Halton Sequences for Mixed Logit
Train, Kenneth
2000-01-01T23:59:59.000Z
Customers’ Choice Among Energy Supplier Simulation based oncustomers’ choice of energy supplier. Surveyed customerspreferences for energy suppliers, such that a mixed logit is
Analysis of fuel shares in the industrial sector
Roop, J.M.; Belzer, D.B.
1986-06-01T23:59:59.000Z
These studies describe how fuel shares have changed over time; determine what factors are important in promoting fuel share changes; and project fuel shares to the year 1995 in the industrial sector. A general characterization of changes in fuel shares of four fuel types - coal, natural gas, oil and electricity - for the industrial sector is as follows. Coal as a major fuel source declined rapidly from 1958 to the early 1970s, with oil and natural gas substituting for coal. Coal's share of total fuels stabilized after the oil price shock of 1972-1973, and increased after the 1979 price shock. In the period since 1973, most industries and the industrial sector as a whole appear to freely substitute natural gas for oil, and vice versa. Throughout the period 1958-1981, the share of electricity as a fuel increased. These observations are derived from analyzing the fuel share patterns of more than 20 industries over the 24-year period 1958 to 1981.
The Continuous Cross-Nested Logit Model: Formulation and Application for Departure Time Choice
Kockelman, Kara M.
The Continuous Cross-Nested Logit Model: Formulation and Application for Departure Time Choice modeling, departure time modeling, continuous logit, continuous cross- nested logit, Bayesian estimation usage). In this paper, the continuous cross-nested logit (CCNL) model is introduced. The CCNL model
The d-Level Nested Logit Model: Assortment and Price Optimization Problems
Topaloglu, Huseyin
The d-Level Nested Logit Model: Assortment and Price Optimization Problems Guang Li Paat, 2013 @ 2:27pm Abstract We provide a new formulation of the d-level nested logit model using a tree the optimal assort- ment. For a d-level nested logit model with n products, the running time of the algorithm
Customer-Specific Taste Parameters and Mixed Logit: Households' Choice of Electricity Supplier
Revelt, David; Train, Kenneth
2000-01-01T23:59:59.000Z
M a y 2000 Keywords: energy suppliers, mixed logit, tastecustomers' choice among energy suppliers in conjoint-typecustomers' choice o f energy supplier and estimate the value
Approximation Methods for Pricing Problems under the Nested Logit Model with Price Bounds
Topaloglu, Huseyin
Approximation Methods for Pricing Problems under the Nested Logit Model with Price Bounds W@orie.cornell.edu November 13, 2012 Abstract We consider two variants of a pricing problem under the nested logit model. In the first variant, the set of products offered to customers is fixed and we want to determine the prices
Capacity Constraints Across Nests in Assortment Optimization Under the Nested Logit Model
Topaloglu, Huseyin
Capacity Constraints Across Nests in Assortment Optimization Under the Nested Logit Model Jacob B Abstract We consider assortment optimization problems when customers choose according to the nested logit in all nests. When each product consumes one unit of capacity, our capacity constraint limits
Random Utility/Multinomial Logit Model Literature Amemiya, Takeshi. 1977. "On a Two-Step Estimation,-I.-E. "Random Utility Model for Sportfishing: Some Preliminary Results for Florida." Marine extensive use of the random utility (or discrete choice) model in recent years, but few applications appear
Estimating long-term world coal production with logit and probit transforms David Rutledge
Weinreb, Sander
from measurements of coal seams. We show that where the estimates based on reserves can be testedEstimating long-term world coal production with logit and probit transforms David Rutledge form 27 October 2010 Accepted 27 October 2010 Available online 4 November 2010 Keywords: Coal reserves
Yaws, C.L.; Yang, H.C.; Hopper, J.R.; Cawley, W.A. (Lamar Univ., Beaumont, TX (US))
1991-01-01T23:59:59.000Z
Saturated liquid densities for organic chemicals are given as functions of temperature using a modified Rackett equation.
The universal radiative transport equation
Preisendorfer, Rudolph W
1959-01-01T23:59:59.000Z
THE UNIVERSAL RADIATIVE TRANSPORT EQUATION Rudolph W.The Universal Radiative Transport Equation Rudolph W.The various radiative transport equations used in general
Solutions of Penrose's Equation
E. N. Glass; Jonathan Kress
1998-09-27T23:59:59.000Z
The computational use of Killing potentials which satisfy Penrose's equation is discussed. Penrose's equation is presented as a conformal Killing-Yano equation and the class of possible solutions is analyzed. It is shown that solutions exist in spacetimes of Petrov type O, D or N. In the particular case of the Kerr background, it is shown that there can be no Killing potential for the axial Killing vector.
Nonlinear gyrokinetic equations
Dubin, D.H.E.; Krommes, J.A.; Oberman, C.; Lee, W.W.
1983-03-01T23:59:59.000Z
Nonlinear gyrokinetic equations are derived from a systematic Hamiltonian theory. The derivation employs Lie transforms and a noncanonical perturbation theory first used by Littlejohn for the simpler problem of asymptotically small gyroradius. For definiteness, we emphasize the limit of electrostatic fluctuations in slab geometry; however, there is a straight-forward generalization to arbitrary field geometry and electromagnetic perturbations. An energy invariant for the nonlinear system is derived, and various of its limits are considered. The weak turbulence theory of the equations is examined. In particular, the wave kinetic equation of Galeev and Sagdeev is derived from an asystematic truncation of the equations, implying that this equation fails to consider all gyrokinetic effects. The equations are simplified for the case of small but finite gyroradius and put in a form suitable for efficient computer simulation. Although it is possible to derive the Terry-Horton and Hasegawa-Mima equations as limiting cases of our theory, several new nonlinear terms absent from conventional theories appear and are discussed.
Burra G. Sidharth
2009-11-10T23:59:59.000Z
We consider the behavior of the particles at ultra relativistic energies, for both the Klein-Gordon and Dirac equations. We observe that the usual description is valid for energies such that we are outside the particle's Compton wavelength. For higher energies however, both the Klein-Gordon and Dirac equations get modified and this leads to some new effects for the particles, including the appearance of anti particles with a slightly different energy.
Applications of Differential Equations
Vickers, James
several techniques for solving commonly-occurring first- order and second-order ordinary differential electrical circuits, projectile motion and Newton's law of cooling recognise and solve second-order ordinary's law of cooling In section 19.1 we introduced Newton's law of cooling. The model equation was d dt = -k
Analysis of fuel shares in the residential sector: 1960 to 1995
Reilly, J.M.; Shankle, S.A.; Pomykala, J.S.
1986-08-01T23:59:59.000Z
Historical and future energy use by fuel type in the residential sector of the United States are examined. Of interest is the likely relative demand for fuels as they affect national policy issues such as the potential shortfall of electric generating capacity in the mid to late 1990's and the ability of the residential sector to switch rapdily among fuels in response to fuel shortages, price increases and other factors. Factors affecting the share of a fuel used rather than the aggregate level of energy use are studied. However, the share of a fuel used is not independent of the level of energy consumption. In the analysis, the level of consumption of each fuel is computed as an intermediate result and is reported for completeness.
Stochastic equations for thermodynamics
Tsekov, R
2015-01-01T23:59:59.000Z
The applicability of stochastic differential equations to thermodynamics is considered and a new form, different from the classical Ito and Stratonovich forms, is introduced. It is shown that the new presentation is more appropriate for the description of thermodynamic fluctuations. The range of validity of the Boltzmann-Einstein principle is also discussed and a generalized alternative is proposed. Both expressions coincide in the small fluctuation limit, providing a normal distribution density.
Syllabus for “Ordinary Differential Equations”
Alan Demlow
2015-01-12T23:59:59.000Z
Syllabus for MA266, Ordinary Differential Equations. (Sections 052 & 091). GENERAL INFORMATION. Course instructor and contact information: Instructor: Dr.
A Master Equation Approach to the `3 + 1' Dirac Equation
Keith A. Earle
2011-02-06T23:59:59.000Z
A derivation of the Dirac equation in `3+1' dimensions is presented based on a master equation approach originally developed for the `1+1' problem by McKeon and Ord. The method of derivation presented here suggests a mechanism by which the work of Knuth and Bahrenyi on causal sets may be extended to a derivation of the Dirac equation in the context of an inference problem.
S. C. Tiwari
2007-06-09T23:59:59.000Z
A generalized harmonic map equation is presented based on the proposed action functional in the Weyl space (PLA, 135, 315, 1989).
Effective equations for quantum dynamics
Benjamin Schlein
2012-08-01T23:59:59.000Z
We report on recent results concerning the derivation of effective evolution equations starting from many body quantum dynamics. In particular, we obtain rigorous derivations of nonlinear Hartree equations in the bosonic mean field limit, with precise bounds on the rate of convergence. Moreover, we present a central limit theorem for the fluctuations around the Hartree dynamics.
INTRODUCTORY LABORATORY 0: DETERMINING AN EQUATION FOR
Minnesota, University of
below are designed to help. Once you are satisfied with an equation, press "Accept Fit Function determine the equations that best represent (fit) the measured data, and compare the resulting Fit Equations with your Prediction Equations. This activity will familiarize you with the procedure for fitting equations
Partial Differential Equations of Physics
Robert Geroch
1996-02-27T23:59:59.000Z
Apparently, all partial differential equations that describe physical phenomena in space-time can be cast into a universal quasilinear, first-order form. In this paper, we do two things. First, we describe some broad features of systems of differential equations so formulated. Examples of such features include hyperbolicity of the equations, constraints and their roles (e.g., in connection with the initial-value formulation), how diffeomorphism freedom is manifest, and how interactions between systems arise and operate. Second, we give a number of examples that illustrate how the equations for physical systems are cast into this form. These examples suggest that the first-order, quasilinear form for a system is often not only the simplest mathematically, but also the most transparent physically.
Entropic corrections to Einstein equations
Hendi, S. H. [Physics Department, College of Sciences, Yasouj University, Yasouj 75914 (Iran, Islamic Republic of); Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Maragha (Iran, Islamic Republic of); Sheykhi, A. [Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Maragha (Iran, Islamic Republic of); Department of Physics, Shahid Bahonar University, P.O. Box 76175-132, Kerman (Iran, Islamic Republic of)
2011-04-15T23:59:59.000Z
Considering the general quantum corrections to the area law of black hole entropy and adopting the viewpoint that gravity interprets as an entropic force, we derive the modified forms of Modified Newtonian dynamics (MOND) theory of gravitation and Einstein field equations. As two special cases we study the logarithmic and power-law corrections to entropy and find the explicit form of the obtained modified equations.
Logit Models for Estimating Urban Area Through Travel
Talbot, Eric
2011-10-21T23:59:59.000Z
of all trips at an external station that are through trips. The second model distributes those through trips at one external station to the other external stations. The models produce separate results for commercial and non- commercial vehicles...-side interview technique at locations (called external stations) where traffic enters and exits the study area. During the daylight hours of a certain day, survey personnel would direct all vehicles or a sample of vehicles leaving the urban area to stop...
Characteristics of rural bank acquisitions: a logit analysis
Applewhite, Jennifer Lynn
1994-01-01T23:59:59.000Z
This study evaluates acquisitions of rural banks by multi-bank holding companies. Evaluation of pre-acquisition characteristics including profitability, size, market concentration, and agricultural lending volume are the basis of the analysis...
How accurate is Limber's equation?
P. Simon
2007-08-24T23:59:59.000Z
The so-called Limber equation is widely used in the literature to relate the projected angular clustering of galaxies to the spatial clustering of galaxies in an approximate way. This paper gives estimates of where the regime of applicability of Limber's equation stops. Limber's equation is accurate for small galaxy separations but breaks down beyond a certain separation that depends mainly on the ratio sigma/R and to some degree on the power-law index, gamma, of spatial clustering xi; sigma is the one-sigma width of the galaxy distribution in comoving distance, and R the mean comoving distance. As rule-of-thumb, a 10% relative error is reached at 260 sigma/R arcmin for gamma~1.6, if the spatial clustering is a power-law. More realistic xi are discussed in the paper. Limber's equation becomes increasingly inaccurate for larger angular separations. Ignoring this effect and blindly applying Limber's equation can possibly bias results for the inferred spatial correlation. It is suggested to use in cases of doubt, or maybe even in general, the exact equation that can easily be integrated numerically in the form given in the paper.
Fulvio Melia
2014-11-21T23:59:59.000Z
The cosmic spacetime is often described in terms of the FRW metric, though the adoption of this elegant and convenient solution to Einstein's equations does not tell us much about the equation of state, p=w rho, in terms of the total energy density rho and pressure p of the cosmic fluid. LCDM and the R_h=ct Universe are both FRW cosmologies that partition rho into (at least) three components, matter rho_m, radiation rho_r, and a poorly understood dark energy rho_de, though the latter goes one step further by also invoking the constraint w=-1/3. This condition is required by the simultaneous application of the Cosmological principle and Weyl's postulate. Model selection tools in one-on-one comparisons favor R_h=ct with a likelihood of ~90% versus only ~10% for LCDM. Nonetheless, the predictions of LCDM often come quite close to those of R_h=ct, suggesting that its parameters are optimized to mimic the w=-1/3 equation of state. In this paper, we demonstrate that the equation of state in R_h=ct helps us to understand why the optimized fraction Omega_m=rho_m/rho in LCDM must be ~0.27, an otherwise seemingly random variable. We show that when one forces LCDM to satisfy the equation of state w=(rho_r/3-rho_de)/rho, the value of the Hubble radius today, c/H_0, can equal its measured value ct_0 only with Omega_m~0.27 when the equation of state for dark energy is w_de=-1. This peculiar value of Omega_m therefore appears to be a direct consequence of trying to fit the data with the equation of state w=(rho_r/3-rho_de)/rho in a Universe whose principal constraint is instead R_h=ct or, equivalently, w=-1/3.
Numerical integration of variational equations
Ch. Skokos; E. Gerlach
2010-09-29T23:59:59.000Z
We present and compare different numerical schemes for the integration of the variational equations of autonomous Hamiltonian systems whose kinetic energy is quadratic in the generalized momenta and whose potential is a function of the generalized positions. We apply these techniques to Hamiltonian systems of various degrees of freedom, and investigate their efficiency in accurately reproducing well-known properties of chaos indicators like the Lyapunov Characteristic Exponents (LCEs) and the Generalized Alignment Indices (GALIs). We find that the best numerical performance is exhibited by the \\textit{`tangent map (TM) method'}, a scheme based on symplectic integration techniques which proves to be optimal in speed and accuracy. According to this method, a symplectic integrator is used to approximate the solution of the Hamilton's equations of motion by the repeated action of a symplectic map $S$, while the corresponding tangent map $TS$, is used for the integration of the variational equations. A simple and systematic technique to construct $TS$ is also presented.
Transport equations in tokamak plasmas
Callen, J. D.; Hegna, C. C.; Cole, A. J. [University of Wisconsin, Madison, Wisconsin 53706-1609 (United States)
2010-05-15T23:59:59.000Z
Tokamak plasma transport equations are usually obtained by flux surface averaging the collisional Braginskii equations. However, tokamak plasmas are not in collisional regimes. Also, ad hoc terms are added for neoclassical effects on the parallel Ohm's law, fluctuation-induced transport, heating, current-drive and flow sources and sinks, small magnetic field nonaxisymmetries, magnetic field transients, etc. A set of self-consistent second order in gyroradius fluid-moment-based transport equations for nearly axisymmetric tokamak plasmas has been developed using a kinetic-based approach. The derivation uses neoclassical-based parallel viscous force closures, and includes all the effects noted above. Plasma processes on successive time scales and constraints they impose are considered sequentially: compressional Alfven waves (Grad-Shafranov equilibrium, ion radial force balance), sound waves (pressure constant along field lines, incompressible flows within a flux surface), and collisions (electrons, parallel Ohm's law; ions, damping of poloidal flow). Radial particle fluxes are driven by the many second order in gyroradius toroidal angular torques on a plasma species: seven ambipolar collision-based ones (classical, neoclassical, etc.) and eight nonambipolar ones (fluctuation-induced, polarization flows from toroidal rotation transients, etc.). The plasma toroidal rotation equation results from setting to zero the net radial current induced by the nonambipolar fluxes. The radial particle flux consists of the collision-based intrinsically ambipolar fluxes plus the nonambipolar fluxes evaluated at the ambipolarity-enforcing toroidal plasma rotation (radial electric field). The energy transport equations do not involve an ambipolar constraint and hence are more directly obtained. The 'mean field' effects of microturbulence on the parallel Ohm's law, poloidal ion flow, particle fluxes, and toroidal momentum and energy transport are all included self-consistently. The final comprehensive equations describe radial transport of plasma toroidal rotation, and poloidal and toroidal magnetic fluxes, as well as the usual particle and energy transport.
Chapter 2' First order Differential Equations I 2,] Linear Equations ...
Alternatively, you can use a numerical approximation method, such as those discussed in. Chapter 8 ... and produce graphs of solutions of differential equations. ..... hand, the effective escape velocity can be signi?cantly reduced if the body is transported a ... the cross section of the (smooth) out?ow stream is smaller than n.
Exact Controllability of the Superlinear Heat Equation
Barbu, V. [Institute of Mathematics of Romanian Academy, Blvd. Carol, 6600 Iasi (Romania)], E-mail: barbu@uaic.ro
2000-07-01T23:59:59.000Z
The exact internal and boundary controllability of parabolic equations with superlinear nonlinearity is studied.
Compatibility of equations with truncated Newton's binomials
Anatoly A. Grinberg
2014-06-19T23:59:59.000Z
The resolvability of equations in integers containing truncated Newton's binomial, is determined by the divisibility of the binomial by the characteristic parameters of the equation, which most often is the binomial exponent. Two types of equations containing binomials from two and three integers are investigated. Conditions of resolvability of the equations are specified based on the characteristics of their parameters.
Melia, Fulvio
2014-01-01T23:59:59.000Z
The cosmic spacetime is often described in terms of the FRW metric, though the adoption of this elegant and convenient solution to Einstein's equations does not tell us much about the equation of state, p=w rho, in terms of the total energy density rho and pressure p of the cosmic fluid. LCDM and the R_h=ct Universe are both FRW cosmologies that partition rho into (at least) three components, matter rho_m, radiation rho_r, and a poorly understood dark energy rho_de, though the latter goes one step further by also invoking the constraint w=-1/3. This condition is required by the simultaneous application of the Cosmological principle and Weyl's postulate. Model selection tools in one-on-one comparisons favor R_h=ct with a likelihood of ~90% versus only ~10% for LCDM. Nonetheless, the predictions of LCDM often come quite close to those of R_h=ct, suggesting that its parameters are optimized to mimic the w=-1/3 equation of state. In this paper, we demonstrate that the equation of state in R_h=ct helps us to under...
2. System boundaries; Balance equations
Zevenhoven, Ron
;5/28 Systems and boundaries /3 An isolated system is a special kind of closed system Pictures: KJ05 Q = heat W Example: an electric hot water heater in a house Â The electric heater is a closed system Â The water1/28 2. System boundaries; Balance equations Ron Zevenhoven Ã?bo Akademi University Thermal and flow
Green Functions of Relativistic Field Equations
Ying-Qiu Gu
2006-12-20T23:59:59.000Z
In this paper, we restudy the Green function expressions of field equations. We derive the explicit form of the Green functions for the Klein-Gordon equation and Dirac equation, and then estimate the decay rate of the solution to the linear equations. The main motivation of this paper is to show that: (1). The formal solutions of field equations expressed by Green function can be elevated as a postulate for unified field theory. (2). The inescapable decay of the solution of linear equations implies that the whole theory of the matter world should include nonlinear interaction.
Langevin Equation on Fractal Curves
Seema Satin; A. D. Gangal
2014-04-28T23:59:59.000Z
We analyse a random motion of a particle on a fractal curve, using Langevin approach. This involves defining a new velocity in terms of mass of the fractal curve, as defined in recent work. The geometry of the fractal curve, hence plays an important role in this analysis. A Langevin equation with a particular noise model is thus proposed and solved using techniques of the newly developed $F^\\alpha$-Calculus .
New flow equation for orifices
Hall, K.R.; Eubank, P.T.; Holste, J.C.
1984-06-01T23:59:59.000Z
Orifices have been used to measure flowrate for thousands of years, but economic pressures recently have dictated a careful evaluation of the procedure. The National Bureau of Standards currently has two major research programs (funded by API and GRI) underway with the goals of increasing the accuracy and range of orifice measurements. The equations presented in this work represent a significant departure from those normally used. The new expressions are equally rigorous and possess many advantages compared with the conventional relationships.
18.03 Differential Equations, Spring 2006
Miller, Haynes
Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary ...
18.03 Differential Equations, Spring 2004
Miller, Haynes R., 1948-
Study of ordinary differential equations, including modeling of physical problems and interpretation of their solutions. Standard solution methods for single first-order equations, including graphical and numerical methods. ...
Padé interpolation for elliptic Painlevé equation
Masatoshi Noumi; Satoshi Tsujimoto; Yasuhiko Yamada
2012-08-08T23:59:59.000Z
An interpolation problem related to the elliptic Painlev\\'e equation is formulated and solved. A simple form of the elliptic Painlev\\'e equation and the Lax pair are obtained. Explicit determinant formulae of special solutions are also given.
Solution of Nonlinear Equations via Optimization
Isaac Siwale
2014-12-22T23:59:59.000Z
from fluid dynamics, medicine, elasticity, combustion, molecular ...... Equation systems emanating from chemical engineering tend to be very complex, with ...
Wave equations with energy dependent potentials
J. Formanek; R. J. Lombard; J. Mares
2003-09-22T23:59:59.000Z
We study wave equations with energy dependent potentials. Simple analytical models are found useful to illustrate difficulties encountered with the calculation and interpretation of observables. A formal analysis shows under which conditions such equations can be handled as evolution equation of quantum theory with an energy dependent potential. Once these conditions are met, such theory can be transformed into ordinary quantum theory.
Inverse Problems for Fractional Diffusion Equations
Zuo, Lihua
2013-06-21T23:59:59.000Z
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.5.3 Derivation of fractional difiusion equations . . . . . . . . . . . 12 1.6 Fractional calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.7 Mittag-Le?er function . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1... point theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Volterra equation of the second kind . . . . . . . . . . . . . . . . . . 6 1.4 Classical difiusion equations . . . . . . . . . . . . . . . . . . . . . . . 6 1.4.1 Derivation...
Four nontrivial solutions for subcritical exponential equations
Mugnai, Dimitri
Four nontrivial solutions for subcritical exponential equations Dimitri Mugnai Dipartimento di@dipmat.unipg.it Abstract We show that a semilinear Dirichlet problem in bounded domains of R2 in presence of subcritical). Equation (3) is a standard example of a subcritical growth, while equation (4) is the model for a critical
Hamilton-Jacobi-Bellman equations for the optimal control of a state equation with
Paris-Sud XI, UniversitÃ© de
Hamilton-Jacobi-Bellman equations for the optimal control of a state equation with memory G is the only viscosity solution of an Hamilton-Jacobi-Bellman equation of the form: v(x, z) + H(x, z, xv(x, z, Hamilton-Jacobi-Bellman equations in infinite dimensions. UniversitÂ´e Paris Dauphine, CEREMADE, Pl. de
The properties of the first equation of the Vlasov chain of equations
E. E. Perepelkin; B. I. Sadovnikov; N. G. Inozemtseva
2015-02-06T23:59:59.000Z
A mathematically rigorous derivation of the first Vlasov equation as a well-known Schr\\"odinger equation for the probabilistic description of a system and families of the classic diffusion equations and heat conduction for the deterministic description of physical systems was inferred. A physical meaning of the phase of the wave function which is a scalar potential of the probabilistic flow velocity is demonstrated. Occurrence of the velocity potential vortex component leads to the Pauli equation for one of the spinar components. A scheme of the construction of the Schr\\"odinger equation solving from the Vlasov equation solving and vice-versa is shown. A process of introduction of the potential to the Schr\\"odinger equation and its interpretation are given. The analysis of the potential properties gives us the Maxwell equation, the equation of the kinematic point movement, and the movement of the medium within electromagnetic fields equation.
Tanmoy Bhattacharya; for the HotQCD collaboration
2015-01-30T23:59:59.000Z
Results for the equation of state in 2+1 flavor QCD at zero net baryon density using the Highly Improved Staggered Quark (HISQ) action by the HotQCD collaboration are presented. The strange quark mass was tuned to its physical value and the light (up/down) quark masses fixed to $m_l = 0.05m_s$ corresponding to a pion mass of 160 MeV in the continuum limit. Lattices with temporal extent $N_t=6$, 8, 10 and 12 were used. Since the cutoff effects for $N_t>6$ were observed to be small, reliable continuum extrapolations of the lattice data for the phenomenologically interesting temperatures range $130 \\mathord{\\rm MeV} < T < 400 \\mathord{\\rm MeV}$ could be performed. We discuss statistical and systematic errors and compare our results with other published works.
Bhattacharya, Tanmoy
2015-01-01T23:59:59.000Z
Results for the equation of state in 2+1 flavor QCD at zero net baryon density using the Highly Improved Staggered Quark (HISQ) action by the HotQCD collaboration are presented. The strange quark mass was tuned to its physical value and the light (up/down) quark masses fixed to $m_l = 0.05m_s$ corresponding to a pion mass of 160 MeV in the continuum limit. Lattices with temporal extent $N_t=6$, 8, 10 and 12 were used. Since the cutoff effects for $N_t>6$ were observed to be small, reliable continuum extrapolations of the lattice data for the phenomenologically interesting temperatures range $130 \\mathord{\\rm MeV} < T < 400 \\mathord{\\rm MeV}$ could be performed. We discuss statistical and systematic errors and compare our results with other published works.
Simultaneous Equation Correspondence to Author:
Ketan P. Dadhania; Parthika A. Nadpara; Yadvendra K. Agrawal; Ketan P. Dadhania
A simple, rapid, accurate, precise, specific and economical spectrophotometric method for simultaneous estimation of Gliclazide (GLC) and Metformin hydrochloride (MET) in combined tablet dosage form has been developed. It employs formation and solving of simultaneous equation using two wavelengths 227.0 nm and 237.5 nm. This method obeys Beer’s law in the employed concentration ranges of 5-25 ?g/ml and 2.5-12.5 ?g/ml for Gliclazide and Metformin hydrochloride, respectively. Results of analysis were validated statistically and by recovery studies. INTRODUCTION: Metformin hydrochloride (N, N-dimethylimidodicarbonimidic diamide hydrochloride or 1, 1-dimethyl biguanide hydrochloride) is oral antihyperglycemic drugs used in the management of type 2 diabetes 1,2. It is an antihyperglycemic agent,
Interaction blending equations enhance reformulated gasoline profitability
Snee, R.D. (Joiner Associates, Madison, WI (United States)); Morris, W.E.; Smith, W.E.
1994-01-17T23:59:59.000Z
The interaction approach to gasoline blending gives refiners an accurate, simple means of re-evaluating blending equations and increasing profitability. With reformulated gasoline specifications drawing near, a detailed description of this approach, in the context of reformulated gasoline is in order. Simple mathematics compute blending values from interaction equations and interaction coefficients between mixtures. A timely example of such interactions is: blending a mixture of catalytically cracked gasoline plus light straight run (LSR) from one tank with alkylate plus reformate from another. This paper discusses blending equations, using interactions, mixture interactions, other blending problems, and obtaining equations.
A counterexample against the Vlasov equation
C. Y. Chen
2009-04-19T23:59:59.000Z
A simple counterexample against the Vlasov equation is put forward, in which a magnetized plasma is perturbed by an electromagnetic standing wave.
Stochastic Master Equations in Thermal Environment
S Attal; C Pellegrini
2010-04-20T23:59:59.000Z
We derive the stochastic master equations which describe the evolution of open quantum systems in contact with a heat bath and undergoing indirect measurements. These equations are obtained as a limit of a quantum repeated measurement model where we consider a small system in contact with an infinite chain at positive temperature. At zero temperature it is well-known that one obtains stochastic differential equations of jump-diffusion type. At strictly positive temperature, we show that only pure diffusion type equations are relevant.
Numerical Solution of Ordinary Di erential Equations
Ordinary di erential equations frequently occur as mathematical models in many branches. of science, engineering and economy. Unfortunately it is seldom that ...
The Fractional Kinetic Equation and Thermonuclear Functions
H. J. Haubold; A. M. Mathai
2000-01-16T23:59:59.000Z
The paper discusses the solution of a simple kinetic equation of the type used for the computation of the change of the chemical composition in stars like the Sun. Starting from the standard form of the kinetic equation it is generalized to a fractional kinetic equation and its solutions in terms of H-functions are obtained. The role of thermonuclear functions, which are also represented in terms of G- and H-functions, in such a fractional kinetic equation is emphasized. Results contained in this paper are related to recent investigations of possible astrophysical solutions of the solar neutrino problem.
SOLVING SYSTEMS OF NONLINEAR EQUATIONS WITH ...
2006-11-02T23:59:59.000Z
Nov 2, 2006 ... an exothermic first-order irreversible reaction. When certain variables are eliminated, the model results in a system of two nonlinear equations.
Scalable Equation of State Capability
Epperly, T W; Fritsch, F N; Norquist, P D; Sanford, L A
2007-12-03T23:59:59.000Z
The purpose of this techbase project was to investigate the use of parallel array data types to reduce the memory footprint of the Livermore Equation Of State (LEOS) library. Addressing the memory scalability of LEOS is necessary to run large scientific simulations on IBM BG/L and future architectures with low memory per processing core. We considered using normal MPI, one-sided MPI, and Global Arrays to manage the distributed array and ended up choosing Global Arrays because it was the only communication library that provided the level of asynchronous access required. To reduce the runtime overhead using a parallel array data structure, a least recently used (LRU) caching algorithm was used to provide a local cache of commonly used parts of the parallel array. The approach was initially implemented in a isolated copy of LEOS and was later integrated into the main trunk of the LEOS Subversion repository. The approach was tested using a simple test. Testing indicated that the approach was feasible, and the simple LRU caching had a 86% hit rate.
Categorical Semantics for Schrödinger's Equation
Stefano Gogioso
2015-02-25T23:59:59.000Z
Applying ideas from monadic dynamics to the well-established framework of categorical quantum mechanics, we provide a novel toolbox for the simulation of finite-dimensional quantum dynamics. We use strongly complementary structures to give a graphical characterisation of quantum clocks, their action on systems and the relevant energy observables, and we proceed to formalise the connection between unitary dynamics and projection-valued spectra. We identify the Weyl canonical commutation relations in the axioms of strong complementarity, and conclude the existence of a dual pair of time/energy observables for finite-dimensional quantum clocks, with the relevant uncertainty principle given by mutual unbias of the corresponding orthonormal bases. We show that Schr\\"odinger's equation can be abstractly formulated as characterising the Fourier transforms of certain Eilenberg-Moore morphisms from a quantum clock to a quantum dynamical system, and we use this to obtain a generalised version of the Feynman's clock construction. We tackle the issue of synchronism of clocks and systems, prove conservation of total energy and give conditions for the existence of an internal time observable for a quantum dynamical system. Finally, we identify our treatment as part of a more general theory of simulated symmetries of quantum systems (of which our clock actions are a special case) and their conservation laws (of which energy is a special case).
Comment on ``Thermodynamically Admissible 13 Moment Equations from the Boltzmann Equation''
, they do not include classical hydrodynam- ics in the limit of small Knudsen numbers. The hydro- dynamic to the equations of hydrodynamics in the limit of small Knudsen numbers. Presently, the R13 equations have
Derivation of Maxwell-like equations from the quaternionic Dirac's equation
A. I. Arbab
2014-09-07T23:59:59.000Z
Expanding the ordinary Dirac's equation, $\\frac{1}{c}\\frac{\\partial\\psi}{\\partial t}+\\vec{\\alpha}\\cdot\\vec{\
Diquark Properties and the TOV Equations
Blaschke, David B; Oztas, A M; Blaschke, David; Fredriksson, Sverker; Oztas, Ahmet Mecit
2001-01-01T23:59:59.000Z
We present various results from including diquark properties and the gap equations into the TOV equations for compact quark objects. One such property is the diquark form factor, which has a strong influence on various quantities. We discuss the consequences for quark stars.
Diquark Properties and the TOV Equations
David Blaschke; Sverker Fredriksson; Ahmet Mecit Oztas
2001-11-30T23:59:59.000Z
We present various results from including diquark properties and the gap equations into the TOV equations for compact quark objects. One such property is the diquark form factor, which has a strong influence on various quantities. We discuss the consequences for quark stars.
Price's Theorem: A General Equation for Response
Walsh, Bruce
12 Price's Theorem: A General Equation for Response It is always difficult, in retrospect, to see situation. Ac- tually, there is, namely Price's Theorem (Price 1970, 1972a), also referred to as the Price Equation. Price's theorem provides a notationally elegant way to describe any selection re- sponse. We
A bi-Hamiltonian supersymmetric geodesic equation
Jonatan Lenells
2008-06-29T23:59:59.000Z
A supersymmetric extension of the Hunter-Saxton equation is constructed. We present its bi-Hamiltonian structure and show that it arises geometrically as a geodesic equation on the space of superdiffeomorphisms of the circle that leave a point fixed endowed with a right-invariant metric.
Geodesic-invariant equations of gravitation
Leonid V. Verozub
2008-02-04T23:59:59.000Z
Einstein's equations of gravitation are not invariant under geodesic mappings, i. e. under a certain class of mappings of the Christoffel symbols and the metric tensor which leave the geodesic equations in a given coordinate system invariant. A theory in which geodesic mappings play the role of gauge transformations is considered.
Comment on ``Discrete Boltzmann Equation for Microfluidics''
Luo, Li-Shi
Comment on ``Discrete Boltzmann Equation for Microfluidics'' In a recent Letter [1], Li and Kwok use a lattice Boltzmann equation (LBE) for microfluidics. Their main claim is that an LBE model for microfluidics can be constructed based on the ``Bhatnagar-Gross-Kooky [sic]'' model by including ``the
The Papapetrou equations and supplementary conditions
O. B. Karpov
2004-06-02T23:59:59.000Z
On the bases of the Papapetrou equations with various supplementary conditions and other approaches a comparative analysis of the equations of motion of rotating bodies in general relativity is made. The motion of a body with vertical spin in a circular orbit is considered. An expression for the spin-orbit force in a post-Newtonian approximation is investigated.
Optimization and Nonlinear Equations Gordon K. Smyth
Smyth, Gordon K.
Optimization and Nonlinear Equations Gordon K. Smyth May 1997 Optimization means to find that value of x which maxÂ imizes or minimizes a given function f(x). The idea of optimization goes to the heart with respect to the components of x. Except in linear cases, optimization and equation solving invariably
Derivation of a Stochastic Neutron Transport Equation
Edward J. Allen
2010-04-14T23:59:59.000Z
Stochastic difference equations and a stochastic partial differential equation (SPDE) are simultaneously derived for the time-dependent neutron angular density in a general three-dimensional medium where the neutron angular density is a function of position, direction, energy, and time. Special cases of the equations are given such as transport in one-dimensional plane geometry with isotropic scattering and transport in a homogeneous medium. The stochastic equations are derived from basic principles, i.e., from the changes that occur in a small time interval. Stochastic difference equations of the neutron angular density are constructed, taking into account the inherent randomness in scatters, absorptions, and source neutrons. As the time interval decreases, the stochastic difference equations lead to a system of Ito stochastic differential equations (SDEs). As the energy, direction, and position intervals decrease, an SPDE is derived for the neutron angular density. Comparisons between numerical solutions of the stochastic difference equations and independently formulated Monte Carlo calculations support the accuracy of the derivations.
Coupled Parabolic Equations for Wave Propagation
Zhao, Hongkai
Coupled Parabolic Equations for Wave Propagation Kai Huang, Knut Solna and Hongkai Zhao #3; April simulation of wave propagation over long distances. The coupled parabolic equations are derived from a two algorithms are important in order to understand wave propagation in complex media. Resolving the wavelength
Dirac Equation in Standard Cosmological Models
M. Sharif
2004-01-15T23:59:59.000Z
The time equation associated to the Dirac Equation (DE) is studied for the radiation-dominated Friedmann-Robertson-Walker (FRW) universe. The results are analysed for small and large values of time. We also incorporate the corrections of the paper studied by Zecca [1] for the matter-dominated FRW universe.
Diffractive Nonlinear Geometrical Optics for Variational Wave Equations and the Einstein Equations
Giuseppe Ali; John K. Hunter
2005-11-02T23:59:59.000Z
We derive an asymptotic solution of the vacuum Einstein equations that describes the propagation and diffraction of a localized, large-amplitude, rapidly-varying gravitational wave. We compare and contrast the resulting theory of strongly nonlinear geometrical optics for the Einstein equations with nonlinear geometrical optics theories for variational wave equations.
A Cartesian grid embedded boundary method for the heat equation and PoissonÃ?s equation in threeÂ85] and extends work of McCorquodale, Colella and Johansen [A Cartesian grid embedded boundary method for the heat and time for the heat equation. Cartesian grid methods for elliptic PDE have a long history beginning with the no
The generalized Schrödinger–Langevin equation
Bargueño, Pedro, E-mail: p.bargueno@uniandes.edu.co [Departamento de Física, Universidad de los Andes, Apartado Aéreo 4976, Bogotá, Distrito Capital (Colombia); Miret-Artés, Salvador, E-mail: s.miret@iff.csic.es [Instituto de Física Fundamental, CSIC, Serrano 123, 28006, Madrid (Spain)
2014-07-15T23:59:59.000Z
In this work, for a Brownian particle interacting with a heat bath, we derive a generalization of the so-called Schrödinger–Langevin or Kostin equation. This generalization is based on a nonlinear interaction model providing a state-dependent dissipation process exhibiting multiplicative noise. Two straightforward applications to the measurement process are then analyzed, continuous and weak measurements in terms of the quantum Bohmian trajectory formalism. Finally, it is also shown that the generalized uncertainty principle, which appears in some approaches to quantum gravity, can be expressed in terms of this generalized equation. -- Highlights: •We generalize the Kostin equation for arbitrary system–bath coupling. •This generalization is developed both in the Schrödinger and Bohmian formalisms. •We write the generalized Kostin equation for two measurement problems. •We reformulate the generalized uncertainty principle in terms of this equation.
Equation of state and helioseismic inversions
Sarbani Basu; J. Christensen-Dalsgaard
1997-02-19T23:59:59.000Z
Inversions to determine the squared isothermal sound speed and density within the Sun often use the helium abundance Y as the second parameter. This requires the explicit use of the equation of state (EOS), thus potentially leading to systematic errors in the results if the equations of state of the reference model and the Sun are not the same. We demonstrate how this potential error can be suppressed. We also show that it is possible to invert for the intrinsic difference in the adiabatic exponent Gamma_1 between two equations of state. When applied to solar data such inversion rules out the EFF equation of state completely, while with existing data it is difficult to distinguish between other equations of state.
New wave equation for ultrarelativistic particles
Ginés R. Pérez Teruel
2014-12-15T23:59:59.000Z
Starting from first principles and general assumptions based on the energy-momentum relation of the Special Theory of Relativity we present a novel wave equation for ultrarelativistic matter. This wave equation arises when particles satisfy the condition, $p>>m$, i.e, when the energy-momentum relation can be approximated by, $E\\simeq p+\\frac{m^{2}}{2p}$. Interestingly enough, such as the Dirac equation, it is found that this wave equation includes spin in a natural way. Furthermore, the free solutions of this wave equation contain plane waves that are completely equivalent to those of the theory of neutrino oscillations. Therefore, the theory reproduces some standard results of the Dirac theory in the limit $p>>m$, but offers the possibility of an explicit Lorentz Invariance Violation of order, $\\mathcal{O}((mc)^{4}/p^{2})$. As a result, the theory could be useful to test small departures from Dirac equation and Lorentz Invariance at very high energies. On the other hand, the wave equation can also describe particles of spin 1 by a simple substitution of the spin operators, $\\boldsymbol{\\sigma}\\rightarrow\\boldsymbol{\\alpha}$. In addition, it naturally admits a Lagrangian formulation and a Hamiltonian formalism. We also discuss the associated conservation laws that arise through the symmetry transformations of the Lagrangian.
Nonlinear time-fractional dispersive equations
P. Artale Harris; R. Garra
2014-10-29T23:59:59.000Z
In this paper we study some cases of time-fractional nonlinear dispersive equations (NDEs) involving Caputo derivatives, by means of the invariant subspace method. This method allows to find exact solutions to nonlinear time-fractional partial differential equations by separating variables. We first consider a third order time-fractional NDE that admits a four-dimensional invariant subspace and we find a similarity solution. We also study a fifth order NDE. In this last case we find a solution involving Mittag-Leffler functions. We finally observe that the invariant subspace method permits to find explicit solutions for a wide class of nonlinear dispersive time-fractional equations.
Parameter estimation in ordinary differential equations
Ng, Chee Loong
2004-09-30T23:59:59.000Z
The parameter estimation problem or the inverse problem of ordinary differential equations is prevalent in many process models in chemistry, molecular biology, control system design and many other engineering applications. It concerns the re...
Inverse backscattering for the acoustic equation
Bulgarian Academy of Sciences. 1113 Sofia .... The natural energy space for equation (1.1) is the completion H of C? ..... Our plan is the following. First we will ...
Equator Appliance: ENERGY STAR Referral (EZ 3720)
Broader source: Energy.gov [DOE]
DOE referred Equator Appliance clothes washer EZ 3720 to EPA, brand manager of the ENERGY STAR program, for appropriate action after DOE testing revealed that the model does not meet ENERGY STAR requirements.
Adaptive biorthogonal spline schemes for advectionreaction equations
equations arise from petroleum reservoir simulation, ground- water contaminant remediation, and many other schemes produce accurate numerical solutions even if large time steps are used. These schemes are explicit numerical difficulties. Standard numerical methods produce either excessive nonphysical oscillations
On Gaussian Beams Described by Jacobi's Equation
Smith, Steven T.
Gaussian beams describe the amplitude and phase of rays and are widely used to model acoustic propagation. This paper describes four new results in the theory of Gaussian beams. (1) A new version of the ?ervený equations ...
The Alternative Form of Fermat's Equation
Anatoly A. Grinberg
2014-09-25T23:59:59.000Z
An alternative form of Fermats equation[1] is proposed. It represents a portion of the identity that includes three terms of Fermats original equation. This alternative form permits an elementary and compact proof of the first case of Fermats Theorem (FT) for a number of specific exponents. Proofs are given for exponents n equal to 3, 5, 7,11 and 13. All these cases have already been proven using the original Fermats equation, not to mention the fact that a complete proof of FT was given by A. Wiles [2]. In view of this, the results presented here carry a purely methodological interest. They illustrate the effectiveness and simplicity of the method,compared with the well-known classical approach. An alternative form of the equation permits use of the criterion of the incompatibility of its terms, avoiding the labor-intensive and sophisticated calculations associated with traditional approach.
On blowup in supercritical wave equations
Roland Donninger; Birgit Schörkhuber
2014-11-28T23:59:59.000Z
We study the blowup behaviour for the focusing energy-supercritical semilinear wave equation in 3 space dimensions without symmetry assumptions on the data. We prove the stability of the ODE blowup profile.
Infrared Evolution Equations: Method and Applications
B. I. Ermolaev; M. Greco; S. I. Troyan
2007-04-03T23:59:59.000Z
It is a brief review on composing and solving Infrared Evolution Equations. They can be used in order to calculate amplitudes of high-energy reactions in different kinematic regions in the double-logarithmic approximation.
Dirac--Lie systems and Schwarzian equations
J. F. Cariñena; J. Grabowski; J. de Lucas; C. Sardón
2014-06-03T23:59:59.000Z
A Lie system is a system of differential equations admitting a superposition rule, i.e., a function describing its general solution in terms of any generic set of particular solutions and some constants. Following ideas going back to the Dirac's description of constrained systems, we introduce and analyse a particular class of Lie systems on Dirac manifolds, called Dirac--Lie systems, which are associated with `Dirac--Lie Hamiltonians'. Our results enable us to investigate constants of the motion, superposition rules, and other general properties of such systems in a more effective way. Several concepts of the theory of Lie systems are adapted to this `Dirac setting' and new applications of Dirac geometry in differential equations are presented. As an application, we analyze traveling wave solutions of Schwarzian equations, but our methods can be applied also to other classes of differential equations important for Physics.
Semimartingales from the Fokker-Planck Equation
Mikami, Toshio [Department of Mathematics, Hokkaido University, Sapporo 060-0810 (Japan)], E-mail: mikami@math.sci.hokudai.ac.jp
2006-03-15T23:59:59.000Z
We show the existence of a semimartingale of which one-dimensional marginal distributions are given by the solution of the Fokker-Planck equation with the pth integrable drift vector (p > 1)
Solutions of systems of ordinary differential equations
Kitchens, Claude Evans
1967-01-01T23:59:59.000Z
SOLUTIONS OF SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS A Thesis By CLAUDE EVANS KITCHENS Submitted to the Graduate College of the Texas A&M University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE May 1967... Major Subject: Mathematics SOLUTIONS OF SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS A Thesis By CLAUDE EVANS KITCHENS Approved as to style and content by: (Chairman of Commi e) (Nember (Hea of Departmen (H er May 1967 ACKNOWLEDGMENTS I wish...
The Raychaudhuri equation for spinning test particles
Mohseni, Morteza
2015-01-01T23:59:59.000Z
We obtain generalized Raychaudhuri equations for spinning test particles corresponding to congruences of particle's world-lines, momentum, and spin. These are physical examples of the Raychaudhuri equation for a non-normalized vector, unit time-like vector, and unit space-like vector. We compute and compare the evolution of expansion-like parameters associated with these congruences for spinning particles confined in the equatorial plane of the Kerr space-time.
POSITIVE EVOLUTION FAMILIES SOLVING NONAUTONOMOUS DIFFERENCE EQUATIONS
. Introduction Our starting point are systems of nonautonomous difference equations of the form (nDE) (t, ft) = 0 equations of type (nDE) have been developed by various authors, see for example [Coo70], [Hal71], [BW81], [Kat70]) were also applied, e.g., by S. Boulite et al. [BMM06] or N. Lan [Lan99]. In order to solve (nDE
Hasan Bulut; Yusuf Pandir; Seyma Tuluce Demiray
2014-02-04T23:59:59.000Z
In this paper, we acquire the soliton solutions of the nonlinear Schrodinger's equation with dual power-law nonlinearity. Primiraly, we use the extended trial equation method to find exact solutions of this equation. Then, we attain some exact solutions including soliton solutions, rational and elliptic function solutions of this equation by using the extended trial equation method.
Crawford, John R.
Using MR equations built from summary data 1 Running head: Using MR equations built from summary, United Kingdom. E-mail: j.crawford@abdn.ac.uk #12;Using MR equations built from summary data 2 Abstract; regression equations; single-case methods #12;Using MR equations built from summary data 3 INTRODUCTION
Hamilton's equations for a fluid membrane
Riccardo Capovilla; Jemal Guven; Efrain Rojas
2005-05-25T23:59:59.000Z
Consider a homogenous fluid membrane described by the Helfrich-Canham energy, quadratic in the mean curvature of the membrane surface. The shape equation that determines equilibrium configurations is fourth order in derivatives and cubic in the mean curvature. We introduce a Hamiltonian formulation of this equation which dismantles it into a set of coupled first order equations. This involves interpreting the Helfrich-Canham energy as an action; equilibrium surfaces are generated by the evolution of space curves. Two features complicate the implementation of a Hamiltonian framework: (i) The action involves second derivatives. This requires treating the velocity as a phase space variable and the introduction of its conjugate momentum. The canonical Hamiltonian is constructed on this phase space. (ii) The action possesses a local symmetry -- reparametrization invariance. The two labels we use to parametrize points on the surface are themselves physically irrelevant. This symmetry implies primary constraints, one for each label, that need to be implemented within the Hamiltonian. The two lagrange multipliers associated with these constraints are identified as the components of the acceleration tangential to the surface. The conservation of the primary constraints imply two secondary constraints, fixing the tangential components of the momentum conjugate to the position. Hamilton's equations are derived and the appropriate initial conditions on the phase space variables are identified. Finally, it is shown how the shape equation can be reconstructed from these equations.
Multilevel bioluminescence tomography based on radiative transfer equation
Soatto, Stefano
, "A fast forward solver of radiative transfer equation," Transport Theory and Statistical Physics 38Multilevel bioluminescence tomography based on radiative transfer equation Part 1: l1 approach for bioluminescence tomography based on radiative transfer equation with the emphasis on improving
Construction of tree volume tables from integration of taper equations
Coffman, Jerry Gale
1973-01-01T23:59:59.000Z
equations and point sampling factors. For. Chron. 47(6): 352-354. 1972. Converting volume equations to compatible taper equations, For. Sci. 18: 241-245. Giurgiu, V. 1963, 0 metoda analitica do intoemire a tabeleor dendrometrice la calculatoarele...
Correspondence between the NLS equation for optical fibers and a class of integrable NLS equations
Domenico Felice; Luigi Barletti
2014-02-05T23:59:59.000Z
The propagation of the optical field complex envelope in a single-mode fiber is governed by a one-dimensional cubic nonlinear Schr\\"odinger equation with a loss term. We present a result about $L^2$-closeness of the solutions of the above-mentioned equation and of a one-dimensional nonlinear Schr\\"odinger equation that is Painlev\\'e integrable.
Evaluation of empirical advance and infiltration equations for furrow irrigation
Blair, Allie William
1982-01-01T23:59:59.000Z
of the differences in accuracy for the following infiltration 19 equations: (a) Kostiakov-Lewis (equation (1)), (b) Horton (equation (2)), (c) Philip (equation (3)), (d) modified Kostiakov-Lewis (equation (4) ), and (e) SCS (equation (5) ) . As mentioned before... obtained from Elliott et al. (1980) . Approximately 37 data sets from blocked furrow infiltration tests at five different farms were evaluated. The furrow width varied from . 76 to 1. 5 meters. The cumulative volume of infiltrated water was measured...
A Least-Squares Transport Equation Compatible with Voids
Hansen, Jon
2014-04-22T23:59:59.000Z
discretization has both the intermediate and thick diffusion limits [6]. Diffu- sion synthetic acceleration (DSA) can be applied to our equation. However, we do not use a consistently-discretized diffusion equation because the consistent P1 equations derived from... transport equation and thereby obtain a “partially-consistent” diffusion equation. This diffusion equation yields an unconditionally effective DSA scheme after an ad hoc modification is made at the boundaries to account for non-standard Dirichlet conditions...
Active-space completely-renormalized equation-of-motioncoupled...
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
space completely-renormalized equation-of-motion coupled-clusterformalism: Excited-state studies of green fluorescent Active-space completely-renormalized equation-of-motion...
Electrolux Gibson Air Conditioner and Equator Clothes Washer...
Broader source: Energy.gov (indexed) [DOE]
Electrolux Gibson Air Conditioner and Equator Clothes Washer Fail DOE Energy Star Testing Electrolux Gibson Air Conditioner and Equator Clothes Washer Fail DOE Energy Star Testing...
A Method of Solving Certain Nonlinear Diophantine Equations
Florentin Smarandache
2009-10-12T23:59:59.000Z
In this paper we propose a method of solving a Nonlinear Diophantine Equation by converting it into a System of Diophantine Linear Equations.
From the Boltzmann equation to fluid mechanics on a manifold
Peter J. Love; Donato Cianci
2012-08-27T23:59:59.000Z
We apply the Chapman-Enskog procedure to derive hydrodynamic equations on an arbitrary surface from the Boltzmann equation on the surface.
Two standard methods for solving the Ito equation
Alvaro Salas Salas
2008-05-21T23:59:59.000Z
In this paper we show some exact solutions for the Ito equation. These solutions are obtained by two methods: the tanh method and the projective Riccati equation method.
Polynomial solutions of certain differential equations arising in physics
Azad, Hassan
Polynomial solutions of certain differential equations arising in physics H. Azad, A. Laradji and M [9], where the authors consider certain equations that arise in mathematical physics
Problems with the Newton-Schrödinger Equations
C. Anastopoulos; B. L. Hu
2014-07-27T23:59:59.000Z
We examine the origin of the Newton-Schr\\"odinger equations (NSEs) that play an important role in alternative quantum theories (AQT), macroscopic quantum mechanics and gravity-induced decoherence. We show that NSEs for individual particles do not follow from general relativity (GR) plus quantum field theory (QFT). Contrary to what is commonly assumed, the NSEs are not the weak-field (WF), non-relativistic (NR) limit of the semi-classical Einstein equation (SCE) (this nomenclature is preferred over the `M\\/oller-Rosenfeld equation') based on GR+QFT. The wave-function in the NSEs makes sense only as that for a mean field describing a system of $N$ particles as $N \\rightarrow \\infty$, not that of a single or finite many particles. From GR+QFT the gravitational self-interaction leads to mass renormalization, not to a non-linear term in the evolution equations of some AQTs. The WF-NR limit of the gravitational interaction in GR+QFT involves no dynamics. To see the contrast, we give a derivation of the equation (i) governing the many-body wave function from GR+QFT and (ii) for the non-relativistic limit of quantum electrodynamics (QED). They have the same structure, being linear, and very different from NSEs. Adding to this our earlier consideration that for gravitational decoherence the master equations based on GR+QFT lead to decoherence in the energy basis and not in the position basis, despite some AQTs desiring it for the `collapse of the wave function', we conclude that the origins and consequences of NSEs are very different, and should be clearly demarcated from those of the SCE equation, the only legitimate representative of semiclassical gravity, based on GR+QFT.
Refined Error Estimates for the Riccati Equation with Applications to the Angular Teukolsky Equation
Felix Finster; Joel Smoller
2015-02-17T23:59:59.000Z
We derive refined rigorous error estimates for approximate solutions of Sturm-Liouville and Riccati equations with real or complex potentials. The approximate solutions include WKB approximations, Airy and parabolic cylinder functions, and certain Bessel functions. Our estimates are applied to solutions of the angular Teukolsky equation with a complex aspherical parameter in a rotating black hole Kerr geometry.
6. CONSTITUTIVE EQUATIONS 6.1 The need for constitutive equations
Cerveny, Vlastislav
6. CONSTITUTIVE EQUATIONS 6.1 The need for constitutive equations Basic principles of continuum mechanics, namely, conservation of mass, balance of momenta, and conservation of energy, discussed, three for linear momentum and one for energy) for 15 unknown field variables, namely, Â· mass density
Chemical potential and the gap equation
Huan Chen; Wei Yuan; Lei Chang; Yu-Xin Liu; Thomas Klahn; Craig D. Roberts
2008-07-17T23:59:59.000Z
In general the kernel of QCD's gap equation possesses a domain of analyticity upon which the equation's solution at nonzero chemical potential is simply obtained from the in-vacuum result through analytic continuation. On this domain the single-quark number- and scalar-density distribution functions are mu-independent. This is illustrated via two models for the gap equation's kernel. The models are alike in concentrating support in the infrared. They differ in the form of the vertex but qualitatively the results are largely insensitive to the Ansatz. In vacuum both models realise chiral symmetry in the Nambu-Goldstone mode and in the chiral limit, with increasing chemical potential, exhibit a first-order chiral symmetry restoring transition at mu~M(0), where M(p^2) is the dressed-quark mass function. There is evidence to suggest that any associated deconfinement transition is coincident and also of first-order.
Electromagnetic field with constraints and Papapetrou equation
Z. Ya. Turakulov; A. T. Muminov
2006-01-12T23:59:59.000Z
It is shown that geometric optical description of electromagnetic wave with account of its polarization in curved space-time can be obtained straightforwardly from the classical variational principle for electromagnetic field. For this end the entire functional space of electromagnetic fields must be reduced to its subspace of locally plane monochromatic waves. We have formulated the constraints under which the entire functional space of electromagnetic fields reduces to its subspace of locally plane monochromatic waves. These constraints introduce variables of another kind which specify a field of local frames associated to the wave and contain some congruence of null-curves. The Lagrangian for constrained electromagnetic field contains variables of two kinds, namely, a congruence of null-curves and the field itself. This yields two kinds of Euler-Lagrange equations. Equations of first kind are trivial due to the constraints imposed. Variation of the curves yields the Papapetrou equations for a classical massless particle with helicity 1.
Some Wave Equations for Electromagnetism and Gravitation
Zi-Hua Weng
2010-08-11T23:59:59.000Z
The paper studies the inferences of wave equations for electromagnetic fields when there are gravitational fields at the same time. In the description with the algebra of octonions, the inferences of wave equations are identical with that in conventional electromagnetic theory with vector terminology. By means of the octonion exponential function, we can draw out that the electromagnetic waves are transverse waves in a vacuum, and rephrase the law of reflection, Snell's law, Fresnel formula, and total internal reflection etc. The study claims that the theoretical results of wave equations for electromagnetic strength keep unchanged in the case for coexistence of gravitational and electromagnetic fields. Meanwhile the electric and magnetic components of electromagnetic waves can not be determined simultaneously in electromagnetic fields.
Deriving the Gross-Pitaevskii equation
Niels Benedikter
2014-04-17T23:59:59.000Z
In experiments, Bose-Einstein condensates are prepared by cooling a dilute Bose gas in a trap. After the phase transition has been reached, the trap is switched off and the evolution of the condensate observed. The evolution is macroscopically described by the Gross-Pitaevskii equation. On the microscopic level, the dynamics of Bose gases are described by the $N$-body Schr\\"odinger equation. We review our article [BdS12] in which we construct a class of initial data in Fock space which are energetically close to the ground state and prove that their evolution approximately follows the Gross-Pitaevskii equation. The key idea is to model two-particle correlations with a Bogoliubov transformation.
Interplay of Boltzmann equation and continuity equation for accelerated electrons in solar flares
Codispoti, Anna
2015-01-01T23:59:59.000Z
During solar flares a large amount of electrons are accelerated within the plasma present in the solar atmosphere. Accurate measurements of the motion of these electrons start becoming available from the analysis of hard X-ray imaging-spectroscopy observations. In this paper, we discuss the linearized perturbations of the Boltzmann kinetic equation describing an ensemble of electrons accelerated by the energy release occurring during solar flares. Either in the limit of high energy or at vanishing background temperature such an equation reduces to a continuity equation equipped with an extra force of stochastic nature. This stochastic force is actually described by the well known energy loss rate due to Coulomb collision with ambient particles, but, in order to match the collision kernel in the linearized Boltzmann equation it needs to be treated in a very specific manner. In the second part of the paper the derived continuity equation is solved with some hyperbolic techniques, and the obtained solution is wr...
Effective equations for GFT condensates from fidelity
Lorenzo Sindoni
2014-08-13T23:59:59.000Z
The derivation of effective equations for group field theories is discussed from a variational point of view, with the action being determined by the fidelity of the trial state with respect to the exact state. It is shown how the maximisation procedure with respect to the parameters of the trial state lead to the expected equations, in the case of simple condensates. Furthermore, we show that the second functional derivative of the fidelity gives a compact way to estimate, within the effective theory itself, the limits of its validity. The generalisation can be extended to include the Nakajima--Zwanzig projection method for general mixed trial states.
Self-consistent scattering theory for the radiative transport equation
Kim, Arnold D.
Self-consistent scattering theory for the radiative transport equation Arnold D. Kim School by the radiative transport equation. We present a theory for the transport equation with an inhomogeneous.5850. 1. INTRODUCTION The radiative transport equation governs light propaga- tion in random media
Wave function derivation of the JIMWLK equation
Alexey V. Popov
2008-12-16T23:59:59.000Z
Using the stationary lightcone perturbation theory, we propose the complete and careful derivation the JIMWLK equation. We show that the rigorous treatment requires the knowledge of a boosted wave function with second order accuracy. Previous wave function approaches are incomplete and implicitly used the time ordered perturbation theory, which requires a usage of an external target field.
Collapsing Solutions of the Maxwell Equations
Budko, N V; Budko, Neil V.; Samokhin, Alexander B.
2006-01-01T23:59:59.000Z
We derive the essential space-time spectrum of the Maxwell equations in linear isotropic inhomogeneous media together with the corresponding essential modes. These modes represent the collapse of the electromagnetic field into a single point in space at a single angular frequency. The location and frequency of the essential mode are random variables obeying the Born statistical postulate.
Collapsing Solutions of the Maxwell Equations
Neil V. Budko; Alexander B. Samokhin
2006-07-04T23:59:59.000Z
We derive the essential space-time spectrum of the Maxwell equations in linear isotropic inhomogeneous media together with the corresponding essential modes. These modes represent the collapse of the electromagnetic field into a single point in space at a single angular frequency. The location and frequency of the essential mode are random variables obeying the Born statistical postulate.
Using MATLAB to solve differential equations numerically
Klein, David
Using MATLAB to solve differential equations numerically Morten BrÃ¸ns Department of Mathematics of the programming language MATLAB. We will focus on practical matters and readers interested in numerical analysis as a mathematical subject should look elsewhere. In the G-databar at DTU, MATLAB can be accessed either by typing Ã?
Thermodynamics of viscoelastic fluids: the temperature equation.
Wapperom, Peter
Thermodynamics of viscoelastic fluids: the temperature equation. Peter Wapperom Martien A. Hulsen and Hydrodynamics Rotterdamseweg 145 2628 AL Delft (The Netherlands) Abstract From the thermodynamics with internal. The well- known stress differential models that fit into the thermodynamic theory will be treated
Identification for a Nonlinear Periodic Wave Equation
Morosanu, C. [Department of Mathematics, University 'Al.I.Cuza', 6600 Iasi (Romania); Trenchea, C. [Institute of Mathematics of Romanian Academy, 6600 Iasi (Romania)
2001-07-01T23:59:59.000Z
This work is concerned with an approximation process for the identification of nonlinearities in the nonlinear periodic wave equation. It is based on the least-squares approach and on a splitting method. A numerical algorithm of gradient type and the numerical implementation are given.
Mathematical analysis for fractional diffusion equations: forward
Boyer, Franck
or dumping WasteGroundwater flow Base rock Underground storage Soil gapsmicro scale about 100m Field: macro-Diffusion equation Result of Field Test (Adams& Gelhar, 1992) t0 t1 t2 t3 t0 Pollution source Model Prediction Univ. #12;· Determination of contamination source t u = u + F We need detailed mathematical researches
EQUATIONS FOR LOWER BOUNDS ON BORDER RANK
Hauenstein, Jonathan
EQUATIONS FOR LOWER BOUNDS ON BORDER RANK JONATHAN D. HAUENSTEIN, CHRISTIAN IKENMEYER, AND J of bilinear maps of border rank at most r. We apply these methods to several cases including the case r = 6 multiplication operator M2, which gives a new proof that the border rank of the multiplication of 2 Ã? 2 matrices
Primes Solutions Of Linear Diophantine Equations
N. A. Carella
2014-04-03T23:59:59.000Z
Let k => 1, m => 1 be small fixed integers, gcd(k, m) = 1. This note develops some techniques for proving the existence of infinitely many primes solutions x = p, and y = q of the linear Diophantine equation y = mx + k.
Optimization of Differential-Algebraic Equation Systems
Grossmann, Ignacio E.
(reactor, column) nu control profiles for optimal operation Constraints: uL u(t) uU zL z(t) z optimal reactor temperature policy optimal column reflux ratio Batch Process Optimization zi,I 0 zi,II 01 Optimization of Differential- Algebraic Equation Systems L. T. Biegler Chemical Engineering
Meromorphic solutions of algebraic differential equations
2005-10-13T23:59:59.000Z
function we mean one that is meromorphic in C. We always use ? to denote .... In § §3 and 4 we give a new proof and a ..... F(y', y, z) = 0 can be regarded as the equation of a family of curves depending on the parameter z. ...... Atomic Energy Agency, Vienna 1976. MR 58 .... Low temperature Physical-technical Institute of the.
On Process Equivalence = Equation Solving in CCS
Bundy, Alan; Monroy, Raul; Green, Ian
turned into equation solving (Lin 1995a). Existing tools for this proof task, such as VPAM (Lin 1993), are highly interactive. We introduce a method that automates the use of UFI. The method uses middle-out reasoning (Bundy et al. 1990a) and, so, is able...
Exact N-envelope-soliton solutions of the Hirota equation
Jian-Jun Shu
2014-03-14T23:59:59.000Z
We discuss some properties of the soliton equations of the type, partial derivative u/partial derivative t = S [u, (u) over bar], where S is a nonlinear operator differential in x, and present the additivity theorems of the class of the soliton equations. On using the theorems, we can construct a new soliton equation through two soliton equations with similar properties. Meanwhile, exact N-envelope-soliton solutions of the Hirota equation are derived through the trace method.
Hammett, Greg
Chapter 3 Landau Fluid Equations The Navier--Stokes equations for neutral fluids are highly for deriving the plasma fluid equations of Braginskii (1965). Plasma waves, especially those driven. The approach to deriving plasma fluid equation by Hammett and Perkins (1990) was to derive the fluid closures
Amplitude equations for a linear wave equation in a weakly curved pipe
Shin-itiro Goto
2009-10-03T23:59:59.000Z
We study boundary effects in a linear wave equation with Dirichlet type conditions in a weakly curved pipe. The coordinates in our pipe are prescribed by a given small curvature with finite range, while the pipe's cross section being circular. Based on the straight pipe case a perturbative analysis by which the boundary value conditions are exactly satisfied is employed. As such an analysis we decompose the wave equation into a set of ordinary differential equations perturbatively. We show the conditions when secular terms due to the curbed boundary appear in the naive peturbative analysis. In eliminating such a secularity with a singular perturbation method, we derive amplitude equations and show that the eigenfrequencies in time are shifted due to the curved boundary.
Schwartz, Peter; Barad, Michael; Colella, Phillip; Ligocki, Terry
2004-01-01T23:59:59.000Z
A Cartesian grid embedded boundary method for the heatA Cartesian Grid Embedded Boundary Method for the HeatError Grid Size Fig. 17. Solution error for heat equation on
Hewett, D.W.; Larson, D.J.; Doss, S. (Lawrence Livermore National Lab., Livermore, CA (United States))
1992-07-01T23:59:59.000Z
We apply a particular version of ADI called Dynamic ADI (DADI) to the strongly coupled 2nd-order partial differential equations that arise from the streamlined Darwin field (SDF) equations. The DADI method a applied in a form that we show is guaranteed to converge to the desired solution of the finite difference equation. We give overviews of our test case, the SDF problem and the DADI method, with some justification for our choice of operator splitting. Finally, we apply DADI to the strongly coupled SDF equations and present the results from our test case. Our implementation requires a factor of 7 less storage and has proven to be a factor of 4 (in the worst case) to several orders of magnitude faster than competing methods. 13 refs., 3 figs., 5 tabs.
E. V. Shiryaeva; M. Yu. Zhukov
2014-10-10T23:59:59.000Z
In paper [S.I. Senashov, A. Yakhno. 2012. SIGMA. Vol.8. 071] the variant of the hodograph method based on the conservation laws for two hyperbolic quasilinear equations of the first order is described. Using these results we propose a method which allows to reduce the Cauchy problem for the two quasilinear PDE's to the Cauchy problem for ODE's. The proposed method is actually some similar method of characteristics for a system of two hyperbolic quasilinear equations. The method can be used effectively in all cases, when the linear hyperbolic equation in partial derivatives of the second order with variable coefficients, resulting from the application of the hodograph method, has an explicit expression for the Riemann-Green function. One of the method's features is the possibility to construct a multi-valued solutions. In this paper we present examples of method application for solving the classical shallow water equations.
Use of the Richards equation in land surface parameterizations Deborah H. Lee1
equation, and an analytical kinematic wave solution of Richards equation. Comparisons show that depth
Solving Partial Differential Equations on Overlapping Grids
Henshaw, W D
2008-09-22T23:59:59.000Z
We discuss the solution of partial differential equations (PDEs) on overlapping grids. This is a powerful technique for efficiently solving problems in complex, possibly moving, geometry. An overlapping grid consists of a set of structured grids that overlap and cover the computational domain. By allowing the grids to overlap, grids for complex geometries can be more easily constructed. The overlapping grid approach can also be used to remove coordinate singularities by, for example, covering a sphere with two or more patches. We describe the application of the overlapping grid approach to a variety of different problems. These include the solution of incompressible fluid flows with moving and deforming geometry, the solution of high-speed compressible reactive flow with rigid bodies using adaptive mesh refinement (AMR), and the solution of the time-domain Maxwell's equations of electromagnetism.
Fundamental Equation of State for Deuterium
Richardson, I. A.; Leachman, J. W., E-mail: jacob.leachman@wsu.edu [HYdrogen Properties for Energy Research (HYPER) Laboratory, School of Mechanical and Materials Engineering, Washington State University, P.O. Box 642920, Pullman, Washington 99164 (United States); Lemmon, E. W. [Applied Chemicals and Materials Division, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305 (United States)] [Applied Chemicals and Materials Division, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305 (United States)
2014-03-15T23:59:59.000Z
World utilization of deuterium is anticipated to increase with the rise of fusion-energy machines such as ITER and NIF. We present a new fundamental equation of state for the thermodynamic properties of fluid deuterium. Differences between thermodynamic properties of orthodeuterium, normal deuterium, and paradeuterium are described. Separate ideal-gas functions were fitted for these separable forms together with a single real-fluid residual function. The equation of state is valid from the melting line to a maximum pressure of 2000 MPa and an upper temperature limit of 600 K, corresponding to available experimental measurements. The uncertainty in predicted density is 0.5% over the valid temperature range and pressures up to 300 MPa. The uncertainties of vapor pressures and saturated liquid densities are 2% and 3%, respectively, while speed-of-sound values are accurate to within 1% in the liquid phase.
Euler's fluid equations: Optimal Control vs Optimization
Darryl D. Holm
2009-09-28T23:59:59.000Z
An optimization method used in image-processing (metamorphosis) is found to imply Euler's equations for incompressible flow of an inviscid fluid, without requiring that the Lagrangian particle labels exactly follow the flow lines of the Eulerian velocity vector field. Thus, an optimal control problem and an optimization problem for incompressible ideal fluid flow both yield the \\emph {same} Euler fluid equations, although their Lagrangian parcel dynamics are \\emph{different}. This is a result of the \\emph{gauge freedom} in the definition of the fluid pressure for an incompressible flow, in combination with the symmetry of fluid dynamics under relabeling of their Lagrangian coordinates. Similar ideas are also illustrated for SO(N) rigid body motion.
Spinning particles and higher spin field equations
Bastianelli, Fiorenzo; Corradini, Olindo; Latini, Emanuele
2015-01-01T23:59:59.000Z
Relativistic particles with higher spin can be described in first quantization using actions with local supersymmetry on the worldline. First, we present a brief review of these actions and their use in first quantization. In a Dirac quantization scheme the field equations emerge as Dirac constraints on the Hilbert space, and we outline how they lead to the description of higher spin fields in terms of the more standard Fronsdal-Labastida equations. Then, we describe how these actions can be extended so that the propagating particle is allowed to take different values of the spin, i.e. carry a reducible representation of the Poincar\\'e group. This way one may identify a four dimensional model that carries the same degrees of freedom of the minimal Vasiliev's interacting higher spin field theory. Extensions to massive particles and to propagation on (A)dS spaces are also briefly commented upon.
Weakly nonlocal fluid mechanics - the Schrodinger equation
P. Van; T. Fulop
2004-06-09T23:59:59.000Z
A weakly nonlocal extension of ideal fluid dynamics is derived from the Second Law of thermodynamics. It is proved that in the reversible limit the additional pressure term can be derived from a potential. The requirement of the additivity of the specific entropy function determines the quantum potential uniquely. The relation to other known derivations of Schr\\"odinger equation (stochastic, Fisher information, exact uncertainty) is clarified.
Bosonic Fradkin-Tseytlin equations unfolded
Oleg Shaynkman
2014-12-24T23:59:59.000Z
We test series of infinite-dimensional algebras as the candidates for higher spin extension of su(k,k). Adjoint and twisted-adjoint representations of su(k,k) on spaces of these algebras are carefully explored. For k=2 corresponding unfolded systems are analyzed and they shown to encode Fradkin-Tseytlin equations for some set of integer spins. In each case spectrum of spins is found.
Comments on the equation rax Reese Scott
Styer, Robert
Comments on the equation Â±rax Â± sby = c. Reese Scott Robert Styer revised 7 Sept 2013 For given not a member of a known infinite family). Some of these anomalous cases are quite high, e.g., (a, b, c, r, s number k such that kc = C, and for every i there exists a j such that kraxi = RAXj and ksbyi = SBYj , 1
Comments on the equation rax Reese Scott
Styer, Robert
, v) = (0, 0) (E.) gcd(ra, sb) = 1, (F.) r = s = 1, (G.) a is prime, (H.) a and b are both prime, (IComments on the equation Â±rax Â± sby = c. Reese Scott Robert Styer revised 1 Aug 2013 For given not a member of a known infinite family). Some of these anomalous cases are quite high, e.g., (a, b, c, r, s
Embeddings for solutions of Einstein equations
S. A. Paston; A. A. Sheykin
2013-06-20T23:59:59.000Z
We study isometric embeddings of some solutions of the Einstein equations with suffciently high symmetries into a flat ambient space. We briefly describe a method for constructing surfaces with a given symmetry. We discuss all minimal embeddings of the Schwarzschild metric obtained using this method and show how the method can be used to construct all minimal embeddings for the Friedmann models. We classify all the embeddings in terms of realizations of symmetries of the corresponding solutions.
Speed selection for coupled wave equations
Mariano Cadoni; Giuseppe Gaeta
2015-01-13T23:59:59.000Z
We discuss models for coupled wave equations describing interacting fields, focusing on the speed of travelling wave solutions. In particular, we propose a general mechanism for selecting and tuning the speed of the corresponding (multi-component) travelling wave solutions under certain physical conditions. A number of physical models (molecular chains, coupled Josephson junctions, propagation of kinks in chains of adsorbed atoms and domain walls) are considered as examples.
Laguerre method to solve parton evolution equations
Mirjalili, A. [Physics Department, Yazd University, P.O.B. 89195-741, Yazd (Iran, Islamic Republic of); School of Particles and Accelerators (IPM), Institute for Research in Fundamental Sciences, 19395-5531, Tehran (Iran, Islamic Republic of); Yazdanpanah, M. M. [Physics Department, Shahid-Bahonar University, Kerman (Iran, Islamic Republic of); School of Particles and Accelerators (IPM), Institute for Research in Fundamental Sciences, 19395-5531, Tehran (Iran, Islamic Republic of); Sharifinejad, H. R. [Physics Department, Yazd University, P.O.B. 89195-741, Yazd (Iran, Islamic Republic of)
2011-05-23T23:59:59.000Z
The DGLAP evolution equations for non-singlet sector of parton density is solved in x-space based on Laguerre polynomial expansion. High numerical accuracy is achieved by expanding over a set of approximately 30 polynomials. The result of evolved parton densities to high energy scales are in good agreement with phenomenological GRV model. To improve the results we can employ a constituent quark model.
Total Operators and Inhomogeneous Proper Values Equations
Jose G. Vargas
2015-03-27T23:59:59.000Z
Kaehler's two-sided angular momentum operator, K + 1, is neither vector-valued nor bivector-valued. It is total in the sense that it involves terms for all three dimensions. Constant idempotents that are "proper functions" of K+1's components are not proper functions of K+1. They rather satisfy "inhomogeneous proper-value equations", i.e. of the form (K + 1)U = {\\mu}U + {\\pi}, where {\\pi} is a scalar. We consider an equation of that type with K+1 replaced with operators T that comprise K + 1 as a factor, but also containing factors for both space and spacetime translations. We study the action of those T's on linear combinations of constant idempotents, so that only the algebraic (spin) part of K +1 has to be considered. {\\pi} is now, in general, a non-scalar member of a Kaehler algebra. We develop the system of equations to be satisfied by the combinations of those idempotents for which {\\pi} becomes a scalar. We solve for its solutions with {\\mu} = 0, which actually also makes {\\pi} = 0: The solutions with {\\mu} = {\\pi} = 0 all have three constituent parts, 36 of them being different in the ensemble of all such solutions. That set of different constituents is structured in such a way that we might as well be speaking of an algebraic representation of quarks. In this paper, however, we refrain from pursuing this identification in order to emphasize the purely mathematical nature of the argument.
Nonholonomic Hamilton-Jacobi equation and Integrability
Tomoki Ohsawa; Anthony M. Bloch
2009-06-18T23:59:59.000Z
We discuss an extension of the Hamilton-Jacobi theory to nonholonomic mechanics with a particular interest in its application to exactly integrating the equations of motion. We give an intrinsic proof of a nonholonomic analogue of the Hamilton--Jacobi theorem. Our intrinsic proof clarifies the difference from the conventional Hamilton-Jacobi theory for unconstrained systems. The proof also helps us identify a geometric meaning of the conditions on the solutions of the Hamilton-Jacobi equation that arise from nonholonomic constraints. The major advantage of our result is that it provides us with a method of integrating the equations of motion just as the unconstrained Hamilton--Jacobi theory does. In particular, we build on the work by Iglesias-Ponte, de Leon, and Martin de Diego so that the conventional method of separation of variables applies to some nonholonomic mechanical systems. We also show a way to apply our result to systems to which separation of variables does not apply.
Macroscopic equations for the adiabatic piston
Massimo Cencini; Luigi Palatella; Simone Pigolotti; Angelo Vulpiani
2007-09-13T23:59:59.000Z
A simplified version of a classical problem in thermodynamics -- the adiabatic piston -- is discussed in the framework of kinetic theory. We consider the limit of gases whose relaxation time is extremely fast so that the gases contained on the left and right chambers of the piston are always in equilibrium (that is the molecules are uniformly distributed and their velocities obey the Maxwell-Boltzmann distribution) after any collision with the piston. Then by using kinetic theory we derive the collision statistics from which we obtain a set of ordinary differential equations for the evolution of the macroscopic observables (namely the piston average velocity and position, the velocity variance and the temperatures of the two compartments). The dynamics of these equations is compared with simulations of an ideal gas and a microscopic model of gas settled to verify the assumptions used in the derivation. We show that the equations predict an evolution for the macroscopic variables which catches the basic features of the problem. The results here presented recover those derived, using a different approach, by Gruber, Pache and Lesne in J. Stat. Phys. 108, 669 (2002) and 112, 1177 (2003).
Solution generating theorems for the TOV equation
Petarpa Boonserm; Matt Visser; Silke Weinfurtner
2007-07-17T23:59:59.000Z
The Tolman-Oppenheimer-Volkov [TOV] equation constrains the internal structure of general relativistic static perfect fluid spheres. We develop several "solution generating" theorems for the TOV, whereby any given solution can be "deformed" to a new solution. Because the theorems we develop work directly in terms of the physical observables -- pressure profile and density profile -- it is relatively easy to check the density and pressure profiles for physical reasonableness. This work complements our previous article [Phys. Rev. D71 (2005) 124307; gr-qc/0503007] wherein a similar "algorithmic" analysis of the general relativistic static perfect fluid sphere was presented in terms of the spacetime geometry -- in the present analysis the pressure and density are primary and the spacetime geometry is secondary. In particular, our "deformed" solutions to the TOV equation are conveniently parameterized in terms of delta rho_c and delta p_c, the finite shift in the central density and central pressure. We conclude by presenting a new physical and mathematical interpretation of the TOV equation -- as an integrability condition on the density and pressure profiles.
Propagation of ultra-short solitons in stochastic Maxwell's equations
Kurt, Levent, E-mail: LKurt@gc.cuny.edu [Department of Science, Borough of Manhattan Community College, City University of New York, New York, New York 10007 (United States)] [Department of Science, Borough of Manhattan Community College, City University of New York, New York, New York 10007 (United States); Schäfer, Tobias [Department of Mathematics, College of Staten Island, City University of New York, Staten Island, New York 10314 (United States)] [Department of Mathematics, College of Staten Island, City University of New York, Staten Island, New York 10314 (United States)
2014-01-15T23:59:59.000Z
We study the propagation of ultra-short short solitons in a cubic nonlinear medium modeled by nonlinear Maxwell's equations with stochastic variations of media. We consider three cases: variations of (a) the dispersion, (b) the phase velocity, (c) the nonlinear coefficient. Using a modified multi-scale expansion for stochastic systems, we derive new stochastic generalizations of the short pulse equation that approximate the solutions of stochastic nonlinear Maxwell's equations. Numerical simulations show that soliton solutions of the short pulse equation propagate stably in stochastic nonlinear Maxwell's equations and that the generalized stochastic short pulse equations approximate the solutions to the stochastic Maxwell's equations over the distances under consideration. This holds for both a pathwise comparison of the stochastic equations as well as for a comparison of the resulting probability densities.
Parallel Solutions of Partial Differential Equations with Adaptive Multigrid Methods
Wieners, Christian
Parallel Solutions of Partial Differential Equations with Adaptive Multigrid Methods results for the solution of partial differential equations based on the software platform UG. State/coarsening, robust parallel multigrid methods, various dis cretizations, dynamic load balancing, mapping and grid
Reduced magnetohydrodynamic equations with coupled Alfvn and sound wave dynamics
kinetic, thermal, electromagnetic, and gravitational forms. As in previous analysis, the equations+ , He+ , and O+ , curvilinear geometry, gravitation, and rotation are also allowed. The equations perturbation may be neglected. For such distur- bances, Faraday's law implies that the perpendicular velocity
Differential form of the Skornyakov-Ter-Martirosyan Equations
Pen'kov, F. M.; Sandhas, W. [Joint Institute for Nuclear Research, Dubna (Russian Federation) and Institute of Nuclear Physics, Almaty (Kazakhstan); Physikalisches Institut, Universitaet Bonn, Bonn (Germany)
2005-12-15T23:59:59.000Z
The Skornyakov-Ter-Martirosyan three-boson integral equations in momentum space are transformed into differential equations. This allows us to take into account quite directly the Danilov condition providing self-adjointness of the underlying three-body Hamiltonian with zero-range pair interactions. For the helium trimer the numerical solutions of the resulting differential equations are compared with those of the Faddeev-type AGS equations.
The Hamilton-Jacobi equation on Lie affgebroids
Juan Carlos Marrero; Diana Sosa
2005-11-03T23:59:59.000Z
The Hamilton-Jacobi equation for a Hamiltonian section on a Lie affgebroid is introduced and some examples are discussed.
SCIENCE ON SATURDAY- "Disastrous Equations: The Role of Mathematics...
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
Equations: The Role of Mathematics in Understanding Tsunami" Professor J. Douglas Wright, Associate Professor Department of Mathematics, Drexel University Presentation:...
Transformations of Heun's equation and its integral relations
Léa Jaccoud El-Jaick; Bartolomeu D. B. Figueiredo
2011-01-26T23:59:59.000Z
We find transformations of variables which preserve the form of the equation for the kernels of integral relations among solutions of the Heun equation. These transformations lead to new kernels for the Heun equation, given by single hypergeometric functions (Lambe-Ward-type kernels) and by products of two hypergeometric functions (Erd\\'elyi-type). Such kernels, by a limiting process, also afford new kernels for the confluent Heun equation.
Wave Propagation Theory 2.1 The Wave Equation
2 Wave Propagation Theory 2.1 The Wave Equation The wave equation in an ideal fluid can be derived #12;66 2. Wave Propagation Theory quantities of the quiescent (time independent) medium are identified perturbations is much smaller than the speed of sound. 2.1.1 The Nonlinear Wave Equation Retaining higher
Discrete Ordinate Method for Solving Inhomogeneous Vector Radiative Transfer Equation
Pattanaik, Sumanta N.
paper.. This type of equation appears when modeling radiative transport in plane parallel media. WeDiscrete Ordinate Method for Solving Inhomogeneous Vector Radiative Transfer Equation We describe here a solution method for equations of the type given by: Âµ I(,Âµ) +I(,Âµ)- () 2 1 -1 Z(,Âµ,Âµ )I(,Âµ )dÂµ
Di usion Approximation of Radiative Transfer Equations in a Channel
Bal, Guillaume
direction. 1 #12; 1 Introduction Radiative transport equations were #12;rst used to describe the propagationDi#11;usion Approximation of Radiative Transfer Equations in a Channel Guillaume Bal Department by a di#11;usion equation. However, the thickness of the crust is of the order of the transport mean free
PARALLEL COMPUTATION OF THE BOLTZMANN TRANSPORT EQUATION FOR MICROSCALE HEAT
Miller, Richard S.
silicon Ã°SiÃ? and silicon dioxide Ã°SiO2Ã?. The equation of phonon radiative transport Ã°ERPTÃ?, in itsPARALLEL COMPUTATION OF THE BOLTZMANN TRANSPORT EQUATION FOR MICROSCALE HEAT TRANSFER fundamental Boltzmann transport equations have been reported [3, 7, 8]. This has consequently instigated a re
Linear Kinetic Heat Transfer: Moment Equations, Boundary Conditions, and Knudsen
Struchtrup, Henning
] and phonons [6], and the radiative transfer equation [7]. The solution of any kinetic equation is usually][25], radiative transfer [7][26], and phonon transport in crystals [6]. Despite the long history, and success method, and the methods employed in [18][19][20], are based solely on the transport equations in the bulk, and
CAMASSA-HOLM TYPE EQUATIONS FOR AXISYMMETRIC POISEUILLE PIPE FLOWS
CAMASSA-HOLM TYPE EQUATIONS FOR AXISYMMETRIC POISEUILLE PIPE FLOWS FRANCESCO FEDELE AND DENYS in non-rotating axisymmetric Poiseuille pipe flows. The associated Navier-Stokes equations are reduced-axisymmetric disturbances. Contents 1. Introduction 1 2. Camassa-Holm type equations for axisymmetric pipe flows 2 3
CAMASSAHOLM TYPE EQUATIONS FOR AXISYMMETRIC POISEUILLE PIPE FLOWS
Boyer, Edmond
CAMASSAÂHOLM TYPE EQUATIONS FOR AXISYMMETRIC POISEUILLE PIPE FLOWS FRANCESCO FEDELE AND DENYS in non-rotating axisymmetric Poiseuille pipe flows. The associated Navier-Stokes equations are reduced-axisymmetric disturbances. Contents 1 Introduction 1 2 Camassa-Holm type equations for axisymmetric pipe flows 2 3 Singular
Original article Comparison of biomass component equations for four
Paris-Sud XI, UniversitÃ© de
Original article Comparison of biomass component equations for four species of northern coniferous compare equations predicting the biomass components (foliage, branches, stem, roots, total aboveground the adjusted R2 for total, aboveground, branch and foliage biomass equations by 2.5 %. Adding tree height
Uniformly Accurate Diffusive Relaxation Schemes for Multiscale Transport Equations
, radiative transfer, and transport equations for waves in random media, have a diffusive scaling that leads #12; 1. Introduction Many transport equations, such as the neutron transport [CZ], radiative transferUniformly Accurate Diffusive Relaxation Schemes for Multiscale Transport Equations Shi JIN y
Hamilton-Jacobi equations on networks Yves Achdou
Paris-Sud XI, UniversitÃ© de
Hamilton-Jacobi equations on networks Yves Achdou , Fabio Camilli , Alessandra Cutr viscosity solution of Hamilton-Jacobi equations on the network and we study related com- parison principles viscosity solution of the Hamilton-Jacobi equation on the network. Keywords Optimal control, graphs
Plane Waves in Isotropic Media 5.1 Maxwell's Equations
Palffy-Muhoray, Peter
Chapter 5 Plane Waves in Isotropic Media 5.1 Maxwell's Equations: Maxwell's equations permeability is isotropic, the last two of Maxwell's equa- tions can be combined to give the wave equation.8) 27 #12;28 CHAPTER 5. PLANE WAVES IN ISOTROPIC MEDIA Finally, using the identity Ã? Ã? A = ( Â· A)- 2
One Dimensional Autonomous Equations Can have only equilibrium attractors
Saleska, Scott
One Dimensional Autonomous Equations ( )x f x Can have only equilibrium attractors: a bounded orbit approaches an equilibrium #12;Two Dimensional Autonomous Equations ( , ) ( , ) x f x y y g x y Can have non-equilibrium attractors: for example, periodic orbits #12;Two Dimensional Autonomous Equations ( , ) ( , ) x f x y y g x y
Theory Revision in Equation Discovery Ljupco Todorovski and Saso Dzeroski
Dzeroski, Saso
. Section 5 presents the experiments with revising the earth-science equation model. The last sectionTheory Revision in Equation Discovery Ljupco Todorovski and Saso Dzeroski Department of Intelligent than from an initial hypothesis in the space of equations. On the other hand, theory revision systems
The Whitham Equation as a Model for Surface Water Waves
Daulet Moldabayev; Henrik Kalisch; Denys Dutykh
2014-10-30T23:59:59.000Z
The Whitham equation was proposed as an alternate model equation for the simplified description of uni-directional wave motion at the surface of an inviscid fluid. As the Whitham equation incorporates the full linear dispersion relation of the water wave problem, it is thought to provide a more faithful description of shorter waves of small amplitude than traditional long wave models such as the KdV equation. In this work, we identify a scaling regime in which the Whitham equation can be derived from the Hamiltonian theory of surface water waves. The Whitham equation is integrated numerically, and it is shown that the equation gives a close approximation of inviscid free surface dynamics as described by the Euler equations. The performance of the Whitham equation as a model for free surface dynamics is also compared to two standard free surface models: the KdV and the BBM equation. It is found that in a wide parameter range of amplitudes and wavelengths, the Whitham equation performs on par with or better than both the KdV and BBM equations.
GLOBAL ATTRACTIVITY OF THE ZERO SOLUTION FOR WRIGHT'S EQUATION
Neumaier, Arnold
GLOBAL ATTRACTIVITY OF THE ZERO SOLUTION FOR WRIGHT'S EQUATION BALÂ´AZS BÂ´ANHELYI, TIBOR CSENDES, TIBOR KRISZTIN, AND ARNOLD NEUMAIERÂ§ Abstract. In 1955 E.M. Wright proved that all solutions oscillating periodic solutions with large amplitudes. Key words. Delayed logistic equation, Wright's equation
Large Solutions for a System of Elliptic Equations
DÃaz, JesÃºs Ildefonso
, along with a heat equation; the equations are nonlinearly coupled through the buoyancy force and viscous-Stokes equations without thermal coupling; but if viscous heating is taken into account, well- posedness is an open). The source terms and | v|2 represent the buoyancy force and viscous heating, respectively. The system (1
BOUNDARY VALUE PROBLEMS FOR THE SHALLOW WATER EQUATIONS WITH TOPOGRAPHY
Temam, Roger
BOUNDARY VALUE PROBLEMS FOR THE SHALLOW WATER EQUATIONS WITH TOPOGRAPHY MING-CHENG SHIUE, JACQUES LAMINIE, ROGER TEMAM, AND JOSEPH TRIBBIA Abstract. In this article, the nonviscous shallow water equations) for subcritical and supercritical flows are associated with these equations. The semi- discrete cental
Song, Xiaoming
2011-04-18T23:59:59.000Z
In this dissertation, I investigate two types of stochastic differential equations driven by fractional Brownian motion and backward stochastic differential equations. Malliavin calculus is a powerful tool in developing ...
On Gaussian Beams Described by Jacobi's Equation
Steven Thomas Smith
2014-04-18T23:59:59.000Z
Gaussian beams describe the amplitude and phase of rays and are widely used to model acoustic propagation. This paper describes four new results in the theory of Gaussian beams. (1) A new version of the \\v{C}erven\\'y equations for the amplitude and phase of Gaussian beams is developed by applying the equivalence of Hamilton-Jacobi theory with Jacobi's equation that connects Riemannian curvature to geodesic flow. Thus the paper makes a fundamental connection between Gaussian beams and an acoustic channel's so-called intrinsic Gaussian curvature from differential geometry. (2) A new formula $\\pi(c/c")^{1/2}$ for the distance between convergence zones is derived and applied to several well-known profiles. (3) A class of "model spaces" are introduced that connect the acoustics of ducting/divergence zones with the channel's Gaussian curvature $K=cc"-(c')^2$. The "model" SSPs yield constant Gaussian curvature in which the geometry of ducts corresponds to great circles on a sphere and convergence zones correspond to antipodes. The distance between caustics $\\pi(c/c")^{1/2}$ is equated with an ideal hyperbolic cosine SSP duct. (4) An "intrinsic" version of \\v{C}erven\\'y's formulae for the amplitude and phase of Gaussian beams is derived that does not depend on an "extrinsic" arbitrary choice of coordinates such as range and depth. Direct comparisons are made between the computational frameworks used by the three different approaches to Gaussian beams: Snell's law, the extrinsic Frenet-Serret formulae, and the intrinsic Jacobi methods presented here. The relationship of Gaussian beams to Riemannian curvature is explained with an overview of the modern covariant geometric methods that provide a general framework for application to other special cases.
Benchmarks for the point kinetics equations
Ganapol, B. [Department of Aerospace and Mechanical Engineering (United States); Picca, P. [Department of Systems and Industrial Engineering, University of Arizona (United States); Previti, A.; Mostacci, D. [Laboratorio di Montecuccolino Alma Mater Studiorum, Universita di Bologna (Italy)
2013-07-01T23:59:59.000Z
A new numerical algorithm is presented for the solution to the point kinetics equations (PKEs), whose accurate solution has been sought for over 60 years. The method couples the simplest of finite difference methods, a backward Euler, with Richardsons extrapolation, also called an acceleration. From this coupling, a series of benchmarks have emerged. These include cases from the literature as well as several new ones. The novelty of this presentation lies in the breadth of reactivity insertions considered, covering both prescribed and feedback reactivities, and the extreme 8- to 9- digit accuracy achievable. The benchmarks presented are to provide guidance to those who wish to develop further numerical improvements. (authors)
The equation of motion of an electron
Kim, K. [Argonne National Laboratory, Argonne, Illinois 60439 and The University of Chicago, Chicago, Illinois 60637 (United States); Sessler, A.M. [Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States)
1999-07-01T23:59:59.000Z
We review the current status of understanding of the equation of motion of an electron. Classically, a consistent, linearized theory exists for an electron of finite extent, as long as the size of the electron is larger than the classical electron radius. Nonrelativistic quantum mechanics seems to offer a fine theory even in the point particle limit. Although there is as yet no convincing calculation, it is probable that a quantum electrodynamical result will be at least as well-behaved as is the nonrelativistic quantum mechanical results. {copyright} {ital 1999 American Institute of Physics.}
The equation of motion of an electron.
Kim, K.-J.
1998-09-02T23:59:59.000Z
We review the current status of understanding of the equation of motion of an electron. Classically, a consistent linearized theory exists for an electron of finite extent, as long as the size of the electron is larger than the classical electron radius. Nonrelativistic quantum mechanics seems to offer a fine theory even in the point particle limit. Although there is as yet no convincing calculation, it is probable that a quantum electrodynamical result will be at least as well-behaved as is the nonrelativistic quantum mechanical results.
Schrödinger-Pauli Equation for the Standard Model Extension CPT-Violating Dirac Equation
Thomas D. Gutierrez
2015-04-06T23:59:59.000Z
It is instructive to investigate the non-relativistic limit of the simplest Standard Model Extension (SME) CPT-violating Dirac-like equation but with minimal coupling to the electromagnetic fields. In this limit, it becomes an intuitive Schr\\"odinger-Pauli-like equation. This is comparable to the free particle treatment as explored by Kostelecky and Lane, but this exercise only considers the $a$ and $b$ CPT-violating terms and $\\vec{p}/m$ terms to first order. Several toy systems are discussed.
Schr\\"odinger-Pauli Equation for the Standard Model Extension CPT-Violating Dirac Equation
Gutierrez, Thomas D
2015-01-01T23:59:59.000Z
It is instructive to investigate the non-relativistic limit of the simplest Standard Model Extension (SME) CPT-violating Dirac-like equation but with minimal coupling to the electromagnetic fields. In this limit, it becomes an intuitive Schr\\"odinger-Pauli-like equation. This is comparable to the free particle treatment as explored by Kostelecky and Lane, but this exercise only considers the $a$ and $b$ CPT-violating terms and $\\vec{p}/m$ terms to first order. Several toy systems are discussed.
Generating functionals and Lagrangian partial differential equations
Vankerschaver, Joris; Liao, Cuicui; Leok, Melvin [Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, Dept. 0112, La Jolla, California 92093-0112 (United States)] [Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, Dept. 0112, La Jolla, California 92093-0112 (United States)
2013-08-15T23:59:59.000Z
The main goal of this paper is to derive an alternative characterization of the multisymplectic form formula for classical field theories using the geometry of the space of boundary values. We review the concept of Type-I/II generating functionals defined on the space of boundary data of a Lagrangian field theory. On the Lagrangian side, we define an analogue of Jacobi's solution to the Hamilton–Jacobi equation for field theories, and we show that by taking variational derivatives of this functional, we obtain an isotropic submanifold of the space of Cauchy data, described by the so-called multisymplectic form formula. As an example of the latter, we show that Lorentz's reciprocity principle in electromagnetism is a particular instance of the multisymplectic form formula. We also define a Hamiltonian analogue of Jacobi's solution, and we show that this functional is a Type-II generating functional. We finish the paper by defining a similar framework of generating functions for discrete field theories, and we show that for the linear wave equation, we recover the multisymplectic conservation law of Bridges.
On unorthodox solutions of the Bloch equations
Alexander Moroz
2012-08-22T23:59:59.000Z
A systematic, rigorous, and complete investigation of the Bloch equations in time-harmonic driving classical field is performed. Our treatment is unique in that it takes full advantage of the partial fraction decomposition over real number field, which makes it possible to find and classify all analytic solutions. Torrey's analytic solution in the form of exponentially damped harmonic oscillations [Phys. Rev. {\\bf 76}, 1059 (1949)] is found to dominate the parameter space, which justifies its use at numerous occasions in magnetic resonance and in quantum optics of atoms, molecules, and quantum dots. The unorthodox solutions of the Bloch equations, which do not have the form of exponentially damped harmonic oscillations, are confined to rather small detunings $\\delta^2\\lesssim (\\gamma-\\gamma_t)^2/27$ and small field strengths $\\Omega^2\\lesssim 8 (\\gamma-\\gamma_t)^2/27$, where $\\gamma$ and $\\gamma_t$ describe decay rates of the excited state (the total population relaxation rate) and of the coherence, respectively. The unorthodox solutions being readily accessible experimentally are characterized by rather featureless time dependence.
Using the scalable nonlinear equations solvers package
Gropp, W.D.; McInnes, L.C.; Smith, B.F.
1995-02-01T23:59:59.000Z
SNES (Scalable Nonlinear Equations Solvers) is a software package for the numerical solution of large-scale systems of nonlinear equations on both uniprocessors and parallel architectures. SNES also contains a component for the solution of unconstrained minimization problems, called SUMS (Scalable Unconstrained Minimization Solvers). Newton-like methods, which are known for their efficiency and robustness, constitute the core of the package. As part of the multilevel PETSc library, SNES incorporates many features and options from other parts of PETSc. In keeping with the spirit of the PETSc library, the nonlinear solution routines are data-structure-neutral, making them flexible and easily extensible. This users guide contains a detailed description of uniprocessor usage of SNES, with some added comments regarding multiprocessor usage. At this time the parallel version is undergoing refinement and extension, as we work toward a common interface for the uniprocessor and parallel cases. Thus, forthcoming versions of the software will contain additional features, and changes to parallel interface may result at any time. The new parallel version will employ the MPI (Message Passing Interface) standard for interprocessor communication. Since most of these details will be hidden, users will need to perform only minimal message-passing programming.
What Are the Limitations of Braginskii's Fluid Equations and Hazeltine's Drift Kinetic Equation?
Simakov, Andrei N. [Los Alamos National Laboratory, Los Alamos, NM 87544 (United States); Catto, Peter J. [MIT Plasma Science and Fusion Center, Cambridge, MA 02139 (United States)
2006-11-30T23:59:59.000Z
The two-fluid equations of Braginskii miss heat-flux terms in the viscosity. In this work we employ drift orderings to recover these missing terms and obtain a fully self-consistent system of short mean-free path two-fluid equations. These equations cannot be recovered from the short mean-free path limit of the well-known drift kinetic formalism of Hazeltine since this formalism is only accurate through first order in the small gyroradius expansion parameter, whereas second order accuracy is required. We propose a way of generalizing this formalism to make it second-order accurate. We also use the results to derive the gyroviscosity and ion perpendicular viscosity for plasmas of arbitrary collisionality, provided the leading order distribution function is velocity-space isotropic. As an application, we consider electrostatic turbulence in a tokamak and use our expressions for ion viscosity in the toroidal angular momentum conservation equation to show that the ion perpendicular viscosity can be important for determining the axisymmetric radial electric field (and, therefore, zonal flow amplitude), especially if the turbulent radial particle flux is small.
Bounding biomass in the Fisher equation
Birch, Daniel A; Young, William R
2007-01-01T23:59:59.000Z
The FKPP equation with a variable growth rate and advection by an incompressible velocity field is considered as a model for plankton dispersed by ocean currents. If the average growth rate is negative then the model has a survival-extinction transition; the location of this transition in the parameter space is constrained using variational arguments and delimited by simulations. The statistical steady state reached when the system is in the survival region of parameter space is characterized by integral constraints and upper and lower bounds on the biomass and productivity that follow from variational arguments and direct inequalities. In the limit of zero-decorrelation time the velocity field is shown to act as Fickian diffusion with an eddy diffusivity much larger than the molecular diffusivity and this allows a one-dimensional model to predict the biomass, productivity and extinction transitions. All results are illustrated with a simple growth and stirring model.
Bounding biomass in the Fisher equation
Daniel A. Birch; Yue-Kin Tsang; William R. Young
2007-03-17T23:59:59.000Z
The FKPP equation with a variable growth rate and advection by an incompressible velocity field is considered as a model for plankton dispersed by ocean currents. If the average growth rate is negative then the model has a survival-extinction transition; the location of this transition in the parameter space is constrained using variational arguments and delimited by simulations. The statistical steady state reached when the system is in the survival region of parameter space is characterized by integral constraints and upper and lower bounds on the biomass and productivity that follow from variational arguments and direct inequalities. In the limit of zero-decorrelation time the velocity field is shown to act as Fickian diffusion with an eddy diffusivity much larger than the molecular diffusivity and this allows a one-dimensional model to predict the biomass, productivity and extinction transitions. All results are illustrated with a simple growth and stirring model.
Radiative Transport Equation in Rotated Reference Frames
George Panasyuk; John C. Schotland; Vadim A. Markel
2005-05-24T23:59:59.000Z
A novel method for solving the linear radiative transport equation (RTE) in a three-dimensional homogeneous medium is proposed and illustrated with numerical examples. The method can be used with an arbitrary phase function A(s,s') with the constraint that it depends only on the angle between the angular variables s and s'. This corresponds to spherically symmetric (on average) random medium constituents. Boundary conditions are considered in the slab and half-space geometries. The approach developed in this paper is spectral. It allows for the expansion of the solution to the RTE in terms of analytical functions of angular and spatial variables to relatively high orders. The coefficients of this expansion must be computed numerically. However, the computational complexity of this task is much smaller than in the standard method of spherical harmonics. The solutions obtained are especially convenient for solving inverse problems associated with radiative transfer.
Schroedinger and Hamilton-Jacobi equations
Milos V. Lokajicek
2006-11-16T23:59:59.000Z
Time-dependent Schroedinger equation represents the basis of any quantum-theoretical approach. The question concerning its proper content in comparison to the classical physics has not been, however, fully answered until now. It will be shown that there is one-to-one physical correspondence between basic solutions (represented always by one Hamiltonian eigenfunction only) and classical ones, as the non-zero quantum potential has not any physical sense, representing only the "numerical" difference between Hamilton principal function and the phase of corresponding wave function in the case of non-inertial motion. Possible interpretation of superposition solutions will be then discussed in the light of this fact. And also different interpretation alternatives of the quantum-mechanical model will be newly analyzed and new attitude to them will be reasoned.
Stochastic evolution equations with random generators
Leon, Jorge A.; Nualart, David
1998-05-01T23:59:59.000Z
maximal inequality for the Skorohod integral deduced from the It ˆ o’s formula for this anticipating stochastic integral. 1. Introduction. In this paper we study nonlinear stochastic evolution equations of the form X t = ? + ? t 0 #3;A#3;s#4;X s +F#3;s#7;X... s #4;#4;ds+ ? t 0 B#3;s#7;X s #4;dW s #7; t ? #6;0#7;T#7;#7;(1.1) whereW is a cylindrical Wiener process on a Hilbert spaceU. The solution pro- cess X = #8;X t #7; t ? #6;0#7;T#7; is a continuous and adapted process taking values in a Hilbert space H...
Universal equations and constants of turbulent motion
Baumert, Helmut Z
2012-01-01T23:59:59.000Z
This paper presents a parameter-free theory of shear-generated turbulence at asymptotically high Reynolds numbers in incompressible fluids. It is based on a two-fluids concept. Both components are materially identical and inviscid. The first component is an ensemble of quasi-rigid dipole-vortex tubes as quasi-particles in chaotic motion. The second is a superfluid performing evasive motions between the tubes. The local dipole motions follow Helmholtz' law. The vortex radii scale with the energy-containing length scale. Collisions between quasi-particles lead either to annihilation (likewise rotation, turbulent dissipation) or to scattering (counterrotation, turbulent diffusion). There are analogies with birth and death processes of population dynamics and their master equations. For free homogeneous decay the theory predicts the TKE to follow 1/t. With an adiabatic condition at the wall it predicts the logarithmic law with von Karman's constant as 1/\\sqrt{2 pi} = 0.399. Likewise rotating couples form dissipat...
Evaluating impedances in a Sacherer integral equation
Zhang, S.Y.; Weng, W.T.
1994-08-01T23:59:59.000Z
In Sacherer integral equation, the beam line density is expanded on the phase deviation {phi}, generating a Hankel spectrum, rather than on the time, which generates a Fourier spectrum. This is a natural choice to deal with the particle evolution in phase space, it however causes complications whenever the impedance corresponding to the spectrum has to be evaluated. In this article, the line density expansion on {phi} is shown to be equivalent to a beam time modulation under an acceptable condition. Therefore for a Hankel spectrum, a number of sidebands, and the corresponding impedance as well, will be involved. For wideband resonators, it is shown that the original Sacherer solution is adequate. For narrowband resonators, the solution had been compromised, therefore a modification may be needed.
Assessment of UF6 Equation of State
Brady, P; Chand, K; Warren, D; Vandersall, J
2009-02-11T23:59:59.000Z
A common assumption in the mathematical analysis of flows of compressible fluids is to treat the fluid as a perfect gas. This is an approximation, as no real fluid obeys the perfect gas relationships over all temperature and pressure conditions. An assessment of the validity of treating the UF{sub 6} gas flow field within a gas centrifuge with perfect gas relationships has been conducted. The definition of a perfect gas is commonly stated in two parts: (1) the gas obeys the thermal equation of state, p = {rho}RT (thermally perfect), and, (2) the gas specific heats are constant (calorically perfect). Analysis indicates the thermally perfect assumption is valid for all flow conditions within the gas centrifuge, including shock fields. The low operating gas pressure is the primary factor in the suitability of the thermally perfect equation of state for gas centrifuge computations. UF{sub 6} is not calorically perfect, as the specific heats vary as a function of temperature. This effect is insignificant within the bulk of the centrifuge gas field, as gas temperatures vary over a narrow range. The exception is in the vicinity of shock fields, where temperature, pressure, and density gradients are large, and the variation of specific heats with temperature should be included in the technically detailed analyses. Results from a normal shock analysis incorporating variable specific heats is included herein, presented in the conventional form of shock parameters as a function of inlet Mach Number. The error introduced by assuming constant specific heats is small for a nominal UF{sub 6} shock field, such that calorically perfect shock relationships can be used for scaling and initial analyses. The more rigorous imperfect gas analysis should be used for detailed analyses.
Exact Solutions of Einstein's Field Equations
P. S. Negi
2004-01-08T23:59:59.000Z
We examine various well known exact solutions available in the literature to investigate the recent criterion obtained in ref. [20] which should be fulfilled by any static and spherically symmetric solution in the state of hydrostatic equilibrium. It is seen that this criterion is fulfilled only by (i) the regular solutions having a vanishing surface density together with the pressure, and (ii) the singular solutions corresponding to a non-vanishing density at the surface of the configuration . On the other hand, the regular solutions corresponding to a non-vanishing surface density do not fulfill this criterion. Based upon this investigation, we point out that the exterior Schwarzschild solution itself provides necessary conditions for the types of the density distributions to be considered inside the mass, in order to obtain exact solutions or equations of state compatible with the structure of general relativity. The regular solutions with finite centre and non-zero surface densities which do not fulfill the criterion [20], in fact, can not meet the requirement of the `actual mass' set up by exterior Schwarzschild solution. The only regular solution which could be possible in this regard is represented by uniform (homogeneous) density distribution. The criterion [20] provides a necessary and sufficient condition for any static and spherical configuration (including core-envelope models) to be compatible with the structure of general relativity. Thus, it may find application to construct the appropriate core-envelope models of stellar objects like neutron stars and may be used to test various equations of state for dense nuclear matter and the models of relativistic stellar structures like star clusters.
Residential mobility and location choice: a nested logit model with sampling of alternatives
Lee, Brian H.; Waddell, Paul
2010-01-01T23:59:59.000Z
Waddell, P. : Modeling residential location in UrbanSim. In:D. (eds. ) Modelling Residential Location Choice. Springer,based model system and a residential location model. Urban
Joint mixed logit models of stated and revealed preferences for alternative-fuel vehicles
Brownston, David; Bunch, David S.; Train, Kenneth
1999-01-01T23:59:59.000Z
for forecasting demand for alternative-fuel vehicles. In:preferences for alternative-fuel vehicles David Brownstonespondents' preferences for alternative-fuel vehicles. The e€
Thermodynamics of Spacetime: The Einstein Equation of State
Ted Jacobson
1995-06-06T23:59:59.000Z
The Einstein equation is derived from the proportionality of entropy and horizon area together with the fundamental relation $\\delta Q=TdS$ connecting heat, entropy, and temperature. The key idea is to demand that this relation hold for all the local Rindler causal horizons through each spacetime point, with $\\delta Q$ and $T$ interpreted as the energy flux and Unruh temperature seen by an accelerated observer just inside the horizon. This requires that gravitational lensing by matter energy distorts the causal structure of spacetime in just such a way that the Einstein equation holds. Viewed in this way, the Einstein equation is an equation of state. This perspective suggests that it may be no more appropriate to canonically quantize the Einstein equation than it would be to quantize the wave equation for sound in air.
Variational Principles for Constrained Electromagnetic Field and Papapetrou Equation
A. T. Muminov
2007-06-28T23:59:59.000Z
In our previous article [4] an approach to derive Papapetrou equations for constrained electromagnetic field was demonstrated by use of field variational principles. The aim of current work is to present more universal technique of deduction of the equations which could be applied to another types of non-scalar fields. It is based on Noether theorem formulated in terms of Cartan' formalism of orthonormal frames. Under infinitesimal coordinate transformation the one leads to equation which includes volume force of spin-gravitational interaction. Papapetrou equation for vector of propagation of the wave is derived on base of the equation. Such manner of deduction allows to formulate more accurately the constraints and clarify equations for the potential and for spin.
Multilevel bioluminescence tomography based on radiative transfer equation Part 1: l1 regularization
Gao, Hao; Zhao, Hongkai
2010-01-01T23:59:59.000Z
problem for the radiative transport equation,” Inv. Prob.the beginning, radiative transport equation (RTE) is used as
E-Print Network 3.0 - approximate kinetic equations Sample Search...
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
equation. Reactor kinetics and Summary: equations, prompt jump approximation; subcritical reactor kinetics, circulating fuel reactor dynamics 5... solution to neutron...
Power-law spatial dispersion from fractional Liouville equation
Tarasov, Vasily E. [Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991 (Russian Federation)] [Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991 (Russian Federation)
2013-10-15T23:59:59.000Z
A microscopic model in the framework of fractional kinetics to describe spatial dispersion of power-law type is suggested. The Liouville equation with the Caputo fractional derivatives is used to obtain the power-law dependence of the absolute permittivity on the wave vector. The fractional differential equations for electrostatic potential in the media with power-law spatial dispersion are derived. The particular solutions of these equations for the electric potential of point charge in this media are considered.
Emergent quantum Euler equation and Bose-Einstein condensates
Maxim V. Eingorn; Vitaliy D. Rusov
2014-03-16T23:59:59.000Z
In this paper, proceeding from the recently developed way of deriving the quantum-mechanical equations from the classical ones, the complete system of hydrodynamical equations, including the quantum Euler equation, is derived for a perfect fluid and an imperfect fluid with pairwise interaction between the particles. For the Bose-Einstein condensate of the latter one the Bogolyubov spectrum of elementary excitations is easily reproduced in the acoustic approximation.
Boundary transfer matrices and boundary quantum KZ equations
Bart Vlaar
2014-10-31T23:59:59.000Z
A simple relation between inhomogeneous transfer matrices and boundary quantum KZ equations is exhibited for quantum integrable systems with reflecting boundary conditions, analogous to an observation by Gaudin for periodic systems. Thus the boundary quantum KZ equations receive a new motivation. We also derive the commutativity of Sklyanin's boundary transfer matrices by merely imposing appropriate reflection equations, i.e. without using the conditions of crossing symmetry and unitarity of the R-matrix.
Stability of drift waves with the integral eigenmode equation
Chen, L.; Ke, F.J.; Xu, M.J.; Tsai, S.T.; Lee, Y.C.; Antonsen, T.M. Jr.
1981-11-01T23:59:59.000Z
An analytical theory on the stability properties of drift-wave eigenmodes in a slab plasma with finite magnetic shear is presented. The corresponding eigenmode equation is the integral equation first given by Coppi, Rosenbluth, and Sagdeev (1967) and rederived here, in a relatively simpler fashion, via the gyrokinetic equation. It is then proved that the universal drift-wave eigenmodes remain absolutely stable and finite electron temperature gradients do not alter the stability.
The fundamental solution of the unidirectional pulse propagation equation
Babushkin, I. [Institute of Mathematics, Humboldt University, Rudower Chaussee 25, 12489 Berlin (Germany)] [Institute of Mathematics, Humboldt University, Rudower Chaussee 25, 12489 Berlin (Germany); Bergé, L. [CEA, DAM, DIF, F-91297 Arpajon (France)] [CEA, DAM, DIF, F-91297 Arpajon (France)
2014-03-15T23:59:59.000Z
The fundamental solution of a variant of the three-dimensional wave equation known as “unidirectional pulse propagation equation” (UPPE) and its paraxial approximation is obtained. It is shown that the fundamental solution can be presented as a projection of a fundamental solution of the wave equation to some functional subspace. We discuss the degree of equivalence of the UPPE and the wave equation in this respect. In particular, we show that the UPPE, in contrast to the common belief, describes wave propagation in both longitudinal and temporal directions, and, thereby, its fundamental solution possesses a non-causal character.
Long-time asymptotics for fully nonlinear homogeneous parabolic equations
Armstrong, Scott N.; Trokhimtchouk, Maxim
2010-01-01T23:59:59.000Z
4), 1333–1362 (1991) S. N. Armstrong, M. Trokhimtchouk 18.are credited. References 1. Armstrong, S.N. : Principalparabolic equations Scott N. Armstrong · Maxim Trokhimtchouk
Generalized Klein-Gordon equations in d dimensions from supersymmetry
Bollini, C.G.; Giambiagi, J.J.
1985-12-15T23:59:59.000Z
The Wess-Zumino model is extended to higher dimensions, leading to a generalized Klein-Gordon equation whose propagator is computed in configuration space.
High-order rogue waves for the Hirota equation
Li, Linjing; Wu, Zhiwei; Wang, Lihong; He, Jingsong, E-mail: hejingsong@nbu.edu.cn
2013-07-15T23:59:59.000Z
The Hirota equation is better than the nonlinear Schrödinger equation when approximating deep ocean waves. In this paper, high-order rational solutions for the Hirota equation are constructed based on the parameterized Darboux transformation. Several types of this kind of solutions are classified by their structures. -- Highlights: •The determinant representation of the N-fold Darboux transformation of the Hirota equation. •Properties of the fundamental pattern of the higher order rogue wave. •Ring structure and triangular structure of the higher order rogue waves.
Differential Equations - Spring 2012, Erik Lundberg, Department of ...
Khan Academy on Differential Equations Online lectures (first one here ) it basically goes through our course in several 10 minute videos - also available on
The Multicomponent KP Hierarchy: Differential Fay Identities and Lax Equations
Lee-Peng Teo
2010-10-28T23:59:59.000Z
In this article, we show that four sets of differential Fay identities of an $N$-component KP hierarchy derived from the bilinear relation satisfied by the tau function of the hierarchy are sufficient to derive the auxiliary linear equations for the wave functions. From this, we derive the Lax representation for the $N$-component KP hierarchy, which are equations satisfied by some pseudodifferential operators with matrix coefficients. Besides the Lax equations with respect to the time variables proposed in \\cite{2}, we also obtain a set of equations relating different charge sectors, which can be considered as a generalization of the modified KP hierarchy proposed in \\cite{3}.
Generalized Harmonic Equations in 3+1 Form
J. David Brown
2011-11-29T23:59:59.000Z
The generalized harmonic equations of general relativity are written in 3+1 form. The result is a system of partial differential equations with first order time and second order space derivatives for the spatial metric, extrinsic curvature, lapse function and shift vector, plus fields that represent the time derivatives of the lapse and shift. This allows for a direct comparison between the generalized harmonic and the Arnowitt-Deser-Misner formulations. The 3+1 generalized harmonic equations are also written in terms of conformal variables and compared to the Baumgarte-Shapiro-Shibata-Nakamura equations with moving puncture gauge conditions.
Structure of equations of macrophysics V. L. Berdichevsky
Berdichevsky, Victor
of external force, dA, and the heat supply, dQ, are zero for an isolated system and the equation of the first
Bifurcations of mutually coupled equations in random graphs
Eduardo Garibaldi; Tiago Pereira
2014-09-19T23:59:59.000Z
We study the behavior of solutions of mutually coupled equations in heterogeneous random graphs. Heterogeneity means that some equations receive many inputs whereas most of the equations are given only with a few connections. Starting from a situation where the isolated equations are unstable, we prove that a heterogeneous interaction structure leads to the appearance of stable subspaces of solutions. Moreover, we show that, for certain classes of heterogeneous networks, increasing the strength of interaction leads to a cascade of bifurcations in which the dimension of the stable subspace of solutions increases. We explicitly determine the bifurcation scenario in terms of the graph structure.
Rational solutions of first-order differential equations
1999-08-19T23:59:59.000Z
Aug 19, 1999 ... [2] A. Eremenko, Meromorphic solutions of algebraic differential equations,. Russian Math. Surveys 37, 4, 1982, 61-95, Errata: 38, 6, 1983.
Universal equations and constants of turbulent motion
Helmut Z. Baumert
2012-03-22T23:59:59.000Z
This paper presents a parameter-free theory of shear-generated turbulence at asymptotically high Reynolds numbers in incompressible fluids. It is based on a two-fluids concept. Both components are materially identical and inviscid. The first component is an ensemble of quasi-rigid dipole-vortex tubes as quasi-particles in chaotic motion. The second is a superfluid performing evasive motions between the tubes. The local dipole motions follow Helmholtz' law. The vortex radii scale with the energy-containing length scale. Collisions between quasi-particles lead either to annihilation (likewise rotation, turbulent dissipation) or to scattering (counterrotation, turbulent diffusion). There are analogies with birth and death processes of population dynamics and their master equations. For free homogeneous decay the theory predicts the TKE to follow 1/t. With an adiabatic condition at the wall it predicts the logarithmic law with von Karman's constant as 1/\\sqrt{2 pi} = 0.399. Likewise rotating couples form dissipative patches almost at rest ($\\rightarrow$ intermittency) wherein the spectrum evolves like an "Apollonian gear" as discussed first by Herrmann, 1990. On this basis the prefactor of the 3D-wavenumber spectrum is predicted as (1/3)(4 pi)^{2/3}=1.8; in the Lagrangian frequency spectrum it is simply 2. The results are situated well within the scatter range of observational, experimental and DNS results.
J. Frauendiener
1997-12-11T23:59:59.000Z
This is the first in a series of articles on the numerical solution of Friedrich's conformal field equations for Einstein's theory of gravity. We will discuss in this paper why one should be interested in applying the conformal method to physical problems and why there is good hope that this might even be a good idea from the numerical point of view. We describe in detail the derivation of the conformal field equations in the spinor formalism which we use for the implementation of the equations, and present all the equations as a reference for future work. Finally, we discuss the implications of the assumptions of a continuous symmetry.
Burns, Michael E.
2004-01-01T23:59:59.000Z
??Maxwell's equations are obtained from Coulomb's Law using special relativity. For the derivation, tensor analysis is used, charge is assumed to be a conserved scalar,… (more)
Stable Difference Schemes for the Neutron Transport Equation
Ashyralyev, Allaberen [Department of Mathematics Fatih University, 34500, Istanbul (Turkey); Department of Mathematics, ITTU, Ashgabat (Turkmenistan); Taskin, Abdulgafur [Department of Mathematics Fatih University, 34500, Istanbul (Turkey)
2011-09-22T23:59:59.000Z
The initial boundary value problem for the neutron transport equation is considered. The first and second orders of accuracy difference schemes for the approximate solution of this problem are presented. In applications, the stability estimates for solutions of difference schemes for the approximate solution of the neutron transport equation are obtained. Numerical techniques are developed and algorithms are tested on an example in MATLAB.
Homogenization of the criticality spectral equation in neutron transport
Bal, Guillaume
for the neutron transport equation in a periodic heterogeneous domain, modeling the criticality study of nuclearHomogenization of the criticality spectral equation in neutron transport Gr'egoire Allaire \\Lambda problem. This result justifies and improves the engineering procedure used in practice for nuclear reactor
Solving the Linear Equation in Reservoir Simulation List of authors
Boyer, Edmond
analogous to those techniques, but ensures that material balance is preserved exactly within each planeSolving the Linear Equation in Reservoir Simulation List of authors: Julien Maes 1 Reservoir, so that solving the linear equations arising in Newtons step is more and more challenging. Simulators
LIMITE SEMI-CLASSIQUE DES EQUATIONS DE SCHRODINGERPOISSON
Alazard, Thomas
. Introduction On s'intÂ´eresse, pour ]0, 1] et x Rn , `a l'analyse BKW des Â´equations : itu + 2 2 u = Vext(t, xÂ´eveloppement BKW des Â´equations de SchrÂ¨odinger non-linÂ´eaires dÂ´elicate. 1 #12;NÂ´eanmoins, on dispose de nombreux
Applying Quadrature Rules with Multiple Nodes to Solving Integral Equations
Hashemiparast, S. M. [Department of Mathematics, Islamic Azad University Karaj Branch, K. N. Toosi University of Technology, Tehran (Iran, Islamic Republic of); Avazpour, L. [Department of Mathematics, K. N. Toosi University of Technology, P.O. Box 16315-1618 (Iran, Islamic Republic of)
2008-09-01T23:59:59.000Z
There are many procedures for the numerical solution of Fredholm integral equations. The main idea in these procedures is accuracy of the solution. In this paper, we use Gaussian quadrature with multiple nodes to improve the solution of these integral equations. The application of this method is illustrated via some examples, the related tables are given at the end.
Multilevel bioluminescence tomography based on radiative transfer equation
Soatto, Stefano
Multilevel bioluminescence tomography based on radiative transfer equation Part 2: total variation with both l1 and total- variation norm for bioluminescence tomography based on radiative transfer equation, Radiative Transfer (Dover Publications, 1960). 14. K. M. Case and P. F. PF Zweifel, Linear Transport Theory
First Order Linear Ordinary Differential Equations in Associative Algebras
Erlebacher, Gordon
. Keywords: associative algebra, factor ring, idempotent, lineal differen- tial equation, nilpotent, spectralFirst Order Linear Ordinary Differential Equations in Associative Algebras G. Erlebacher and G(t) in an associative but non-commutative algebra A, where the bi(t) form a set of commutative A-valued functions
A reciprocal transformation for the Geng-Xue equation
Li, Nianhua, E-mail: linianh@163.com; Niu, Xiaoxing [Department of Mathematics, China University of Mining and Technology, Beijing 100083 (China)] [Department of Mathematics, China University of Mining and Technology, Beijing 100083 (China)
2014-05-15T23:59:59.000Z
In this paper, we construct a reciprocal transformation for the Geng-Xue equation and show that, with help of this transformation, we relate the first negative flow of the modified Boussinesq hierarchy to the Geng-Xue equation. Furthermore, we analyze the construction of conserved quantities and present new ones.
The nonlinear Schrodinger equation with a strongly anisotropic harmonic potential
Méhats, Florian
The nonlinear Schr¨odinger equation with general nonlinearity and har- monic confining potential is considered is shown to be propagated, and the lower dimensional modulation wave function again satisfies a nonlinear Schr¨odinger equation. The main tools of the analysis are energy and Strichartz estimates as well
EFFECTIVE MAXWELL EQUATIONS FROM TIME-DEPENDENT DENSITY FUNCTIONAL THEORY
Bigelow, Stephen
EFFECTIVE MAXWELL EQUATIONS FROM TIME-DEPENDENT DENSITY FUNCTIONAL THEORY WEINAN E, JIANFENG LU and magnetic fields are derived starting from time-dependent density functional theory. Effective permittivity with the density functional theory [2Â4] instead of the many-body SchrÂ¨odinger or Dirac equations. This is because
Asymptotic Solutions of Hamilton-Jacobi Equations with State Constraints
Mitake, Hiroyoshi [Waseda University, Department of Pure and Applied Mathematics (Japan)], E-mail: take_take_hiro2@akane.waseda.jp
2008-12-15T23:59:59.000Z
We study Hamilton-Jacobi equations in a bounded domain with the state constraint boundary condition. We establish a general convergence result for viscosity solutions of the Cauchy problem for Hamilton-Jacobi equations with the state constraint boundary condition to asymptotic solutions as time goes to infinity.
Hamilton-Jacobi equations with discontinuous source terms Nao Hamamuki
Ishii, Hitoshi
Hamilton-Jacobi equations with discontinuous source terms Nao Hamamuki We study the initial-value problem for the Hamilton-Jacobi equation of the form { tu(x, t) + H(x, xu(x, t)) = 0 in Rn Ã? (0, T), u control problem with a semicontinuous running cost function. References [1] Y. Giga, N. Hamamuki, Hamilton
THE HAMILTON-JACOBI EQUATION, INTEGRABILITY, AND NONHOLONOMIC SYSTEMS
FassÃ², Francesco
THE HAMILTON-JACOBI EQUATION, INTEGRABILITY, AND NONHOLONOMIC SYSTEMS LARRY BATES, FRANCESCO FASSÃ? why it appears there should not be an analogue of a complete integral for the Hamilton-Jacobi equation for integrable nonholonomic systems. February 7, 2014 1. Introduction The Hamilton-Jacobi theory is at the heart
The Dirac equation in D-dimensional spherically symmetric spacetimes
A. Lopez-Ortega
2009-06-15T23:59:59.000Z
We expound in detail a method frequently used to reduce the Dirac equation in D-dimensional (D >= 4) spherically symmetric spacetimes to a pair of coupled partial differential equations in two variables. As a simple application of these results we exactly calculate the quasinormal frequencies of the uncharged Dirac field propagating in the D-dimensional Nariai spacetime.
Invariant measures for a stochastic porous medium equation
RÃ¶ckner, Michael
Invariant measures for a stochastic porous medium equation Giuseppe Da Prato (Scuola Normale AMS :76S05,35J25, 37L40 . 1 Introduction The porous medium equation X t = (Xm ), m N, (1 Brownian motion in H and C is a positive definite bounded operator on H of trace class. To be more concrete
$(1+1)$ dimensional Dirac equation with non Hermitian interaction
A. Sinha; P. Roy
2005-11-29T23:59:59.000Z
We study $(1+1)$ dimensional Dirac equation with non Hermitian interactions, but real energies. In particular, we analyze the pseudoscalar and scalar interactions in detail, illustrating our observations with some examples. We also show that the relevant hidden symmetry of the Dirac equation with such an interaction is pseudo supersymmetry.
SPECTRA OF CRITICAL EXPONENTS IN NONLINEAR HEAT EQUATIONS WITH ABSORPTION
Bath, University of
SPECTRA OF CRITICAL EXPONENTS IN NONLINEAR HEAT EQUATIONS WITH ABSORPTION V.A. GALAKTIONOV AND P of the classical porous medium equation with absorption u t = #1;u m u p in R N #2; R+ change their large-time behaviour at the critical absorption exponent p 0 = m+2=N . We show that, actually, there exists an in#12
TIME-PERIODIC SOUND WAVE PROPAGATION COMPRESSIBLE EULER EQUATIONS
A PARADIGM FOR TIME-PERIODIC SOUND WAVE PROPAGATION IN THE COMPRESSIBLE EULER EQUATIONS BLAKE consistent with time-periodic sound wave propagation in the 3 Ã? 3 nonlinear compressible Euler equations description of shock-free waves that propagate through an oscillating entropy field without breaking or dis
Electron Spin Precession for the Time Fractional Pauli Equation
Hosein Nasrolahpour
2011-04-05T23:59:59.000Z
In this work, we aim to extend the application of the fractional calculus in the realm of quantum mechanics. We present a time fractional Pauli equation containing Caputo fractional derivative. By use of the new equation we study the electron spin precession problem in a homogeneous constant magnetic field.
Capillary waves in the subcritical nonlinear Schroedinger equation
Kozyreff, G. [Optique Nonlineaire Theorique, Universite Libre de Bruxelles (U.L.B.), CP 231, B-1050 Brussels (Belgium)
2010-01-15T23:59:59.000Z
We expand recent results on the nonlinear Schroedinger equation with cubic-quintic nonlinearity to show that some solutions are described by the Bernoulli equation in the presence of surface tension. As a consequence, capillary waves are predicted and found numerically at the interface between regions of large and low amplitude.
Static Solutions of Einstein's Equations with Spherical Symmetry
Iftikhar Ahmad; Maqsoom Fatima; Najam-ul-Basat
2014-05-02T23:59:59.000Z
The Schwarzschild solution is a complete solution of Einstein's field equations for a static spherically symmetric field. The Einstein's field equations solutions appear in the literature, but in different ways corresponding to different definitions of the radial coordinate. We attempt to compare them to the solutions with nonvanishing energy density and pressure. We also calculate some special cases with changes in spherical symmetry.
Einstein equations in the null quasi-spherical gauge
Robert Bartnik
1997-05-29T23:59:59.000Z
The structure of the full Einstein equations in a coordinate gauge based on expanding null hypersurfaces foliated by metric 2-spheres is explored. The simple form of the resulting equations has many applications -- in the present paper we describe the structure of timelike boundary conditions; the matching problem across null hypersurfaces; and the propagation of gravitational shocks.
The modified equation for spinless particles and superalgebra
Sadeghi, J.; Rostami, M. [Department of Physics, Islamic Azad University, Ayatollah Amoli Branch, P.O. Box 678, Amol (Iran, Islamic Republic of)] [Department of Physics, Islamic Azad University, Ayatollah Amoli Branch, P.O. Box 678, Amol (Iran, Islamic Republic of); Sadeghi, Z. [Young Researchers Club, Islamic Azad University, Ayatollah Amoli Branch, Amol (Iran, Islamic Republic of)] [Young Researchers Club, Islamic Azad University, Ayatollah Amoli Branch, Amol (Iran, Islamic Republic of)
2013-09-15T23:59:59.000Z
In this paper we consider modified wave equations for spinless particles in an external magnetic field. We consider 4-potentials which guarantee Lorentz' and Coulomb's conditions. The new variable for modified wave equation leads us to consider the associated Laguerre differential equation. We take advantage of the factorization method in Laguerre differential equation and solve the modified equation. In order to obtain the wave function, energy spectrum and its quantization, we will establish conditions for the orbital quantum number. We account such orbital quantum number and obtain the raising and lowering operators. If we want to have supersymmetry partners, we need to apply the shape invariance condition. This condition for the partner potential will help us find the limit of ? as ?=±?(l)
Symmetries of Differential equations and Applications in Relativistic Physics
Paliathanasis, Andronikos
2015-01-01T23:59:59.000Z
In this thesis, we study the one parameter point transformations which leave invariant the differential equations. In particular we study the Lie and the Noether point symmetries of second order differential equations. We establish a new geometric method which relates the point symmetries of the differential equations with the collineations of the underlying manifold where the motion occurs. This geometric method is applied in order the two and three dimensional Newtonian dynamical systems to be classified in relation to the point symmetries; to generalize the Newtonian Kepler-Ermakov system in Riemannian spaces; to study the symmetries between classical and quantum systems and to investigate the geometric origin of the Type II hidden symmetries for the homogeneous heat equation and for the Laplace equation in Riemannian spaces. At last but not least, we apply this geometric approach in order to determine the dark energy models by use the Noether symmetries as a geometric criterion in modified theories of gra...
Gibbon, J. D.
The Kinematic Wave Equation (KWE) In Tuesday's interrupted lecture we derived the Kinematic Wave refer to partial derivatives. Kinematic waves occur when we take Q = Q(), in which case t + c()x = 0 (2) where the propagation velocity is c() = dQ/d. (2) is called the Kinematic Wave Equation (KWE). We wish
Paris-Sud XI, Université de
on the 500±67300 km, 4° inclination EQUATOR-S orbit show that the increase of the energetic electron ¯ux of electrons in the outer radiation belt has been attributed to Pc 5 band ULF waves excited by high speed solar wind ¯ow associated with magnetic storms (Rostoker et al., 1998). The main features
An improved viscosity equation to characterize shear-thinning fluids
Allen, E.
1995-11-01T23:59:59.000Z
An improved viscosity equation is proposed for shear-thinning polymer solutions, using a kinetic approach to model the rate of formation and loss of interactive bonding during shear flow. The bonds are caused by temporary polymer entanglements in polymer solutions, and by coordination bonding in metal ion cross-linked gels. The equation characterizes the viscosity of shear-thinning fluids over a wide range of shear rates, from the zero shear region through to infinite shear viscosity. The equation has been used to characterize fluid data from a wide range of fluids. Recent work indicates that a range of polymer solutions, polymer-based drilling fluids and frac-gels do not have a measurable yield stress, and that the equations which use extrapolated values of yield stress can be significantly in error. The new equation is compared with the Carreau and Cross equations, using the correlation procedure of Churchill and Usagi. It gives a significantly better fit to the data (by up to 50%) over a wide range of shear rates. The improved equation can be used for evaluating the fluid viscosity during the flow of polymeric fluids, in a range of oilfield applications including drilling, completion, stimulation and improved recovery (IOR) processes.
Discrete KP equation with self-consistent sources
Adam Doliwa; Runliang Lin
2014-04-05T23:59:59.000Z
We show that the discrete Kadomtsev-Petviashvili (KP) equation with sources obtained recently by the "source generalization" method can be incorporated into the squared eigenfunction symmetry extension procedure. Moreover, using the known correspondence between Darboux-type transformations and additional independent variables, we demonstrate that the equation with sources can be derived from Hirota's discrete KP equations but in a space of higher dimension. In this way we uncover the origin of the source terms as coming from multidimensional consistency of the Hirota system itself.
Harmonic coordinates in the string and membrane equations
Chun-Lei He; Shou-Jun Huang
2010-04-16T23:59:59.000Z
In this note, we first show that the solutions to Cauchy problems for two versions of relativistic string and membrane equations are diffeomorphic. Then we investigate the coordinates transformation presented in Ref. [9] (see (2.20) in Ref. [9]) which plays an important role in the study on the dynamics of the motion of string in Minkowski space. This kind of transformed coordinates are harmonic coordinates, and the nonlinear relativistic string equations can be straightforwardly simplified into linear wave equations under this transformation.
On the Boltzmann equation, quantitative studies and hydrodynamical limits
Briant, Marc
2014-11-11T23:59:59.000Z
work in collaboration with S. Merino-Aceituno and C. Mouhot. Chapter 6 establishes a Cauchy theory on a quantic version of the Boltz- mann equation and discusses the phenomenon of Bose-Einstein condensate. It is original work and its arXiv link is: http... with the mathematical treatment of kinetic theory and focuses more precisely on the Boltzmann equation. The latter equation describes the evolution in position and velocity of rarefied gas particles with a statistical point of view. It plays a central role...
Balmer and Rydberg Equations for Hydrogen Spectra Revisited
Raji Heyrovska
2011-05-22T23:59:59.000Z
Balmer equation for the atomic spectral lines was generalized by Rydberg. Here it is shown that 1) while Bohr's theory explains the Rydberg constant in terms of the ground state energy of the hydrogen atom, quantizing the angular momentum does not explain the Rydberg equation, 2) on reformulating Rydberg's equation, the principal quantum numbers are found to correspond to integral numbers of de Broglie waves and 3) the ground state energy of hydrogen is electromagnetic like that of photons and the frequency of the emitted or absorbed light is the difference in the frequencies of the electromagnetic energy levels.
Asymptotic Preserving Unified Gas Kinetic Scheme for Grey Radiative Transfer Equations
Xu, Kun
The solutions of radiative transport equations can cover both optical thin and optical thick regimes due equations, where the radiation transport equation is coupled with the material thermal energy equation(2013), 138-156] from a one-dimensional linear radiation transport equation to a nonlinear two
J. Frauendiener
1997-12-11T23:59:59.000Z
This is the second in a series of articles on the numerical solution of Friedrich's conformal field equations for Einstein's theory of gravity. We will discuss in this paper the numerical methods used to solve the system of evolution equations obtained from the conformal field equations. In particular we discuss in detail the choice of gauge source functions and the treatment of the boundaries. Of particular importance is the process of ``radiation extraction'' which can be performed in a straightforward way in the present formalism.
Essential Differential Equations September 2013 Lecturer David Silvester
Silvester, David J.
Essential Differential Equations September 2013 Lecturer David Silvester Office Alan Turing 1Â5 Classes Tues 3Â4 Alan Turing G.207 Thur 1Â3 Alan Turing G.205 Assessment Week 7 Test 20% Week 10
Development of one-equation transition/turbulence models
Edwards, J.R.; Roy, C.J.; Blottner, F.G.; Hassan, H.A.
2000-01-14T23:59:59.000Z
This paper reports on the development of a unified one-equation model for the prediction of transitional and turbulent flows. An eddy viscosity--transport equation for nonturbulent fluctuation growth based on that proposed by Warren and Hassan is combined with the Spalart-Allmaras one-equation model for turbulent fluctuation growth. Blending of the two equations is accomplished through a multidimensional intermittency function based on the work of Dhawan and Narasimha. The model predicts both the onset and extent of transition. Low-speed test cases include transitional flow over a flat plate, a single element airfoil, and a multi-element airfoil in landing configuration. High-speed test cases include transitional Mach 3.5 flow over a 5{degree} cone and Mach 6 flow over a flared-cone configuration. Results are compared with experimental data, and the grid-dependence of selected predictions is analyzed.
Center Manifold Analysis of Delayed Lienard Equation and Its Applications
Zhao, Siming
2010-01-14T23:59:59.000Z
state. It has both practical and theoretical importance in determining the criticality of the Hopf bifurcation. For such purpose, center manifold analysis on the bifurcation line is required. This thesis uses operator differential equation formulation...
Intro to Differential Equations MATH 2070 (Winter 2012)
Hagler, Jim
Intro to Differential Equations MATH 2070 (Winter 2012) Solving Linear Systems -- Complex to . 3. Write Yc (t) = et Vc = e(+i)t Vc = et (cos (t) + i sin (t)) (Vre + iVim) where both Vre and Vim
Equator Appliance: ENERGY STAR Referral (EZ 3720 CEE)
Broader source: Energy.gov [DOE]
DOE referred the matter of Equator clothes washer model EZ 3720 CEE to the EPA for appropriate action after DOE testing showed that the model does not meet the ENERGY STAR specification.
Hyperbolic Equations for Vacuum Gravity Using Special Orthonormal Frames
Frank B. Estabrook; R. Steve Robinson; Hugo D. Wahlquist
2004-09-29T23:59:59.000Z
By adopting Nester's higher dimensional special orthonormal frames (HSOF) the tetrad equations for vacuum gravity are put into first order symmetric hyperbolic (FOSH) form with constant coefficients, independent of any time slicing or coordinate specialization.
A piecewise linear finite element discretization of the diffusion equation
Bailey, Teresa S
2006-10-30T23:59:59.000Z
it discretizes the diffusion equation on an arbitrary polyhedral mesh. We implemented our method in the KULL software package being developed at Lawrence Livermore National Laboratory. This code previously utilized Palmer's method as its diffusion solver, which...
Exact controllability of the superlinear heat equation 1 Statement of ...
2008-05-11T23:59:59.000Z
... it depends on z. This is a key point in this proof that will ..... [5] S. Anita and V. Barbu, Null controllability of nonlinear convective heat equation. ESAIM: COCV 5
STABILITY OF EQUILIBRIA IN ONE DIMENSION FOR DIBLOCK COPOLYMER EQUATION
Sander, Evelyn
STABILITY OF EQUILIBRIA IN ONE DIMENSION FOR DIBLOCK COPOLYMER EQUATION Olga Stulov Department for numerically. The various sets of the solutions of the linearized model were found by means of software AUTO
Periodic solutions of Schrodinger equation in Hilbert space
A. A. Boichuk; A. A. Pokutnyi
2012-09-03T23:59:59.000Z
Necessary and sufficient conditions for existence of boundary value problem of Schrodinger equation are obtained in linear and nonlinear cases. Periodic analytical solutions are represented using generalized Green's operator
Gravitation and Thermodynamics: The Einstein Equation of State Revisited
Jarmo Makela; Ari Peltola
2008-08-19T23:59:59.000Z
We perform an analysis where Einstein's field equation is derived by means of very simple thermodynamical arguments. Our derivation is based on a consideration of the properties of a very small, spacelike two-plane in a uniformly accelerating motion.
A new equation of state for dark energy
Dragan Slavkov Hajdukovic
2009-11-04T23:59:59.000Z
In the contemporary Cosmology, dark energy is modeled as a perfect fluid, having a very simple equation of state: pressure is proportional to dark energy density. As an alternative, I propose a more complex equation of state, with pressure being function of three variables: dark energy density, matter density and the size of the Universe. One consequence of the new equation is that, in the late-time Universe, cosmological scale factor is linear function of time; while the standard cosmology predicts an exponential function.The new equation of state allows attributing a temperature to the physical vacuum, a temperature proportional to the acceleration of the expansion of the Universe. The vacuum temperature decreases with the expansion of the Universe, approaching (but never reaching) the absolute zero.
A unifying framework for watershed thermodynamics: balance equations for mass,
Hassanizadeh, S. Majid
A unifying framework for watershed thermodynamics: balance equations for mass, momentum, energy Hassanizadehb a Centre for Water Research, Department of Environmental Engineering, The University of Western Australia, 6907 Nedlands, Australia b Department of Water Management, Environmental and Sanitary Engineering
A new approach to deformation equations of noncommutative KP hierarchies
Aristophanes Dimakis; Folkert Muller-Hoissen
2007-03-21T23:59:59.000Z
Partly inspired by Sato's theory of the Kadomtsev-Petviashvili (KP) hierarchy, we start with a quite general hierarchy of linear ordinary differential equations in a space of matrices and derive from it a matrix Riccati hierarchy. The latter is then shown to exhibit an underlying 'weakly nonassociative' (WNA) algebra structure, from which we can conclude, refering to previous work, that any solution of the Riccati system also solves the potential KP hierarchy (in the corresponding matrix algebra). We then turn to the case where the components of the matrices are multiplied using a (generalized) star product. Associated with the deformation parameters, there are additional symmetries (flow equations) which enlarge the respective KP hierarchy. They have a compact formulation in terms of the WNA structure. We also present a formulation of the KP hierarchy equations themselves as deformation flow equations.
LONGTIME ENERGY CONSERVATION OF NUMERICAL METHODS FOR OSCILLATORY DIFFERENTIAL EQUATIONS
TÃ¼bingen, UniversitÃ¤t
LONGÂTIME ENERGY CONSERVATION OF NUMERICAL METHODS FOR OSCILLATORY DIFFERENTIAL EQUATIONS ERNSTÂtime energy conservation, secondÂorder symmetric methods, frequency expansion, backward error analysis, Fermi
Multiscale numerical methods for some types of parabolic equations
Nam, Dukjin
2009-05-15T23:59:59.000Z
parabolic equations in strongly channelized media. We concentrate on showing that the solution depends on the steady state solution smoothly. As for the first problem, we obtain quantitive estimates for the convergence of the correctors and some parts...
A BIFURCATION RESULT FOR NON-LOCAL FRACTIONAL EQUATIONS
, minimal surfaces, materials science and water waves. This is one of the reason why, recently, non studied non-local fractional Laplacian equations with superlinear and subcritical or critical
Compressed absorbing boundary conditions for the Helmholtz equation
Bélanger-Rioux, Rosalie
2014-01-01T23:59:59.000Z
Absorbing layers are sometimes required to be impractically thick in order to offer an accurate approximation of an absorbing boundary condition for the Helmholtz equation in a heterogeneous medium. It is always possible ...
Generating expansion model incorporating compact DC power flow equations
Nderitu, D.G.; Sparrow, F.T.; Yu, Z. [Purdue Inst. for Interdisciplinary Engineering Studies, West Lafayette, IN (United States)
1998-12-31T23:59:59.000Z
This paper presents a compact method of incorporating the spatial dimension into the generation expansion problem. Compact DC power flow equations are used to provide real-power flow coordination equations. Using these equations the marginal contribution of a generator to th total system loss is formulated as a function of that generator`s output. Incorporating these flow equations directly into the MIP formulation of the generator expansion problem results in a model that captures a generator`s true net marginal cost, one that includes both the cost of generation and the cost of transport. This method contrasts with other methods that iterate between a generator expansion model and an optimal power flow model. The proposed model is very compact and has very good convergence performance. A case study with data from Kenya is used to provide a practical application to the model.
A GPU Parallelized Spectral Method For Elliptic Equations.
2013-04-29T23:59:59.000Z
ence methods [6], finite element methods [24, 14, 13], Fourier spectral methods .... stored on the GPU once and for all, in order to minimize data transfer between the ..... The spectrum of the Chebyshev collocation operator for the heat equation.
Math 331 Ordinary Differential Equations Fall 2014 Instructor Amites Sarkar
Sarkar, Amites
Math 331 Ordinary Differential Equations Fall 2014 Instructor Amites Sarkar Text Differential Bond Hall. My phone number is 650 7569 and my e-mail is amites.sarkar@wwu.edu Relation to Overall
Lattice Boltzmann equation simulations of turbulence, mixing, and combustion
Yu, Huidan
2006-04-12T23:59:59.000Z
We explore the capability of lattice Boltzmann equation (LBE) method for complex fluid flows involving turbulence, mixing, and reaction. In the first study, LBE schemes for binary scalar mixing and multi-component reacting flow with reactions...
Wave-Particle Duality and the Hamilton-Jacobi Equation
Gregory I. Sivashinsky
2009-12-28T23:59:59.000Z
The Hamilton-Jacobi equation of relativistic quantum mechanics is revisited. The equation is shown to permit solutions in the form of breathers (oscillating/spinning solitons), displaying simultaneous particle-like and wave-like behavior. The de Broglie wave thus acquires a clear deterministic meaning of a wave-like excitation of the classical action function. The problem of quantization in terms of the breathing action function and the double-slit experiment are discussed.
Complete radiative terms for the electron/electronic energy equation
Stanley, S.A.; Carlson, L.A. [Univ of California, San Diego, CA (United States)
1994-10-01T23:59:59.000Z
A derivation of the radiative terms in the electron/electronic energy equation is presented, properly accounting for the effects of absorption and emission of radiation on the individual energy modes of the gas. This electron/electronic energy equation with the complete radiative terms has successfully been used to model the radiation-dominated precursor ahead of the bow shock of a hypersonic vehicle entering the Earth`s atmosphere. 8 refs.
Hypersonic expansion of the Fokker--Planck equation
Fernandez-Feria, R.
1989-02-01T23:59:59.000Z
A systematic study of the hypersonic limit of a heavy species diluted in a much lighter gas is made via the Fokker--Planck equation governing its velocity distribution function. In particular, two different hypersonic expansions of the Fokker--Planck equation are considered, differing from each other in the momentum equation of the heavy gas used as the basis of the expansion: in the first of them, the pressure tensor is neglected in that equation while, in the second expansion, the pressure tensor term is retained. The expansions are valid when the light gas Mach number is O(1) or larger and the difference between the mean velocities of light and heavy components is small compared to the light gas thermal speed. They can be applied away from regions where the spatial gradient of the distribution function is very large, but it is not restricted with respect to the temporal derivative of the distribution function. The hydrodynamic equations corresponding to the lowest order of both expansions constitute two different hypersonic closures of the moment equations. For the subsequent orders in the expansions, closed sets of moment equations (hydrodynamic equations) are given. Special emphasis is made on the order of magnitude of the errors of the lowest-order hydrodynamic quantities. It is shown that if the heat flux vanishes initially, these errors are smaller than one might have expected from the ordinary scaling of the hypersonic closure. Also it is found that the normal solution of both expansions is a Gaussian distribution at the lowest order.
The confluent supersymmetry algorithm for Dirac equations with pseudoscalar potentials
Contreras-Astorga, Alonso, E-mail: aloncont@iun.edu; Schulze-Halberg, Axel, E-mail: axgeschu@iun.edu, E-mail: xbataxel@gmail.com [Department of Mathematics and Actuarial Science and Department of Physics, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States)
2014-10-15T23:59:59.000Z
We introduce the confluent version of the quantum-mechanical supersymmetry formalism for the Dirac equation with a pseudoscalar potential. Application of the formalism to spectral problems is discussed, regularity conditions for the transformed potentials are derived, and normalizability of the transformed solutions is established. Our findings extend and complement former results [L. M. Nieto, A. A. Pecheritsin, and B. F. Samsonov, “Intertwining technique for the one-dimensional stationary Dirac equation,” Ann. Phys. 305, 151–189 (2003)].
Solutions of differential equations by linear programming techniques
Saye, Jake Lee
2012-06-07T23:59:59.000Z
. INTRODUCTION II. LINEAR PROGRAMMING General Discussion. Theory of Linear ProSrsmming. a Duality . The Simplex Method anA LP/90. III. LINEAR DIFFZREKTAL EQUATIONS. General Discussion. A Limital Solution to a Differential Equation IV. THE ~ PROGRAMING... be traced back much further. A study of mathematical game theory was initiated. in 1928 by Von Neumann. In 1944 Von Neumann and Morgenstern published the book, Theory of Games and. Economic Behavior which is an economic application of minimax theory...
Mpemba effect, Newton cooling law and heat transfer equation
Vladan Pankovic; Darko V. Kapor
2012-12-11T23:59:59.000Z
In this work we suggest a simple theoretical solution of the Mpemba effect in full agreement with known experimental data. This solution follows simply as an especial approximation (linearization) of the usual heat (transfer) equation, precisely linearization of the second derivation of the space part of the temperature function (as it is well-known Newton cooling law can be considered as the effective approximation of the heat (transfer) equation for constant space part of the temperature function).
Wave Equation for Sound in Fluids with Vorticity
Santiago Esteban Perez Bergliaffa; Katrina Hibberd; Michael Stone; Matt Visser
2001-06-13T23:59:59.000Z
We use Clebsch potentials and an action principle to derive a closed system of gauge invariant equations for sound superposed on a general background flow. Our system reduces to the Unruh (1981) and Pierce (1990) wave equations when the flow is irrotational, or slowly varying. We illustrate our formalism by applying it to waves propagating in a uniformly rotating fluid where the sound modes hybridize with inertial waves.
Dark energy models with variable equation of state parameter
Anil Kumar Yadav; Farook Rahaman; Saibal Ray
2010-09-24T23:59:59.000Z
The dark energy models with variable equation of state parameter $\\omega$ is investigated by using law of variation of Hubble's parameter that yields the constant value of deceleration parameter. The equation of state parameter $\\omega$ is found to be time dependent and its existing range for this model is consistent with the recent observations of SN Ia data, SN Ia data (with CMBR anisotropy) and galaxy clustering statistics. The physical significance of the dark energy models has also been discussed.
Multibump solutions for quasilinear elliptic equations with critical growth
Liu, Jiaquan, E-mail: jiaquan@math.pku.edu.cn [LMAM, School of Mathematical Science, Peking University, Beijing 100871 (China)] [LMAM, School of Mathematical Science, Peking University, Beijing 100871 (China); Wang, Zhi-Qiang, E-mail: zhi-qiang.wang@usu.edu [Chern Institute of Mathematics, Nankai University, Tianjin 300071, People's Republic of China and Department of Mathematics and Statistics, Utah State University, Logan, Utah 84322 (United States)] [Chern Institute of Mathematics, Nankai University, Tianjin 300071, People's Republic of China and Department of Mathematics and Statistics, Utah State University, Logan, Utah 84322 (United States); Wu, Xian, E-mail: wuxian2001@yahoo.com.cn [Department of Mathematics, Yunnan Normal University, Kunming, Yunnan 650092 (China)] [Department of Mathematics, Yunnan Normal University, Kunming, Yunnan 650092 (China)
2013-12-15T23:59:59.000Z
The current paper is concerned with constructing multibump solutions for a class of quasilinear Schrödinger equations with critical growth. This extends the classical results of Coti Zelati and Rabinowitz [Commun. Pure Appl. Math. 45, 1217–1269 (1992)] for semilinear equations as well as recent work of Liu, Wang, and Guo [J. Funct. Anal. 262, 4040–4102 (2012)] for quasilinear problems with subcritical growth. The periodicity of the potentials is used to glue ground state solutions to construct multibump bound state solutions.
New Curved Spacetime Dirac Equations - On the Anomalous Gyromagnetic Ratio
G. G. Nyambuya
2008-09-06T23:59:59.000Z
I propose three new curved spacetime versions of the Dirac Equation. These equations have been developed mainly to try and account in a natural way for the observed anomalous gyromagnetic ratio of Fermions. The derived equations suggest that particles including the Electron which is thought to be a point particle do have a finite spatial size which is the reason for the observed anomalous gyromagnetic ratio. A serendipitous result of the theory, is that, two of the equation exhibits an asymmetry in their positive and negative energy solutions the first suggestion of which is clear that a solution to the problem as to why the Electron and Muon - despite their acute similarities - exhibit an asymmetry in their mass is possible. The Mourn is often thought as an Electron in a higher energy state. Another of the consequences of three equations emanating from the asymmetric serendipity of the energy solutions of two of these equations, is that, an explanation as to why Leptons exhibit a three stage mass hierarchy is possible.
New look at 3-D Navier-Stokes equation
Tomasz Dlotko
2015-01-09T23:59:59.000Z
We propose a new way of looking at the Navier-Stokes equation (N-S) in dimension three. That problem is a {\\it critical limit}, as $\\alpha\\to 0^+$, of the regular approximations in which the $-\\Delta$ operator is replaced with its fractional power $(-\\Delta)^{1+\\alpha}, \\alpha>0$ small. For such approximations the nonlinearity of the classical N-S becomes {\\it subcritical}, that means, it is {\\it subordinated} to that main part operator $(-\\Delta)^{1+\\alpha}$ relatively to the known $L^2$ a priori estimate. Using Dan Henry's {\\it semigroup approach} we construct regular solutions to the fractional approximations. Such solutions are unique, smooth and regularized through the equation in time. A solution to the N-S equation is obtained next as a limit of the regular solutions to subcritical equations when the exponent $\\alpha$ of $(-\\Delta)^{1+\\alpha}$ tends to $0^+$. Unfortunately, when passing to that limit we are loosing several nice properties of the approximating solutions; in particular uniqueness. Moreover, since the nonlinearity of the N-S equation is of {\\it quadratic type}, the solutions corresponding to small initial data and small $f$ are shown to be global in time and regular. The way of looking at the N-S equation as a limit of subcritical approximations seems to be new in the literature.
Non-linear equation: energy conservation and impact parameter dependence
Andrey Kormilitzin; Eugene Levin
2010-09-08T23:59:59.000Z
In this paper we address two questions: how energy conservation affects the solution to the non-linear equation, and how impact parameter dependence influences the inclusive production. Answering the first question we solve the modified BK equation which takes into account energy conservation. In spite of the fact that we used the simplified kernel, we believe that the main result of the paper: the small ($\\leq 40%$) suppression of the inclusive productiondue to energy conservation, reflects a general feature. This result leads us to believe that the small value of the nuclear modification factor is of a non-perturbative nature. In the solution a new scale appears $Q_{fr} = Q_s \\exp(-1/(2 \\bas))$ and the production of dipoles with the size larger than $2/Q_{fr}$ is suppressed. Therefore, we can expect that the typical temperature for hadron production is about $Q_{fr}$ ($ T \\approx Q_{fr}$). The simplified equation allows us to obtain a solution to Balitsky-Kovchegov equation taking into account the impact parameter dependence. We show that the impact parameter ($b$) dependence can be absorbed into the non-perturbative $b$ dependence of the saturation scale. The solution of the BK equation, as well as of the modified BK equation without $b$ dependence, is only accurate up to $\\pm 25%$.
A comparison of the point kinetics equations with the QUANDRY analytic nodal diffusion method
Velasquez, Arthur
1993-01-01T23:59:59.000Z
The point kinetics equations were incorporated into QUANDRY, a nuclear reactor analysis computer program which uses the analytic nodal method to solve the neutron diffusion equation. Both the point kinetics equations, solved using the IMSL MATH...
Generalized solution to multispecies transport equations coupled with a first-order reaction network
Clement, Prabhakar
Generalized solution to multispecies transport equations coupled with a first-order reaction for deriving analytical solutions to multispecies transport equations coupled with multiparent, serial multispecies transport equations with different retardation factors. Mathematical steps are provided
Jiang, Lijian
2009-05-15T23:59:59.000Z
. These methods employ limited single or multiple global information. We apply these numerical methods to partial differential equations (elliptic, parabolic and wave equations) with continuum scales. To compute the solution of partial differential equations on a...
E-Print Network 3.0 - atmospheric diffusion equation Sample Search...
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grey atmospheres Defining the radiation field (specific intensity, moments, fluxes) Equation... equation. Basic assumptions for a magnetized fluid Derivation of the ... Source:...
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CONTRACT DE-AC02-76CH03073 Summary: , steady-state axisymmetric angular momentum transport equation equates angular momentum flux through... -integrated torque, then the...
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cancer equation Search Powered by Explorit Topic List Advanced Search Sample search results for: algebraic cancer equation Page: << < 1 2 3 4 5 > >> 1 Cancer Treatment Using...
Open systems dynamics: Simulating master equations in the computer
Carlos Navarrete-Benlloch
2015-04-21T23:59:59.000Z
Master equations are probably the most fundamental equations for anyone working in quantum optics in the presence of dissipation. In this context it is then incredibly useful to have efficient ways of coding and simulating such equations in the computer, and in this notes I try to introduce in a comprehensive way how do I do so, focusing on Matlab, but making it general enough so that it can be directly translated to any other language or software of choice. I inherited most of my methods from Juan Jos\\'{e} Garc\\'{\\i}a-Ripoll (whose numerical abilities I cannot praise enough), changing them here and there to accommodate them to the way my (fairly limited) numerical brain works, and to connect them as much as possible to how I understand the theory behind them. At present, the notes focus on how to code master equations and find their steady state, but I hope soon I will be able to update them with time evolution methods, including how to deal with time-dependent master equations. During the last 4 years I've tested these methods in various different contexts, including circuit quantum electrodynamics, the laser problem, optical parametric oscillators, and optomechanical systems. Comments and (constructive) criticism are greatly welcome, and will be properly credited and acknowledged.
Dirac equation in low dimensions: The factorization method
J. A. Sanchez-Monroy; C. J. Quimbay
2014-09-30T23:59:59.000Z
We present a general approach to solve the (1+1) and (2+1)-dimensional Dirac equation in the presence of static scalar, pseudoscalar and gauge potentials, for the case in which the potentials have the same functional form and thus the factorization method can be applied. We show that the presence of electric potentials in the Dirac equation leads to a two Klein-Gordon equations including an energy-dependent potential. We then generalize the factorization method for the case of energy-dependent Hamiltonians. Additionally, the shape invariance is generalized for a specific class of energy-dependent Hamiltonians. We also present a condition for the absence of the Klein's paradox (stability of the Dirac sea), showing how Dirac particles in low dimensions can be confined for a wide family of potentials.
Painleve Analysis and Similarity Reductions for the Magma Equation
Shirley E. Harris; Peter A. Clarkson
2006-10-05T23:59:59.000Z
In this paper, we examine a generalized magma equation for rational values of two parameters, $m$ and $n$. Firstly, the similarity reductions are found using the Lie group method of infinitesimal transformations. The Painlev\\'e ODE test is then applied to the travelling wave reduction, and the pairs of $m$ and $n$ which pass the test are identified. These particular pairs are further subjected to the ODE test on their other symmetry reductions. Only two cases remain which pass the ODE test for all such symmetry reductions and these are completely integrable. The case when $m=0$, $n=-1$ is related to the Hirota-Satsuma equation and for $m=\\tfrac12$, $n=-\\tfrac12$, it is a real, generalized, pumped Maxwell-Bloch equation.
Generalized linear Boltzmann equations for particle transport in polycrystals
Jens Marklof; Andreas Strömbergsson
2015-02-13T23:59:59.000Z
The linear Boltzmann equation describes the macroscopic transport of a gas of non-interacting point particles in low-density matter. It has wide-ranging applications, including neutron transport, radiative transfer, semiconductors and ocean wave scattering. Recent research shows that the equation fails in highly-correlated media, where the distribution of free path lengths is non-exponential. We investigate this phenomenon in the case of polycrystals whose typical grain size is comparable to the mean free path length. Our principal result is a new generalized linear Boltzmann equation that captures the long-range memory effects in this setting. A key feature is that the distribution of free path lengths has an exponential decay rate, as opposed to a power-law distribution observed in a single crystal.
Conservative Moment Equations for Neutrino Radiation Transport with Limited Relativity
Endeve, Eirik; Mezzacappa, Anthony
2012-01-01T23:59:59.000Z
We derive conservative, multidimensional, energy-dependent moment equations for neutrino transport in core-collapse supernovae and related astrophysical systems, with particular attention to the consistency of conservative four-momentum and lepton number transport equations. After taking angular moments of conservative formulations of the general relativistic Boltzmann equation, we specialize to a conformally flat spacetime, which also serves as the basis for four further limits. Two of these---the multidimensional special relativistic case, and a conformally flat formulation of the spherically symmetric general relativistic case---are given in appendices for the sake of comparison with extant literature. The third limit is a weak-field, `pseudo-Newtonian' approach \\citep{kim_etal_2009,kim_etal_2012} in which the source of the gravitational potential includes the trace of the stress-energy tensor (rather than just the mass density), and all orders in fluid velocity $v$ are retained. Our primary interest here ...
On the Thermal Symmetry of the Markovian Master Equation
B. A. Tay; T. Petrosky
2012-07-25T23:59:59.000Z
The quantum Markovian master equation of the reduced dynamics of a harmonic oscillator coupled to a thermal reservoir is shown to possess thermal symmetry. This symmetry is revealed by a Bogoliubov transformation that can be represented by a hyperbolic rotation acting on the Liouville space of the reduced dynamics. The Liouville space is obtained as an extension of the Hilbert space through the introduction of tilde variables used in the thermofield dynamics formalism. The angle of rotation depends on the temperature of the reservoir, as well as the value of Planck's constant. This symmetry relates the thermal states of the system at any two temperatures. This includes absolute zero, at which purely quantum effects are revealed. The Caldeira-Leggett equation and the classical Fokker-Planck equation also possess thermal symmetry. We compare the thermal symmetry obtained from the Bogoliubov transformation in related fields and discuss the effects of the symmetry on the shape of a Gaussian wave packet.
The Schroedinger equation with friction from the quantum trajectory perspective
Garashchuk, Sophya; Dixit, Vaibhav; Gu Bing; Mazzuca, James [Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208 (United States)
2013-02-07T23:59:59.000Z
Similarity of equations of motion for the classical and quantum trajectories is used to introduce a friction term dependent on the wavefunction phase into the time-dependent Schroedinger equation. The term describes irreversible energy loss by the quantum system. The force of friction is proportional to the velocity of a quantum trajectory. The resulting Schroedinger equation is nonlinear, conserves wavefunction normalization, and evolves an arbitrary wavefunction into the ground state of the system (of appropriate symmetry if applicable). Decrease in energy is proportional to the average kinetic energy of the quantum trajectory ensemble. Dynamics in the high friction regime is suitable for simple models of reactions proceeding with energy transfer from the system to the environment. Examples of dynamics are given for single and symmetric and asymmetric double well potentials.
Trapping Regions for the Navier-Stokes Equations
Craig Alan Feinstein
2014-10-27T23:59:59.000Z
In 1999, J.C. Mattingly and Ya. G. Sinai used elementary methods to prove the existence and uniqueness of smooth solutions to the 2D Navier-Stokes equations with periodic boundary conditions. And they were almost successful in proving the existence and uniqueness of smooth solutions to the 3D Navier-Stokes equations using the same strategy. In this paper, we modify their technique to obtain a simpler proof of one of their results. We also argue that there is no logical reason why the 3D Navier-Stokes equations must always have solutions, even when the initial velocity vector field is smooth; if they do always have solutions, it is due to probability and not logic.
Multi-time Schrödinger equations cannot contain interaction potentials
Petrat, Sören, E-mail: petrat@math.lmu.de [Mathematisches Institut, Ludwig-Maximilians-Universität, Theresienstr. 39, 80333 München (Germany)] [Mathematisches Institut, Ludwig-Maximilians-Universität, Theresienstr. 39, 80333 München (Germany); Tumulka, Roderich, E-mail: tumulka@math.rutgers.edu [Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway, New Jersey 08854-8019 (United States)] [Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway, New Jersey 08854-8019 (United States)
2014-03-15T23:59:59.000Z
Multi-time wave functions are wave functions that have a time variable for every particle, such as ?(t{sub 1},x{sub 1},...,t{sub N},x{sub N}). They arise as a relativistic analog of the wave functions of quantum mechanics but can be applied also in quantum field theory. The evolution of a wave function with N time variables is governed by N Schrödinger equations, one for each time variable. These Schrödinger equations can be inconsistent with each other, i.e., they can fail to possess a joint solution for every initial condition; in fact, the N Hamiltonians need to satisfy a certain commutator condition in order to be consistent. While this condition is automatically satisfied for non-interacting particles, it is a challenge to set up consistent multi-time equations with interaction. We prove for a wide class of multi-time Schrödinger equations that the presence of interaction potentials (given by multiplication operators) leads to inconsistency. We conclude that interaction has to be implemented instead by creation and annihilation of particles, which, in fact, can be done consistently [S. Petrat and R. Tumulka, “Multi-time wave functions for quantum field theory,” Ann. Physics (to be published)]. We also prove the following result: When a cut-off length ? > 0 is introduced (in the sense that the multi-time wave function is defined only on a certain set of spacelike configurations, thereby breaking Lorentz invariance), then the multi-time Schrödinger equations with interaction potentials of range ? are consistent; however, in the desired limit ? ? 0 of removing the cut-off, the resulting multi-time equations are interaction-free, which supports the conclusion expressed in the title.
Thermodynamically constrained correction to ab initio equations of state
French, Martin; Mattsson, Thomas R. [HEDP Theory, Sandia National Laboratories, Albuquerque, New Mexico 87185-1189 (United States)
2014-07-07T23:59:59.000Z
We show how equations of state generated by density functional theory methods can be augmented to match experimental data without distorting the correct behavior in the high- and low-density limits. The technique is thermodynamically consistent and relies on knowledge of the density and bulk modulus at a reference state and an estimation of the critical density of the liquid phase. We apply the method to four materials representing different classes of solids: carbon, molybdenum, lithium, and lithium fluoride. It is demonstrated that the corrected equations of state for both the liquid and solid phases show a significantly reduced dependence of the exchange-correlation functional used.
Combined Field Integral Equation Based Theory of Characteristic Mode
Qi I. Dai; Qin S. Liu; Hui Gan; Weng Cho Chew
2015-03-04T23:59:59.000Z
Conventional electric field integral equation based theory is susceptible to the spurious internal resonance problem when the characteristic modes of closed perfectly conducting objects are computed iteratively. In this paper, we present a combined field integral equation based theory to remove the difficulty of internal resonances in characteristic mode analysis. The electric and magnetic field integral operators are shown to share a common set of non-trivial characteristic pairs (values and modes), leading to a generalized eigenvalue problem which is immune to the internal resonance corruption. Numerical results are presented to validate the proposed formulation. This work may offer efficient solutions to characteristic mode analysis which involves electrically large closed surfaces.
Illite Dissolution Rates and Equation (100 to 280 dec C)
DOE Data Explorer [Office of Scientific and Technical Information (OSTI)]
Carroll, Susan
The objective of this suite of experiments was to develop a useful kinetic dissolution expression for illite applicable over an expanded range of solution pH and temperature conditions representative of subsurface conditions in natural and/or engineered geothermal reservoirs. Using our new data, the resulting rate equation is dependent on both pH and temperature and utilizes two specific dissolution mechanisms (a “neutral” and a “basic” mechanism). The form of this rate equation should be easily incorporated into most existing reactive transport codes for to predict rock-water interactions in EGS shear zones.
Solitary Waves of the MRLW Equation by Variational Iteration Method
Hassan, Saleh M. [Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451 (Saudi Arabia); Department of Mathematics, College of Science, Ain Shams University, Abbassia 11566, Cairo (Egypt); Alamery, D. G. [Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451 (Saudi Arabia)
2009-09-09T23:59:59.000Z
In a recent publication, Soliman solved numerically the modified regularized long wave (MRLW) equation by using the variational iteration method (VIM). In this paper, corrected numerical results have been computed, plotted, tabulated, and compared with not only the exact analytical solutions but also the Adomian decomposition method results. Solitary wave solutions of the MRLW equation are exactly obtained as a convergent series with easily computable components. Propagation of single solitary wave, interaction of two and three waves, and also birth of solitons have been discussed. Three invariants of motion have been evaluated to determine the conservation properties of the problem.
Singular eigenfunctions for the three-dimensional radiative transport equation
Manabu Machida
2013-09-07T23:59:59.000Z
Case's method obtains solutions to the radiative transport equation as superpositions of elementary solutions when the specific intensity depends on one spatial variable. In this paper, we find elementary solutions when the specific intensity depends on three spatial variables in three-dimensional space. By using the reference frame whose z-axis lies in the direction of the wave vector, the angular part of each elementary solution becomes the singular eigenfunction for the one-dimensional radiative transport equation. Thus Case's method is generalized.
Quantum Master Equation of Particle in Gas Environment
Lajos Diosi
1994-03-23T23:59:59.000Z
The evolution of the reduced density operator $\\rho$ of Brownian particle is discussed in single collision approach valid typically in low density gas environments. This is the first succesful derivation of quantum friction caused by {\\it local} environmental interactions. We derive a Lindblad master equation for $\\rho$, whose generators are calculated from differential cross section of a single collision between Brownian and gas particles, respectively. The existence of thermal equilibrium for $\\rho$ is proved. Master equations proposed earlier are shown to be particular cases of our one.
Averaged equations for Josephson junction series arrays with LRC load
Kurt Wiesenfeld; James W. Swift
1994-08-26T23:59:59.000Z
We derive the averaged equations describing a series array of Josephson junctions shunted by a parallel inductor-resistor-capacitor load. We assume that the junctions have negligable capacitance ($\\beta = 0$), and derive averaged equations which turn out to be completely tractable: in particular the stability of both in-phase and splay states depends on a single parameter, $\\del$. We find an explicit expression for $\\delta$ in terms of the load parameters and the bias current. We recover (and refine) a common claim found in the technical literature, that the in-phase state is stable for inductive loads and unstable for capacitive loads.
On the wave equation in spacetimes of Goedel type
P. Marecki
2012-01-24T23:59:59.000Z
We analyze the d'Alembert equation in the Goedel-type spacetimes with spherical and Lobachevsky sections (with sufficiently rapid rotation). By separating the $t$ and $x_3$ dependence we reduce the problem to a group-theoretical one. In the spherical case solutions have discrete frequencies, and involve spin-weighted spherical harmonics. In the Lobachevsky case we give simple formulas for obtaining all the solutions belonging to the $D^\\pm_\\la$ sectors of the irreducible unitary representations of the reduced Lorentz group. The wave equation enforces restrictions on $\\la$ and the allowed (here: continuous) spectrum of frequencies.
A Note on Equations for Steady-State Optimal Landscapes
Liu, H.H.
2010-06-15T23:59:59.000Z
Based on the optimality principle (that the global energy expenditure rate is at its minimum for a given landscape under steady state conditions) and calculus of variations, we have derived a group of partial differential equations for describing steady-state optimal landscapes without explicitly distinguishing between hillslopes and channel networks. Other than building on the well-established Mining's equation, this work does not rely on any empirical relationships (such as those relating hydraulic parameters to local slopes). Using additional constraints, we also theoretically demonstrate that steady-state water depth is a power function of local slope, which is consistent with field data.
Illite Dissolution Rates and Equation (100 to 280 dec C)
Carroll, Susan
2014-10-17T23:59:59.000Z
The objective of this suite of experiments was to develop a useful kinetic dissolution expression for illite applicable over an expanded range of solution pH and temperature conditions representative of subsurface conditions in natural and/or engineered geothermal reservoirs. Using our new data, the resulting rate equation is dependent on both pH and temperature and utilizes two specific dissolution mechanisms (a “neutral” and a “basic” mechanism). The form of this rate equation should be easily incorporated into most existing reactive transport codes for to predict rock-water interactions in EGS shear zones.
An analytically solvable eigenvalue problem for the linear elasticity equations.
Day, David Minot; Romero, Louis Anthony
2004-07-01T23:59:59.000Z
Analytic solutions are useful for code verification. Structural vibration codes approximate solutions to the eigenvalue problem for the linear elasticity equations (Navier's equations). Unfortunately the verification method of 'manufactured solutions' does not apply to vibration problems. Verification books (for example [2]) tabulate a few of the lowest modes, but are not useful for computations of large numbers of modes. A closed form solution is presented here for all the eigenvalues and eigenfunctions for a cuboid solid with isotropic material properties. The boundary conditions correspond physically to a greased wall.
Hamilton-Jacobi-Bellman equations for Quantum Filtering and Control
J. Gough; V. P. Belavkin; O. G. Smolyanov
2005-02-24T23:59:59.000Z
We exploit the separation of the filtering and control aspects of quantum feedback control to consider the optimal control as a classical stochastic problem on the space of quantum states. We derive the corresponding Hamilton-Jacobi-Bellman equations using the elementary arguments of classical control theory and show that this is equivalent, in the Stratonovich calculus, to a stochastic Hamilton-Pontryagin setup. We show that, for cost functionals that are linear in the state, the theory yields the traditional Bellman equations treated so far in quantum feedback.
Self-adjointness and conservation laws of difference equations
Linyu Peng
2014-05-20T23:59:59.000Z
A general theorem on conservation laws for arbitrary difference equations is proved. The theorem is based on an introduction of an adjoint system related with a given difference system, and it does not require the existence of a difference Lagrangian. It is proved that the system, combined by the original system and its adjoint system, is governed by a variational principle, which inherits all symmetries of the original system. Noether's theorem can then be applied. With some special techniques, e.g. self-adjointness properties, this allows us to obtain conservation laws for difference equations, which are not necessary governed by Lagrangian formalisms.
Equation calculates activated carbon's capacity for adsorbing pollutants
Yaws, C.L.; Bu, L.; Nijhawan, S. (Lamar Univ., Beaumont, TX (United States))
1995-02-13T23:59:59.000Z
Adsorption on activated carbon is an effective method for removing volatile organic compound (VOC) contaminants from gases. A new, simple equation has been developed for calculating activated carbon's adsorption capacity as a function of the VOC concentration in the gas. The correlation shows good agreement with experimental results. Results from the equation are applicable for conditions commonly encountered in air pollution control techniques (25 C, 1 atm). The only input parameters needed are VOC concentrations and a table of correlation coefficients for 292 C[sub 8]-C[sub 14] compounds. The table is suitable for rapid engineering usage with a personal computer or hand calculator.
Disappearance of fusionlike residues and the nuclear equation of state
Xu, H.M.; Lynch, W.G.; Danielewicz, P.; Bertsch, G.F. (National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI (USA) Department of Physics, Michigan State University, East Lansing, MI (USA))
1990-08-13T23:59:59.000Z
The cross sections for massive residues from {sup 40}Ca+{sup 40}Ca and {sup 40}Ar+{sup 27}Al collisions were calculated with an improved Boltzmann-Uehling-Uhlenbeck equation. The calculated residue cross sections decrease with incident energy, an effect which does not appear related to the residue excitation energy. Larger residue cross sections result from calculations with larger in-medium nucleon-nucleon cross sections or with equations of state which are less attractive at subnuclear density. This dual sensitivity may be eliminated by measurements of observables associated with the coincident light particles.
The Runge-Kutta equations through the eighth order
Smitherman, John Alvis
2012-06-07T23:59:59.000Z
such as the orbiting of space vehicles. While there are different methods which lend themselves to solving differential equations, one of the most highly regarded processes is the Runge-Kutta [1] [2] method. Froberg [3] states in his book, "This is one of the most... or Also, where Similarly, Now, equation (2. 7) ? = Df df dx D f + ? Df, df 2gf 2 az dx D = ~ ? + f- ' , ax az/ ? = D f + D f + ( ? ) Df + 3'D ? )(Df) ~ d f 3 Bf 2 &Sf&2 [ Bf& d az l axe [ a. J dx (2. 5) may be rewritten as z(x, +h) = z...
Discrete symmetry in graphene: the Dirac equation and beyond
Sadurní, Emerson; Rosado, Alfonso
2014-01-01T23:59:59.000Z
In this pedagogical paper we review the discrete symmetries of the Dirac equation using elementary tools, but in a comparative order: the usual 3 + 1 dimensional case and the 2 + 1 dimensional case. Motivated by new applications of the 2d Dirac equation in condensed matter, we further analyze the discrete symmetries of a full tight-binding model in hexagonal lattices without conical approximations. We touch upon an effective CPT symmetry breaking that occurs when deformations and second-neighbor corrections are considered.
On the Sackur-Tetrode equation in an expanding universe
S. H. Pereira
2011-10-07T23:59:59.000Z
In this work we investigate the thermodynamic properties satisfied by an expanding universe filled with a monoatomic ideal gas. We show that the equations for the energy density, entropy density and chemical potential remain the same of an ideal gas confined to a constant volume V . In particular the Sackur-Tetrode equation for the entropy of the ideal gas is also valid in the case of an expanding universe, provided that the constant value that represents the current entropy of the universe is appropriately chosen.
Overland flow modelling with the Shallow Water Equation using a well balanced numerical scheme
Paris-Sud XI, UniversitÃ© de
or kinematic waves equations, and using either finite volume or finite difference method. We compare these four show that, for relatively simple configurations, kinematic waves equations solved with finite volume; finite differ- ences scheme; kinematic wave equations; shallow water equations; comparison of numerical
Bailey, Teresa S
2008-10-10T23:59:59.000Z
of the Piecewise Linear Discontinuous Finite Element Method (PWLD) applied to the particle transport equation in two-dimensional cylindrical (RZ) and three-dimensional Cartesian (XYZ) geometries. We have designed this method to be applicable to radiative... ..................................................... 12 Coupling the radiation transport equation to the Euler equations.. 16 Limit of the radiative transfer equations ........................................ 19 Summary...
Perturbation theory for the diffusion equation by use of the moments of the generalized
Fantini, Sergio
of the radiative transfer equation and the solution of the Fredholm equation of the second kind given a suitable solution of the radiative transfer equation for the calculation of the multiple integrals or on transport theory. While analyti- cal solutions of the diffusion equation (DE) are found in the literature
Math 314 Boundary Value Problems Spring 2008 Elementary Partial Differential Equations
Muraki, David J.
worksheet. Textbook: Applied Partial Differential Equations, DuChateau & Zachmann, Dover. Prerequisites
Three-dimensional h-adaptivity for the multigroup neutron diffusion equations Yaqi Wang a
Bangerth, Wolfgang
(Bell and Glasstone, 1970; Duderstadt and Martin, 1979), an equation that is extraordinarily complicated
Lessard, Jean-Philippe
Recent advances about the uniqueness of the slowly oscillating periodic solutions of Wright's equation Jean-Philippe Lessard Abstract An old conjecture in delay equations states that Wright's equation to rigorously compute a global continuous branch of SOPS of Wright's equation. Using this method, we show
Gas Generation Equations for CRiSP 1.6 April 21, 1998 1 Gas Generation Equations for CRiSP 1.6
Washington at Seattle, University of
Gas Generation Equations for CRiSP 1.6 April 21, 1998 1 Gas Generation Equations for CRiSP 1.6 Theory For CRiSP.1.6 new equations have been implemented for gas production from spill. As a part of the US Army Corps' Gas Abatement study, Waterways Experiment Station (WES) has developed these new
SINGULAR FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND EMISSIONS DERIVATIVES
Carmona, Rene
SINGULAR FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND EMISSIONS DERIVATIVES RENÂ´E CARMONA and why they appear naturally as models for the valuation of CO2 emission allowances. Single phase cap is motivated by the mathematical analysis of the emissions markets, as implemented for example in the European
Solution generating theorems for the Tolman-Oppenheimer-Volkov equation
Boonserm, Petarpa; Visser, Matt; Weinfurtner, Silke [School of Mathematics, Statistics, and Computer Science, Victoria University of Wellington, PO Box 600, Wellington (New Zealand)
2007-08-15T23:59:59.000Z
The Tolman-Oppenheimer-Volkov (TOV) equation constrains the internal structure of general relativistic static perfect fluid spheres. We develop several 'solution generating' theorems for the TOV equation, whereby any given solution can be deformed into a new solution. Because the theorems we develop work directly in terms of the physical observables--pressure profile and density profile--it is relatively easy to check the density and pressure profiles for physical reasonableness. This work complements our previous article [Phys. Rev. D 71, 124037 (2005)] wherein a similar algorithmic analysis of the general relativistic static perfect fluid sphere was presented in terms of the spacetime geometry--in the present analysis the pressure and density are primary and the spacetime geometry is secondary. In particular, our deformed solutions to the TOV equation are conveniently parametrized in terms of {delta}{rho}{sub c} and {delta}p{sub c}, the finite shift in the central density and central pressure. We conclude by presenting a new physical and mathematical interpretation for the TOV equation--as an integrability condition on the density and pressure profiles.
Constraints on Equation of State for Cavitating Flows with Thermodynamic
Paris-Sud XI, UniversitÃ© de
, Equation of State, Entropy Conditions, Mixture Sound Speed Notations c speed of sound Corresponding author dynamic viscosity Subscripts and superscripts L liquid value V vapour value 1 Introduction The simulation the cavity character- istics. For such fluids, the liquid-vapour density ratio is lower than in cold water
Green function diagonal for a class of heat equations
Grzegorz Kwiatkowski; Sergey Leble
2011-12-15T23:59:59.000Z
A construction of the heat kernel diagonal is considered as element of generalized Zeta function, that, being meromorfic function, its gradient at the origin defines determinant of a differential operator in a technique for regularizing quadratic path integral. Some classes of explicit expression in the case of finite-gap potential coefficient of the heat equation are constructed.
Global existence for the primitive equations with small anisotropic viscosity
Charve, FrÃ©dÃ©ric
diffusivity, and the horizontal viscosity and horizontal thermal diffusivity of size where 0 and no vertical thermal diffusivity and we also suppose that the horizontal viscosity and thermal diffusivity go , Van-Sang Ngo RÂ´esumÂ´e: Dans cet article, nous considÂ´erons le syst`eme des Â´equations prim- itives
Getting Started with Differential Equations in Maple September 2003
Weckesser, Warren
order equations here. First, we need to load the "DEtools" library: > with(DEtools): Let's define to Inline by using the menu bar to select Options -> Plot Display -> Inline Let's add a solution curve "linecolor=blue" tells the command to draw the solution curve in black. (The default line color is yellow
Getting Started with Differential Equations in Maple September 2003
Weckesser, Warren
order equations here. First, we need to load the "DEtools" library: > with(DEtools): Let's define to Inline by using the menu bar to select Options > Plot Display > Inline Let's add a solution curve "linecolor=blue" tells the command to draw the solution curve in black. (The default line color is yellow
Iterative Solution of Elliptic Equations with a Small Parameter
Segatti, Antonio
and engineering are modelled by partial differ- ential equations involving a small parameter defining a certain are positive semi-definite linear partial differential operators, such that the operator t2 L1 +L0 is coercive the properties of the operators Li and the vectors x and b describe the unknown u and the load f with respect
Supplementary material Boundary conditions and numerical solution of Equation 4
Neufeld, Jerome A.
Supplementary Material for Particle Mass Yield from -Caryophyllene Ozonolysis Qi Chen1 , Yongjie Li in a continuously mixed flow reactor (CMFR) The mass balance of organic aerosol in a CMFR is described by the following equation: org, CMFR org, inflow org, CMFR org org, CMFR CMFR CMFR dM M M F M dt = - + - (A1
Radiative transport limit for the random Schrödinger equation
Guillaume Bal; George Papanicolaou; Leonid Ryzhik
2001-08-14T23:59:59.000Z
We give a detailed mathematical analysis of the radiative transport limit for the average phase space density of solutions of the Schroedinger equation with time dependent random potential. Our derivation is based on the construction of an approximate martingale for the random Wigner distribution.
A genus six cyclic tetragonal reduction of the Benney equations
Matthew England; John Gibbons
2009-03-30T23:59:59.000Z
A reduction of Benney's equations is constructed corresponding to Schwartz-Christoffel maps associated with a family of genus six cyclic tetragonal curves. The mapping function, a second kind Abelian integral on the associated Riemann surface, is constructed explicitly as a rational expression in derivatives of the Kleinian sigma-function of the curve.
Optimum Aerodynamic Design using the Navier--Stokes Equations
Pierce, Niles A.
Optimum Aerodynamic Design using the Navier--Stokes Equations A. JAMESON \\Lambda ; N.A. PIERCE y factors such as aerodynamic effiÂ ciency, structural weight, stability and control, and the volume the disciplines. The development of accurate and efficient methods for aerodynamic shape optimization represents
Generalized Digital Trees and Their Difference-Differential Equations
Flajolet, Philippe
Generalized Digital Trees and Their Difference- Differential Equations Philippe Flajolet a tree partitioning process in which n elements are split into b at the root of a tree (b a design. This extends some familiar tree data structures of computer science like the digital trie and the digital
Rigid Shape Interpolation Using Normal Equations William Baxter
Boyer, Edmond
Rigid Shape Interpolation Using Normal Equations William Baxter OLM Digital, Inc. Pascal Barla INRIA Bordeaux University Ken-ichi Anjyo OLM Digital, Inc. Figure 1: Rigid Morphing with large rotations works well and is a very practical way e-mail: baxter@olm.co.jp e-mail: pascal.barla@labri.fr e
Conformal welding and the sewing equations Eric Schippers
Schippers, Eric
Conformal welding and the sewing equations Eric Schippers Department of Mathematics University of Manitoba Winnipeg Rutgers 2014 Eric Schippers (Manitoba) Conformal welding Rutgers 1 / 41 #12;Introduction Schippers (Manitoba) Conformal welding Rutgers 2 / 41 #12;Introduction Our work in general We began
CAMASSAHOLM EQUATIONS AND VORTEXONS FOR AXISYMMETRIC PIPE FLOWS
CAMASSAÂHOLM EQUATIONS AND VORTEXONS FOR AXISYMMETRIC PIPE FLOWS FRANCESCO FEDELE AND DENYS DUTYKH state in non-rotating Poiseuille pipe flows. In particular, we show that the associated Navier they correspond to localized toroidal vortices that concentrate near the pipe boundaries (wall vortexons) or wrap
Multi-peak solution for nonlinear magnetic Choquard type equation
Sun, Xiaomei, E-mail: xmsunn@gmail.com [College of Science, Huazhong Agricultural University, Wuhan 430070 (China) [College of Science, Huazhong Agricultural University, Wuhan 430070 (China); Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071 (China); Zhang, Yimin, E-mail: zhangyimin@wipm.ac.cn [Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071 (China)] [Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071 (China)
2014-03-15T23:59:59.000Z
In this paper, we study a class of nonlinear magnetic Choquard type equation involving a magnetic potential and nonlocal nonlinearities. By using the method of penalization argument, we show that there exists a family of solutions having multiple concentration regions which are concentrate at the minimum points of potential V.
Gravitational lens equation for embedded lenses; magnification and ellipticity
Chen, B. [Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, 440 West Brooks, Norman, Oklahoma 73019 (United States); Mathematics Department, University of Oklahoma, 601 Elm Avenue, Norman, Oklahoma 73019 (United States); Kantowski, R.; Dai, X. [Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, 440 West Brooks, Norman, Oklahoma 73019 (United States)
2011-10-15T23:59:59.000Z
We give the lens equation for light deflections caused by point mass condensations in an otherwise spatially homogeneous and flat universe. We assume the signal from a distant source is deflected by a single condensation before it reaches the observer. We call this deflector an embedded lens because the deflecting mass is part of the mean density. The embedded lens equation differs from the conventional lens equation because the deflector mass is not simply an addition to the cosmic mean. We prescribe an iteration scheme to solve this new lens equation and use it to compare our results with standard linear lensing theory. We also compute analytic expressions for the lowest order corrections to image amplifications and distortions caused by incorporating the lensing mass into the mean. We use these results to estimate the effect of embedding on strong lensing magnifications and ellipticities and find only small effects, <1%, contrary to what we have found for time delays and for weak lensing, {approx}5%.
Topological horseshoes in travelling waves of discretized nonlinear wave equations
Chen, Yi-Chiuan, E-mail: YCChen@math.sinica.edu.tw [Institute of Mathematics, Academia Sinica, Taipei 10617, Taiwan (China)] [Institute of Mathematics, Academia Sinica, Taipei 10617, Taiwan (China); Chen, Shyan-Shiou, E-mail: sschen@ntnu.edu.tw [Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan (China)] [Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan (China); Yuan, Juan-Ming, E-mail: jmyuan@pu.edu.tw [Department of Financial and Computational Mathematics, Providence University, Shalu, Taichung 43301, Taiwan (China)] [Department of Financial and Computational Mathematics, Providence University, Shalu, Taichung 43301, Taiwan (China)
2014-04-15T23:59:59.000Z
Applying the concept of anti-integrable limit to coupled map lattices originated from space-time discretized nonlinear wave equations, we show that there exist topological horseshoes in the phase space formed by the initial states of travelling wave solutions. In particular, the coupled map lattices display spatio-temporal chaos on the horseshoes.
2D dilaton-gravity from 5D Einstein equations
P. F. González-Díaz
1993-07-16T23:59:59.000Z
A semiclassical two-dimensional dilaton-gravity model is obtained by dimensional reduction of the spherically symmetric five-dimensional Einstein equations and used to investigate black hole evaporation. It is shown that this model prevents the formation of naked singularity and allows spacetime wormholes to contribute the process of formation and evaporation of black holes.
Hylomorphic solitons for the generalized KdV equation
Vieri Benci; Donato Fortunato
2014-10-13T23:59:59.000Z
In this paper we prove the existence of hylomorphic solitons in the generalized KdV equation. A soliton is called hylomorphic if it is a solitary wave whose stability is due to a particular relation between energy and another integral of motion which we call hylenic charge.
Adaptive Calculation of Variable Coefficients Elliptic Differential Equations via Wavelets
Averbuch, Amir
Description Generating a "good" discrete representation for continuous operators is one of the basic problemsAdaptive Calculation of Variable Coefficients Elliptic Differential Equations via Wavelets Amir rather than in the original physical space can speed up the performance of the sparse solver by a factor
Multilevel Methods to Solve the Neutron Di usion Equation ?
MarÃn, JosÃ©
: multilevel methods, neutron di#11;usion equation, iterative methods. 1 Introduction A nuclear power plant the reactor core, and a turbo- generator [15]. The primary energy in a nuclear power plant is generated to simulate the nuclear plants behaviour as accurately as possible. These simulators con- sist mainly of two
Boundary quantum Knizhnik-Zamolodchikov equations and Bethe vectors
Nicolai Reshetikhin; Jasper Stokman; Bart Vlaar
2014-07-18T23:59:59.000Z
Solutions to boundary quantum Knizhnik-Zamolodchikov equations are constructed as bilateral sums involving "off-shell" Bethe vectors in case the reflection matrix is diagonal and only the 2-dimensional representation of $U_q(\\hat{\\frak{sl}(2)})$ is involved. We also consider their rational and classical degenerations.
The Cauchy problem for Liouville equation and Bryant surfaces
GÃ¡lvez, JosÃ© Antonio
The Cauchy problem for Liouville equation and Bryant surfaces JosÂ´e A. GÂ´alveza and Pablo Mirab by R. Bryant in his 1987's seminal paper [Bry], in which he derived a holomorphic representation . After Bryant's work, the above class of surfaces has become a fashion research topic, and has received
Global Nonexistence for Abstract Evolution Equations with Positive Initial Energy
Pucci, Patrizia
of the initial value problem for abstract evolution equations of the form Putt + Q(t)ut + A(t, u) = F(t, u), t J appropriately small positive values. His analysis primarily considers linear wave operators, and moreover Scientifica e Tecnologica under the auspices of the Gruppo Nazionale di Analisi Funzionale e sue Applicazioni
Effective Maxwell equations from time-dependent density functional theory
Weinan E; Jianfeng Lu; Xu Yang
2010-10-23T23:59:59.000Z
The behavior of interacting electrons in a perfect crystal under macroscopic external electric and magnetic fields is studied. Effective Maxwell equations for the macroscopic electric and magnetic fields are derived starting from time-dependent density functional theory. Effective permittivity and permeability coefficients are obtained.
On the Fokker-Planck Equation for Stochastic Hybrid Systems
Boyer, Edmond
On the Fokker-Planck Equation for Stochastic Hybrid Systems: Application to a Wind Turbine Model- speed wind turbine, with a switching controller that combines stall regulation and pitch control FPE is stated. Then the theory is applied to a variable-speed wind turbine model, yielding
HAMILTON JACOBI EQUATIONS ON METRIC SPACES AND TRANSPORT ENTROPY INEQUALITIES
Boyer, Edmond
HAMILTON JACOBI EQUATIONS ON METRIC SPACES AND TRANSPORT ENTROPY INEQUALITIES N. GOZLAN, C. ROBERTO, P-M. SAMSON Abstract. We prove an Hopf-Lax-Oleinik formula for the solutions of some Hamilton that the log-Sobolev inequality is equivalent to an hypercontractivity property of the Hamilton-Jacobi semi
Hamilton-Jacobi equations constrained on networks Yves Achdou
Paris-Sud XI, UniversitÃ© de
Hamilton-Jacobi equations constrained on networks Yves Achdou , Fabio Camilli , Alessandra Cutr, the value function is continuous. We define a notion of constrained viscosity solution of Hamilton- Jacobi in particular that the value function is the unique constrained viscosity solution of the Hamilton
Hamilton-Jacobi equations with jumps: asymptotic stability
Amir Mahmood; Saima Parveen
2009-09-05T23:59:59.000Z
The asymptotic stability of a global solution satisfying Hamilton-Jacobi equations with jumps will be analyzed in dependence on the strong dissipativity of the jump control function and using orbits of the differentiable flows to describe the corresponding characteristic system.
On formation of equation of state of evolving quantum field
A. V. Leonidov; A. A. Radovskaya
2014-12-13T23:59:59.000Z
Stylized model of evolution of matter created in ultra relativistic heavy ion collisions is considered. Systematic procedure of computing quantum corrections in the framework of Keldysh formalism is formulated. Analytical expressions for formation of equations of state taking into account leading quantum corrections is worked out, complete description of subleasing corrections and analytical expressions for some of them is presented.
Loss of regularity for Kolmogorov equations Martin Hairer1
Hairer, Martin
.jentzen (at) sam.math.ethz.ch 4 Program in Applied and Computational Mathematics, Princeton University, this observation has the consequence that there exists a stochastic differential equation (SDE) with globally on regularity analysis of linear PDEs, on the literature on regularity analysis of stochastic differential
Homogenized Maxwell's Equations; a Model for Varistor Ceramics
Birnir, BjÃ¶rn
from [3] of the electric field as a function of the current density for Zinc Oxide, ZnHomogenized Maxwell's Equations; a Model for Varistor Ceramics BjÂ¨orn Birnir Niklas Wellander and lower bounds are obtained for the effective conductivity in the varistor. These two bounds
Homogenized Maxwell's Equations; a Model for Varistor Ceramics
Birnir, BjÃ¶rn
from [3] of the electric field as a function of the current density for Zinc Oxide, ZnHomogenized Maxwell's Equations; a Model for Varistor Ceramics BjË? orn Birnir Niklas Wellander and lower bounds are obtained for the effective conductivity in the varistor. These two bounds
Relativistic static fluid spheres with a linear equation of state
B. V. Ivanov
2001-07-10T23:59:59.000Z
It is shown that almost all known solutions of the kind mentioned in the title are easily derived in a unified manner when a simple ansatz is imposed on the metric. The Whittaker solution is an exception, replaced by a new solution with the same equation of state.
Gaussian Beams For the Wave Equation Nicolay M. Tanushev
Soatto, Stefano
Gaussian Beams For the Wave Equation Nicolay M. Tanushev September 20, 2007 Abstract High frequency rely on approximate solution methods to describe the wave field in this regime. Gaussian beams can form integral superpositions of such Gaussian beams to generate more general high frequency
Alternative Discrete Energy Solutions to the Free Particle Dirac Equation
Thomas Edward Brennan
2013-11-15T23:59:59.000Z
The usual method of solving the free particle Dirac equation results in the so called continuum energy solutions. Here, we take a different approach and find a set of solutions with quantized energies which are proportional to the total angular momentum.
ENERGY CONSERVATION AND ONSAGER'S CONJECTURE FOR THE EULER EQUATIONS
Shvydkoy, Roman
ENERGY CONSERVATION AND ONSAGER'S CONJECTURE FOR THE EULER EQUATIONS A. CHESKIDOV, P. CONSTANTIN, S occurs when h 1/3. Eyink [14] proved energy conservation under a stronger assumption. Subsequently, Constantin, E and Titi [9] proved energy conservation for u in the Besov space B 3,, > 1/3. More recently
A Debugging Scheme for Declarative Equation Based Modeling Languages
Zhao, Yuxiao
examine the particular debugging problems posed by Modelica, a declarative equation based modeling language. A brief overview of the Modelica language is also given. We also present our view of the issues, bipartite graphs, graph decomposition techniques, static analysis, debug- ging, Modelica. 1 Introduction
A Debugging Scheme for Declarative Equation Based Modeling Languages
Burns, Peter
examine the particular debugging problems posed by Modelica, a declarative equation based modeling language. A brief overview of the Modelica language is also given. We also present our view of the issues, bipartite graphs, graph decomposition techniques, static analysis, debug- ging, Modelica 1 Introduction
Learning Computational Methods for Partial Differential Equations from the Web
Jaun, André
Learning Computational Methods for Partial Differential Equations from the Web Andr´e Jaun1 , Johan@fusion.kth.se, Web-page: http://pde.fusion.kth.se 2 Center for Educational Development, Chalmers, SE 412 96 G the web1 and has been tested with postgraduate students from re- mote universities. Short video
Integral equations for shape and impedance reconstruction in corrosion detection
Cakoni, Fioralba
Integral equations for shape and impedance reconstruction in corrosion detection Fioralba Cakoni of the method. 1 Introduction We consider an inverse problem originating from corrosion detection. Let D R2 Angewandte Mathematik, UniversitÃ¤t GÃ¶ttingen, 37083 GÃ¶ttingen, Germany 1 #12;part c affected by corrosion
Numerical solutions to integral equations of the Fredholm type
Pullin, John Henry
1966-01-01T23:59:59.000Z
of the principal founders of the theory of integral equations are Vito Volterra (1860-1940), Ivar Fredholm (1866-1927), David Hilbert (1862-1943), and Erhard Schmidt (b. 1876). It was Volterra who recognised the importance of the theory, but Fredholm...
The Fundamental Solution to the Wright-fisher Equation
Stroock, Daniel W.
The Wright–Fisher equation, which was introduced as a model to study demography in the presence of diffusion, has had a renaissance as a model for the migration of alleles in the genome. Our goal in this paper is to give ...
GLOBAL ATTRACTIVITY OF THE ZERO SOLUTION FOR WRIGHT'S EQUATION
Csendes, Tibor
GLOBAL ATTRACTIVITY OF THE ZERO SOLUTION FOR WRIGHT'S EQUATION BALÂ´AZS BÂ´ANHELYI, TIBOR CSENDES, TIBOR KRISZTIN, AND ARNOLD NEUMAIERÂ§ Abstract. In a paper published in 1955, E.M. Wright proved that all oscillating periodic solution, Wright's conjecture, verified computational techniques, computer-assisted proof
Another method to solve Dirac's one-electron equation numerically
K V Koshelev
2008-11-24T23:59:59.000Z
One more mode developed to get eigen energies and states for the one-electron Dirac's equation with spherically symmetric bound potential. For the particular case of the Coulomb potential it was shown that the method is free of so called spurious states. The procedure could be adapted to receive highly exited states with great precision.
Nonlinear analysis of a reaction-diffusion system: Amplitude equations
Zemskov, E. P., E-mail: zemskov@ccas.ru [Russian Academy of Sciences, Dorodnicyn Computing Center (Russian Federation)
2012-10-15T23:59:59.000Z
A reaction-diffusion system with a nonlinear diffusion term is considered. Based on nonlinear analysis, the amplitude equations are obtained in the cases of the Hopf and Turing instabilities in the system. Turing pattern-forming regions in the parameter space are determined for supercritical and subcritical instabilities in a two-component reaction-diffusion system.
Energy Conserving Equations of Motion for Gear Systems
Barber, James R.
: 10.1115/1.1891815 1 Introduction The undesirable noise and vibration caused by gears in a large critically on the high frequency response. A primary source of gear noise and vibration is the varying meshEnergy Conserving Equations of Motion for Gear Systems Sejoong Oh Senior Engineer General Motors
ALSEP Thermal Performance at Off-Equator Latitudes
Rathbun, Julie A.
CONFIGURATION 33 THERMAL ANALYSIS 35 4. 1 SOLAR HEATING OF CENTRAL STATION ENCLOSURE AT LUNAR NOON 35 4.2 SOLAR HEATING OF CENTRAL STATION ENCLOSURE AT LUNAR SUNSET 35 DISCUSSION 40 5. 1 MODIFICATIONS TO CENTRAL.6 EFFECT OF OFF-EQUATOR DEPLOYMENT ON PDM PANEL 58 REFERENCES 59 #12;: : t ~ ALSEP Thermal Performance
A Superposition Strategy for Abductive Reasoning in Ground Equational Logic
Paris-Sud XI, UniversitÃ© de
A Superposition Strategy for Abductive Reasoning in Ground Equational Logic Mnacho Echenim, Nicolas Abduction has been introduced by Peirce [8] as the process of inferring plausible hypotheses from data. There exists an extensive amount of research on abductive reasoning, mainly in propositional logic
Accurate solution and approximations of the linearized bgk equation ...
Wei Li
2015-01-30T23:59:59.000Z
Jan 7, 2015 ... We present an accurate and efficient high-order collocation method to solve the integral equation with a singular kernel ..... where A is an N ? N matrix whose element is amn ? An?ym?, and b and c are ...... some classical problems in flow and heat transfer. .... Algorithms for the numerical solution of a finite-.
Control of the Wave Equation by Time-Dependent Coefficient
in the area of smart materials. The properties of these materials can be changed by the application that the problem considered here is different from the con- trol of structures by a system of smart material sensors and actuators. The smart material can be piezo-electric, in which case, the governing equations
Control of the Wave Equation by TimeDependent Coefficient
in the area of smart materials. The properties of these materials can be changed by the application that the problem considered here is different from the conÂ trol of structures by a system of smart material sensors and actuators. The smart material can be piezoÂelectric, in which case, the governing equations
Analytic solution of nonlinear fractional Burgers-type equation by invariant subspace method
P. Artale Harris; R. Garra
2013-06-08T23:59:59.000Z
In this paper we study the analytic solutions of Burgers-type nonlinear fractional equations by means of the Invariant Subspace Method. We first study a class of nonlinear equations directly related to the time-fractional Burgers equation. Some generalizations linked to the forced time-fractional Burgers equations and variable-coefficient diffusion are also considered. Finally we study a Burgers-type equation involving both space and time-fractional derivatives.
Donchev, Veliko, E-mail: velikod@ie.bas.bg [Laboratory “Physical Problems of Electron and Ion Technologies,” Institute of Electronics, Bulgarian Academy of Sciences, 72 Tzarigradsko shosse, 1784 Sofia (Bulgaria)] [Laboratory “Physical Problems of Electron and Ion Technologies,” Institute of Electronics, Bulgarian Academy of Sciences, 72 Tzarigradsko shosse, 1784 Sofia (Bulgaria)
2014-03-15T23:59:59.000Z
We find variational symmetries, conserved quantities and identities for several equations: envelope equation, Böcher equation, the propagation of sound waves with losses, flow of a gas with losses, and the nonlinear Schrödinger equation with losses or gains, and an electro-magnetic interaction. Most of these equations do not have a variational description with the classical variational principle and we find such a description with the generalized variational principle of Herglotz.
Methods for diffusive relaxation in the Pn equation
Hauck, Cory D [Los Alamos National Laboratory; Mcclarren, Ryan G [Los Alamos National Laboratory; Lowrie, Robert B [Los Alamos National Laboratory
2008-01-01T23:59:59.000Z
We present recent progress in the development of two substantially different approaches for simulating the so-called of P{sub N} equations. These are linear hyperbolic systems of PDEs that are used to model particle transport in a material medium, that in highly collisional regimes, are accurately approximated by a simple diffusion equation. This limit is based on a balance between function values and gradients of certain variables in the P{sub N} system. Conventional reconstruction methods based on upwinding approximate such gradients with an error that is dependent on the size of the computational mesh. Thus in order to capture the diffusion limit, a given mesh must resolve the dynamics of the continuum equation at the level of the mean-free-path, which tends to zero in the diffusion limit. The two methods analyzed here produce accurate solutions in both collisional and non-collisional regimes; in particular, they do not require resolution of the mean-free-path in order to properly capture the diffusion limit. The first method is a straight-forward application of the discrete Galerkin (DG) methodology, which uses additional variables in each computational cell to capture the balance between function values and gradients, which are computed locally. The second method uses a temporal splitting of the fast and slow dynamics in the P{sub N} system to derive so-called regularized equations for which the diffusion limit is built-in. We focus specifically on the P{sub N} equations for one-dimensional, slab geometries. Preliminary results for several benchmark problems are presented which highlight the advantages and disadvantages of each method. Further improvements and extensions are also discussed.
Support Operators Method for the Diffusion Equation in Multiple Materials
Winters, Andrew R. [Los Alamos National Laboratory; Shashkov, Mikhail J. [Los Alamos National Laboratory
2012-08-14T23:59:59.000Z
A second-order finite difference scheme for the solution of the diffusion equation on non-uniform meshes is implemented. The method allows the heat conductivity to be discontinuous. The algorithm is formulated on a one dimensional mesh and is derived using the support operators method. A key component of the derivation is that the discrete analog of the flux operator is constructed to be the negative adjoint of the discrete divergence, in an inner product that is a discrete analog of the continuum inner product. The resultant discrete operators in the fully discretized diffusion equation are symmetric and positive definite. The algorithm is generalized to operate on meshes with cells which have mixed material properties. A mechanism to recover intermediate temperature values in mixed cells using a limited linear reconstruction is introduced. The implementation of the algorithm is verified and the linear reconstruction mechanism is compared to previous results for obtaining new material temperatures.
Hydrodynamic Burnett equations for inelastic Maxwell models of granular gases
Nagi Khalil; Vicente Garzó; Andrés Santos
2014-05-06T23:59:59.000Z
The hydrodynamic Burnett equations and the associated transport coefficients are exactly evaluated for generalized inelastic Maxwell models. In those models, the one-particle distribution function obeys the inelastic Boltzmann equation, with a velocity-independent collision rate proportional to the $\\gamma$ power of the temperature. The pressure tensor and the heat flux are obtained to second order in the spatial gradients of the hydrodynamic fields with explicit expressions for all the Burnett transport coefficients as functions of $\\gamma$, the coefficient of normal restitution, and the dimensionality of the system. Some transport coefficients that are related in a simple way in the elastic limit become decoupled in the inelastic case. As a byproduct, existing results in the literature for three-dimensional elastic systems are recovered, and a generalization to any dimension of the system is given. The structure of the present results is used to estimate the Burnett coefficients for inelastic hard spheres.
Gauge Drivers for the Generalized Harmonic Einstein Equations
Lee Lindblom; Keith D. Matthews; Oliver Rinne; Mark A. Scheel
2007-11-13T23:59:59.000Z
The generalized harmonic representation of Einstein's equation is manifestly hyperbolic for a large class of gauge conditions. Unfortunately most of the useful gauges developed over the past several decades by the numerical relativity community are incompatible with the hyperbolicity of the equations in this form. This paper presents a new method of imposing gauge conditions that preserves hyperbolicity for a much wider class of conditions, including as special cases many of the standard ones used in numerical relativity: e.g., K-freezing, Gamma-freezing, Bona-Masso slicing, conformal Gamma-drivers, etc. Analytical and numerical results are presented which test the stability and the effectiveness of this new gauge driver evolution system.
Deformation Quantization, Quantization, and the Klein-Gordon Equation
P. Tillman
2007-02-28T23:59:59.000Z
The aim of this proceeding is to give a basic introduction to Deformation Quantization (DQ) to physicists. We compare DQ to canonical quantization and path integral methods. It is described how certain issues such as the roles of associativity, covariance, dynamics, and operator orderings are understood in the context of DQ. Convergence issues in DQ are mentioned. Additionally, we formulate the Klein-Gordon (KG) equation in DQ. Original results are discussed which include the exact construction of the Fedosov star-product on the dS and AdS space-times. Also, the KG equation is written down for these space-times. This is a proceedings to the Second International Conference on Quantum Theories and Renormalization Group in Gravity and Cosmology.
Vorticity Preserving Flux Corrected Transport Scheme for the Acoustic Equations
Lung, Tyler B. [Los Alamos National Laboratory; Roe, Phil [University of Michigan; Morgan, Nathaniel R. [Los Alamos National Laboratory
2012-08-15T23:59:59.000Z
Long term research goals are to develop an improved cell-centered Lagrangian Hydro algorithm with the following qualities: 1. Utilizes Flux Corrected Transport (FCT) to achieve second order accuracy with multidimensional physics; 2. Does not rely on the one-dimensional Riemann problem; and 3. Implements a form of vorticity control. Short term research goals are to devise and implement a 2D vorticity preserving FCT solver for the acoustic equations on an Eulerian mesh: 1. Develop a flux limiting mechanism for systems of governing equations with symmetric wave speeds; 2. Verify the vorticity preserving properties of the scheme; and 3. Compare the performance of the scheme to traditional MUSCL-Hancock and other algorithms.
Boundary quantum Knizhnik-Zamolodchikov equations and fusion
Nicolai Reshetikhin; Jasper Stokman; Bart Vlaar
2014-12-19T23:59:59.000Z
In this paper we extend our previous results concerning Jackson integral solutions of the boundary quantum Knizhnik-Zamolodchikov equations with diagonal K-operators to higher-spin representations of quantum affine $\\mathfrak{sl}_2$. First we give a systematic exposition of known results on $R$-operators acting in the tensor product of evaluation representations in Verma modules over quantum $\\mathfrak{sl}_2$. We develop the corresponding fusion of $K$-operators, which we use to construct diagonal $K$-operators in these representations. We construct Jackson integral solutions of the associated boundary quantum Knizhnik-Zamolodchikov equations and explain how in the finite-dimensional case they can be obtained from our previous results by the fusion procedure.
An iterative technique for solving equations of statistical equilibrium
L. B. Lucy
2001-03-21T23:59:59.000Z
Superlevel partitioning is combined with a simple relaxation procedure to construct an iterative technique for solving equations of statistical equilibrium. In treating an $N$-level model atom, the technique avoids the $N^{3}$ scaling in computer time for direct solutions with standard linear equation routines and also does not fail at large $N$ due to the accumulation of round-off errors. In consequence, the technique allows detailed model atoms with $N \\ga 10^{3}$, such as those required for iron peak elements, to be incorporated into diagnostic codes for analysing astronomical spectra. Tests are reported for a 394-level Fe II ion and a 1266-level Ni I--IV atom.
Applications of a nonlinear evolution equation II: the EMC effect
Chen, Xurong; Wang, Rong; Zhang, Pengming; Zhu, Wei
2013-01-01T23:59:59.000Z
The EMC effect is studied by using the GLR-MQ-ZSR equation with minimum number of free parameters, where the nuclear shadowing effect is a dynamical evolution result of the equation, and nucleon swelling and Fermi motion in the nuclear environment deform the input parton distributions. Parton distributions of both proton and nucleus are predicted in a unified framework. We show that the parton recombination as a higher twist correction plays an essential role in the evolution of parton distributions either of proton or nucleus. We find that the nuclear antishadowing contributes a part of enhancement of the ratio of the structure functions around $x\\sim 0.1$, while the other part origins from the deformation of the nuclear valence quark distributions. We point out that the nuclear shadowing and antishadowing effects in the gluon distribution are not stronger than that in the quark distributions.
Applications of a nonlinear evolution equation II: the EMC effect
Xurong Chen; Jianhong Ruan; Rong Wang; Pengming Zhang; Wei Zhu
2014-09-10T23:59:59.000Z
The EMC effect is studied by using the GLR-MQ-ZSR equation with minimum number of free parameters, where the nuclear shadowing effect is a dynamical evolution result of the equation, and nucleon swelling and Fermi motion in the nuclear environment deform the input parton distributions. Parton distributions of both proton and nucleus are predicted in a unified framework. We show that the parton recombination as a higher twist correction plays an essential role in the evolution of parton distributions either of proton or nucleus. We find that the nuclear antishadowing contributes a part of enhancement of the ratio of the structure functions around $x\\sim 0.1$, while the other part origins from the deformation of the nuclear valence quark distributions. We point out that the nuclear shadowing and antishadowing effects in the gluon distribution are not stronger than that in the quark distributions.
Ergodicity for Nonlinear Stochastic Equations in Variational Formulation
Barbu, Viorel [Faculty of Mathematics, University Al. I. Cuza, 6600 Iasi (Romania)], E-mail: barbu@uaic.ro; Da Prato, Giuseppe [Scuola Normale Superiore, 56126 Pisa (Italy)], E-mail: daprato@sns.it
2006-03-15T23:59:59.000Z
This paper is concerned with nonlinear partial differential equations of the calculus of variation (see [13]) perturbed by noise. Well-posedness of the problem was proved by Pardoux in the seventies (see [14]), using monotonicity methods.The aim of the present work is to investigate the asymptotic behaviour of the corresponding transition semigroup P{sub t}. We show existence and, under suitable assumptions, uniqueness of an ergodic invariant measure {nu}. Moreover, we solve the Kolmogorov equation and prove the so-called 'identite du carre du champs'. This will be used to study the Sobolev space W{sup 1,2}(H,{nu}) and to obtain information on the domain of the infinitesimal generator of P{sub t}.
Probability representation of quantum evolution and energy level equations for optical tomograms
Ya. A. Korennoy; V. I. Man'ko
2011-01-13T23:59:59.000Z
The von Neumann evolution equation for density matrix and the Moyal equation for the Wigner function are mapped onto evolution equation for optical tomogram of quantum state. The connection with known evolution equation for symplectic tomogram of the quantum state is clarified. The stationary states corresponding to quantum energy levels are associated with the probability representation of the von Neumann and Moyal equations written for the optical tomograms. Classical Liouville equation for optical tomogram is obtained. Example of parametric oscillator is considered in detail.
Lattice Boltzmann computations for reaction-diffusion equations
Ponce Dawson, S.; Chen, S.; Doolen, G.D. (Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States))
1993-01-15T23:59:59.000Z
A lattice Boltzmann model for reaction-diffusion systems is developed. The method provides an efficient computational scheme for simulating a variety of problems described by the reaction-diffusion equations. Diffusion phenomena, the decay to a limit cycle, and the formation of Turing patterns are studied. The results of lattice Boltzmann calculations are compared with the lattice gas method and with theoretical predictions, showing quantitative agreement. The model is extended to include velocity convection in chemically reacting fluid flows.
Oppenheimer-Volkoff Equation in Relativistic MOND Theory
Xing-hua Jin; Xin-zhou Li
2006-06-23T23:59:59.000Z
In this paper, we discuss the internal and external metric of the semi-realistic stars in relativistic MOND theory. We show the Oppenheimer-Volkoff equation in relativistic MOND theory and get the metric and pressure inside the stars to order of post-Newtonian corrections. We study the features of motion around the static, spherically symmetric stars by Hamilton-Jacobi mothod, and find there are only some small corrections in relativistic MOND theory.
1-D Dirac Equation, Klein Paradox and Graphene
S. P. Bowen
2008-07-23T23:59:59.000Z
Solutions of the one dimensional Dirac equation with piece-wise constant potentials are presented using standard methods. These solutions show that the Klein Paradox is non-existent and represents a failure to correctly match solutions across a step potential. Consequences of this exact solution are studied for the step potential and a square barrier. Characteristics of massless Dirac states and the momentum linear band energies for Graphene are shown to have quite different current and momentum properties.
Field Equations and Conservation Laws in the Nonsymmetric Gravitational Theory
J. Legare; J. W. Moffat
1994-12-08T23:59:59.000Z
The field equations in the nonsymmetric gravitational theory are derived from a Lagrangian density using a first-order formalism. Using the general covariance of the Lagrangian density, conservation laws and tensor identities are derived. Among these are the generalized Bianchi identities and the law of energy-momentum conservation. The Lagrangian density is expanded to second-order, and treated as an ``Einstein plus fields'' theory. From this, it is deduced that the energy is positive in the radiation zone.
On the Solutions of Einstein Equations with Massive Point Source
P. P. Fiziev
2004-12-30T23:59:59.000Z
We show that Einstein equations are compatible with the presence of massive point particles and find corresponding two parameter family of their solutions which depends on the bare mechanical mass $M_0>0$ and the Keplerian mass $M
Regional Monte Carlo solution of elliptic partial differential equations
Booth, T.E.
1981-01-01T23:59:59.000Z
A continuous random walk procedure for solving some elliptic partial differential equations at a single point is generalized to estimate the solution everywhere. The Monte Carlo method described here is exact (except at the boundary) in the sense that the only error is the statistical sampling error that tends to zero as the sample size increases. A method to estimate the error introduced at the boundary is provided so that the boundary error can always be made less than the statistical error.
The Nuclear Equation of State at high densities
Christian Fuchs
2006-10-10T23:59:59.000Z
Ab inito calculations for the nuclear many-body problem make predictions for the density and isospin dependence of the nuclear equation-of-state (EOS) far away from the saturation point of nuclear matter. I compare predictions from microscopic and phenomenological approaches. Constraints on the EOS derived from heavy ion reactions, in particular from subthreshold kaon production, as well as constraints from neutron stars are discussed.
Nuclear Shadowing and Antishadowing in a Unitarized BFKL Equation
Jianhong Ruan; Zhenqi Shen; Wei Zhu
2008-01-22T23:59:59.000Z
The nuclear shadowing and antishadowing effects are explained by a unitarized BFKL equation. The $Q^2$- and $x$-variations of the nuclear parton distributions are detailed based on the level of the unintegrated gluon distribution. In particular, the asymptotical behavior of the unintegrated gluon distribution near the saturation limit in nuclear targets is studied. Our results in the nuclear targets are insensitive to the input distributions if the parameters are fixed by the data of a free proton.
A note on the Lyapunov Equation Alessandro Abate
Abate, Alessandro
A note on the Lyapunov Equation Alessandro Abate a.abate@tudelft.nl Delft Center for Systems and Control, TU Delft October 27, 2011 Â Ac.Yr. 2011/12, 1e Sem. Q1 Â Note Â sc4026 #12;A. Abate Consider/12, 1e Sem. Q1 Â Note Â sc4026 1 #12;A. Abate Consider the following operations: AX + XAT = -Q2 AXX-1
Determination of soil parameters for wave equation analysis
Berger, William John
1973-01-01T23:59:59.000Z
Determination of Soil Parameters for Wave Equation Analysis (August 1973) William J. Berger, B. S. , Texas A&M University; Directed by: Dr. Harry M. Coyle Load distribution versus depth data are used from static load test results and the amount of load... provided by Dr. Harry M. Coyle, Chairman of the writer's Graduate Advisory Committee and chief investigator for the project. Dr. Robert M. Olson snd Dr. Christopher C. Mathewson, members of the writer' s Graduate Advisory Committee, also furnished...
Parallel algorithm and computer architecture for solving Burgers' equation
Lie, Heung-Wai
1988-01-01T23:59:59.000Z
approaches namely time marching method and boundary value technique are used to formulate tbe matrix equation. Both computer simulations analytical results are presented. Simulation results indicate that the performance of the Textured Decomposition... OF FIGIJRES Figure 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. Domain oi interest Finite difference mesh and nonmenclature Diagonal dominant matrix discretizstion (DDD...
Initial data for Einstein's equations with superposed gravitational waves
Harald P. Pfeiffer; Lawrence E. Kidder; Mark A. Scheel; Deirdre Shoemaker
2005-02-22T23:59:59.000Z
A method is presented to construct initial data for Einstein's equations as a superposition of a gravitational wave perturbation on an arbitrary stationary background spacetime. The method combines the conformal thin sandwich formalism with linear gravitational waves, and allows detailed control over characteristics of the superposed gravitational wave like shape, location and propagation direction. It is furthermore fully covariant with respect to spatial coordinate changes and allows for very large amplitude of the gravitational wave.
Modified Bloch equations in presence of a nonstationary bath
Jyotipratim Ray Chaudhuri; Suman Kumar Banik; Bimalendu Deb; Deb Shankar Ray
1999-02-11T23:59:59.000Z
Based on the system-reservoir description we propose a simple solvable microscopic model for a nonequilibrium bath. This captures the essential features of a nonstationary quantum Markov process. We establish an appropriate generalization of the fluctuation-dissipation relation pertaining to this process and explore the essential modifications of the Bloch equations to reveal the nonexponential decay of the Bloch vector components and transient spectral broadening in resonance fluorescence. We discuss a simple experimental scheme to verify the theoretical results.
Evaluation of a land management based infiltration equation on rangelands
Bouraoui, Faycal
1990-01-01T23:59:59.000Z
de Tunis Chair of Advisory Committee: Mary Leigh Wolfe SPUR is the newest model developed for use on rangelands. It is a comprehensive model simulating all the broad aspects of the range ecosystem. The original SPUR model computes the runoff... of the equations. Aase et al. (1973), Hanks (1974), de Jong and McDonald (1975), Hanson (1976), Ritchie et al. (1976) and Rasmusssen and Hanks (1978) developed such models to predict evapotranspiration from native rangelands. However, rangeland managers were...
Motion estimation using the differential epipolar equation Dep. Inteligencia Artificial
Baumela, Luis
Science University of Oxford 19 Parks Rd, Oxford (UK) lourdes@robots.ox.ac.uk P. Bustos Dep. Inform of Oxford 19 Parks Rd, Oxford (UK) ian@robots.ox.ac.uk Abstract We consider the motion estimation problem of the projection equation (t)m(t) = P(t)X = [Q(t) | T(t)] X, viz: ( + t + O(t2 ))(m + mt + O(t2 )) = ([Q | T] + [ Q
Iterative solution of ordinary differential equations with polynomial coefficients
Forehand, Jimmie Charles Rhea
1965-01-01T23:59:59.000Z
ITERATIVE SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS WITH POLYNOMIAL COEFFICIENTS A Thesis By JIMMIE CHARLES RHEA FOREHAND Submitted to the Graduate College of the Texas A&M University in partial fulfillment of the requirements... for the degree of MASTER OF SCIENCE August 1965 Major Subject Mathematics FAMILIES OF FIFTH ORDER RUNGE-KUTTA FORMULAS A Thesis By HARRY PAUL KONEN 4 0 0 IXI v 0 Approved as to style and content by: (Chairman of Committee) (Head of Departmen...
Master equation approach to protein folding and kinetic traps
Marek Cieplak; Malte Henkel; Jan Karbowski; Jayanth R. Banavar
1998-04-21T23:59:59.000Z
The master equation for 12-monomer lattice heteropolymers is solved numerically and the time evolution of the occupancy of the native state is determined. At low temperatures, the median folding time follows the Arrhenius law and is governed by the longest relaxation time. For good folders, significant kinetic traps appear in the folding funnel whereas for bad folders, the traps also occur in non-native energy valleys.
Fractional Equations of Kicked Systems and Discrete Maps
Vasily E. Tarasov; George M. Zaslavsky
2011-07-20T23:59:59.000Z
Starting from kicked equations of motion with derivatives of non-integer orders, we obtain "fractional" discrete maps. These maps are generalizations of well-known universal, standard, dissipative, kicked damped rotator maps. The main property of the suggested fractional maps is a long-term memory. The memory effects in the fractional discrete maps mean that their present state evolution depends on all past states with special forms of weights. These forms are represented by combinations of power-law functions.
Dirac Equation in Noncommutative Space for Hydrogen Atom
T. C. Adorno; M. C. Baldiotti; M. Chaichian; D. M. Gitman; A. Tureanu
2009-07-06T23:59:59.000Z
We consider the energy levels of a hydrogen-like atom in the framework of $\\theta $-modified, due to space noncommutativity, Dirac equation with Coulomb field. It is shown that on the noncommutative (NC) space the degeneracy of the levels $2S_{1/2}, 2P_{1/2}$ and $ 2P_{3/2}$ is lifted completely, such that new transition channels are allowed.
The wave equation on static singular space-times
Eberhard Mayerhofer
2008-02-12T23:59:59.000Z
The first part of my thesis lays the foundations to generalized Lorentz geometry. The basic algebraic structure of finite-dimensional modules over the ring of generalized numbers is investigated. The motivation for this part of my thesis evolved from the main topic, the wave equation on singular space-times. The second and main part of my thesis is devoted to establishing a local existence and uniqueness theorem for the wave equation on singular space-times. The singular Lorentz metric subject to our discussion is modeled within the special algebra on manifolds in the sense of Colombeau. Inspired by an approach to generalized hyperbolicity of conical-space times due to Vickers and Wilson, we succeed in establishing certain energy estimates, which by a further elaborated equivalence of energy integrals and Sobolev norms allow us to prove existence and uniqueness of local generalized solutions of the wave equation with respect to a wide class of generalized metrics. The third part of my thesis treats three different point value resp. uniqueness questions in algebras of generalized functions
KAM theory and the 3D Euler equation
Boris Khesin; Sergei Kuksin; Daniel Peralta-Salas
2014-07-22T23:59:59.000Z
We prove that the dynamical system defined by the hydrodynamical Euler equation on any closed Riemannian 3-manifold $M$ is not mixing in the $C^k$ topology ($k > 4$ and non-integer) for any prescribed value of helicity and sufficiently large values of energy. This can be regarded as a 3D version of Nadirashvili's and Shnirelman's theorems showing the existence of wandering solutions for the 2D Euler equation. Moreover, we obtain an obstruction for the mixing under the Euler flow of $C^k$-neighborhoods of divergence-free vectorfields on $M$. On the way we construct a family of functionals on the space of divergence-free $C^1$ vectorfields on the manifold, which are integrals of motion of the 3D Euler equation. Given a vectorfield these functionals measure the part of the manifold foliated by ergodic invariant tori of fixed isotopy types. We use the KAM theory to establish some continuity properties of these functionals in the $C^k$-topology. This allows one to get a lower bound for the $C^k$-distance between a divergence-free vectorfield (in particular, a steady solution) and a trajectory of the Euler flow.
Horizon entropy and higher curvature equations of state
Raf Guedens; Ted Jacobson; Sudipta Sarkar
2012-01-02T23:59:59.000Z
The Clausius relation between entropy change and heat flux has previously been used to derive Einstein's field equations as an equation of state. In that derivation the entropy is proportional to the area of a local causal horizon, and the heat is the energy flux across the horizon, defined relative to an approximate boost Killing vector. We examine here whether a similar derivation can be given for extensions beyond Einstein gravity to include higher derivative and higher curvature terms. We review previous proposals which, in our opinion, are problematic or incomplete. Refining one of these, we assume that the horizon entropy depends on an approximate local Killing vector in a way that mimics the diffeomorphism Noether charge that yields the entropy of a stationary black hole. We show how this can be made to work if various restrictions are imposed on the nature of the horizon slices and the approximate Killing vector. Also, an integrability condition on the assumed horizon entropy density must hold. This can yield field equations of a Lagrangian constructed algebraically from the metric and Riemann tensor, but appears unlikely to allow for derivatives of curvature in the Lagrangian.
The Einstein Equation on the 3-Brane World
Shiromizu, T; Sasaki, M; Shiromizu, Tetsuya; Maeda, Kei-ichi; Sasaki, Misao
2000-01-01T23:59:59.000Z
We carefully investigate the gravitational equations of the brane world, in which all the matter forces except gravity are confined on the 3-brane in a 5-dimensional spacetime with $Z_2$ symmetry. We derive the effective gravitational equations on the brane, which reduce to the conventional Einstein equations in the low energy limit. From our general argument we conclude that the first Randall & Sundrum-type theory (RS1) [hep-ph/9905221] predicts that the brane with the negative tension is an anti-gravity world and hence should be excluded from the physical point of view. Their second-type theory (RS2)[hep-th/9906064] where the brane has the positive tension provides the correct signature of gravity. In this latter case, if the bulk spacetime is exactly anti-de Sitter, generically the matter on the brane is required to be spatially homogeneous because of the Bianchi identities. By allowing deviations from anti-de Sitter in the bulk, the situation will be relaxed and the Bianchi identities give just the re...
Equations of a Moving Mirror and the Electromagnetic Field
Luis Octavio Castaños; Ricardo Weder
2014-10-28T23:59:59.000Z
We consider a slab of a material that is linear, isotropic, non-magnetizable, ohmic, and electrically neutral when it is at rest. The slab interacts with the electromagnetic field through radiation pressure. Using a relativistic treatment, we deduce the exact equations governing the dynamics of the field and of the slab, as well as, approximate equations to first order in the velocity and the acceleration of the slab. As a consequence of the motion of the slab, the field must satisfy a wave equation with damping and slowly varying coefficients plus terms that are small when the time-scale of the evolution of the mirror is much smaller than that of the field. Moreover, the dynamics of the mirror involve a time-dependent mass arising from the interaction with the field and it is related to the effective mass of mechanical oscillators used in optomechanics. By the same reason, the mirror is subject to a velocity dependent force which is related to the much sought cooling of mechanical oscillators in optomechanics.
Time-periodic solutions of the Benjamin-Ono equation
Ambrose , D.M.; Wilkening, Jon
2008-04-01T23:59:59.000Z
We present a spectrally accurate numerical method for finding non-trivial time-periodic solutions of non-linear partial differential equations. The method is based on minimizing a functional (of the initial condition and the period) that is positive unless the solution is periodic, in which case it is zero. We solve an adjoint PDE to compute the gradient of this functional with respect to the initial condition. We include additional terms in the functional to specify the free parameters, which, in the case of the Benjamin-Ono equation, are the mean, a spatial phase, a temporal phase and the real part of one of the Fourier modes at t = 0. We use our method to study global paths of non-trivial time-periodic solutions connecting stationary and traveling waves of the Benjamin-Ono equation. As a starting guess for each path, we compute periodic solutions of the linearized problem by solving an infinite dimensional eigenvalue problem in closed form. We then use our numerical method to continue these solutions beyond the realm of linear theory until another traveling wave is reached (or until the solution blows up). By experimentation with data fitting, we identify the analytical form of the solutions on the path connecting the one-hump stationary solution to the two-hump traveling wave. We then derive exact formulas for these solutions by explicitly solving the system of ODE's governing the evolution of solitons using the ansatz suggested by the numerical simulations.
Equation of state and QCD transition at finite temperature
Bazavov, A; Bhattacharya, T; Cheng, M; Christ, N H; DeTar, C; Ejiri, S; Gottlieb, S; Gupta, R; Heller, U M; Huebner, K; Jung, C; Karsch, F; Laermann, E; Levkova, L; Miao, C; Mawhinney, R D; Petreczky, P; Schmidt, C; Soltz, R A; Soeldner, W; Sugar, R; Toussaint, D; Vranas, P
2009-03-25T23:59:59.000Z
We calculate the equation of state in 2+1 flavor QCD at finite temperature with physical strange quark mass and almost physical light quark masses using lattices with temporal extent N{sub {tau}} = 8. Calculations have been performed with two different improved staggered fermion actions, the asqtad and p4 actions. Overall, we find good agreement between results obtained with these two O(a{sup 2}) improved staggered fermion discretization schemes. A comparison with earlier calculations on coarser lattices is performed to quantify systematic errors in current studies of the equation of state. We also present results for observables that are sensitive to deconfining and chiral aspects of the QCD transition on N{sub {tau}} = 6 and 8 lattices. We find that deconfinement and chiral symmetry restoration happen in the same narrow temperature interval. In an Appendix we present a simple parametrization of the equation of state that can easily be used in hydrodynamic model calculations. In this parametrization we also incorporated an estimate of current uncertainties in the lattice calculations which arise from cutoff and quark mass effects. We estimate these systematic effects to be about 10 MeV.
Thermodynamic route to field equations in Lanczos-Lovelock gravity
Paranjape, Aseem; Sarkar, Sudipta; Padmanabhan, T. [Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai-400 005 (India); IUCAA, Post Bag 4, Ganeshkhind, Pune-411 007 (India)
2006-11-15T23:59:59.000Z
Spacetimes with horizons show a resemblance to thermodynamic systems and one can associate the notions of temperature and entropy with them. In the case of Einstein-Hilbert gravity, it is possible to interpret Einstein's equations as the thermodynamic identity TdS=dE+PdV for a spherically symmetric spacetime and thus provide a thermodynamic route to understand the dynamics of gravity. We study this approach further and show that the field equations for the Lanczos-Lovelock action in a spherically symmetric spacetime can also be expressed as TdS=dE+PdV with S and E given by expressions previously derived in the literature by other approaches. The Lanczos-Lovelock Lagrangians are of the form L=Q{sub a}{sup bcd}R{sup a}{sub bcd} with {nabla}{sub b}Q{sub a}{sup bcd}=0. In such models, the expansion of Q{sub a}{sup bcd} in terms of the derivatives of the metric tensor determines the structure of the theory and higher order terms can be interpreted as quantum corrections to Einstein gravity. Our result indicates a deep connection between the thermodynamics of horizons and the allowed quantum corrections to standard Einstein gravity, and shows that the relation TdS=dE+PdV has a greater domain of validity than Einstein's field equations.
THE METHOD OF CONJUGATE RESIDUALS FOR SOLVING THE GALERKIN EQUATIONS ASSOCIATED WITH SYMMETRIC
Plato, Robert
kind integral equations, conjugate gradient type methods, Galerkin method, regularization schemesTHE METHOD OF CONJUGATE RESIDUALS FOR SOLVING THE GALERKIN EQUATIONS ASSOCIATED WITH SYMMETRIC, the method of conjugate residuals is consid- ered. An a posteriori stopping rule is introduced
Takeshi Fukuyama; Alexander J. Silenko
2013-11-09T23:59:59.000Z
General classical equation of spin motion is explicitly derived for a particle with magnetic and electric dipole moments in electromagnetic fields. Equation describing the spin motion relatively the momentum direction in storage rings is also obtained.
Property estimation using inverse methods for elliptic and parabolic partial differential equations
Parmekar, Sandeep
1994-01-01T23:59:59.000Z
In this work we use inverse methods to estimate flow coefficients in both elliptic and parabolic partial differential equations. An algorithm is developed to solve a one layer problem for elliptic and parabolic partial differential equations...
PERIODIC SOLUTIONS WITH NONCONSTANT SIGN IN ABEL EQUATIONS OF THE SECOND KIND
PolitÃ¨cnica de Catalunya, Universitat
PERIODIC SOLUTIONS WITH NONCONSTANT SIGN IN ABEL EQUATIONS OF THE SECOND KIND JOSEP M. OLM, XAVIER, is equivalent. Key words and phrases. Abel differential equations, periodic solutions. 1 #12;2 JOSEP M. OLM
Solution of symmetry equation and hierarchy of self dual Yang-Mills systems
A. N. Leznov
2008-02-11T23:59:59.000Z
The solution of symmetry equation of Yang-Mills self dual system is found in explicit form of its raising Hamiltonian operator. Thus explicit form of equations of self dual Yang Mills hierarchy is constructed.
Linearisation of the (M,K)-reduced non-autonomous discrete periodic KP equation
Shinsuke Iwao
2009-12-17T23:59:59.000Z
The (M,K)-reduced non-autonomous discrete KP equation is linearised on the Picard group of an algebraic curve. As an application, we construct theta function solutions to the initial value problem of some special discrete KP equation.
Solutions and Generalizations of Partial Differential Equations Occurring in Petroleum Engineering
Dacunha, Jeffrey
2014-07-08T23:59:59.000Z
to derive the hyperbolic diffusion equation (a generalization of the parabolic diffusion equation) which takes into account a finite propagation speed for pressure propagation in the fluid. We develop the mathematical theory used to solve the diffusion...
E-Print Network 3.0 - adsorption isotherm equation Sample Search...
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
equation Page: << < 1 2 3 4 5 > >> 1 Experimental Study of Water Vapor Adsorption on Geothermal Summary: -Halsey-Hill (FHH) equation was found to fit the water adsorption isotherms...
Classes of Exact Solutions to Regge-Wheeler and Teukolsky Equations
P. P. Fiziev
2009-03-17T23:59:59.000Z
The Regge-Wheeler equation describes axial perturbations of Schwarzschild metric in linear approximation. Teukolsky Master Equation describes perturbations of Kerr metric in the same approximation. We present here unified description of all classes of exact solutions to these equations in terms of the confluent Heun's functions. Special attention is paid to the polynomial solutions, which yield novel applications of Teukolsky Master Equation for description of relativistic jets and astrophysical explosions.
Muraki, David J.
, and office hours Â TBA Readings: Applied Partial Differential Equations (required) P DuChateau & D Zachmann
Elliptic (N,N^\\prime)-Soliton Solutions of the lattice KP Equation
Sikarin Yoo-Kong; Frank Nijhoff
2011-11-22T23:59:59.000Z
Elliptic soliton solutions, i.e., a hierarchy of functions based on an elliptic seed solution, are constructed using an elliptic Cauchy kernel, for integrable lattice equations of Kadomtsev-Petviashvili (KP) type. This comprises the lattice KP, modified KP (mKP) and Schwarzian KP (SKP) equations as well as Hirota's bilinear KP equation, and their successive continuum limits. The reduction to the elliptic soliton solutions of KdV type lattice equations is also discussed.
Existence, uniqueness, and longtime behavior for a nonlinear Volterra integrodifferential equation
Colli, Pierluigi
equation et + · q = g in × (0, +) where · is the spatial divergence operator and g is the heat supply
Subcritical solution of the Yang-Mills Schroedinger equation in the Coulomb gauge
D. Epple; H. Reinhardt; W. Schleifenbaum; A. P. Szczepaniak
2007-12-21T23:59:59.000Z
In the Hamiltonian approach to Coulomb gauge Yang-Mills theory, the functional Schroedinger equation is solved variationally resulting in a set of coupled Dyson-Schwinger equations. These equations are solved self-consistently in the subcritical regime defined by infrared finite form factors. It is shown that the Dyson-Schwinger equation for the Coulomb form factor fails to have a solution in the critical regime where all form factors have infrared divergent power laws.
Subcritical solution of the Yang-Mills Schroedinger equation in the Coulomb gauge
Epple, D.; Reinhardt, H.; Schleifenbaum, W.; Szczepaniak, A. P. [Institut fuer Theoretische Physik, Tuebingen University, Auf der Morgenstelle 14 D-72076 Tuebingen (Germany); Physics Department and Nuclear Theory Center Indiana University, Bloomington, Indiana 47405 (United States)
2008-04-15T23:59:59.000Z
In the Hamiltonian approach to Coulomb gauge Yang-Mills theory, the functional Schroedinger equation is solved variationally resulting in a set of coupled Dyson-Schwinger equations. These equations are solved self-consistently in the subcritical regime defined by infrared-finite form factors. It is shown that the Dyson-Schwinger equation for the Coulomb form factor fails to have a solution in the critical regime where all form factors have infrared divergent power laws.
De Saporta, BenoÃ®te
Renewal theorem for a system of renewal equations ThÂ´eor`eme de renouvellement pour un syst`eme d show that the classical renewal theorems of Feller hold in the case of a system of renewal equations of renewal equations of the following type: Zi(t) = Gi(t) + p k=1 - Zk(t - u)Fik(du), t R, 1 i p, (1
A wave equation including leptons and quarks for the standard model of quantum physics in
Boyer, Edmond
A wave equation including leptons and quarks for the standard model of quantum physics in Clifford-m@orange.fr August 27, 2014 Abstract A wave equation with mass term is studied for all particles and an- tiparticles of color and antiquarks u and d. This wave equation is form invariant under the Cl 3 group generalizing
Tolman-Oppenheimer-Volkoff Equations in Modified Gauss-Bonnet Gravity
D. Momeni; R. Myrzakulov
2014-10-02T23:59:59.000Z
Based on a stringy inspired Gauss-Bonnet (GB) modification of classical gravity, we constructed a model for neutron stars. We derived the modified forms of Tolman-Oppenheimer-Volkoff (TOV) equations for a generic function of $f(G)$ gravity. The hydrostatic equations remained unchanged but the dynamical equations for metric functions are modified due to the effects of GB term.
Tolman-Oppenheimer-Volkoff Equations in Modified Gauss-Bonnet Gravity
Momeni, D
2014-01-01T23:59:59.000Z
Based on a stringy inspired Gauss-Bonnet (GB) modification of classical gravity, we constructed a model for neutron stars. We derived the modified forms of Tolman-Oppenheimer-Volkoff (TOV) equations for a generic function of $f(G)$ gravity. The hydrostatic equations remained unchanged but the dynamical equations for metric functions are modified due to the effects of GB term.
Botti, Silvana
Motivation Green's functions The GW Approximation The Bethe-Salpeter Equation Introduction to Green=whiteMotivation Green's functions The GW Approximation The Bethe-Salpeter Equation Outline 1 Motivation 2 Green's functions 3 The GW Approximation 4 The Bethe-Salpeter Equation #12;bg=whiteMotivation Green's functions
Self-similar solutions for a fractional thin film equation governing hydraulic fractures
Boyer, Edmond
Self-similar solutions for a fractional thin film equation governing hydraulic fractures C. Imbert equation governing hydraulic fractures are constructed. One of the boundary con- ditions, which accounts, 35R11, 35C06 Keywords: Hydraulic fractures, higher order equation, thin films, fractional Laplacian
ON THE DIOPHANTINE EQUATION x2 SAMIR SIKSEK AND JOHN E. CREMONA
Cremona, John
ON THE DIOPHANTINE EQUATION x2 + 7 = ym SAMIR SIKSEK AND JOHN E. CREMONA Abstract. In this paper we study the equation x2 +7 = ym , in integers x, y, m with m 3, using a Frey curve and Ribet's level. Key words and phrases. Diophantine equations, Frey curves. The first author's work is funded
ON THE DIOPHANTINE EQUATION x2 SAMIR SIKSEK AND JOHN E. CREMONA
Siksek, Samir
ON THE DIOPHANTINE EQUATION x2 + 7 = ym SAMIR SIKSEK AND JOHN E. CREMONA Abstract. In this paper we study the equation x2 +7 = ym , in integers x, y, m with m 3, using a Frey curve and Ribet's level. Primary 11G30, Secondary 11D41. Key words and phrases. Diophantine equations, Frey curves. The first
ON THE DIOPHANTINE EQUATION x 2 + 7 = y m SAMIR SIKSEK AND JOHN E. CREMONA
Cremona, John
ON THE DIOPHANTINE EQUATION x 2 + 7 = y m SAMIR SIKSEK AND JOHN E. CREMONA Abstract. In this paper we study the equation x 2 +7 = y m , in integers x, y, m with m # 3, using a Frey curve and Ribet. Key words and phrases. Diophantine equations, Frey curves. The first author's work is funded
E. Minguzzi
2014-10-01T23:59:59.000Z
A mechanical covariant equation is introduced which retains all the effectingness of the Lagrange equation while being able to describe in a unified way other phenomena including friction, non-holonomic constraints and energy radiation (Lorentz-Abraham-Dirac force equation). A quantization rule adapted to the dissipative degrees of freedom is proposed which does not pass through the variational formulation.
HYDRODYNAMIC LIMITS FOR KINETIC EQUATIONS AND THE DIFFUSIVE APPROXIMATION OF RADIATIVE
Tzavaras, Athanasios E.
HYDRODYNAMIC LIMITS FOR KINETIC EQUATIONS AND THE DIFFUSIVE APPROXIMATION OF RADIATIVE TRANSPORT . The radiative transport equations, satisfied by the Wigner function for random acoustic waves, present#usive approximation of the radiative transport equation. 1. Introduction We consider a class of kinetic models
On a Generalized Boltzmann Equation for Non-Classical Particle Transport
Goudon, Thierry
equations. Diffusion asymptotics. Radiative transfer. Neutron transport. AMS Subject classification. 35Q99On a Generalized Boltzmann Equation for Non-Classical Particle Transport Martin Frank1 and Thierry of collisional transport equations is broken by the introduction of the memory terms. Key words. Transport
A GEOMETRIC DERIVATION OF THE LINEAR BOLTZMANN EQUATION FOR A PARTICLE INTERACTING WITH A
Paris-Sud XI, UniversitÃ© de
] the radiative transport equation in the spatially homogenous case. Later Ho, Landau and Wilkins studied in [29 Boltzmann equation was derived in the radiative transport limit by Bal, Papanicolaou and Ryzhik [5A GEOMETRIC DERIVATION OF THE LINEAR BOLTZMANN EQUATION FOR A PARTICLE INTERACTING WITH A GAUSSIAN
Three-dimensional optical tomography with the equation of radiative transfer
Hielscher, Andreas
on a transport-backtransport method applied to the two-dimensional time-dependent equation of radiative transferThree-dimensional optical tomography with the equation of radiative transfer Gassan S. Abdoulaev reconstruction scheme that is based on the time-independent equation of radiative transfer (ERT) and allows
Analytical study of the energy rate balance equation for the magnetospheric storm-ring current
Paris-Sud XI, UniversitÃ© de
Analytical study of the energy rate balance equation for the magnetospheric storm-ring current A. L of the analytical integration of the energy rate balance equation, assum- ing that the input energy rate of the energy function to ht times a constant factor in the energy rate balance equation (e.g. Gonzalez et al
Averaging out Inhomogeneous Newtonian Cosmologies: I. Fluid Mechanics and the Navier-Stokes Equation
Roustam Zalaletdinov
2002-12-18T23:59:59.000Z
The basic concepts and equations of classical fluid mechanics are presented in the form necessary for the formulation of Newtonian cosmology and for derivation and analysis of a system of the averaged Navier-Stokes-Poisson equations. A special attention is paid to the analytic formulation of the definitions and equations of moving fluids and to their physical content.
Ergodicity of Hamilton-Jacobi equations with a non coercive non convex Hamiltonian in R2
Boyer, Edmond
Ergodicity of Hamilton-Jacobi equations with a non coercive non convex Hamiltonian in R2 /Z2 Pierre of Hamilton-Jacobi equations with a non coercive, non convex Hamiltonian in the torus R2/Z2. We give nonreson moyenne temporelle de solutions d'Â´equations de Hamilton-Jacobi pour un hamiltonien non convexe et non
Hamilton-Jacobi equations for optimal control on junctions and Yves Achdou
Boyer, Edmond
Hamilton-Jacobi equations for optimal control on junctions and networks Yves Achdou , Salom. A notion of viscosity solution of Hamilton-Jacobi equations on the network has been proposed in earlier of optimal control. Keywords Optimal control, networks, Hamilton-Jacobi equations, viscosity solutions AMS 34
Hamilton-Jacobi Equations on a Manifold and Applications to Grid Generation or Re nement.
Hamilton-Jacobi Equations on a Manifold and Applications to Grid Generation or Re#28;nement. Ph Hamilton-Jacobi equations on a manifold, typically on the graph of some previously computed function z method. Keywords: Hamilton-Jacobi equations, viscosity solutions, level set method, adaptative meshes
System of two Hamilton-Jacobi equations for complex-valued travel time
Cerveny, Vlastislav
System of two Hamilton-Jacobi equations for complex-valued travel time Lud#20;ek Klime#20;s. In real space, the eikonal equation for complex{valued travel time represents the system of two Hamilton of this system of Hamilton{Jacobi equations does not propagate along rays, and has to be solved by more global
Dark-energy equation of state: how far can we go from ??
Hrvoje Stefancic
2006-09-28T23:59:59.000Z
The equation of state of dark energy is investigated to determine how much it may deviate from the equation of state of the cosmological constant (CC). Two aspects of the problem are studied: the "expansion" around the vacuum equation of state and the problem of the crossing of the cosmological constant boundary.
Energy conservation equations and interaction contributions at a structural interface between two
Cerveny, Vlastislav
Energy conservation equations and interaction contributions at a structural interface between twoÂmails: johana@seis.karlov.mff.cuni.cz, vcerveny@seis.karlov.mff.cuni.cz Summary Energy conservation equations is to investigate numeriÂ cally the energy conservation equations and the interaction contributions. An attempt
ON LANDAU-LIFSHITZ EQUATIONS OF NO-EXCHANGE ENERGY MODELS IN FERROMAGNETICS
Yan, Baisheng
ON LANDAU-LIFSHITZ EQUATIONS OF NO-EXCHANGE ENERGY MODELS IN FERROMAGNETICS Wei Deng and Baisheng for such equations of models with the exchange energy. Problems turn out quite different and challeng- ing for Landau-Lifshitz equations of no-exchange energy models because the usual methods based on certain compactness do not apply
On an inverse problem: the recovery of non-smooth solutions to backward heat equation
Daripa, Prabir
On an inverse problem: the recovery of non-smooth solutions to backward heat equation Fabien Ternat solu- tions of backward heat equation. In this paper, we test the viability of using these techniques to recover non-smooth solutions of backward heat equation. In particular, we numerically integrate
Shape-from-shading using the Heat Equation Antonio Robles-Kelly1
Robles-Kelly, Antonio
of these contributions, we pose the problem of surface normal recovery as that of solving the steady state heat equationShape-from-shading using the Heat Equation Antonio Robles-Kelly1 and Edwin R. Hancock 2 1 NICTA directions to shape-from-shading, namely the use of the heat equation to smooth the field of surface normals
On an inverse problem: Recovery of non-smooth solutions to backward heat equation
Daripa, Prabir
On an inverse problem: Recovery of non-smooth solutions to backward heat equation Fabien Ternat 2011 Accepted 2 November 2011 Available online 11 November 2011 Keywords: Heat equation Inverse problem and CrankNicolson schemes and applied successfully to solve for smooth solutions of backward heat equation
Âdifferential equations that model steadyÂstate combined conductiveÂradiative heat transfer. This system of equationsÂBrakhage algorithm. Key words. conductiveÂradiative heat transfer, multilevel algorithm, compact fixed point problems integroÂdifferential equations that model steadyÂstate combined conductiveÂradiative heat transfer
A Numerical Test of Air-Void Spacing Equations Kenneth A. Snyder
Bentz, Dale P.
and Pigeon. Each proposed spacing equation attempts to characterize the true \\spacing" of entrained air voids: entrained air voids; concrete; freeze-thaw; spacing equations 1 #12;1 Introduction The ecacy of entrained of these equations attempts to characterize the \\spacing" of voids in air-entrained concrete, even though
Dickinson, Brenton J
2010-01-01T23:59:59.000Z
??The Family Forest Research Center recently conducted a mail survey of about 1,400 Massachusetts landowners. Respondents were given questions about themselves and their land and… (more)
Bains, Amrit Anoop Singh
2010-10-12T23:59:59.000Z
technical challenges, which has lead to escalation of danger on a construction site. Data from OSHA show that crane accidents have increased rapidly from 2000 to 2004. By analyzing the characteristics of all the crane accident inspections, we can better...
Fusion of heavy ions by means of the Langevin equation
Mahboub, K.; Zerarka, A.; Foester, V.G. [Departement de Physique Nucleaire, Universite Med Khider, B P 145 Biskra 07000 (Algeria)
2005-06-01T23:59:59.000Z
The Langevin equation was used to describe fusion dynamics in two systems, {sup 64}Ni+{sup 100}Mo and {sup 64}Ni+{sup 96}Zr. The corresponding fusion cross sections were calculated for different energies, and the mean angular momentum and its dependence on energy were also obtained. We were able to reproduce experimental fusion cross sections at high energies with the one-body dissipation mechanism. Attention was focused on the fusion barrier calculated with the Yukawa-plus-exponential method.
Multigrid elliptic equation solver with adaptive mesh refinement
J. David Brown; Lisa L. Lowe
2005-03-22T23:59:59.000Z
In this paper we describe in detail the computational algorithm used by our parallel multigrid elliptic equation solver with adaptive mesh refinement. Our code uses truncation error estimates to adaptively refine the grid as part of the solution process. The presentation includes a discussion of the orders of accuracy that we use for prolongation and restriction operators to ensure second order accurate results and to minimize computational work. Code tests are presented that confirm the overall second order accuracy and demonstrate the savings in computational resources provided by adaptive mesh refinement.
Stability analysis of buried flexible pipes: a biaxial buckling equation
Chau, Melissa Tuyet-Mai
1990-01-01T23:59:59.000Z
loading are (see Appendix B for derivations) 29 rN. . +Ne~e+rp, = 0 rNes, e + Ne, a+ rpa = 0 r M*, *, +?M*a, *e + Me, ee +?e ? (?*P*, * +?N*eP*, e + - NaPe, e) 2 +r p. Ps+r pePa+r p. = o 2 2 2 (27) Introduction of Eqs. (20) and (25) into Eqs. (27...STABILITY ANALYSIS OF BURIED FLEXIBLE PIPES: A BIAXIAL BUCKLING EQUATION A Thesis by MELISSA TUYET-MAI CHAU Submitted to the Office of Graduate Studies of Texas AkM University in partial fulfillment of the requirements for the degree...
Fragment Isotope Distributions and the Isospin Dependent Equation of State
W. P. Tan; B-A. Li; R. Donangelo; C. K. Gelbke; M-J. van Goetherm; X. D. Liu; W. G. Lynch; S. Souza; M. B. Tsang; G. Verde; A. Wagner; N. S. Xu
2001-04-21T23:59:59.000Z
Calculations predict a connection between the isotopic composition of particles emitted during an energetic nucleus-nucleus collision and the density dependence of the asymmetry term of the nuclear equation of state (EOS). This connection is investigated for central 112Sn+112Sn and 124Sn+124Sn collisions at E/A=50 MeV in the limit of an equilibrated freezeout condition. Comparisons between measured isotopic yields ratios and theoretical predictions in the equilibrium limit are used to assess the sensitivity to the density dependence of the asymmetry term of the EOS. This analysis suggests that such comparisons may provide an opportunity to constrain the asymmetry term of the EOS.
Analysis of moving mesh partial differential equations with spatial smoothing
Huang, Weizhang; Russell, Robert D.
1997-06-01T23:59:59.000Z
ANALYSIS OF MOVING MESH PARTIAL DIFFERENTIAL EQUATIONS WITH SPATIAL SMOOTHING#3; WEIZHANG HUANGy AND ROBERT D. RUSSELLz SIAM J. NUMER. ANAL. c© 1997 Society for Industrial and Applied Mathematics Vol. 34, No. 3, pp. 1106{1126, June 1997 013 Abstract.... report NM-N8902, CWI, Amsterdam, 1989. [CD85] G. F. CAREY AND H. T. DINH, Grading functions and mesh redistribution, SIAM J. Numer. Anal., 22 (1985), pp. 1028{1040. [DD87] E. A. DORFI AND L. O’C. DRURY, Simple adaptive grids for 1-D initial value problems...
Heart simulation with surface equations for using on MCNP code
Rezaei-Ochbelagh, D.; Salman-Nezhad, S. [Department of Physics, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil (Iran, Islamic Republic of); Asadi, A. [Department of biology, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil (Iran, Islamic Republic of); Rahimi, A. [Razi Hospital, Rasht (Iran, Islamic Republic of)
2011-12-26T23:59:59.000Z
External photon beam radiotherapy is carried out in a way to achieve an 'as low as possible' a dose in healthy tissues surrounding the target. One of these surroundings can be heart as a vital organ of body. As it is impossible to directly determine the absorbed dose by heart, using phantoms is one way to acquire information around it. The other way is Monte Carlo method. In this work we have presented a simulation of heart geometry by introducing of different surfaces in MCNP code. We used 14 surface equations in order to determine human heart modeling. Those surfaces are borders of heart walls and contents.
Some iterative techniques for solving simultaneous linear equations
Nolen, James Henry
2012-06-07T23:59:59.000Z
E16 ~ 7) END JACOSI e GAUSS-SEI DEL e AND KACZMARZ TECHNIQUES FOR SOLVING SIMULTANEOUS LINEAR EQUAT IQNS EPSILON = 0 99999999E-05 AND ITMAX 25 THE ORIGINAL MATRIX OF COEFFICIENTS 0 ~ 09999999E 01 0 ~ 20000000E 01 0 ~ 30000000E 01 0 ~ 40000000E... 01 Oe500OQQOOE 01 Oe20000000E 01 0 ~ 30000000E 01 0 ~ 40000000E 01 0 ~ 50000000E 01 Oe09999999E 01 Oe40000000E 01 0e09999999E 01 Oe 3000000OE 01 0 ~ 50000000E Ol 0 ~ 20000000E 01 Oq 20000000E 01 0 ~ 50000000E 01 0 ~ 09999999E 01 0 ~ 400QOQOOE 01 0...
An improved nonlinear optical pulse propagation equation M. Trippenbacha
Band, Yehuda B.
the wave equation for the electric field r2 ? Ã¾ o2 oz2 Ã? 1 c2 o2 ot2 ~EEÃ°x; y; z; tÃ? Â¼ 4p c2 o2 ot2 ~PPL Ã°x; y; z; tÃ? Ã¾ ~PPNL Ã°x; y; z; tÃ? ; Ã°1Ã? where ~PPL and ~PPNL are the linear and nonlinear ~PPL Ã°~kk; xÃ? Ã¾ ~PPNL Ã°~kk; xÃ? : Ã°2Ã? We first consider the
Equation of State of Graphite-like BC,
Solozhenko,V.; Kurakevych, O.; Solozhenko, E.; Chen, J.; Parise, J.
2006-01-01T23:59:59.000Z
The compressibility of turbostratic boron-substituted graphite (t-BC) was measured up to 12 GPa at room temperature using energy-dispersive X-ray powder diffraction with synchrotron radiation. A fit to the experimental p-V data using Birch-Murnaghan equation of state gives values of the t-BC bulk modulus 23(2) GPa and its pressure derivative 8.0(6). These values point to a higher compressibility of t-BC as compared to turbostratic graphite.
Modified definition of group velocity and electromagnetic energy conservation equation
Changbiao Wang
2015-01-19T23:59:59.000Z
The classical definition of group velocity has two flaws: (a) the group velocity can be greater than the phase velocity in a non-dispersive, lossless, non-conducting, anisotropic uniform medium; (b) the definition is not consistent with the principle of relativity for a plane wave in a moving isotropic uniform medium. To remove the flaws, a modified definition is proposed. A criterion is set up to identify the justification of group velocity definition. A "superluminal power flow" is constructed to show that the electromagnetic energy conservation equation cannot uniquely define the power flow if the principle of Fermat is not taken into account.
ZM theory II: Hamilton's and Lagrange's equations of motion
Yaneer Bar-Yam
2006-03-03T23:59:59.000Z
We show that considering time measured by an observer to be a function of a cyclical field (an abstract version of a clock) is consistent with Hamilton's and Lagrange's equations of motion for a one dimensional space manifold. The derivation may provide a simple understanding of the conventions that are used in defining the relationship between independent and dependent variables in the Lagrangian and Hamiltonian formalisms. These derivations of the underlying principles of classical mechanics are steps on the way to discussions of physical laws and interactions in ZM theory.
State-Constrained Optimal Control Problems of Impulsive Differential Equations
Forcadel, Nicolas, E-mail: forcadel@ceremade.dauphine.fr [Universite Paris-Dauphine, Ceremade (France); Rao Zhiping, E-mail: Zhiping.Rao@ensta-paristech.fr; Zidani, Hasnaa, E-mail: Hasnaa.Zidani@ensta-paristech.fr [ENSTA ParisTech and INRIA-Saclay, Equipe COMMANDS (France)
2013-08-01T23:59:59.000Z
The present paper studies an optimal control problem governed by measure driven differential systems and in presence of state constraints. The first result shows that using the graph completion of the measure, the optimal solutions can be obtained by solving a reparametrized control problem of absolutely continuous trajectories but with time-dependent state-constraints. The second result shows that it is possible to characterize the epigraph of the reparametrized value function by a Hamilton-Jacobi equation without assuming any controllability assumption.
Boussinesq-equation and rans hybrid wave model
Sitanggang, Khairil Irfan
2009-05-15T23:59:59.000Z
? parenleftbigg??u i? ?xj + ??uj? ?xi parenrightbigg ? k3 ?2 braceleftbigg C1 parenleftbigg??u i? ?xl ??ul? ?xj + ??uj? ?xl ??ul? ?xi ? 2 3 ??ul? ?xk ??uk? ?xl ?ij parenrightbigg + C2 parenleftbigg??u i? ?xk ??uj? ?xk ? 1 3 ??ul? ?xk ??ul? ?xk ?ij parenrightbigg... +C 3 parenleftbigg??u k? ?xi ??uk? ?xj ? 1 3 ??ul? ?xk ??ul? ?xk ?ij parenrightbiggbracerightbigg , (2.13) where the turbulence kinetic energy k and the turbulence energy dissipation rate ? are obtained by solving the k?? equation: ?k ?t +?uj? ?k ?xj...
On the global solutions of the Higgs boson equation
Karen Yagdjian
2010-10-03T23:59:59.000Z
In this article we study global in time (not necessarily small) solutions of the equation for the Higgs boson in the Minkowski and in the de Sitter spacetimes. We reveal some qualitative behavior of the global solutions. In particular, we formulate sufficient conditions for the existence of the zeros of global solutions in the interior of their supports, and, consequently, for the creation of the so-called bubbles, which have been studied in particle physics and inflationary cosmology. We also give some sufficient conditions for the global solution to be an oscillatory in time solution.
Neumann domination for the Yang-Mills heat equation
Nelia Charalambous; Leonard Gross
2014-05-30T23:59:59.000Z
Long time existence and uniqueness of solutions to the Yang-Mills heat equation have been proven over a compact 3-manifold with boundary for initial data of finite energy. In the present paper we improve on previous estimates by using a Neumann domination technique that allows us to get much better pointwise bounds on the magnetic field. As in the earlier work, we focus on Dirichlet, Neumann and Marini boundary conditions. In addition, we show that the Wilson Loop functions, gauge invariantly regularized, converge as the parabolic time goes to infinity.
On isotropic metric of Schwarzschild solution of Einstein equation
T. Mei
2006-10-24T23:59:59.000Z
The known static isotropic metric of Schwarzschild solution of Einstein equation cannot cover with the range of r<2MG, a new isotropic metric of Schwarzschild solution is obtained. The new isotropic metric has the characters: (1) It is dynamic and periodic. (2) It has infinite singularities of the spacetime. (3) It cannot cover with the range of 0
Geomorphic Equations and Methods for Natural Channel Design
Shelley, John Edwin
2012-05-31T23:59:59.000Z
significant predictors of the Q1.2. This led to Equation 2.2: 1.26 3.17 1.101.2Q 0.00258 CDA MAP L?? (2.2) Sy bol Watershed Characteristic Units DA Contributing Drainage Area mi 2 Sh Basin Shape Factor -- Sl Average Slope of Main Channel ft/mi SP........................................................................................... 97 6.4 BSCR by Grain Size .............................................................................................................. 98 vi List of Figures 1.1 A restored chute on the Missouri River in Saline, MO...
Beale-Kato-Majda type condition for Burgers equation
Ben Goldys; Misha Neklyudov
2008-12-23T23:59:59.000Z
We consider a multidimensional Burgers equation on the torus $\\mathbb{T}^d$ and the whole space $\\Rd$. We show that, in case of the torus, there exists a unique global solution in Lebesgue spaces. For a torus we also provide estimates on the large time behaviour of solutions. In the case of $\\Rd$ we establish the existence of a unique global solution if a Beale-Kato-Majda type condition is satisfied. To prove these results we use the probabilistic arguments which seem to be new.
The equation-transform model for Dirac–Morse problem including Coulomb tensor interaction
Ortakaya, Sami, E-mail: sami.ortakaya@yahoo.com
2013-11-15T23:59:59.000Z
The approximate solutions of Dirac equation with Morse potential in the presence of Coulomb-like tensor potential are obtained by using Laplace transform (LT) approach. The energy eigenvalue equation of the Dirac particles is found and some numerical results are obtained. By using convolution integral, the corresponding radial wave functions are presented in terms of confluent hypergeometric functions. -- Highlights: •The Dirac equation with tensor interaction is solved by using Laplace transform. •For solving this equation, we introduce the equation-transform model. •Numerical results and plots for pseudospin and spin symmetric solutions are given. •The obtained numerical results by using transform method are compared with orthogonal polynomial method.
Wave equations with non-commutative space and time
Verch, Rainer
2015-01-01T23:59:59.000Z
The behaviour of solutions to the partial differential equation $(D + \\lambda W)f_\\lambda = 0$ is discussed, where $D$ is a normal hyperbolic partial differential operator, or pre-normal hyperbolic operator, on $n$-dimensional Minkowski spacetime. The potential term $W$ is a $C_0^\\infty$ kernel operator which, in general, will be non-local in time, and $\\lambda$ is a complex parameter. A result is presented which states that there are unique advanced and retarded Green's operators for this partial differential equation if $|\\lambda|$ is small enough (and also for a larger set of $\\lambda$ values). Moreover, a scattering operator can be defined if the $\\lambda$ values admit advanced and retarded Green operators. In general, however, the Cauchy-problem will be ill-posed, and examples will be given to that effect. It will also be explained that potential terms arising from non-commutative products on function spaces can be approximated by $C_0^\\infty$ kernel operators and that, thereby, scattering by a non-commu...
Nonequilibrium equation of state in suspensions of active colloids
Félix Ginot; Isaac Theurkauff; Demian Levis; Christophe Ybert; Lydéric Bocquet; Ludovic Berthier; Cécile Cottin-Bizonne
2014-11-26T23:59:59.000Z
Active colloids constitute a novel class of materials composed of colloidal-scale particles locally converting chemical energy into motility, mimicking micro-organisms. Evolving far from equilibrium, these systems display structural organizations and dynamical properties distinct from thermalized colloidal assemblies. Harvesting the potential of this new class of systems requires the development of a conceptual framework to describe these intrinsically nonequilibrium systems. We use sedimentation experiments to probe the nonequilibrium equation of state of a bidimensional assembly of active Janus microspheres, and conduct computer simulations of a model of self-propelled hard disks. Self-propulsion profoundly affects the equation of state, but these changes can be rationalized using equilibrium concepts. We show that active colloids behave, in the dilute limit, as an ideal gas with an activity-dependent effective temperature. At finite density, increasing the activity is similar to increasing adhesion between equilibrium particles. We quantify this effective adhesion and obtain a unique scaling law relating activity and effective adhesion in both experiments and simulations. Our results provide a new and efficient way to understand the emergence of novel phases of matter in active colloidal suspensions.
Plasma equilibria with multiple ion species: Equations and algorithm
Galeotti, L.; Ceccherini, F. [Department of Physics, University of Pisa, Largo B. Pontecorvo 3, Pisa 56127 (Italy); Tri Alpha Energy, Inc., P.O. Box 7010, Rancho Santa Margarita, California 92688 (United States); Barnes, D. C. [Tri Alpha Energy, Inc., P.O. Box 7010, Rancho Santa Margarita, California 92688 (United States); Pegoraro, F. [Department of Physics, University of Pisa, Largo B. Pontecorvo 3, Pisa 56127 (Italy)
2011-08-15T23:59:59.000Z
Axisymmetric equilibrium of a magnetically confined plasma with multiple ion species is considered. To describe hot plasmas with isothermal surfaces, we adopt a formulation consistent with zero poloidal ion flow. This formulation includes all magnetic field components and also correctly includes all effects of toroidal ion rotation. There are two free surface functions for each species and a third which is determined by a differential equation relating surface functions per species. We have developed and implemented an algorithm for the solution of the resulting nonlinear equations and found solutions with large charge and mass contrast among the ion species for both compact (r = 0 included) and annular (r = 0 excluded) domains. Our solution method allows for arbitrary domain shapes, includes far-field conditions, and treats any combination of electrically conducting or insulating walls. Appropriate surface functions are used to describe the transition from closed to open field plasma in a reasonable manner. Solutions for advanced fuel cycle fusion systems (both D-{sup 3}He and p-{sup 11}B) are presented to illustrate the power of the method. Finally, we briefly discuss the special issues associated with obtaining very elongated solutions and describe the algorithm for implementing these features.
Minimal Liouville Gravity correlation numbers from Douglas string equation
Alexander Belavin; Boris Dubrovin; Baur Mukhametzhanov
2014-09-11T23:59:59.000Z
We continue the study of $(q,p)$ Minimal Liouville Gravity with the help of Douglas string equation. We generalize the results of \\cite{Moore:1991ir}, \\cite{Belavin:2008kv}, where Lee-Yang series $(2,2s+1)$ was studied, to $(3,3s+p_0)$ Minimal Liouville Gravity, where $p_0=1,2$. We demonstrate that there exist such coordinates $\\tau_{m,n}$ on the space of the perturbed Minimal Liouville Gravity theories, in which the partition function of the theory is determined by the Douglas string equation. The coordinates $\\tau_{m,n}$ are related in a non-linear fashion to the natural coupling constants $\\lambda_{m,n}$ of the perturbations of Minimal Lioville Gravity by the physical operators $O_{m,n}$. We find this relation from the requirement that the correlation numbers in Minimal Liouville Gravity must satisfy the conformal and fusion selection rules. After fixing this relation we compute three- and four-point correlation numbers when they are not zero. The results are in agreement with the direct calculations in Minimal Liouville Gravity available in the literature \\cite{Goulian:1990qr}, \\cite{Zamolodchikov:2005sj}, \\cite{Belavin:2006ex}.
New, improved equation solves for volatile oil, condensate reserves
Walsh, M.P. (Petroleum Recovery Research Inst., Austin, TX (United States))
1994-08-22T23:59:59.000Z
A new generalized material-balance equation (GMBE) can be applied to the full range of reservoir fluids, including volatile oil and gas condensate. The GMBE replaces the nearly 60-year-old conventional material-balance equation (CMBE). Material balance methods are routinely used by petroleum engineers to estimate reserves. The so-called straight-line methods are the most common. Two of the most popular are: P/z-plot for estimating gas reserves in a dry-gas reservoir; and Havlena and Odeh method for estimating original oil-in-place (N) and original gas-in-place (G) in a black-oil reservoir. A major shortcoming of these and other straight-line methods is that none apply to the full range of reservoir fluids and very few, if any, deal satisfactorily with volatile oil and rich gas condensate. Also, the limits of the methods are not well defined. As drilling goes deeper and more volatile oil and gas-condensate reservoirs are discovered, there is a growing need for a general straight-line method to estimate N and G. For the GMBE, no restrictions are placed on the initial fluid compositions.
Equation of state and phase diagram of FeO
Fischer, Rebecca A.; Campbell, Andrew J.; Shofner, Gregory A.; Lord, Oliver T.; Dera, Przemyslaw; Prakapenka, Vitali B. (Bristol); (Maryland); (UC)
2012-04-11T23:59:59.000Z
Wuestite, Fe{sub 1-x}O, is an important component in the mineralogy of Earth's lower mantle and may also be a component in the core. Therefore the high pressure, high temperature behavior of FeO, including its phase diagram and equation of state, is essential knowledge for understanding the properties and evolution of Earth's deep interior. We performed X-ray diffraction measurements using a laser-heated diamond anvil cell to achieve simultaneous high pressures and temperatures. Wuestite was mixed with iron metal, which served as our pressure standard, under the assumption that negligible oxygen dissolved into the iron. Our data show a positive slope for the subsolidus phase boundary between the B1 and B8 structures, indicating that the B1 phase is stable at the P-T conditions of the lower mantle and core. We have determined the thermal equation of state of B1 FeO to 156 GPa and 3100 K, finding an isothermal bulk modulus K{sub 0} = 149.4 {+-} 1.0 GPa and its pressure derivative K'{sub 0} = 3.60 {+-} 0.4. This implies that 7.7 {+-} 1.1 wt.% oxygen is required in the outer core to match the seismologically-determined density, under the simplifying assumption of a purely Fe-O outer core.
Barhorst, Alan Andrew
1989-01-01T23:59:59.000Z
of the system being studied. II. 4 Methods Based On Lagrange's Equation (Energy Methods) Lagrange's equations or the Euler-Lagrange difl'erential equations were derived independently by Euler and Lagrange. They derived the differential equations when... to derive the difi'erential equation that the curve must satisfy. Lagrange started developing a. new calculus rel'erred to as the calculus of variations to solve the minimization problem. He too derived the Euler-Lagrange differential equation...
The Gross-Pitaevskii equations and beyond for inhomogeneous condensed bosons
G. G. N. Angilella; S. Bartalini; F. S. Cataliotti; I. Herrera; N. H. March; R. Pucci
2006-05-22T23:59:59.000Z
A simple derivation of the static Gross-Pitaevskii (GP) equation is given from an energy variational principle. The result is then generalized heuristically to the time-dependent GP form. With this as background, a number of different experimental areas explored very recently are reviewed, in each case contact being established between the measurements and the predictions of the GP equations. The various limitations of these equations as used on dilute inhomogeneous condensed Boson atomic gases are then summarized, reference also being made to the fact that there is no many-body wave function underlying the GP formulation. This then leads into a discussion of a recently proposed integral equation, derived by taking the Bogoliubov-de Gennes equation as starting point. Some limitations of the static GP differential equation are thereby removed, though it is a matter of further study to determine whether a correlated wave function exists as underpinning for the integral equation formulation.
On the ineffectiveness of constant rotation in the primitive equations and their symmetry analysis
Cardoso-Bihlo, Elsa Dos Santos
2015-01-01T23:59:59.000Z
Modern weather and climate prediction models are based on a system of nonlinear partial differential equations called the primitive equations. Lie symmetries of the primitive equations are computed and the structure of its maximal Lie invariance algebra, which is infinite dimensional, is studied. The maximal Lie invariance algebra for the case of a nonzero constant Coriolis parameter is mapped to the case of vanishing Coriolis force. The same mapping allows one to transform the constantly rotating primitive equations to the equations in a resting reference frame. This mapping is used to obtain exact solutions for the rotating case from exact solutions from the nonrotating equations. Another important result of the paper is the computation of the complete point symmetry group of the primitive equations using the algebraic method.
Ng, Chung-Sang
of motion, an energy equation can be derived. It is simply the continuity equation of energy density, which is the sum of kinetic energy density mU2 /2, magnetic energy density B2 /2Âµ0, and the internal energy density p/( -1). The total energy obtained by integrating the energy density over the whole space
Neutron star equations of state with optical potential constraint
Antic, Sofija
2015-01-01T23:59:59.000Z
Nuclear matter and neutron stars are studied in the framework of an extended relativistic mean-field (RMF) model with higher-order derivative and density dependent couplings of nucleons to the meson fields. The derivative couplings lead to an energy dependence of the scalar and vector self-energies of the nucleons. It can be adjusted to be consistent with experimental results for the optical potential in nuclear matter. Several parametrisations, which give identical predictions for the saturation properties of nuclear matter, are presented for different forms of the derivative coupling functions. The stellar structure of spherical, non-rotating stars is calculated for these new equations of state (EoS). A substantial softening of the EoS and a reduction of the maximum mass of neutron stars is found if the optical potential constraint is satisfied.
Neutron star equations of state with optical potential constraint
Sofija Antic; Stefan Typel
2015-01-29T23:59:59.000Z
Nuclear matter and neutron stars are studied in the framework of an extended relativistic mean-field (RMF) model with higher-order derivative and density dependent couplings of nucleons to the meson fields. The derivative couplings lead to an energy dependence of the scalar and vector self-energies of the nucleons. It can be adjusted to be consistent with experimental results for the optical potential in nuclear matter. Several parametrisations, which give identical predictions for the saturation properties of nuclear matter, are presented for different forms of the derivative coupling functions. The stellar structure of spherical, non-rotating stars is calculated for these new equations of state (EoS). A substantial softening of the EoS and a reduction of the maximum mass of neutron stars is found if the optical potential constraint is satisfied.
Thermodynamics of apparent horizon and modified Friedman equations
Ahmad Sheykhi
2010-12-02T23:59:59.000Z
Starting from the first law of thermodynamics, $dE=T_hdS_h+WdV$, at apparent horizon of a FRW universe, and assuming that the associated entropy with apparent horizon has a quantum corrected relation, $S=\\frac{A}{4G}-\\alpha \\ln \\frac{A}{4G}+\\beta \\frac{4G}{A}$, we derive modified Friedmann equations describing the dynamics of the universe with any spatial curvature. We also examine the time evolution of the total entropy including the quantum corrected entropy associated with the apparent horizon together with the matter field entropy inside the apparent horizon. Our study shows that, with the local equilibrium assumption, the generalized second law of thermodynamics is fulfilled in a region enclosed by the apparent horizon.
Monte Carlo solution of a semi-discrete transport equation
Urbatsch, T.J.; Morel, J.E.; Gulick, J.C.
1999-09-01T23:59:59.000Z
The authors present the S{sub {infinity}} method, a hybrid neutron transport method in which Monte Carlo particles traverse discrete space. The goal of any deterministic/stochastic hybrid method is to couple selected characters from each of the methods in hopes of producing a better method. The S{sub {infinity}} method has the features of the lumped, linear-discontinuous (LLD) spatial discretization, yet it has no ray-effects because of the continuous angular variable. They derive the S{sub {infinity}} method for the solid-state, mono-energetic transport equation in one-dimensional slab geometry with isotropic scattering and an isotropic internal source. They demonstrate the viability of the S{sub {infinity}} method by comparing their results favorably to analytic and deterministic results.
A Simple Proof of the Ramsey Savings Equation
El-Hodiri, Mohamed
1978-01-01T23:59:59.000Z
have: d U’=U’L,dt dd--(U’fa V’) O, B- U+ V-eU’-a(U’f,,- V’) O. U’f.- V’=0. * Received by the editors, April 15, 1976. " Department of Economics, University of Kansas, Lawrence, Kansas 66045. The purpose of this note is purely pedantic since it reveals... Euler’s equations are necessary conditions for an extremum. 169 D ow nl oa de d 01 /2 3/ 15 to 1 29 .2 37 .4 6. 10 0. R ed ist rib ut io n su bje ct to SIA M lic en se or co py rig ht; se e h ttp ://w ww .si am .or g/j ou rna ls/ ojs a.p hp...
Linear multistep methods for integrating reversible differential equations
Wyn Evans; Scott Tremaine
1999-06-24T23:59:59.000Z
This paper studies multistep methods for the integration of reversible dynamical systems, with particular emphasis on the planar Kepler problem. It has previously been shown by Cano & Sanz-Serna that reversible linear multisteps for first-order differential equations are generally unstable. Here, we report on a subset of these methods -- the zero-growth methods -- that evade these instabilities. We provide an algorithm for identifying these rare methods. We find and study all zero-growth, reversible multisteps with six or fewer steps. This select group includes two well-known second-order multisteps (the trapezoidal and explicit midpoint methods), as well as three new fourth-order multisteps -- one of which is explicit. Variable timesteps can be readily implemented without spoiling the reversibility. Tests on Keplerian orbits show that these new reversible multisteps work well on orbits with low or moderate eccentricity, although at least 100 steps/radian are required for stability.
Adsorption of a fluid in an aerogel: integral equation approach
V. Krakoviack; E. Kierlik; M. -l. Rosinberg; G. Tarjus
2008-01-01T23:59:59.000Z
We present a theoretical study of the phase diagram and the structure of a fluid adsorbed in high-porosity aerogels by means of an integral-equation approach combined with the replica formalism. To simulate a realistic gel environment, we use an aerogel structure factor obtained from an off-lattice diffusion-limited cluster-cluster aggregation process. The predictions of the theory are in qualitative agreement with the experimental results, showing a substantial narrowing of the gas-liquid coexistence curve (compared to that of the bulk fluid), associated with weak changes in the critical density and temperature. The influence of the aerogel structure (nontrivial short-range correlations due to connectedness, long-range fractal behavior of the silica strands) is shown to be important at low fluid densities. I.
Surface electromagnetic wave equations in a warm magnetized quantum plasma
Li, Chunhua; Yang, Weihong [Department of Modern Physics, University of Science and Technology of China, 230026 Hefei (China); Wu, Zhengwei, E-mail: wuzw@ustc.edu.cn [Department of Modern Physics, University of Science and Technology of China, 230026 Hefei (China); Department of Physics and Materials Science, City University of Hong Kong, Tat Chee Avenue, Kowloon (Hong Kong); Center of Low Temperature Plasma Application, Yunnan Aerospace Industry Company, Kunming, 650229 Yunnan (China); Chu, Paul K. [Department of Physics and Materials Science, City University of Hong Kong, Tat Chee Avenue, Kowloon (Hong Kong)
2014-07-15T23:59:59.000Z
Based on the single-fluid plasma model, a theoretical investigation of surface electromagnetic waves in a warm quantum magnetized inhomogeneous plasma is presented. The surface electromagnetic waves are assumed to propagate on the plane between a vacuum and a warm quantum magnetized plasma. The quantum magnetohydrodynamic model includes quantum diffraction effect (Bohm potential), and quantum statistical pressure is used to derive the new dispersion relation of surface electromagnetic waves. And the general dispersion relation is analyzed in some special cases of interest. It is shown that surface plasma oscillations can be propagated due to quantum effects, and the propagation velocity is enhanced. Furthermore, the external magnetic field has a significant effect on surface wave's dispersion equation. Our work should be of a useful tool for investigating the physical characteristic of surface waves and physical properties of the bounded quantum plasmas.
Generalized Darboux transformation and localized waves in coupled Hirota equations
Xin Wang; Yuqi Li; Yong Chen
2014-04-28T23:59:59.000Z
In this paper, we construct a generalized Darboux transformation to the coupled Hirota equations with high-order nonlinear effects like the third dispersion, self-steepening and inelastic Raman scattering terms. As application, an Nth-order localized wave solution on the plane backgrounds with the same spectral parameter is derived through the direct iterative rule. In particular, some semi-rational, multi-parametric localized wave solutions are obtained: (1) Vector generalization of the first- and the second-order rogue wave solution; (2) Interactional solutions between a dark-bright soliton and a rogue wave, two dark-bright solitons and a second-order rogue wave; (3) Interactional solutions between a breather and a rogue wave, two breathers and a second-order rogue wave. The results further reveal the striking dynamic structures of localized waves in complex coupled systems.
Complex roots in the inhour equation of coupled reactors
Yeh, Elizabeth Ching
2012-06-07T23:59:59.000Z
in this report: dT. p +y ? 8 c T + Z ~ T (t-r)P (r)dr k& dt A j A k kj D N +E 1. Ci i=1 dC . Bji ~ = ? T ? X. . C dt h j ji ji where amplitude function of neutron flux in module j amplitude function of delayed neutron precursors, module j, group i... . ) 10 With the above substitution Equation (1) reads: dT. p. -I y. ? E. N --T. + I 1. , 0, . + 3 j 1 j dt A. j . ji ji j i=1 E1 e k-1 A k k' kj At criticality, p. = 0, and we obtain the criticality condition of the system: 10 110 210 MLO 120 0...