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.
Logit Models for Estimating Urban Area Through Travel
Talbot, Eric
2011-10-21T23:59:59.000Z
LOGIT MODELS FOR ESTIMATING URBAN AREA THROUGH TRAVEL A Thesis by ERIC TALBOT Submitted to the Office of Graduate Studies of Texas A&M University in partial fulfillment of the requirements for the degree... of MASTER OF SCIENCE August 2010 Major Subject: Civil Engineering LOGIT MODELS FOR ESTIMATING URBAN AREA THROUGH TRAVEL A Thesis by ERIC TALBOT Submitted to the Office of Graduate Studies of Texas A...
Characteristics of rural bank acquisitions: a logit analysis
Applewhite, Jennifer Lynn
1994-01-01T23:59:59.000Z
interstate acquisition of their banks, the rate of acquisitions soared. In 1978, Maine enacted legislation permitting interstate banking on a reciprocal basis. Until mid-1982, Maine was the only state with such a law. In 1982, both New York and Alaska... of U. S. banks using comparative performance profiles and logit analysis. Characteristics of acquired and acquiring banks are compared for five years before the acquisitions and found to have significantly different rates of return on assets...
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
Aristophanes Dimakis; Folkert Mueller-Hoissen
2014-09-27T23:59:59.000Z
It is shown that higher Bruhat orders admit a decomposition into a higher Tamari order, the corresponding dual Tamari order, and a "mixed order". We describe simplex equations (including the Yang-Baxter equation) as realizations of higher Bruhat orders. Correspondingly, a family of "polygon equations" realizes higher Tamari orders. They generalize the well-known pentagon equation. The structure of simplex and polygon equations is visualized in terms of deformations of maximal chains in posets forming 1-skeletons of polyhedra. The decomposition of higher Bruhat orders induces a reduction of the N-simplex equation to the (N+1)-gon equation, its dual, and a compatibility equation.
Relativistic quaternionic wave equation
Schwartz, C
2006-01-01T23:59:59.000Z
Majorana representation of the Dirac equation, i ? ? ? ? ? = m ? , where all four of the gamma matrices
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.
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.
Loinger, A
2015-01-01T23:59:59.000Z
The physical results of quantum field theory are independent of the various specializations of Dirac's gamma-matrices, that are employed in given problems. Accordingly, the physical meaning of Majorana's equation is very dubious,considering that it is a consequence of ad hoc matrix representations of the gamma-operators. Therefore, it seems to us that this equation cannot give the equation of motion of the neutral WIMPs (weakly interacting massive particles), the hypothesized constitutive elements of the Dark Matter.
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.
Relativistic Guiding Center Equations
White, R. B. [PPPL; Gobbin, M. [Euratom-ENEA Association
2014-10-01T23:59:59.000Z
In toroidal fusion devices it is relatively easy that electrons achieve relativistic velocities, so to simulate runaway electrons and other high energy phenomena a nonrelativistic guiding center formalism is not sufficient. Relativistic guiding center equations including flute mode time dependent field perturbations are derived. The same variables as used in a previous nonrelativistic guiding center code are adopted, so that a straightforward modifications of those equations can produce a relativistic version.
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.
Solving Symbolic Equations with PRESS
Sterling, L.; Bundy, Alan; Byrd, L.; O'Keefe, R.; Silver, B.
1982-01-01T23:59:59.000Z
We outline a program, PRESS (PRolog Equation Solving System) for solving symbolic, transcendental, non-differential equations. The methods used for solving equations are described, together with the service facilities. The ...
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
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.
Evangelos Chaliasos
2006-11-12T23:59:59.000Z
As we know, from the Einstein equations the vanishing of the four-divergence of the energy-momentum tensor follows. This is the case because the four-divergence of the Einstein tensor vanishes identically. Inversely, we find that from the vanishing of the four-divergence of the energy-momentum tensor not only the Einstein equations follow. Besides, the so-named anti-Einstein equations follow. These equations must be considered as complementary to the Einstein equations. And while from the Einstein equations the energy density (or the pressure) can be found, from the anti-Einstein equations the pressure (or the energy density) can be also found, without having to use an additional (but arbitrary) equation of state.
Noncommutativity and the Friedmann Equations
Sabido, M.; Socorro, J. [Physics Department of the Division of Science and Engineering of the University of Guanajuato, Campus Leon P.O. Box E-143, 37150 Leon Gto. (Mexico); Guzman, W. [Instituto de Fisica, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, 21945-970, Rio de Janeiro (Brazil)
2010-07-12T23:59:59.000Z
In this paper we study noncommutative scalar field cosmology, we find the noncommutative Friedmann equations as well as the noncommutative Klein-Gordon equation, interestingly the noncommutative contributions are only present up to second order in the noncommutitive parameter.
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.
Chapter Two Model Equations and
Xue, Ming
after Miller and White (1984). Equations (1.2.30), (1.2.31), (1.2.33), (1.2.34), (1.2.38), and (1. They are the equation for y-velocity v, and the equations for the conservation of water vapour, cloud water and rain humidity of water vapour, cloud water and rain water respectively. The momentum equations (2.1.1) to (2
Assignment II Saha & Boltzmann equations
Spoon, Henrik
Assignment II Saha & Boltzmann equations January 21, 2002 This assignment is meant to give you some practical experience in using the Saha and Boltzmann equations that govern the level populations in atoms;s =kT the partition function of ionization stage r. The Saha equation: N r+1 N r = 2U r+1 U r P e #18
Natale, Michael J.
the smaller cloaked vessel before she had a chance to de-cloak and fire, the Enterprise had virtually disabled the scoutship. Now, the innocent people on Omnicron I could at least get a break from the barrage of disrupter fire from orbit, and the Enterprise... into destroying the Klingon vessel. But, if they were going to threaten innocents on Omnicron I, then the Enterprise could play the role of executioner adequately. "Mr. Sulu, fire main phasers!" "Locking phasers.....firing, sir!" The Human Equation Page...
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.
Martin Frimmer; Lukas Novotny
2014-09-26T23:59:59.000Z
Coherent control of a quantum mechanical two-level system is at the heart of magnetic resonance imaging, quantum information processing, and quantum optics. Among the most prominent phenomena in quantum coherent control are Rabi oscillations, Ramsey fringes and Hahn echoes. We demonstrate that these phenomena can be derived classically by use of a simple coupled harmonic oscillator model. The classical problem can be cast in a form that is formally equivalent to the quantum mechanical Bloch equations with the exception that the longitudinal and the transverse relaxation times ($T_1$ and $T_2$) are equal. The classical analysis is intuitive and well suited for familiarizing students with the basic concepts of quantum coherent control, while at the same time highlighting the fundamental differences between classical and quantum theories.
Energy Conservation Equations of Motion
Vinokurov, Nikolay A
2015-01-01T23:59:59.000Z
A conventional derivation of motion equations in mechanics and field equations in field theory is based on the principle of least action with a proper Lagrangian. With a time-independent Lagrangian, a function of coordinates and velocities that is called energy is constant. This paper presents an alternative approach, namely derivation of a general form of equations of motion that keep the system energy, expressed as a function of generalized coordinates and corresponding velocities, constant. These are Lagrange equations with addition of gyroscopic forces. The important fact, that the energy is defined as the function on the tangent bundle of configuration manifold, is used explicitly for the derivation. The Lagrangian is derived from a known energy function. A development of generalized Hamilton and Lagrange equations without the use of variational principles is proposed. The use of new technique is applied to derivation of some equations.
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.
Media with no Fresnel equation
Peinke, Joachim
Media with no Fresnel equation Alberto Favaro & Ismo V. Lindell Outline Part 1: Local linear media Part 2: Jump conditions Part 3: media with no G(q) Conclusions Electromagnetic media with no Fresnel with no Fresnel equation Alberto Favaro & Ismo V. Lindell Outline Part 1: Local linear media Part 2: Jump
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
Optimal control, parabolic equations, st
2008-12-22T23:59:59.000Z
In this paper we study the optimal control problem of the heat equation by a distributed control over a subset of the domain, in the presence of a state constraint.
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.
Chapter Two Model Equations and
Xue, Ming
was established after Miller and White (1984). Equations (1.2.30), (1.2.31), (1.2.33), (1.2.34), (1.2.38), and (1, and the equations for the conservation of water vapour, cloud water and rain water. Ice phase is not included in our model at the moment. Variables q v , q c and q r are the specific humidity of water vapour, cloud water
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.
SOLVING SYSTEMS OF NONLINEAR EQUATIONS WITH ...
2006-11-02T23:59:59.000Z
Nov 2, 2006 ... A method for finding all roots of a system of nonlinear equations is described ... Nonlinear systems of equations, global optimization, continuous ...
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.
Exact Vacuum Solutions to the Einstein Equation
Ying-Qiu Gu
2007-06-17T23:59:59.000Z
In this paper, we present a framework for getting a series of exact vacuum solutions to the Einstein equation. This procedure of resolution is based on a canonical form of the metric. According to this procedure, the Einstein equation can be reduced to some 2-dimensional Laplace-like equations or rotation and divergence equations, which are much convenient for the resolution.
Fourier's Law from Closure Equations
Jean Bricmont; Antti Kupiainen
2006-09-01T23:59:59.000Z
We give a rigorous derivation of Fourier's law from a system of closure equations for a nonequilibrium stationary state of a Hamiltonian system of coupled oscillators subjected to heat baths on the boundary. The local heat flux is proportional to the temperature gradient with a temperature dependent heat conductivity and the stationary temperature exhibits a nonlinear profile.
Evolution equation for quantum entanglement
Loss, Daniel
LETTERS Evolution equation for quantum entanglement THOMAS KONRAD1 , FERNANDO DE MELO2,3 , MARKUS of the time evolution of this resource under realistic conditions--that is, when corrupted by environment describes the time evolution of entanglement on passage of either component through an arbitrary noisy
Lyapunov Exponents for Burgers' Equation
Alexei Kourbatov
2015-02-23T23:59:59.000Z
We establish the existence, uniqueness, and stability of the stationary solution of the one-dimensional viscous Burgers equation with the Dirichlet boundary conditions on a finite interval. We obtain explicit formulas for solutions and analytically determine the Lyapunov exponents characterizing the asymptotic behavior of arbitrary solutions approaching the stationary one.
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.
London's Equation from Abelian Projection
V. Dzhunushaliev; D. Singleton
2002-04-05T23:59:59.000Z
Confinement in non-Abelian gauge theories, such as QCD, is often explained using an analogy to type II superconductivity. In this analogy the existence of the ``Meissner'' effect for quarks with respect to the QCD vacuum is an important element. Here we show that using the ideas of Abelian projection it is possible to arrive at an effective London equation from a non-Abelian gauge theory. (London's equation gave a phenomenological description of the Meissner effect prior to the Ginzburg-Landau or BCS theory of superconductors). The Abelian projected gauge field acts as the E&M field in normal superconductivity, while the remaining non-Abelian components form a gluon condensate which is described via an effective scalar field. This effective scalar field plays a role similar to the scalar field in Ginzburg-Landau theory.
Iterative solutions of simultaneous equations
Laycock, Guyron Brantley
1962-01-01T23:59:59.000Z
ITERATIVE SOLUTIONS OP SIKJLTANEOUS EQUATIONS G~cn Hrantlep I aycock Approved. as to style snd, content by& (Chairman of Committee) E. c. (Head. of Department August 1/62 ACKNOWLEDGEMENT The author wishes to thank Dr. Hi A. Luther for his time sn4.... . . . ~ ~ . . ~ III. JACOBI AND 6AUSS-SEIDEL METHODS I V ~ C ONCLUS I GN ~ ~ ~ a ~ ~ ~ t ~ ~ ~ ~ a ~ 1 ~ ~ ~ ~ ~ ~ 9 ~ . ~ 18 V BIBLIOGRAPHY ~ ~ ~ o ~ ~ t ~ ~ ~ ~ 1 ~ ~ ~ VI ~ APPENDIX ~ ~ o ~ ~ e ~ o ~ ~ o o ~ ~ ~ . 22 Px'ogl am Lisliiixlgs...
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 .
Fritz, J.N.; Olinger, B.
1984-03-15T23:59:59.000Z
The volume of sodium in the bcc structure was measured at 293 K to 9 GPa using a high pressure, x-ray diffraction technique. The compression of NaF was used as the pressure gauge. These data, the shock compression data of Rice and Bakanova et al., and the melting curve data of Luedemann and Kennedy, and Ivanov et al., are all used to establish a model for the equation of state of sodium.
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. ...
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 ...
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.
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.
The Schrodinger equation and negative energies
S. Bruce
2008-06-30T23:59:59.000Z
We present a nonrelativistic wave equation for the electron in (3+1)-dimensions which includes negative-energy eigenstates. We solve this equation for three well-known instances, reobtaining the corresponding Pauli equation (but including negative-energy eigenstates) in each case.
Quadratic Equation over Associative D-Algebra
Aleks Kleyn
2015-05-30T23:59:59.000Z
In this paper, I treat quadratic equation over associative $D$-algebra. In quaternion algebra $H$, the equation $x^2=a$ has either $2$ roots, or infinitely many roots. Since $a\\in R$, $aalgebra, the equation $$(x-b)(x-a)+(x-a)(x-c)=0$$ $b\
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.
Evolution equation of moving defects: dislocations and inclusions
Markenscoff, Xanthippi
2010-01-01T23:59:59.000Z
9483-8 ORIGINAL PAPER Evolution equation of moving defects:Springerlink.com Abstract Evolution equations, or equationsof dissipation, and the evolution equation for a plane
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.
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.
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,
Equivalence of the Husain and the Pleba?ski equations
M. Jakimowicz; J. Tafel
2006-03-31T23:59:59.000Z
We show that Husain's reduction of the self-dual Einstein equations is equivalent to the Pleba\\'nski equation. The B\\"acklund transformation between these equations is found. Contact symmetries of the Husain equation are derived.
A MULTIDIMENSIONAL NONLINEAR SIXTH-ORDER QUANTUM DIFFUSION EQUATION
heat equation tn = n. The second one is the fourth-order DerridaLebowitzSpeerSpohn (DLSS) equation
A New Integral Equation for the Spheroidal equations in case of m equal 1
Guihua Tian; Shuquan Zhong
2012-01-05T23:59:59.000Z
The spheroidal wave functions are investigated in the case m=1. The integral equation is obtained for them. For the two kinds of eigenvalues in the differential and corresponding integral equations, the relation between them are given explicitly. Though there are already some integral equations for the spheroidal equations, the relation between their two kinds of eigenvalues is not known till now. This is the great advantage of our integral equation, which will provide useful information through the study of the integral equation. Also an example is given for the special case, which shows another way to study the eigenvalue problem.
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.
Linear Equation in Finite Dimensional Algebra
Aleks Kleyn
2012-04-30T23:59:59.000Z
In the paper I considered methods for solving equations of the form axb+cxd=e in the algebra which is finite dimensional over the field.
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.
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).
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.
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{\
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
Relativistic Wave Equations and Compton Scattering
B. A. Robson; S. H. Sutanto
2006-05-25T23:59:59.000Z
The recently proposed eight-component relativistic wave equation is applied to the scattering of a photon from a free electron (Compton scattering). It is found that in spite of the considerable difference in the structure of this equation and that of Dirac the cross section is given by the Klein-Nishina formula.
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.
CONTROL VALVE TESTING PROCEDURES AND EQUATIONS
Rahmeyer, William J.
APPENDIX A CONTROL VALVE TESTING PROCEDURES AND EQUATIONS FOR LIQUID FLOWS #12;APPENDIX A CONTROL VALVE TESTING PROCEDURES AND EQUATIONS FOR LIQUID FLOWS 2 Cv Q P Sg net gpm net = / Cv = Q P / Sg 75 is used to relate the pressure loss of a valve to the discharge of the valve at a given valve opening
Additive Relation and Algebraic System of Equations
Ziqian Wu
2012-03-01T23:59:59.000Z
Additive relations are defined over additive monoids and additive operation is introduced over these new relations then we build algebraic system of equations. We can generate profuse equations by additive relations of two variables. To give an equation with several known parameters is to give an additive relation taking these known parameters as its variables or value and the solution of the equation is just the reverse of this relation which always exists. We show a core result in this paper that any additive relation of many variables and their inverse can be expressed in the form of the superposition of additive relations of one variable in an algebraic system of equations if the system satisfies some conditions. This result means that there is always a formula solution expressed in the superposition of additive relations of one variable for any equation in this system. We get algebraic equations if elements of the additive monoid are numbers and get operator equations if they are functions.
The Cauchy Problem of the Ward equation
Derchyi Wu
2008-06-02T23:59:59.000Z
We generalize the results of Villarroel, Fokas and Ioannidou, Dai, Terng and Uhlenbeck to study the inverse scattering problem of the Ward equation with non-small data and solve the Cauchy problem of the Ward equation with a non-small purely continuous scattering data.
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.
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
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
PhotovoltaicsPhotovoltaics: the equations for solar: the equations for solar--cell designcell design
Pulfrey, David L.
design LECTURE 5 · photovoltaic effect · the equation set · simplifying the equation set · absorption, Germany 90 MW Sarnia, Ontario 5kW Boston Massachusetts http://256.com/solar/ #12;3 The Photovoltaic EffectThe Photovoltaic EffectSec. 7.0 Is the full Device Equation Set needed to design and analyze a cell like this one
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.
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.
Classical non-Markovian Boltzmann equation
Alexanian, Moorad, E-mail: alexanian@uncw.edu [Department of Physics and Physical Oceanography, University of North Carolina Wilmington, Wilmington, North Carolina 28403-5606 (United States)
2014-08-01T23:59:59.000Z
The modeling of particle transport involves anomalous diffusion, (x²(t) ) ? t{sup ?} with ? ? 1, with subdiffusive transport corresponding to 0 < ? < 1 and superdiffusive transport to ? > 1. These anomalies give rise to fractional advection-dispersion equations with memory in space and time. The usual Boltzmann equation, with only isolated binary collisions, is Markovian and, in particular, the contributions of the three-particle distribution function are neglected. We show that the inclusion of higher-order distribution functions give rise to an exact, non-Markovian Boltzmann equation with resulting transport equations for mass, momentum, and kinetic energy with memory in both time and space. The two- and the three-particle distribution functions are considered under the assumption that the two- and the three-particle correlation functions are translationally invariant that allows us to obtain advection-dispersion equations for modeling transport in terms of spatial and temporal fractional derivatives.
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.
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.
Uniqueness theorems for equations of Keldysh Type
Thomas H. Otway
2010-05-25T23:59:59.000Z
A fundamental result that characterizes elliptic-hyperbolic equations of Tricomi type, the uniqueness of classical solutions to the open Dirichlet problem, is extended to a large class of elliptic-hyperbolic equations of Keldysh type. The result implies the non-existence of classical solutions to the closed Dirichlet problem for this class of equations. A uniqueness theorem is also proven for a mixed Dirichlet-Neumann problem. A generalized uniqueness theorem for the adjoint operator leads to the existence of distribution solutions to the closed Dirichlet problem in a special case.
Supersymmetric Ito equation: Bosonization and exact solutions
Ren Bo; Yu Jun [Institute of Nonlinear Science, Shaoxing University, Shaoxing 312000 (China); Lin Ji [Institute of Nonlinear Physics, ZheJiang Normal University, Jinhua, 321004 (China)
2013-04-15T23:59:59.000Z
Based on the bosonization approach, the N=1 supersymmetric Ito (sIto) system is changed to a system of coupled bosonic equations. The approach can effectively avoid difficulties caused by intractable fermionic fields which are anticommuting. By solving the coupled bosonic equations, the traveling wave solutions of the sIto system are obtained with the mapping and deformation method. Some novel types of exact solutions for the supersymmetric system are constructed with the solutions and symmetries of the usual Ito equation. In the meanwhile, the similarity reduction solutions of the model are also studied with the Lie point symmetry theory.
THE DIFFUSION APPROXIMATION FOR THE LINEAR BOLTZMANN EQUATION
THE DIFFUSION APPROXIMATION FOR THE LINEAR BOLTZMANN EQUATION WITH VANISHING SCATTERING COEFFICIENT equation, Diffusion approximation, Neutron transport equation, Radiative transfer equation subject, 23], neutron transport theory [27]. A typical model linear Boltzmann equation is (t +· x)f(t,x,)= 1
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.
Spatially Discrete FitzHugh-Nagumo Equations
Elmer, Christopher E.; Van Vleck, Erik
2005-04-05T23:59:59.000Z
We consider pulse and front solutions to a spatially discrete FitzHugh--Nagumo equation that contains terms to represent both depolarization and hyperpolarization of the nerve axon. We demonstrate a technique for deriving ...
SESAME equation of state for epoxy
Boettger, J.C.
1994-03-01T23:59:59.000Z
A new SESAME equation of state (EOS) for epoxy has been generated using the computer program GRIZZLY. This new EOS has been added to the SESAME EOS library as material number 7603.
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 ...
Chemical equation set and complete figures set
Meskhidze, Nicholas
represents the electronic supplement of our article "Observed and simulated global distribution and budget Equations 5 Propane (C3H8) Comparison of simulated and observed C3H8 mixing ratios in pmol/mol for all
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.
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.
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 ...
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)
Quantum Statistical Mechanics. II. Stochastic Schrodinger Equation
Phil Attard
2014-06-02T23:59:59.000Z
The stochastic dissipative Schrodinger equation is derived for an open quantum system consisting of a sub-system able to exchange energy with a thermal reservoir. The resultant evolution of the wave function also gives the evolution of the density matrix, which is an explicit, stochastic form of the Lindblad master equation. A quantum fluctuation-dissipation theorem is also derived. The time correlation function is discussed.
Optimization of the back equation of state
Iglesias-Silva, Gustavo Arturo
1983-01-01T23:59:59.000Z
its validity over the entire PVT diagram. First, the equation is extrapolated to high densities, pressures, and temperatures using data from Robertson et al. (1969) up to 10 000 bars, Michels et al. (1949) up to 2 900 bars and 423 K, and Van.... Rundel1 (Member) ABSTRACT Optimization of the Back . Equation of State (May 1983) Gustavo Arturo Iglesias-Silva, B. S. Instituto Politecnico Nacional, Mexico Chairman of Advisory Committee: Dr. Kenneth R. Hall An accurate representation of PVT...
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.
Nonlinear quantum equations: Classical field theory
Rego-Monteiro, M. A.; Nobre, F. D. [Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro - RJ (Brazil)] [Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro - RJ (Brazil)
2013-10-15T23:59:59.000Z
An exact classical field theory for nonlinear quantum equations is presented herein. It has been applied recently to a nonlinear Schrödinger equation, and it is shown herein to hold also for a nonlinear generalization of the Klein-Gordon equation. These generalizations were carried by introducing nonlinear terms, characterized by exponents depending on an index q, in such a way that the standard, linear equations, are recovered in the limit q? 1. The main characteristic of this field theory consists on the fact that besides the usual ?(x(vector sign),t), a new field ?(x(vector sign),t) needs to be introduced in the Lagrangian, as well. The field ?(x(vector sign),t), which is defined by means of an additional equation, becomes ?{sup *}(x(vector sign),t) only when q? 1. The solutions for the fields ?(x(vector sign),t) and ?(x(vector sign),t) are found herein, being expressed in terms of a q-plane wave; moreover, both field equations lead to the relation E{sup 2}=p{sup 2}c{sup 2}+m{sup 2}c{sup 4}, for all values of q. The fact that such a classical field theory works well for two very distinct nonlinear quantum equations, namely, the Schrödinger and Klein-Gordon ones, suggests that this procedure should be appropriate for a wider class nonlinear equations. It is shown that the standard global gauge invariance is broken as a consequence of the nonlinearity.
Finite Element Analysis of the Schroedinger Equation
Avtar S. Sehra
2007-04-17T23:59:59.000Z
The purpose of this work is to test the application of the finite element method to quantum mechanical problems, in particular for solving the Schroedinger equation. We begin with an overview of quantum mechanics, and standard numerical techniques. We then give an introduction to finite element analysis using the diffusion equation as an example. Three numerical time evolution methods are considered: the (tried and tested) Crank-Nicolson method, the continuous space-time method, and the discontinuous space-time method.
Black hole initial data without elliptic equations
István Rácz; Jeffrey Winicour
2015-02-24T23:59:59.000Z
We explore whether a new method to solve the constraints of Einstein's equations, which does not involve elliptic equations, can be applied to provide initial data for black holes. We show that this method can be successfully applied to a nonlinear perturbation of a Schwarzschild black hole by establishing the well-posedness of the resulting constraint problem. We discuss its possible generalization to the boosted, spinning multiple black hole problem.
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
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.
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...
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.
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...
approximate kinetic equations: Topics by E-print Network
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
is unbounded. As example, we study the Fokker Planck equation where eqilibrium. Keywords. maximum entropy, moment methods, Fokker-Planck equation, exact solution, Grad expansion of...
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.
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
Fourier transform of the 3d NS equations The 3d NS equations are
Salmon, Rick
1 Fourier transform of the 3d NS equations The 3d NS equations are (1) vi t + vj vi xj = - p xi easily add it in at the end. Our interest is in the advection and pressure terms. Introducing the Fourier transforms (2) vi x( ) = ui k( )eikx k p x( ) = p k( )eikx k we obtain the Fourier transform of (1
Measuring the dark matter equation of state
Serra, Ana Laura
2011-01-01T23:59:59.000Z
The nature of the dominant component of galaxies and clusters remains unknown. While the astrophysics comunity supports the cold dark matter (CDM) paradigm as a clue factor in the current cosmological model, no direct CDM detections have been performed. Faber and Visser 2006 have suggested a simple method for measuring the dark matter equation of state. By combining kinematical and gravitational lensing data it is possible to test the widely adopted assumption of pressureless dark matter. According to this formalism, we have measured the dark matter equation of state for first time using improved techniques. We have found that the value of the equation of state parameter is consistent with pressureless dark matter within the errors. Nevertheless the measured value is lower than expected. This fact follows from the well known differences between the masses determinated by lensing and kinematical methods. We have tested our techniques using simulations and we have also analyzed possible sources of errors that c...
QCD evolution equations from conformal symmetry
V. M. Braun; A. N. Manashov
2014-08-28T23:59:59.000Z
QCD evolution equations in $\\text{MS}$-like schemes can be recovered from the same equations in a modified theory, QCD in non-integer $d=4-2\\epsilon$ dimensions, which enjoys exact scale and conformal invariance at the critical point. Restrictions imposed by the conformal symmetry of the modified theory allow one to obtain complete evolution kernels in integer (physical) dimensions at the given order of perturbation theory from the spectrum of anomalous dimensions added by the calculation of the special conformal anomaly at one order less. We use this technique to derive two-loop evolution equations for flavor-nonsinglet quark-antiquark light-ray operators that encode the scale dependence of generalized hadron parton distributions.
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.
Generalized equation of state for dark energy
Barboza, E. M. Jr.; Alcaniz, J. S. [Observatorio Nacional, 20921-400, Rio de Janeiro - RJ (Brazil); Zhu, Z.-H. [Department of Astronomy, Beijing Normal University, Beijing 100875 (China); Silva, R. [Departamento de Fisica, Universidade Federal do Rio Grande do Norte, 59072-970 Natal - RN (Brazil); Departamento de Fisica, Universidade do Estado do Rio Grande do Norte, 59610-210, Mossoro - RN (Brazil)
2009-08-15T23:59:59.000Z
A generalized parametrization w{sub {beta}}(z) for the dark energy equation of state is proposed and some of its cosmological consequences are investigated. We show that in the limit of the characteristic dimensionless parameter {beta}{yields}+1, 0 and -1 some well-known equation of state parametrizations are fully recovered whereas for other values of {beta} the proposed parametrization admits a wider and new range of cosmological solutions. We also discuss possible constraints on the w{sub {beta}}(z) parameters from current observational data.
Multiverse rate equation including bubble collisions
Michael P. Salem
2013-02-19T23:59:59.000Z
The volume fractions of vacua in an eternally inflating multiverse are described by a coarse-grain rate equation, which accounts for volume expansion and vacuum transitions via bubble formation. We generalize the rate equation to account for bubble collisions, including the possibility of classical transitions. Classical transitions can modify the details of the hierarchical structure among the volume fractions, with potential implications for the staggering and Boltzmann-brain issues. Whether or not our vacuum is likely to have been established by a classical transition depends on the detailed relationships among transition rates in the landscape.
Changing the Equation in STEM Education
Broader source: Energy.gov [DOE]
Editor's Note: This is a cross post of an announcement that the White House featured on its blog last week. Check out the video below for Secretary Chu's thoughts on how an education in math and science helps students understand the world and deal with the pressing issues of our time. Today, President Obama announced the launch of Change the Equation, a CEO-led effort to dramatically improve education in science, technology, engineering, and math (STEM), as part of his “Educate to Innovate” campaign. Change the Equation is a non-profit organization dedicated to mobilizing the business community to improve the quality of STEM education in the United States.
Gribov gap equation at finite temperature
Fabrizio Canfora; Pablo Pais; Patricio Salgado-Rebolledo
2014-06-05T23:59:59.000Z
In this paper the Gribov gap equation at finite temperature is analyzed. The solutions of the gap equation (which depend explicitly on the temperature) determine the structure of the gluon propagator within the semi-classical Gribov approach. The present analysis is consistent with the standard confinement scenario for low temperatures, while for high enough temperatures, deconfinement takes place and a free gluon propagator is obtained. It also suggests the presence of the so-called semi-quark-gluon-plasma phase in between the confined and quark-gluon plasma phases.
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.
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...
SUBELLIPTIC ESTIMATES FOR FULLY NONLINEAR EQUATIONS ...
In a Carnot group G there is an interesting class of equations related to ( 1.1 ) , and ..... interesting four-dimensional group of step 7 = 3, the cycle of — ngel group. ... function is alsopÀ -convex, the more delicate reverse implication has been.
The Kinematic Algebras from the Scattering Equations
Monteiro, Ricardo
2013-01-01T23:59:59.000Z
We study kinematic algebras associated to the recently proposed scattering equations, which arise in the description of the scattering of massless particles. In particular, we describe the role that these algebras play in the BCJ duality between colour and kinematics in gauge theory, and its relation to gravity. We find that the scattering equations are a consistency condition for a self-dual-type vertex which is associated to each solution of those equations. We also identify an extension of the anti-self-dual vertex, such that the two vertices are not conjugate in general. Both vertices correspond to the structure constants of Lie algebras. We give a prescription for the use of the generators of these Lie algebras in trivalent graphs that leads to a natural set of BCJ numerators. In particular, we write BCJ numerators for each contribution to the amplitude associated to a solution of the scattering equations. This leads to a decomposition of the determinant of a certain kinematic matrix, which appears natur...
Grad-Shafranov equation with anisotropic pressure
V. S. Beskin; I. V. Kuznetsova
2000-04-16T23:59:59.000Z
The most general form of the nonrelativistic Grad-Shafranov equation describing anisotropic pressure effects is formulated within the double adiabatic approximation. It gives a possibility to analyze quantitatively how the anisotropic pressure affects the 2D structure of the ideal magnetohydrodynamical flows.
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
SYSTEMS OF FUNCTIONAL EQUATIONS MICHAEL DRMOTA
Drmota, Michael
of planted plane trees. Hence the corresponding generating function y(x) satis#12;es the functional equation the asymptotic properties of the coeÃ?cients of generating functions which satisfy a system of functional a recursive description then the generating function y(x) = P o2Y x joj = P n#21;0 yn x n satis#12;es
Inverse Problems for Fractional Diffusion Equations
Zuo, Lihua
2013-06-21T23:59:59.000Z
and preliminaries in Section 1 and 2, in the third section we consider our first inverse boundary problem. This is where an unknown boundary condition is to be determined from overposed data in a time- fractional diffusion equation. Based upon the fundamental...
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.
Spectral equivalences from Bethe Ansatz equations
Dorey, P; Tateo, R; Dorey, Patrick; Dunning, Clare; Tateo, Roberto
2001-01-01T23:59:59.000Z
The one-dimensional Schr\\"odinger equation for the potential $x^6+\\alpha x^2 +l(l+1)/x^2$ has many interesting properties. For certain values of the parameters l and alpha the equation is in turn supersymmetric (Witten), quasi-exactly solvable (Turbiner), and it also appears in Lipatov's approach to high energy QCD. In this paper we signal some further curious features of these theories, namely novel spectral equivalences with particular second- and third-order differential equations. These relationships are obtained via a recently-observed connection between the theories of ordinary differential equations and integrable models. Generalised supersymmetry transformations acting at the quasi-exactly solvable points are also pointed out, and an efficient numerical procedure for the study of these and related problems is described. Finally we generalise slightly and then prove a conjecture due to Bessis, Zinn-Justin, Bender and Boettcher, concerning the reality of the spectra of certain PT-symmetric quantum-mecha...
Pointwise Fourier Inversion: a Wave Equation Approach
Pointwise Fourier Inversion: a Wave Equation Approach Mark A. Pinsky1 Michael E. Taylor2. A general criterion for pointwise Fourier inversion 2. Pointwise Fourier inversion on Rn (n = 3) 3. Fourier inversion on R2 4. Fourier inversion on Rn (general n) 5. Fourier inversion on spheres 6. Fourier inversion
Pointwise Fourier Inversion: a Wave Equation Approach
Pointwise Fourier Inversion: a Wave Equation Approach Mark A. Pinsky 1 Michael E. Taylor 2. A general criterion for pointwise Fourier inversion 2. Pointwise Fourier inversion on R n (n = 3) 3. Fourier inversion on R 2 4. Fourier inversion on R n (general n) 5. Fourier inversion on spheres 6. Fourier
Effective Evolution Equations from Quantum Dynamics
Niels Benedikter; Marcello Porta; Benjamin Schlein
2015-02-09T23:59:59.000Z
In these notes we review the material presented at the summer school on "Mathematical Physics, Analysis and Stochastics" held at the University of Heidelberg in July 2014. We consider the time-evolution of quantum systems and in particular the rigorous derivation of effective equations approximating the many-body Schr\\"odinger dynamics in certain physically interesting regimes.
Evolution equations in QCD and QED
M. Slawinska
2008-05-12T23:59:59.000Z
Evolution equations of YFS and DGLAP types in leading order are considered. They are compared in terms of mathematical properties and solutions. In particular, it is discussed how the properties of evolution kernels affect solutions. Finally, comparison of solutions obtained numerically are presented.
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
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.
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
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.
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.
Geodesic equations and algebro-geometric methods
Hackmann, Eva
2015-01-01T23:59:59.000Z
For an investigation of the physical properties of gravitational fields the observation of massive test particles and light is very useful. The characteristic features of a given space-time may be decoded by studying the complete set of all possible geodesic motions. Such a thorough analysis can be accomplished most effectively by using analytical methods to solve the geodesic equation. In this contribution, the use of elliptic functions and their generalizations for solving the geodesic equation in a wide range of well known space-times, which are part of the general Pleba\\'nski-Demia\\'nski family of solutions, will be presented. In addition, the definition and calculation of observable effects like the perihelion shift will be presented and further applications of the presented methods will be outlined.
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.
Semirelativistic Bound-State Equations: Trivial Considerations
Wolfgang Lucha; Franz F. Schöberl
2014-07-17T23:59:59.000Z
Observing renewed interest in long-standing (semi-) relativistic descriptions of bound states, we would like to make a few comments on the eigenvalue problem posed by the spinless Salpeter equation and, illustrated by the examples of the nonsingular Woods-Saxon potential and the singular Hulth\\'en potential, recall elementary tools that practitioners looking for analytic albeit approximate solutions might find useful in their quest.
Solving the Schrödinger Equation with Power Anharmonicity
Vladimir B. Belyaev; Andrej Babi?
2014-09-17T23:59:59.000Z
We present an application of a nonstandard approximate method---the finite-rank approximation---to solving the time-independent Schr\\"odinger equation for a bound-state problem. The method is illustrated on the example of a three-dimensional isotropic quantum anharmonic oscillator with additive cubic or quartic anharmonicity. Approximate energy eigenvalues are obtained and convergence of the method is discussed.
Generalized bootstrap equations for N=4 SCFT
Luis F. Alday; Agnese Bissi
2014-04-23T23:59:59.000Z
We study the consistency of four-point functions of half-BPS chiral primary operators of weight p in four-dimensional N=4 superconformal field theories. The resulting conformal bootstrap equations impose non-trivial bounds for the scaling dimension of unprotected local operators transforming in various representations of the R-symmetry group. These bounds generalize recent bounds for operators in the singlet representation, arising from consistency of the four-point function of the stress-energy tensor multiplet.
SESAME equation of state number 7740: Polycarbonate
Boettger, J.C.
1991-06-01T23:59:59.000Z
An equation of state (EOS) for polycarbonate (a widely used polymer) has been generated with the computer code GRIZZLY and will be added to the SESAME library as material number 7740. Although a number of the input parameter used in the calculations are based on rough estimates. 7740 provides a good match to experimental Hugoniot data and should be reliable on or near the principal Hugoniot. 6 refs., 1 fig.
Jacobi equations and particle accelerator beam dynamics
Ricardo Gallego Torrome
2012-03-27T23:59:59.000Z
A geometric formulation of the linear beam dynamics in accelerator physics is presented. In particular, it is proved that the linear transverse and longitudinal dynamics can be interpret geometrically as an approximation to the Jacobi equation of an affine averaged Lorentz connection. We introduce a specific notion reference trajectory as integral curves of the main velocity vector field. A perturbation caused by the statistical nature of the bunch of particles is considered.
Freeze Out and the Boltzmann Transport Equation
L. P. Csernai; V. K. Magas; E. Molnar; A. Nyiri; K. Tamosiunas
2005-02-20T23:59:59.000Z
Recently several works have appeared in the literature that addressed the problem of Freeze Out in energetic heavy ion reaction and aimed for a description based on the Boltzmann Transport Equation (BTE). In this paper we develop a dynamical Freeze-Out description, starting from the BTE, pointing out the basic limitations of the BTE approach, and the points where the BTE approach should be modified.
Modified Boltzmann Transport Equation and Freeze Out
Csernai, L P; Molnár, E; Nyiri, A; Tamosiunas, K
2005-01-01T23:59:59.000Z
We study Freeze Out process in high energy heavy ion reaction. The description of the process is based on the Boltzmann Transport Equation (BTE). We point out the basic limitations of the BTE approach and introduce Modified BTE. The Freeze Out dynamics is presented in the 4-dimensional space-time in a layer of finite thickness, and we employ Modified BTE for the realistic Freeze Out description.
Modified Boltzmann Transport Equation and Freeze Out
L. P. Csernai; V. K. Magas; E. Molnar; A. Nyiri; K. Tamosiunas
2005-05-26T23:59:59.000Z
We study Freeze Out process in high energy heavy ion reaction. The description of the process is based on the Boltzmann Transport Equation (BTE). We point out the basic limitations of the BTE approach and introduce Modified BTE. The Freeze Out dynamics is presented in the 4-dimensional space-time in a layer of finite thickness, and we employ Modified BTE for the realistic Freeze Out description.
Solutions of systems of ordinary differential equations
Kitchens, Claude Evans
1967-01-01T23:59:59.000Z
Engineering. This thesis would not have been possible without their guidance and patience. ACKNOWLEDGMENTS LIST OF TABLES CHAPTER I CHAPTER II CHAPTER III CHAPTER IV CHAPTER V CHAPTER VI REFERENCES APPENDIX TABLE OF CONTENTS INTRODUCTION LINEAR... FOR THE BEAM PROBLEM ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 21 CHAPTER I INTRODUCTION The ob]ective of this research was to investigate the feasibility of finding numerical solutions of systems of ordinary linear differ- ential equations with appropriate boundary...
Lyapunov Functionals for the Enskog Equation
Zhenglu Jiang
2006-08-27T23:59:59.000Z
Two Lyapunov functionals are presented for the Enskog equation. One is to describe interactions between particles with various velocities and another is to measure the $L^1$ distance between two classical solutions. The former yields the time-asymptotic convergence of global classical solutions to the collision free motion while the latter is applied into the verification of the $L^1$ stability of global classical solutions.
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.
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.
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
Orbital stability of periodic waves for the nonlinear Schrodinger equation
Gallay, Thierry
Orbital stability of periodic waves for the nonlinear SchrË?odinger equation Thierry Gallay Institut: Thierry Gallay, Thierry.Gallay@ujfÂgrenoble.fr Keywords: Nonlinear SchrË?odinger equation, periodic waves
Orbital stability of periodic waves for the nonlinear Schrodinger equation
Orbital stability of periodic waves for the nonlinear SchrÂ¨odinger equation Thierry Gallay Institut: Thierry Gallay, Thierry.Gallay@ujf-grenoble.fr Keywords: Nonlinear SchrÂ¨odinger equation, periodic waves
Orbital stability of periodic waves for the nonlinear Schrodinger equation
Boyer, Edmond
Orbital stability of periodic waves for the nonlinear Schr¨odinger equation Thierry Gallay Institut: Thierry Gallay, Thierry.Gallay@ujf-grenoble.fr Keywords: Nonlinear Schr¨odinger equation, periodic waves
Infinite-dimensional symmetry for wave equation with additional condition
Irina Yehorchenko; Alla Vorobyova
2009-10-13T23:59:59.000Z
Symmetries for wave equation with additional conditions are found. Some conditions yield infinite-dimensional symmetry algebra for the nonlinear equation. Ansatzes and solutions corresponding to the new symmetries were constructed.
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.
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.
Stabilization for the semilinear wave equation with geometric control condition
Paris-Sud XI, Université de
'attracteur global compact pour l'´equation des ondes sont aussi donn´ees. 1 Introduction In this article, we
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
Transport equations in tokamak plasmasa... J. D. Callen,b
Callen, James D.
Transport equations in tokamak plasmasa... J. D. Callen,b C. C. Hegna, and A. J. Cole University; published online 8 April 2010 Tokamak plasma transport equations are usually obtained by flux surface averaging the collisional Braginskii equations. However, tokamak plasmas are not in collisional regimes
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
Spectral discretization of Darcy's equations with pressure dependent porosity
Paris-Sud XI, Université de
Spectral discretization of Darcy's equations with pressure dependent porosity by Mejdi Aza¨iez1 and the pressure p of the fluid. This system is an extension of Darcy's equations, which model the flow of the resulting system of equations which takes into account the axisymmetry of the domain and of the flow. We
Mortar spectral element discretization of Darcy's equations in nonhomogeneous medium
Paris-Sud XI, Université de
Mortar spectral element discretization of Darcy's equations in nonhomogeneous medium Mouna Daadaa Cedex 05 France. daadaa@ann.jussieu.fr 4 mai 2010 Abstract : We consider Darcy's equations. They turn out to be in good coherency with the theoretical results. R´esum´e : Les ´equations de Darcy mod
IDENTIFICATION OF MOBILITIES FOR THE BUCKLEYLEVERETT EQUATION BY FRONT TRACKING
IDENTIFICATION OF MOBILITIES FOR THE BUCKLEYLEVERETT EQUATION BY FRONT TRACKING VIDAR HAUGSE Multi--phase flow in porous media is modelled by Darcy's law. This empirical relation relates is also used to solve the saturation equation in a commercial reservoir simulator [1]. 2. Equations
VISCOSITY SOLUTIONS OF HAMILTON-JACOBI EQUATIONS, AND ASYMPTOTICS FOR
Gomes, Diogo
VISCOSITY SOLUTIONS OF HAMILTON-JACOBI EQUATIONS, AND ASYMPTOTICS FOR HAMILTONIAN SYSTEMS DIOGO:dgomes@math.ist.utl.pt Abstract. In this paper we apply the theory of viscosity solu- tions of Hamilton-Jacobi equations) that are characteristics of viscosity solutions of Hamilton-Jacobi equations, (2) H(P + Dxu, x) = H
VISCOSITY SOLUTIONS OF HAMILTON-JACOBI EQUATIONS, AND ASYMPTOTICS FOR
VISCOSITY SOLUTIONS OF HAMILTON-JACOBI EQUATIONS, AND ASYMPTOTICS FOR HAMILTONIAN SYSTEMS DIOGO. In this paper we apply the theory of viscosity solu- tions of Hamilton-Jacobi equations to understand) with cer- tain minimizing properties) and viscosity solutions of Hamilton-Jacobi equations (2) H(P + Dxu, x
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.
A Fractional Lie Group Method For Anomalous Diffusion Equations
Guo-cheng Wu
2010-09-21T23:59:59.000Z
Lie group method provides an efficient tool to solve a differential equation. This paper suggests a fractional partner for fractional partial differential equations using a fractional characteristic method. A space-time fractional diffusion equation is used as an example to illustrate the effectiveness of the Lie group method.
Developments of the Price equation and natural selection under uncertainty
Grafen, Alan
success, following Darwin (1859). Here, this project is pursued by developing the Price equation, ¢rstDevelopments of the Price equation and natural selection under uncertainty Alan Grafen Department to employ these approaches. Here, a new theore- tical development arising from the Price equation provides
Heavy tailed K distributions imply a fractional advection dispersion equation
Meerschaert, Mark M.
Dispersion Equation (FADE) to model contaminant transport in porous media. This equation characterizes, and Particle Jumps Equations of contaminant transport in porous media are based on assumptions about hydraulic governing groundwater flow (e.g., Freeze and Cherry, 1979): h K v - = (1) where v is average velocity
4. Reaction equilibria 4.1 The Saha equation
Pohl, Martin Karl Wilhelm
4. Reaction equilibria 4.1 The Saha equation If particles and radiation are in equilibrium volume with all electrons, and thus d3 x = n-1 e . Hence we finally derive the Saha equation that, using into Saha's equation then gives the ionization fraction = Ni+1 Ni + Ni+1 2 1 - 10-7 3 · 10-4 (4
Solution of the Percus-Yevick equation for hard discs
M. Adda-Bedia; E. Katzav; D. Vella
2008-01-31T23:59:59.000Z
We solve the Percus-Yevick equation in two dimensions by reducing it to a set of simple integral equations. We numerically obtain both the pair correlation function and the equation of state for a hard disc fluid and find good agreement with available Monte-Carlo calculations. The present method of resolution may be generalized to any even dimension.
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
Alexander Gorbatsievich; Ernst Schmutzer
2012-05-17T23:59:59.000Z
The equations of motion of $N$ gravitationally bound bodies are derived from the field equations of Projective Unified Field Theory. The Newtonian and the post-Newtonian approximations of the field equations and of the equations of motion of this system of bodies are studied in detail. In analyzing some experimental data we performed some numeric estimates of the ratio of the inertial mass to the scalaric mass of matter.
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.
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.... The functions F#3;s#7;?#7; x#4; and B#3;s#7;?#7; x#4; are predictable processes satisfying suitable Lipschitz–type conditions and taking values in H and L 2 #3;U#7;H#4;, respectively. We will assume that A#3;s#7;?#4; is a random family of unbounded operators...
Efficient Solution of the Simplified PN Equations
Hamilton, Steven P [ORNL; Evans, Thomas M [ORNL
2015-01-01T23:59:59.000Z
In this paper we show new solver strategies for the multigroup SPN equations for nuclear reactor analysis. By forming the complete matrix over space, moments, and energy a robust set of solution strategies may be applied. Power iteration, shifted power iteration, Rayleigh quotient iteration, Arnoldi's method, and a generalized Davidson method, each using algebraic and physics-based multigrid preconditioners, have been compared on C5G7 MOX test problem as well as an operational PWR model. Our results show that the most ecient approach is the generalized Davidson method, that is 30{40 times faster than traditional power iteration and 6{10 times faster than Arnoldi's method.
Variational Approach for Fractional Partial Differential Equations
Guo-cheng Wu
2010-06-25T23:59:59.000Z
Fractional variational approach has gained much attention in recent years. There are famous fractional derivatives such as Caputo derivative, Riesz derivative and Riemann-Liouville derivative. Several versions of fractional variational principles are proposed. However, it becomes difficult to apply the existing fractional variational theories to fractional differential models, due to the definitions of fractional variational derivatives which not only contain the left fractional derivatives but also appear right ones. In this paper, a new definition of fractional variational derivative is introduced by using a modified Riemann-Liouville derivative and the fractional Euler-Lagrange principle is established for fractional partial differential equations.
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.
Tracking Land Cover Change in a Mixed Logit Model: Recognizing Temporal and Spatial Effects
Kockelman, Kara M.
, but high residential densities can impede future development. Model application produces graphic in order to demonstrate compliance with air quality- related planning standards. Moreover, with further
Residential mobility and location choice: a nested logit model with sampling of alternatives
Lee, Brian H.; Waddell, Paul
2010-01-01T23:59:59.000Z
empirical results from the Puget Sound region. Environ.residences from the central Puget Sound region. It usesapplication in the Central Puget Sound region The NL model
Numerical Experiments with AMLET, a New Monte Carlo Algorithm for Estimating Mixed Logit Models
Toint, Philippe
th International Conference on Travel Behaviour Research Lucerne, 1015. August 2003 #12 at the 10 th International Conference on Travel Behaviour Research, Lucerne, August 2003. 1 Research Fellow
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
Z .Social Networks 21 1999 3766 primer: logit models for social networks
Fienberg, Stephen E.
a,b,) , Stanley Wasserman b,c,d,1 , Bradley Crouch b,2 a Department of Educational Psychology, Uni: Jossey-Bass, pp. 156192; Fienberg, S.E., Meyer, M.M., Wasserman, S., 1985. Statistical analysis
Computationally Efficient Technique for Nonlinear Poisson-Boltzmann Equation
Sanjay Kumar Khattri
2006-05-26T23:59:59.000Z
Discretization of non-linear Poisson-Boltzmann Equation equations results in a system of non-linear equations with symmetric Jacobian. The Newton algorithm is the most useful tool for solving non-linear equations. It consists of solving a series of linear system of equations (Jacobian system). In this article, we adaptively define the tolerance of the Jacobian systems. Numerical experiment shows that compared to the traditional method our approach can save a substantial amount of computational work. The presented algorithm can be easily incorporated in existing simulators.
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.
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.
Field Equations in the Complex Quaternion Spaces
Zi-Hua Weng
2015-04-06T23:59:59.000Z
The paper aims to adopt the complex quaternion and octonion to formulate the field equations for electromagnetic and gravitational fields. Applying the octonionic representation enables one single definition to combine some physics contents of two fields, which were considered to be independent of each other in the past. J. C. Maxwell applied simultaneously the vector terminology and the quaternion analysis to depict the electromagnetic theory. This method edified the paper to introduce the quaternion and octonion spaces into the field theory, in order to describe the physical feature of electromagnetic and gravitational fields, while their coordinates are able to be the complex number. The octonion space can be separated into two subspaces, the quaternion space and the S-quaternion space. In the quaternion space, it is able to infer the field potential, field strength, field source, field equations, and so forth, in the gravitational field. In the S-quaternion space, it is able to deduce the field potential, field strength, field source, and so forth, in the electromagnetic field. The results reveal that the quaternion space is appropriate to describe the gravitational features; meanwhile the S-quaternion space is proper to depict the electromagnetic features.
A Modified Equation for Neural Conductance and Resonance
M. Robert Showalter
1999-05-06T23:59:59.000Z
A modified equation, the S-K equation, fits data that the current neural conduction equation, the K-R equation, does not. The S-K equation is a modified Heaviside equation, based on a new interpretation of cross terms. Elements of neural anatomy and function are reviewed to put the S-K equation into context. The fit between S-K and resonance-like neural data is then shown. Appendix 1: Derivation of crossterms that represent combinations of physical laws for a line conductor of finite length. Appendix 2: Evaluation of crossterms that represent combinations of physical laws according to consistency arguments. Appendix 3: Some background on resonance. Appendix 4: Web access to some brain modeling, correspondence with NATURE, and discussion of the work in George Johnson's New York Times forums.
Nonlinear Integral-Equation Formulation of Orthogonal Polynomials
Carl M. Bender; E. Ben-Naim
2006-11-15T23:59:59.000Z
The nonlinear integral equation P(x)=\\int_alpha^beta dy w(y) P(y) P(x+y) is investigated. It is shown that for a given function w(x) the equation admits an infinite set of polynomial solutions P(x). For polynomial solutions, this nonlinear integral equation reduces to a finite set of coupled linear algebraic equations for the coefficients of the polynomials. Interestingly, the set of polynomial solutions is orthogonal with respect to the measure x w(x). The nonlinear integral equation can be used to specify all orthogonal polynomials in a simple and compact way. This integral equation provides a natural vehicle for extending the theory of orthogonal polynomials into the complex domain. Generalizations of the integral equation are discussed.
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.
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.
Emergence of wave equations from quantum geometry
Majid, Shahn [School of Mathematical Sciences, Queen Mary University of London, 327 Mile End Rd, London E1 4NS (United Kingdom)
2012-09-24T23:59:59.000Z
We argue that classical geometry should be viewed as a special limit of noncommutative geometry in which aspects which are inter-constrained decouple and appear arbitrary in the classical limit. In particular, the wave equation is really a partial derivative in a unified extra-dimensional noncommutative geometry and arises out of the greater rigidity of the noncommutative world not visible in the classical limit. We provide an introduction to this 'wave operator' approach to noncommutative geometry as recently used[27] to quantize any static spacetime metric admitting a spatial conformal Killing vector field, and in particular to construct the quantum Schwarzschild black hole. We also give an introduction to our related result that every classical Riemannian manifold is a shadow of a slightly noncommutative one wherein the meaning of the classical Ricci tensor becomes very natural as the square of a generalised braiding.
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.
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.
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.
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.
Solutions for a Schroedinger equation with a nonlocal term
Lenzi, E. K.; Oliveira, B. F. de; Evangelista, L. R. [Departamento de Fisica, Universidade Estadual de Maringa, Avenida Colombo, 5790 -87020-900 Maringa, Parana (Brazil); Silva, L. R. da [Departamento de Fisica, Universidade Federal do Rio Grande do Norte, 59072-970 Natal-RN (Brazil)
2008-03-15T23:59:59.000Z
We obtain time dependent solutions for a Schroendiger equation in the presence of a nonlocal term by using the Green function approach. These solutions are compared with recent results obtained for the fractional Schroedinger equation as well as for the usual one. The nonlocal term incorporated in the Schroedinger equation may also be related to the spatial and time fractional derivative and introduces different regimes of spreading of the solution with the time evolution.
An Equation of Motion with Quantum Effect in Spacetime
Jyh-Yang Wu
2009-05-26T23:59:59.000Z
In this paper, we shall present a new equation of motion with Quantum effect in spacetime. To do so, we propose a classical-quantum duality. We also generalize the Schordinger equation to the spacetime and obtain a relativistic wave equation. This will lead a generalization of Einstein's formula $E=m_0c^2$ in the spacetime. In general, we have $E=m_0c^2 + \\frac{\\hbar^2}{12m_0}R$ in a spacetime.
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}.
A Least-Squares Transport Equation Compatible with Voids
Jon Hansen; Jacob Peterson; Jim Morel; Jean Ragusa; Yaqi Wang
2014-09-01T23:59:59.000Z
Standard second-order self-adjoint forms of the transport equation, such as the evenparity, odd-parity, and self-adjoint angular flux equation, cannot be used in voids. Perhaps more important, they experience numerical convergence difficulties in near-voids. Here we present a new form of a second-order self-adjoint transport equation that has an advantage relative to standard forms in that it can be used in voids or near-voids. Our equation is closely related to the standard least-squares form of the transport equation with both equations being applicable in a void and having a nonconservative analytic form. However, unlike the standard least-squares form of the transport equation, our least-squares equation is compatible with source iteration. It has been found that the standard least-squares form of the transport equation with a linear-continuous finite-element spatial discretization has difficulty in the thick diffusion limit. Here we extensively test the 1D slab-geometry version of our scheme with respect to void solutions, spatial convergence rate, and the intermediate and thick diffusion limits. We also define an effective diffusion synthetic acceleration scheme for our discretization. Our conclusion is that our least-squares Sn formulation represents an excellent alternative to existing second-order Sn transport formulations
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.
An extension of the Derrida-Lebowitz-Speer-Spohn equation
Charles Bordenave; Pierre Germain; Thomas Trogdon
2015-04-19T23:59:59.000Z
Derrida, Lebowitz, Speer and Spohn have proposed a simplified model to describe the low temperature Glauber dynamics of an anchored Toom interface. We show how the derivation of the Derrida-Lebowitz-Speer-Spohn equation can be prolonged to obtain a new equation, generalizing the models obtained in the paper by these authors. We then investigate its properties from both an analytical and numerical perspective. Specifically, a numerical method is presented to approximate solutions of the prolonged equation. Using this method, we investigate the relationship between the solutions of the prolonged equation and the Tracy--Widom GOE distribution.
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.
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.
On the running coupling in the JIMWLK equation
T. Lappi; H. Mäntysaari
2012-12-19T23:59:59.000Z
We propose a new method to implement the running coupling constant in the JIMWLK equation, imposing the scale dependence on the correlation function of the random noise in the Langevin formulation. We interpret this scale choice as the transverse momentum of the emitted gluon in one step of the evolution and show that it is related to the "Balitsky" prescription for the BK equation. This slows down the evolution speed of a practical solution of the JIMWLK equation, bringing it closer to the x-dependence inferred from fits to HERA data. We further study our proposal by a numerical comparison of the BK and JIMWLK equations.
Evolution equation for 3-quark Wilson loop operator
R. E. Gerasimov; A. V. Grabovsky
2012-12-07T23:59:59.000Z
The evolution equation for the 3 quark Wilson loop operator has been derived in the leading logarithm approximation within Balitsky high energy operator expansion.
Stabilization for the semilinear wave equation with geometric control condition
Joly, Romain
applica- tions `a la contr^olabilit´e et `a l'existence d'attracteur global compact pour l'´equation des
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
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
Solving the BuckleyLeverett Equation with Gravity in a Heterogeneous Porous Medium
Eindhoven, Technische Universiteit
be described by two equations for conservation of mass and two equations for Darcy's law. These equa tionsSolving the BuckleyLeverett Equation with Gravity in a Heterogeneous Porous Medium E equation is a nonlinear hyperbolic conservation law, known as the BuckleyLeverett equation. This equation
Astrophysical Gyrokinetics: Basic Equations and Linear Theory
Gregory G. Howes; Steven C. Cowley; William Dorland; Gregory W. Hammett; Eliot Quataert; Alexander A. Schekochihin
2006-05-04T23:59:59.000Z
Magnetohydrodynamic (MHD) turbulence is encountered in a wide variety of astrophysical plasmas, including accretion disks, the solar wind, and the interstellar and intracluster medium. On small scales, this turbulence is often expected to consist of highly anisotropic fluctuations with frequencies small compared to the ion cyclotron frequency. For a number of applications, the small scales are also collisionless, so a kinetic treatment of the turbulence is necessary. We show that this anisotropic turbulence is well described by a low frequency expansion of the kinetic theory called gyrokinetics. This paper is the first in a series to examine turbulent astrophysical plasmas in the gyrokinetic limit. We derive and explain the nonlinear gyrokinetic equations and explore the linear properties of gyrokinetics as a prelude to nonlinear simulations. The linear dispersion relation for gyrokinetics is obtained and its solutions are compared to those of hot-plasma kinetic theory. These results are used to validate the performance of the gyrokinetic simulation code {\\tt GS2} in the parameter regimes relevant for astrophysical plasmas. New results on global energy conservation in gyrokinetics are also derived. We briefly outline several of the problems to be addressed by future nonlinear simulations, including particle heating by turbulence in hot accretion flows and in the solar wind, the magnetic and electric field power spectra in the solar wind, and the origin of small-scale density fluctuations in the interstellar medium.
A JUSTIFICATION OF EDDY CURRENTS MODEL FOR THE MAXWELL EQUATIONS
Buffa, Annalisa
A JUSTIFICATION OF EDDY CURRENTS MODEL FOR THE MAXWELL EQUATIONS H. AMMARI, A. BUFFA, AND J.-C. NÂ1823 Abstract. This paper is concerned with the approximation of the Maxwell equations by the eddy currents model, which appears as a correction of the quasi-static model. The eddy currents model is obtained
Kalman filtering the delay-difference equation: practical approaches
Kalman filtering the delay-difference equation: practical approaches and simulations Daniel K.-Recently, J. J. Pella showed how the Kalman filter could be applied to production modeling to esti- mate apply these methods to the Deriso-Schnute delay-difference equation. The Kalman filter approach
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
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.
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
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
Boundary value problems for the one-dimensional Willmore equation
Grunau, Hans-Christoph
Boundary value problems for the one-dimensional Willmore equation Klaus Deckelnick and HansÂknown that the corresponding surface has to satisfy the Willmore equation H + 2H(H2 - K) = 0 on , (1) e-mail: Klaus Willmore surfaces of prescribed genus has been proved by Simon [Sn] and Bauer & Kuwert [BK]. Also, local
Boundary value problems for the onedimensional Willmore equation
Grunau, Hans-Christoph
Boundary value problems for the oneÂdimensional Willmore equation Klaus Deckelnick # and Hans--known that the corresponding surface # has to satisfy the Willmore equation #H + 2H(H 2 -K) = 0 on #, (1) # eÂmail: Klaus Willmore surfaces of prescribed genus has been proved by Simon [Sn] and Bauer & Kuwert [BK]. Also, local
On thermodynamically consistent schemes for phase field equations
Fife, Paul
and at the phase change front. A somewhat different approach of Charach and Zemel [2] combines bal- ance equationsOn thermodynamically consistent schemes for phase field equations C. Charach and P. C. Fife thermodynamics. The principal applications are to the solidification of a pure material and of a binary alloy
ON WAVELET FUNDAMENTAL SOLUTIONS TO THE HEAT EQUATION ---HEATLETS
Soatto, Stefano
ON WAVELET FUNDAMENTAL SOLUTIONS TO THE HEAT EQUATION --- HEATLETS JIANHONG SHEN AND GILBERT STRANG Abstract. We present an application of wavelet theory in partial differential equaÂ tions. We study the wavelet fundamental solutions to the heat equation. The heat evolution of an initial wavelet state
Radio Interferometry & The Measurement Equation -1 School of Physics
Tittley, Eric
Radio Interferometry & The Measurement Equation - 1 School of Physics and Astronomy An Introduction to Radio Interferometry and The Measurement Equation Formalism Pedagogical Seminar Louise M. Ker March 2010 Abstract The next generation of radio telescopes, such as LOFAR, e-Merlin, ASKAP, MeerKat and even- tually
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.
Photovoltaic translation equations: A new approach. Final subcontract report
Anderson, A.J. [Sunset Technology, Highlands Ranch, CO (United States)] [Sunset Technology, Highlands Ranch, CO (United States)
1996-01-01T23:59:59.000Z
New equations were developed for the purpose of evaluating the performance of photovoltaic cells, modules, panels, and arrays. These equations enable the performance values determined at one condition of temperature and irradiance to be translated to any other condition of temperature and irradiance.
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
VISCOSITY SOLUTIONS TO DEGENERATE COMPLEX MONGE-AMP`ERE EQUATIONS
Boyer, Edmond
VISCOSITY SOLUTIONS TO DEGENERATE COMPLEX MONGE-AMP`ERE EQUATIONS PHILIPPE EYSSIDIEUX, VINCENT an alternative approach based on the concept of viscosity solutions and compare systematically viscosity concepts PDE approach to second-order degenerate elliptic equations is the method of viscosity solutions
Fractional Method of Characteristics for Fractional Partial Differential Equations
Guo-cheng Wu
2010-07-10T23:59:59.000Z
The method of characteristics has played a very important role in mathematical physics. Preciously, it was used to solve the initial value problem for partial differential equations of first order. In this paper, we propose a fractional method of characteristics and use it to solve some fractional partial differential equations.
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.
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.
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.
MATH 100 Introduction to the Profession Linear Equations in MATLAB
Fasshauer, Greg
's input-output model in economics, electric circuit problems, the steady-state analysis of a systemMATH 100 Â Introduction to the Profession Linear Equations in MATLAB Greg Fasshauer Department;Chapter 5 of Experiments with MATLAB Where do systems of linear equations come up? fasshauer@iit.edu MATH
A New Wide Range Equation of State for Helium-4
Ortiz Vega, Diego O
2013-08-01T23:59:59.000Z
A multiparametric and fundamental equation of state is presented for the fluid thermodynamic properties of helium. The equation is valid for temperatures from the ?- line (~2.17 K) to 1500 K and for pressures up to 2000 MPa. The formulation can...
On a nonlocal dispersive equation modeling particle suspensions
Zumbrun, Kevin
On a nonlocal dispersive equation modeling particle suspensions Kevin Zumbrun July, 1996 Abstract: We study a nonlocal, scalar conservation law, u t + ((K a \\Lambda u)u) x = 0, modeling sedimentation, and \\Lambda represents convolution. We show this to be a dispersive regularization of the Hopf equation, u
Lyapunov control of bilinear Schrodinger equations Mazyar Mirrahimi a
Paris-Sud XI, Université de
Lyapunov control of bilinear Schr¨odinger equations Mazyar Mirrahimi a , Pierre Rouchon b , Gabriel´ee Cedex, France Abstract A Lyapunov-based approach for trajectory tracking of the Schr¨odinger equation Lyapunov function, Adiabatic invariants, Tracking. 1 Introduction Controllability of a finite dimensional
Mickens, R.E.
1997-12-12T23:59:59.000Z
The major thrust of this proposal was to continue our investigations of so-called non-standard finite-difference schemes as formulated by other authors. These schemes do not follow the standard rules used to model continuous differential equations by discrete difference equations. The two major aspects of this procedure consist of generalizing the definition of the discrete derivative and using a nonlocal model (on the computational grid or lattice) for nonlinear terms that may occur in the differential equations. Our aim was to investigate the construction of nonstandard finite-difference schemes for several classes of ordinary and partial differential equations. These equations are simple enough to be tractable, yet, have enough complexity to be both mathematically and scientifically interesting. It should be noted that all of these equations differential equations model some physical phenomena under an appropriate set of experimental conditions. The major goal of the project was to better understand the process of constructing finite-difference models for differential equations. In particular, it demonstrates the value of using nonstandard finite-difference procedures. A secondary goal was to construct and study a variety of analytical techniques that can be used to investigate the mathematical properties of the obtained difference equations. These mathematical procedures are of interest in their own right and should be a valuable contribution to the mathematics research literature in difference equations. All of the results obtained from the research done under this project have been published in the relevant research/technical journals or submitted for publication. Our expectation is that these results will lead to improved finite difference schemes for the numerical integration of both ordinary and partial differential equations. Section G of the Appendix gives a concise summary of the major results obtained under funding by the grant.
Sensitivity of rocky planet structures to the equation of state
Swift, D C
2009-06-10T23:59:59.000Z
Structures were calculated for Mercury, Venus, Earth, the Moon, and Mars, using a core-mantle model and adjusting the core radius to reproduce the observed mass and diameter of each body. Structures were calculated using Fe and basalt equations of state of different degrees of sophistication for the core and mantle. The choice of equation of state had a significant effect on the inferred structure. For each structure, the moment of inertia ratio was calculated and compared with observed values. Linear Grueneisen equations of state fitted to limited portions of shock data reproduced the observed moments of inertia significantly better than did more detailed equations of state incorporating phase transitions, presumably reflecting the actual compositions of the bodies. The linear Grueneisen equations of state and corresponding structures seem however to be a reasonable starting point for comparative simulations of large-scale astrophysical impacts.
Heat Equations with Fractional White Noise Potentials
Hu, Y. [Department of Mathematics, University of Kansas, 405 Snow Hall, Lawrence, KS 66045-2142 (United States)], E-mail: hu@math.ukans.edu
2001-07-01T23:59:59.000Z
This paper is concerned with the following stochastic heat equations: ({partial_derivative}u{sub t}(x))/({partial_derivative}t=1/2 u{sub t}(x)+{omega}{sup H}.u{sub t}(x)), x element of {sup d}, t>0, where w{sup H} is a time independent fractional white noise with Hurst parameter H=(h{sub 1}, h{sub 2},..., h{sub d}) , or a time dependent fractional white noise with Hurst parameter H=(h{sub 0}, h{sub 1},..., h{sub d}) . Denote | H | =h{sub 1}+h{sub 2}+...+h{sub d} . When the noise is time independent, it is shown that if 1/2
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
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
Equations, States, and Lattices of Infinite-Dimensional Hilbert Spaces
Norman D. Megill; Mladen Pavicic
2001-01-21T23:59:59.000Z
We provide several new results on quantum state space, on lattice of subspaces of an infinite dimensional Hilbert space, and on infinite dimensional Hilbert space equations as well as on connections between them. In particular we obtain an n-variable generalized orthoarguesian equation which holds in any infinite dimensional Hilbert space. Then we strengthen Godowski's result by showing that in an ortholattice on which strong states are defined Godowski's equations as well as the orthomodularity hold. We also prove that all 6- and 4-variable orthoarguesian equations presented in the literature can be reduced to new 4- and 3-variable ones, respectively and that Mayet's examples follow from Godowski's equations. To make a breakthrough in testing these massive equations we designed several novel algorithms for generating Greechie diagrams with an arbitrary number of blocks and atoms (currently testing with up to 50) and for automated checking of equations on them. A way of obtaining complex infinite dimensional Hilbert space from the Hilbert lattice equipped with several additional conditions and without invoking the notion of state is presented. Possible repercussions of the results to quantum computing problems are discussed.
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.
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.
Generalized Ehrenfest's Equations and phase transition in Black Holes
Mohammad Bagher Jahani Poshteh; Behrouz Mirza; Fatemeh Oboudiat
2015-03-09T23:59:59.000Z
We generalize Ehrenfest's equations to systems having two work terms, i.e. systems with three degrees of freedom. For black holes with two work terms we obtain nine equations instead of two to be satisfied at the critical point of a second order phase transition. We finally generalize this method to a system with an arbitrary number of degrees of freedom and found there is $\\frac{N(N+1)^{2}}{2}$ equations to be satisfied at the point of a second order phase transition where $N$ is number of work terms in the first law of thermodynamics.
A Least-Squares Transport Equation Compatible with Voids
Hansen, Jon
2014-04-22T23:59:59.000Z
. DERIVATION OF EQUATION Let us begin the derivation of our least-squares equation with the first-order monoenergetic transport equation, L? = S? + q 4pi = ?s?+ q 4pi = Q , (2.1) where ? (n/cm2-s-str) is the angular flux, ? (n/cm2-s) is the scalar flux defined... by ? = ? 4pi ? d?, q (n/cm 3-s) is the distributed source, and L is the streaming plus removal operator, L = ?? ? · ?? ? + ?t , (2.2) S is the scattering operator, S = ?s 4pi ? 4pi d? , (2.3) ?t (cm?1) denotes the macroscopic total cross section and ?s...
On equations of motion in twist-four evolution
Yao Ji; A. V. Belitsky
2014-10-23T23:59:59.000Z
Explicit diagrammatic calculation of evolution equations for high-twist correlation functions is a challenge already at one-loop order in QCD coupling. The main complication being quite involved mixing pattern of the so-called non-quasipartonic operators. Recently, this task was completed in the literature for twist-four nonsinglet sector. Presently, we elaborate on a particular component of renormalization corresponding to the mixing of gauge-invariant operators with QCD equations of motion. These provide an intrinsic contribution to evolution equations yielding total result in agreement with earlier computations that bypassed explicit analysis of Feynman graphs.
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.
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
Essential Differential Equations September 2013 Lecturer David Silvester
Silvester, David J.
Essential Differential Equations September 2013 Lecturer David Silvester Office Alan Turing 15 Classes Tues 34 Alan Turing G.207 Thur 13 Alan Turing G.205 Assessment Week 7 Test 20% Week 10
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
On the Stochastic Burgers’ Equation in the Real Line
Gyö ngy, Istvá n; Nualart, David
1999-01-01T23:59:59.000Z
Burgers’ equation, space#1;time white noise. 782 STOCHASTIC BURGERS EQUATION 783 equations, #2;u #2; 2 u #2; g #1; #2; f t , x , u t , x #2; t , x , u t , xŽ . Ž .Ž . Ž .2 #2; t #2; x#2; x 1.1Ž . #2; 2W #2; #3; t , x , u t , x ,Ž .Ž . #2; t#2; x #3; #4;is... in the following stochastic partial differential equation: #2;u #2; 2 u #2; g #1; #2; f t , x , u t , x #2; t , x , u t , xŽ . Ž .Ž . Ž .2 #2; t #2; x#2; x 2.1Ž . #2; 2W #2; #3; t , x , u t , x ,Ž .Ž . #2; t#2; x ¨I. GYONGY AND D. NUALART784 #3; #4; Ž . Ž . 2Ž .t#6...
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.
Sandia National Laboratories: governing WEC equations of motion...
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
governing WEC equations of motion in six degrees of freedom Sandia, NREL Release Wave Energy Converter Modeling and Simulation Code: WEC-Sim On July 29, 2014, in Computational...
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
Energy Flow in Extended Gradient Partial Differential Equations
Energy Flow in Extended Gradient Partial Differential Equations Th. Gallay S. Slijepâ??atiment 425 BijeniÅ¸cka 30 FÂ91405 Orsay, France 10000 Zagreb, Croatia Thierry.Gallay@math.uÂpsud.fr slijepce
Stability of Propagating Fronts in Damped Hyperbolic Equations
Stability of Propagating Fronts in Damped Hyperbolic Equations Th. Gallay, G. Raugel Analyse Num'erique et EDP CNRS et Universit'e de ParisÂSud FÂ91405 Orsay Cedex, France Thierry.Gallay
Numerical solution of plasma fluid equations using locally refined grids
Colella, P., LLNL
1997-01-26T23:59:59.000Z
This paper describes a numerical method for the solution of plasma fluid equations on block-structured, locally refined grids. The plasma under consideration is typical of those used for the processing of semiconductors. The governing equations consist of a drift-diffusion model of the electrons and an isothermal model of the ions coupled by Poisson's equation. A discretization of the equations is given for a uniform spatial grid, and a time-split integration scheme is developed. The algorithm is then extended to accommodate locally refined grids. This extension involves the advancement of the discrete system on a hierarchy of levels, each of which represents a degree of refinement, together with synchronization steps to ensure consistency across levels. A brief discussion of a software implementation is followed by a presentation of numerical results.
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.
Multiscale numerical methods for some types of parabolic equations
Nam, Dukjin
2009-05-15T23:59:59.000Z
method. The goal of the second problem is to develop efficient multiscale numerical techniques for solving turbulent diffusion equations governed by celluar flows. The solution near the separatrices can be approximated by the solution of a system of one...
Exponential Time Decay Estimates for the Landau Equation on Torus
Kung-Chien Wu
2013-01-04T23:59:59.000Z
We study the time decay estimates for the linearized Landau equation on torus when the initial perturbation is not necessarily smooth. Our result reveals the kinetic and fluid aspects of the equation. We design a Picard-type iteration and Mixture lemma for constructing the increasingly regular kinetic like waves, they are carried by transport equations and have exponential time decay rate. The fluid like waves are constructed as part of the long-wave expansion in the spectrum of the Fourier mode for the space variable and the time decay rate depends on the size of the domain. The Mixture lemma plays an important role in this paper, this lemma is parallel to Boltzmann equation but the proof is more challenge.
Exact Vacuum Solutions of Jordan, Brans-Dicke Field Equations
Sergey Kozyrev
2005-12-04T23:59:59.000Z
We present the static spherically symmetric vacuum solutions of the Jordan, Brans-Dicke field equations. The new solutions are obtained by considering a polar Gaussian, isothermal and radial hyperbolic metrics.
Quicksilver Solutions of a q-difference first Painlevé equation
Nalini Joshi
2014-07-07T23:59:59.000Z
In this paper, we present new, unstable solutions, which we call quicksilver solutions, of a $q$-difference Painlev\\'e equation in the limit as the independent variable approaches infinity. The specific equation we consider in this paper is a discrete version of the first Painlev\\'e equation ($q\\Pon$), whose phase space (space of initial values) is a rational surface of type $A_7^{(1)}$. We describe four families of almost stationary behaviours, but focus on the most complicated case, which is the vanishing solution. We derive this solution's formal power series expansion, describe the growth of its coefficients and show that, while the series is divergent, there exist true analytic solutions asymptotic to such a series in a certain $q$-domain. The method, while demonstrated for $q\\Pon$, is also applicable to other $q$-difference Painlev\\'e equations.
Numerical Analysis and Partial Differential Equations March 12, 2009
Elliott, Charles
Equations . . . . . . . . . . . . . . . . . . . . . 71 6 Finite element error analysis 74 6.1 Galerkin.1 A Boundary Value Problem . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 A Finite Element Method) . . . . . . . . . . . . . . . . . . . . 12 2.4 Finite Element Method . . . . . . . . . . . . . . . . . . . . . . . . . 12 II Finite Element
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.
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
Positive Lyapunov exponents for continuous quasiperiodic Schroedinger equations
Bjerkloev, Kristian [Department of Mathematics, University of Toronto, Toronto Ontario, M5S 3G3 (Canada)
2006-02-15T23:59:59.000Z
We prove that the continuous one-dimensional Schroedinger equation with an analytic quasi-periodic potential has positive Lyapunov exponents in the bottom of the spectrum for large couplings.
A fast enriched FEM for Poisson equations involving interfaces
Huynh, Thanh Le Ngoc
2008-01-01T23:59:59.000Z
We develop a fast enriched finite element method for solving Poisson equations involving complex geometry interfaces by using regular Cartesian grids. The presence of interfaces is accounted for by developing suitable jump ...
Construction of tree volume tables from integration of taper equations
Coffman, Jerry Gale
1973-01-01T23:59:59.000Z
August 1973 Major Subject: Forest Science CONSTRUCTION OF TREE VOLUME TABLES FROM INTEGRATION OF TAPER EqUATIONS A Thesis by JERRY GALE COFFMAN Approved as to style and content by: , . . -('7)i- 7 Jf A~(''~--- (Chairman of Committee) (8 ad... of Dsp ar tment) (Member) (Member August 1973 488899 ABSTRACT Construction of Tree Volume Tables From Integration of Taper Equations. (August. 1973) Jerry Gale Coffman, B. S. F. , University of Arkansas at Monticello; Directed by: Dr. De~id M...
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.
Laplace Operators on Fractals and Related Functional Equations
Gregory Derfel; Peter Grabner; Fritz Vogl
2012-06-06T23:59:59.000Z
We give an overview over the application of functional equations, namely the classical Poincar\\'e and renewal equations, to the study of the spectrum of Laplace operators on self-similar fractals. We compare the techniques used to those used in the euclidean situation. Furthermore, we use the obtained information on the spectral zeta function to define the Casimir energy of fractals. We give numerical values for this energy for the Sierpi\\'nski gasket.
MAXWELL-LORENTZ EQUATIONS IN GENERAL FRENET-SERRET COORDINATES
Kabel, A
2004-09-17T23:59:59.000Z
We consider the trajectory of a charged particle in an arbitrary external magnetic field. A local orthogonal coordinate system is given by the tangential, curvature, and torsion vectors. We write down Maxwell's equations in this coordinate system. The resulting partial differential equations for the magnetic fields fix conditions among its local multipole components, which can be viewed as a generalization of the usual multipole expansion of the fields of magnetic elements.
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.
A Maxwell's equations, Coulomb gauge analysis of two scatterers
Crowell, Kelly Jean
1990-01-01T23:59:59.000Z
A MAXWELL'S EQUATIONS, COULOMB GAUGE ANALYSIS OF TWO SCATTERERS A Thesis by KELLY JEAN CROWELL Submitted to the Office of Graduate Studies of Texas ASM University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE... May 1990 Major Subject: Electrical Engineering A MAXWELL'S EQUATIONS, COULOMB GAUGE ANALYSIS OF TWO SCATTERERS A Thesis by KELLY JEAN CROWELL Approved as to style and content by: Robert D. Nevels (Chairman of Committee) D. R. Halverson...
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)].
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).
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 $\\pm 25%$.
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.
The quantummechanical wave equations from a relativistic viewpoint
Engel Roza
2007-07-19T23:59:59.000Z
A derivation is presented of the quantummechanical wave equations based upon the Equity Principle of Einstein's General Relativity Theory. This is believed to be more generic than the common derivations based upon Einstein's energy relationship for moving particles. It is shown that Schrodinger's Equation, if properly formulated, is relativisticly covariant. This makes the critisized Klein-Gordon Equation for spinless massparticles obsolete. Therefore Dirac's Equation is presented from a different viewpoint and it is shown that the relativistic covariance of Schrodinger's Equation gives a natural explanation for the dual energy outcome of Dirac's derivation and for the nature of antiparticles. The propagation of wave functions in an energy field is studied in terms of propagation along geodesic lines in curved space-time, resulting in an equivalent formulation as with Feynman's path integral. It is shown that Maxwell's wave equation fits in the developed framework as the massless limit of moving particles. Finally the physical appearance of electrons is discussed including a quantitative calculation of the jitter phenomenon of a free moving electron.
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
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...
Long time behavior and stability of special solutions of nonlinear partial differential equations.
Demirkaya, Aslihan
2011-04-21T23:59:59.000Z
In this dissertation, in the first part, I study the long-time behavior of the solutions of the Kuramoto-Sivashinsky equation and the Burgers-Sivashinsky equation. First, I work on a two-dimensional modified KS equation ...
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.
Open systems dynamics: Simulating master equations in the computer
Carlos Navarrete-Benlloch
2015-04-22T23:59:59.000Z
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\\'ia-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.
Bifurcations of traveling wave solutions for an integrable equation
Li Jibin [Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004 (China) and Kunming University of Science and Technology, Kunming, Yunnan 650093 (China); Qiao Zhijun [Department of Mathematics, University of Texas Pan-American, 1201 West University Drive, Edinburg, Texas 78541 (United States)
2010-04-15T23:59:59.000Z
This paper deals with the following equation m{sub t}=(1/2)(1/m{sup k}){sub xxx}-(1/2)(1/m{sup k}){sub x}, which is proposed by Z. J. Qiao [J. Math. Phys. 48, 082701 (2007)] and Qiao and Liu [Chaos, Solitons Fractals 41, 587 (2009)]. By adopting the phase analysis method of planar dynamical systems and the theory of the singular traveling wave systems to the traveling wave solutions of the equation, it is shown that for different k, the equation may have infinitely many solitary wave solutions, periodic wave solutions, kink/antikink wave solutions, cusped solitary wave solutions, and breaking loop solutions. We discuss in a detail the cases of k=-2,-(1/2),(1/2),2, and parametric representations of all possible bounded traveling wave solutions are given in the different (c,g)-parameter regions.
Properties of the Boltzmann equation in the classical approximation
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Tanji, Naoto; Epelbaum, Thomas; Gelis, Francois; Wu, Bin
2014-12-01T23:59:59.000Z
We study the Boltzmann equation with elastic point-like scalar interactions in two different versions of the the classical approximation. Although solving numerically the Boltzmann equation with the unapproximated collision term poses no problem, this allows one to study the effect of the ultraviolet cutoff in these approximations. This cutoff dependence in the classical approximations of the Boltzmann equation is closely related to the non-renormalizability of the classical statistical approximation of the underlying quantum field theory. The kinetic theory setup that we consider here allows one to study in a much simpler way the dependence on the ultraviolet cutoff, since onemore »has also access to the non-approximated result for comparison.« less
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.
Properties of the Boltzmann equation in the classical approximation
Tanji, Naoto [Nishina Center, RIKEN, Wako (Japan). Theoretical Research Division; Brookhaven National Lab. (BNL), Upton, NY (United States); Epelbaum, Thomas [Institut de Physique Theorique (France); Gelis, Francois [Institut de Physique Theorique (France); Wu, Bin [Institut de Physique Theorique (France)
2014-12-01T23:59:59.000Z
We study the Boltzmann equation with elastic point-like scalar interactions in two different versions of the the classical approximation. Although solving numerically the Boltzmann equation with the unapproximated collision term poses no problem, this allows one to study the effect of the ultraviolet cutoff in these approximations. This cutoff dependence in the classical approximations of the Boltzmann equation is closely related to the non-renormalizability of the classical statistical approximation of the underlying quantum field theory. The kinetic theory setup that we consider here allows one to study in a much simpler way the dependence on the ultraviolet cutoff, since one has also access to the non-approximated result for comparison.
Artificial Neural Networks for Solving Ordinary and Partial Differential Equations
I. E. Lagaris; A. Likas; D. I. Fotiadis
1997-05-19T23:59:59.000Z
We present a method to solve initial and boundary value problems using artificial neural networks. A trial solution of the differential equation is written as a sum of two parts. The first part satisfies the boundary (or initial) conditions and contains no adjustable parameters. The second part is constructed so as not to affect the boundary conditions. This part involves a feedforward neural network, containing adjustable parameters (the weights). Hence by construction the boundary conditions are satisfied and the network is trained to satisfy the differential equation. The applicability of this approach ranges from single ODE's, to systems of coupled ODE's and also to PDE's. In this article we illustrate the method by solving a variety of model problems and present comparisons with finite elements for several cases of partial differential equations.
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.
Pointwise Behavior of the Linearized Boltzmann Equation on Torus
Kung-Chien Wu
2013-01-04T23:59:59.000Z
We study the pointwise behavior of the linearized Boltzmann equation on torus for non-smooth initial perturbation. The result reveals both the fluid and kinetic aspects of this model. The fluid-like waves are constructed as part of the long-wave expansion in the spectrum of the Fourier mode for the space variable, the time decay rate of the fluid-like waves depends on the size of the domain. We design a Picard-type iteration for constructing the increasingly regular kinetic-like waves, which are carried by the transport equations and have exponential time decay rate. Moreover, the mixture lemma plays an important role in constructing the kinetic-like waves, we supply a new proof of this lemma to avoid constructing explicit solution of the damped transport equations
Charged anisotropic matter with linear or nonlinear equation of state
Varela, Victor; Rahaman, Farook; Ray, Saibal; Chakraborty, Koushik; Kalam, Mehedi [Institute of Mathematics, Kings College, University of Aberdeen, Aberdeen AB24 3UE (United Kingdom); Department of Mathematics, Jadavpur University, Kolkata 700 032, West Bengal (India); Department of Physics, Government College of Engineering and Ceramic Technology, Kolkata 700 010, West Bengal (India); Department of Physics, Government Training College, Hooghly 712103 (India)
2010-08-15T23:59:59.000Z
Ivanov pointed out substantial analytical difficulties associated with self-gravitating, static, isotropic fluid spheres when pressure explicitly depends on matter density. Simplifications achieved with the introduction of electric charge were noticed as well. We deal with self-gravitating, charged, anisotropic fluids and get even more flexibility in solving the Einstein-Maxwell equations. In order to discuss analytical solutions we extend Krori and Barua's method to include pressure anisotropy and linear or nonlinear equations of state. The field equations are reduced to a system of three algebraic equations for the anisotropic pressures as well as matter and electrostatic energy densities. Attention is paid to compact sources characterized by positive matter density and positive radial pressure. Arising solutions satisfy the energy conditions of general relativity. Spheres with vanishing net charge contain fluid elements with unbounded proper charge density located at the fluid-vacuum interface. Notably the electric force acting on these fluid elements is finite, although the acting electric field is zero. Net charges can be huge (10{sup 19}C) and maximum electric field intensities are very large (10{sup 23}-10{sup 24} statvolt/cm) even in the case of zero net charge. Inward-directed fluid forces caused by pressure anisotropy may allow equilibrium configurations with larger net charges and electric field intensities than those found in studies of charged isotropic fluids. Links of these results with charged strange quark stars as well as models of dark matter including massive charged particles are highlighted. The van der Waals equation of state leading to matter densities constrained by cubic polynomial equations is briefly considered. The fundamental question of stability is left open.
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.
E. V. Shiryaeva; M. Yu. Zhukov
2014-10-17T23:59:59.000Z
The paper presents the solutions for the zonal electrophoresis equations are obtained by analytical and numerical methods. The method proposed by the authors is used. This method allows to reduce the Cauchy problem for two hyperbolic quasilinear PDE's to the Cauchy problem for ODE's. In some respect, this method is analogous to the method of characteristics for two hyperbolic equations. The method is effectively applicable in all cases when the explicit expression for the Riemann-Green function of some linear second order PDE, resulting from the use of the hodograph method for the original equations, is known. One of the method advantages is the possibility of constructing a multi-valued solutions. Compared with the previous authors paper, in which, in particular, the shallow water equations are studied, here we investigate the case when the Riemann-Green function can be represent as the sum of the terms each of them is a product of two multipliers depended on different variables. The numerical results for zonal electrophoresis equations are presented. For computing the different initial data (periodic, wave packet, the Gaussian distribution) are used.
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.
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.
Fluid equations in the presence of electron cyclotron current drive
Jenkins, Thomas G.; Kruger, Scott E. [Tech-X Corporation, 5621 Arapahoe Avenue, Boulder, Colorado 80303 (United States)
2012-12-15T23:59:59.000Z
Two-fluid equations, which include the physics imparted by an externally applied radiofrequency source near electron cyclotron resonance, are derived in their extended magnetohydrodynamic forms using the formalism of Hegna and Callen [Phys. Plasmas 16, 112501 (2009)]. The equations are compatible with the closed fluid/drift-kinetic model developed by Ramos [Phys. Plasmas 17, 082502 (2010); 18, 102506 (2011)] for fusion-relevant regimes with low collisionality and slow dynamics, and they facilitate the development of advanced computational models for electron cyclotron current drive-induced suppression of neoclassical tearing modes.
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.
2+1 dimensional solution of Einstein Cartan equations
M. Hortacsu; H. T. Ozcelik; N. Ozdemir
2008-07-28T23:59:59.000Z
In this work a static solution of Einstein-Cartan (EC) equations in 2+1 dimensional space-time is given by considering classical spin-1/2 field as external source for torsion of the space-time. Here, the torsion tensor is obtained from metricity condition for the connection and the static spinor field is determined as the solution of Dirac equation in 2+1 spacetime with non-zero cosmological constant and torsion. The torsion itself is considered as a non-dynamical field.
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.
Probing the softest region of the nuclear equation of state
Li, Ba; Ko, Che Ming.
1998-01-01T23:59:59.000Z
th s Ma l y t lead the throug RAPID COMMUNICATIONS PHYSICAL REVIEW C SEPTEMBER 1998VOLUME 58, NUMBER 3 model ART @11#, which treats consistently the final freeze- out. The possibility of describing the main features of lattice QCD phase...-2813/98/58~3!/1382~3!/$15.00 e nuclear equation of state d C. M. Ko A&M University, College Station, Texas 77843 y 1998! for baryons is introduced in order to generate a soft recent lattice QCD calculations of baryon-free matter , we find that although this equation...
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.
On the Equation of State of the Gluon Plasma
Zwanziger, Daniel [New York University, New York, NY 10003 (United States)
2007-02-27T23:59:59.000Z
We consider a local, renormalizable, BRST-invariant action for QCD in Coulomb gauge that contains auxiliary bose and fermi ghost fields. It possess a non-perturbative vacuum that spontaneously breaks BRST-invariance. The vacuum condition leads to a gap equation that introduces a mass scale. Calculations are done to one-loop order in a perturbative expansion about this vacuum. They are free of the finite-T infrared divergences found by Linde and which occur in the order g6 corrections to the Stefan-Boltzmann equation of state. We obtain a finite result for these corrections.
Efficiency of Carnot Cycle with Arbitrary Gas Equation of State
Paulus C. Tjiang; Sylvia H. Sutanto
2006-03-27T23:59:59.000Z
The derivation of the efficiency of Carnot cycle is usually done by calculating the heats involved in two isothermal processes and making use of the associated adiabatic relation for a given working substance's equation of state, usually the ideal gas. We present a derivation of Carnot efficiency using the same procedure with Redlich-Kwong gas as working substance to answer the calculation difficulties raised by Agrawal and Menon. We also show that using the same procedure, the Carnot efficiency may be derived regardless of the functional form of the gas equation of state.
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.
Evolution equation of entanglement for multi-qubit systems
Michael Siomau; Stephan Fritzsche
2010-11-24T23:59:59.000Z
We discuss entanglement evolution of a multi-qubit system when one of its qubits is subjected to a general noisy channel. For such a system, an evolution equation of entanglement for a lower bound for multi-qubit concurrence is derived. Using this evolution equation, the entanglement dynamics of an initially mixed three-qubit state composed of a GHZ and a W state is analyzed if one of the qubits is affected by a phase, an amplitude or a generalized amplitude damping channel.
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.
A new vapor pressure equation originating at the critical point
Nuckols, James William
1976-01-01T23:59:59.000Z
- tence curve has been developed from critical scaling theory. The agreement between published vapor pressures and vapor pressures predicted by this equation is very good, especially in the critical region where many other vapor pressure equations fail... vapor pressure data f' or Ar, N2, 02H6, and H20, w1th the parameters ai to a being determined by an unweighted least squares curve 5 fit. The method of least squares has been described adequately elsewhere, e. g. Wylie (1966), and the theory w111...
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
A Block-Based Parallel Adaptive Scheme for Solving the 4D Vlasov Equation
Genaud, Stéphane
phenomena in plasma physics such as controlled thermonuclear fusion. This equation is defined in the phase
Jozef Klacka
2002-01-07T23:59:59.000Z
Relativistically covariant form of equation of motion for real particle (body) under the action of electromagnetic radiation is derived. Equation of motion in the proper frame of the particle uses the radiation pressure cross section 3 $\\times$ 3 matrix. Obtained covariant equation of motion is compared with another covariant equation of motion which was presented more than one year ago.
Math 314 Boundary Value Problems Spring 2008 Elementary Partial Differential Equations
Muraki, David J.
worksheet. Textbook: Applied Partial Differential Equations, DuChateau & Zachmann, Dover. Prerequisites
ERROR ESTIMATES FOR A TIME DISCRETIZATION METHOD FOR THE RICHARDS' EQUATION
Eindhoven, Technische Universiteit
. The continuity condition t() + · (q) = 0 combined with Darcy law (1.1) leads to Richards' equation (1.2) tERROR ESTIMATES FOR A TIME DISCRETIZATION METHOD FOR THE RICHARDS' EQUATION IULIU SORIN POP' equation. Written in its saturation-based form, this nonlinear para- bolic equation models water flow
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
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
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.
Surface plasmon for graphene in the Dirac equation model
M. Bordag
2012-12-09T23:59:59.000Z
We consider single-layer plane graphene with electronic excitations described by the Dirac equation. Using a known representation of the polarization tensor in terms of the spinor loop we show the existence of surface modes, i.e., of undamped in time excitations of the \\elm field, propagating along the graphene. These show up in the TE polarization and exist at zero temperature.
Group classification of heat conductivity equations with a nonlinear source
Zhdanov, Renat
Group classification of heat conductivity equations with a nonlinear source R.Z. Zhdanov Institute. It is shown that there are three, seven, twenty eight and twelve inequivalent classes of partial differential to the class under study and admitting symmetry group of the dimension higher than four is locally equivalent
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
Chaos expansion of heat equations with white noise potentials
Hu, Yaozhong
2002-02-01T23:59:59.000Z
The asymptotic behavior as t --> infinity of the solution to the following stochastic heat equations [GRAPHICS] is investigated, where w is a space-time white noise or a space white noise. The use of lozenge means that the stochastic integral of 10...
On the WDVV equations in five-dimensional gauge theories
L. K. Hoevenaars; R. Martini
2003-01-15T23:59:59.000Z
It is well-known that the perturbative prepotentials of four-dimensional N=2 supersymmetric Yang-Mills theories satisfy the generalized WDVV equations, regardless of the gauge group. In this paper we study perturbative prepotentials of the five-dimensional theories for some classical gauge groups and determine whether or not they satisfy the WDVV system.
Multiple solutions of CCD equations for PPP model of benzene
Podeszwa, R; Jankowski, K; Rubiniec, K; Podeszwa, Rafa{\\l}; Stolarczyk, Leszek Z.; Jankowski, Karol; Rubiniec, Krzysztof
2002-01-01T23:59:59.000Z
To gain some insight into the structure and physical significance of the multiple solutions to the coupled-cluster doubles (CCD) equations corresponding to the Pariser-Parr-Pople (PPP) model of cyclic polyenes, complete solutions to the CCD equations for the A^{-}_{1g} states of benzene are obtained by means of the homotopy method. By varying the value of the resonance integral beta from -5.0 eV to -0.5 eV, we cover the so-called weakly, moderately, and strongly correlated regimes of the model. For each value of beta 230 CCD solutions are obtained. It turned out, however, that only for a few solutions a correspondence with some physical states can be established. It has also been demonstrated that, unlike for the standard methods of solving CCD equations, some of the multiple solutions to the CCD equations can be attained by means of the iterative process based on Pulay's direct inversion in the iterative subspace (DIIS) approach.
FREQUENCY SHAPED LINEAR OPTIMAL CONTROL WXTH TRANSFER FUNCTION RICCATI EQUATIONS*
Moore, John Barratt
and numerical tool in optimal control problems associated with linear systems having state space descriptions optimal controllers for known multivariable linear stochastic systems. There are some inherent robustnessFREQUENCY SHAPED LINEAR OPTIMAL CONTROL WXTH TRANSFER FUNCTION RICCATI EQUATIONS* John B. Moore** D
SESAME equation of state number 8020: Polyetheretherketone (PEEK)
Boettger, J.C.; Johnson, J.D.
1993-12-01T23:59:59.000Z
A new SESAME equation of state (EOS) for the polymer polyetheretherketone (PEEK) has been generated using the computer program GRIZZLY. This new EOS has been added to the SESAME EOS library as material number 8020. A few general guidelines for estimating the thermodynamic parameters for polymers needed to generate an EOS with GRIZZLY are suggested.
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
Reducing Equational Theories for the Decision of Static Equivalence #
Treinen, Ralf - Laboratoire Preuves, Programmes et SystÃ¨mes, UniversitÃ© Paris 7
Reducing Equational Theories for the Decision of Static Equivalence # Steve Kremer 1 , Antoine, CNRS, France Abstract. Static equivalence is a well established notion of indistinÂ guishability of sequences of terms which is useful in the symbolic analysis of cryptographic protocols. Static equivalence
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
Collective perspective on advances in Dyson-Schwinger Equation QCD
Adnan Bashir; Lei Chang; Ian C. Cloet; Bruno El-Bennich; Yu-xin Liu; Craig D. Roberts; Peter C. Tandy
2012-01-16T23:59:59.000Z
We survey contemporary studies of hadrons and strongly interacting quarks using QCD's Dyson-Schwinger equations, addressing: aspects of confinement and dynamical chiral symmetry breaking; the hadron spectrum; hadron elastic and transition form factors, from small- to large-Q^2; parton distribution functions; the physics of hadrons containing one or more heavy quarks; and properties of the quark gluon plasma.
A Note Basis Properties for Fractional Hydrogen Atom Equation
E. Bas; F. Metin
2013-07-24T23:59:59.000Z
In this paper, spectral analysis of fractional Sturm Liouville problem defined on (0,1], having the singularity of type at zero and research the fundamental properties of the eigenfunctions and eigenvalues for the operator. We show that the eigenvalues and eigenfunctions of the problem are real and orthogonal, respectively. Furthermore,we give some important theorems and lemmas for fractional hydrogen atom equation.
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.
Alternative Discrete Energy Solutions to the Free Particle Dirac Equation
Brennan, Thomas Edward
2011-01-01T23:59:59.000Z
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.
Fast numerical treatment of nonlinear wave equations by spectral methods
Skjaeraasen, Olaf [ProsTek, Institute for Energy Technology, P.O. Box 40, N-2027 Kjeller (Norway); Robinson, P. A. [School of Physics, University of Sydney, New South Wales 2006 (Australia); Newman, D. L. [Center for Integrated Plasma Studies, University of Colorado at Boulder, Boulder, Colorado 80309 (United States)
2011-02-15T23:59:59.000Z
A method is presented that accelerates spectral methods for numerical solution of a broad class of nonlinear partial differential wave equations that are first order in time and that arise in plasma wave theory. The approach involves exact analytical treatment of the linear part of the wave evolution including growth and damping as well as dispersion. After introducing the method for general scalar and vector equations, we discuss and illustrate it in more detail in the context of the coupling of high- and low-frequency plasma wave modes, as modeled by the electrostatic and electromagnetic Zakharov equations in multiple dimensions. For computational efficiency, the method uses eigenvector decomposition, which is particularly advantageous when the wave damping is mode-dependent and anisotropic in wavenumber space. In this context, it is shown that the method can significantly speed up numerical integration relative to standard spectral or finite difference methods by allowing much longer time steps, especially in the limit in which the nonlinear Schroedinger equation applies.
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
Numerical treatment of interfaces for second-order wave equations
F. Parisi; M. Cécere; M. Iriondo; O. Reula
2014-06-12T23:59:59.000Z
In this article we develop a numerical scheme to deal with interfaces between touching numerical grids when solving the second-order wave equation. We show that it is possible to implement an interface scheme of "penalty" type for the second-order wave equation, similar to the ones used for first-order hyperbolic and parabolic equations, and the second-order scheme used by Mattsson et al (2008). These schemes, known as SAT schemes for finite difference approximations and penalties for spectral ones, and ours share similar properties but in our case one needs to pass at the interface a smaller amount of data than previously known schemes. This is important for multi-block parallelizations in several dimensions, for it implies that one obtains the same solution quality while sharing among different computational grids only a fraction of the data one would need for a comparable (in accuracy) SAT or Mattsson et al.'s scheme. The semi-discrete approximation used here preserves the norm and uses standard finite-difference operators satisfying summation by parts. For the time integrator we use a semi-implicit IMEX Runge-Kutta method. This is crucial, since the explicit Runge-Kutta method would be impractical given the severe restrictions that arise from the stiff parts of the equations.
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
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.
RESOLVENT OPERATORS AND WEAK SOLUTIONS OF INTEGRODIFFERENTIAL EQUATIONS
Liu, James H.
, see [9]. Let u be the internal energy and f be the external heat with the heat flux q(t, x) = -Eux., James Madison University, Harrisonburg, VA 22807 ABSTRACT Equations from heat conduction(A ), and , denotes the pairing between X and its dual X . The result also enables us to unify many concepts about
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
An Explicitly Correlated Wavelet Method for the Electronic Schroedinger Equation
Bachmayr, Markus [RWTH Aachen, Aachen Institute for Advanced Study in Computational Engineering Sciences, Schinkelstr. 2, 52062 Aachen (Germany)
2010-09-30T23:59:59.000Z
A discretization for an explicitly correlated formulation of the electronic Schroedinger equation based on hyperbolic wavelets and exponential sum approximations of potentials is described, covering mathematical results as well as algorithmic realization, and discussing in particular the potential of methods of this type for parallel computing.
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.
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.
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
An extended Dirac equation in noncommutative space-time
R. Vilela Mendes
2015-02-01T23:59:59.000Z
Stabilizing, by deformation, the algebra of relativistic quantum mechanics a non-commutative space-time geometry is obtained. The exterior algebra of this geometry leads to an extended massless Dirac equation which has both a massless and a large mass solution. The nature of the solutions is discussed, as well as the effects of coupling the two solutions.
An extended Dirac equation in noncommutative space-time
Mendes, R Vilela
2015-01-01T23:59:59.000Z
Stabilizing, by deformation, the algebra of relativistic quantum mechanics a non-commutative space-time geometry is obtained. The exterior algebra of this geometry leads to an extended massless Dirac equation which has both a massless and a large mass solution. The nature of the solutions is discussed, as well as the effects of coupling the two solutions.
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
Exact controllability of the superlinear heat equation 1 Statement of ...
2008-05-11T23:59:59.000Z
y Xr (0,T ;V')? C(1+ a ?)K [ F Lr (Lr (V) + y L2(H2)?C(H1)]. ... Assume p be a solution of (2.1) associated to p0 ? L2(?) and f ? L2(Q). ...... J.-P. Puel and E. Zuazua, Approximate controllability of the semilinear heat equation. Proc. Roy. Soc.
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 GPU Parallelized Spectral Method For Elliptic Equations.
2013-04-29T23:59:59.000Z
The method is applicable to elliptic equations with general boundary conditions in ... §Department of Mathematics, Purdue University, West Lafayette, IN 47907 ..... Computer. Physics Communications, 182(12):2454–2463, December 2011. ... International Journal for Numerical Methods in Engineering, 80(10):1295–1321,
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.
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
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
ON THE CONSTRUCTION OF DISCRETIZATIONS OF ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS
Doedel, Eusebius
on the occasion of his 60th Birthday Algorithmic aspects of a class of #12;nite element collocation methods of matching points and the number of collocation points for each #12;nite element. For linear equations. Keywords. Elliptic PDEs, Collocation Methods, Finite Di#11;erence Methods, Nested Dis- section, Finite
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
Infinite energy solutions of the twodimensional NavierStokes equations
Gallay, Thierry
Infinite energy solutions of the twoÂdimensional NavierÂStokes equations Thierry Gallay UniversitÂMartinÂd'Hâ??eres, France Thierry.Gallay@ujfÂgrenoble.fr Abstract These notes are based on a series of lectures delivered
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
VISCOSITY SOLUTIONS OF HAMILTONJACOBI EQUATIONS WITH DISCONTINUOUS COEFFICIENTS
VISCOSITY SOLUTIONS OF HAMILTONJACOBI EQUATIONS WITH DISCONTINUOUS COEFFICIENTS GIUSEPPE MARIA of viscosity solution to the Cauchy problem, and that the front tracking algorithm yields an L contractive semigroup. We define a viscosity solution by treating the discontinuities in the coefficients analogously
Global existence of reaction-diffusion equations over multiple domains
Ryan, John Maurice-Car
2006-04-12T23:59:59.000Z
Systems of semilinear parabolic differential equations arise in the modelling of many chemical and biological systems. We consider m component systems of the form ut = D?u + f (t, x, u) ?uk/?? =0 k =1, ...m where u(t, x...
Fractional Variational Iteration Method for Fractional Nonlinear Differential Equations
Guo-cheng Wu
2010-07-12T23:59:59.000Z
Recently, fractional differential equations have been investigated via the famous variational iteration method. However, all the previous works avoid the term of fractional derivative and handle them as a restricted variation. In order to overcome such shortcomings, a fractional variational iteration method is proposed. The Lagrange multipliers can be identified explicitly based on fractional variational theory.
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.
On the Fokker-Planck Equation for Stochastic Hybrid Systems
Boyer, Edmond
a natural framework for power sys- tems modeling and control, since it allows to simultaneously capture both in the field of power systems can be found in [6]. More generally, such models appear in various applicationOn the Fokker-Planck Equation for Stochastic Hybrid Systems: Application to a Wind Turbine Model
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%.
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.
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.
Combinatorial Dyson-Schwinger equations in noncommutative field theory
Adrian Tanasa; Dirk Kreimer
2009-07-13T23:59:59.000Z
We give here the Hopf algebra structure describing the noncommutative renormalization of a recently introduced translation-invariant model on Moyal space. We define Hochschild one-cocyles $B_+^\\gamma$ which allows us to write down the combinatorial Dyson-Schwinger equations for noncommutative quantum field theory. One- and two-loops examples are explicitly worked out.
SINGULAR FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND EMISSIONS DERIVATIVES
Carmona, Rene
SINGULAR FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND EMISSIONS DERIVATIVES REN´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
Poisson-Nernst-Planck equations in a ball
Z. Schuss J. Cartailler; D. Holcman
2015-05-07T23:59:59.000Z
The Poisson Nernst-Planck equations for charge concentration and electric potential in a ball is a model of electro-diffusion of ions in the head of a neuronal dendritic spine. We study the relaxation and the steady state when an initial charge of ions is injected into the ball. The steady state equation is similar to the Liouville-Gelfand-Bratu-type equation with the difference that the boundary condition is Neumann, not Dirichlet and there a minus sign in the exponent of the exponential term. The entire boundary is impermeable to the ions and the electric field satisfies the compatibility condition of Poisson's equation. We construct a steady radial solution and find that the potential is maximal in the center and decreases toward the boundary. We study the limit of large charge in dimension 1,2 and 3. For the case of a small absorbing window in the sphere, we find the escape rate of an ion from the steady density.
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...
On Numerical Methods for Hyperbolic Conservation Laws and Related Equations
Bürger, Raimund
A classical kinematical model of sedimentation of small equal-sized particles dispersed in a viscous fluidOn Numerical Methods for Hyperbolic Conservation Laws and Related Equations Modelling Sedimentation with nonlocal flux, systems of nonlinear conservation modelling the sedimentation of polydisperse suspensions
Performance of various computers using standard linear equations
Dongarra, J. (Univ. of Tennessee, TN (US))
1989-01-01T23:59:59.000Z
This report compares the performance of different computer systems in solving dense systems of linear equations. The comparison involves approximately one hundred computers, ranging from a CRAY Y-MP to scientific workstations such as the Apollo and Sun to IBM PCs.
Well-posedness of Einstein's Equation with Redshift Data
Christopher Winfield
2011-11-22T23:59:59.000Z
We study the solvability of a system of ordinary differential equations derived from null geodesics of the LTB metric with data given in terms of a so-called redshift parameter. Data is introduced along these geodesics by the luminosity distance function. We check our results with luminosity distance depending on the cosmological constant and with the well-known FRW model.
The sunrise amplitude equation applied to an Egyptian temple
Sparavigna, Amelia Carolina
2012-01-01T23:59:59.000Z
An equation, fundamental for solar energy applications, can be used to determine the sunrise amplitude at given latitude. It is therefore suitable for being applied to archaeoastronomical calculations concerning the orientation of towns, worship places and buildings. Here it is discussed the case of the Great Temple of Amarna, Egypt, oriented toward the sunrise on the winter solstice.
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.
Boltzmann Equation for Relativistic Neutral Scalar Field in Non-equilibrium Thermo Field Dynamics
Yuichi Mizutani; Tomohiro Inagaki
2011-03-18T23:59:59.000Z
A relativistic neutral scalar field is investigated on the basis of the Schwinger-Dyson equation in the non-equilibrium thermo field dynamics. A time evolution equation for a distribution function is obtained from a diagonalization condition for the Schwinger-Dyson equation. An explicit expression of the time evolution equation is calculated in the $\\lambda\\phi^4$ interaction model at the 2-loop level. The Boltzmann equation is derived for the relativistic scalar field. We set a simple initial condition and numerically solve the Boltzmann equation and show the time evolution of the distribution function and the relaxation time.
Numerical solutions to integral equations of the Fredholm type
Pullin, John Henry
1966-01-01T23:59:59.000Z
%Y ) RETURN AK~SIN(X+Y) RETURN AK~EXP( ABS(X Y)) RETURN AK~(SIN&X-Y })442/&X-Y) RETURN END PROGRAM TO CALCULATE SHIFTED CHEBYSHEV POLYNOMIALS SUBROUT I NE CHES &Me X ~ TM ) DI MENS I QN TM (2D ) IF(M 1)2&3 ~ 2 2 TM(1) = I ~ IF(M 2)4e5 ~ 4 4 TM&2... FUNCTION AK(XeY AN) GO TO &)o2o3)sN 1 AK&I ~ 3 ' +X+Y RETURN 2 AK~SIN&X+Y) RETURN 3 AK~X+Y RETVRN END C THIS FUNCTION CONTAINS THE MAIN FUNCTION OF THE INTEGRAL C EQUATIONS IF IT IS ZERO WE HAVE A HOMOGENEOVS EQUATIONS FUNCTION FOFX(N ~ X) GO...
Multipole matrix elements of Green function of Laplace equation
Karol Makuch; Przemys?aw Górka
2015-01-02T23:59:59.000Z
Multipole matrix elements of Green function of Laplace equation are calculated. The multipole matrix elements of Green function in electrostatics describe potential on a sphere which is produced by a charge distributed on the surface of a different (possibly overlapping) sphere of the same radius. The matrix elements are defined by double convolution of two spherical harmonics with the Green function of Laplace equation. The method we use relies on the fact that in the Fourier space the double convolution has simple form. Therefore we calculate the multipole matrix from its Fourier transform. An important part of our considerations is simplification of the three dimensional Fourier transformation of general multipole matrix by its rotational symmetry to the one-dimensional Hankel transformation.
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.
Multiphase weakly nonlinear geometric optics for Schrodinger equations
Rémi Carles; Eric Dumas; Christof Sparber
2009-02-17T23:59:59.000Z
We describe and rigorously justify the nonlinear interaction of highly oscillatory waves in nonlinear Schrodinger equations, posed on Euclidean space or on the torus. Our scaling corresponds to a weakly nonlinear regime where the nonlinearity affects the leading order amplitude of the solution, but does not alter the rapid oscillations. We consider initial states which are superpositions of slowly modulated plane waves, and use the framework of Wiener algebras. A detailed analysis of the corresponding nonlinear wave mixing phenomena is given, including a geometric interpretation on the resonance structure for cubic nonlinearities. As an application, we recover and extend some instability results for the nonlinear Schrodinger equation on the torus in negative order Sobolev spaces.
Dirac Equation on a Curved 2+1 Dimensional Hypersurface
Mehmet Ali Olpak
2011-12-22T23:59:59.000Z
Interest on 2 + 1 dimensional electron systems has increased considerably after the realization of novel properties of graphene sheets, in which the behaviour of electrons is effectively described by relativistic equations. Having this fact in mind, the following problem is studied in this work: when a spin 1/2 particle is constrained to move on a curved surface, is it possible to describe this particle without giving reference to the dimensions external to the surface? As a special case of this, a relativistic spin 1/2 particle which is constrained to move on a 2 + 1 dimensional hypersurface of the 3 + 1 dimensional Minkowskian spacetime is considered, and an effective Dirac equation for this particle is derived using the so-called thin layer method. Some of the results are compared with those obtained in a previous work by M. Burgess and B. Jensen.
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.
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.
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 integrable evolution equation for surface waves in deep water
R. Kraenkel; H. Leblond; M. A. Manna
2011-01-30T23:59:59.000Z
In order to describe the dynamics of monochromatic surface waves in deep water, we derive a nonlinear and dispersive system of equations for the free surface elevation and the free surface velocity from the Euler equations in infinite depth. From it, and using a multiscale perturbative methods, an asymptotic model for small-aspect-ratio waves is derived. The model is shown to be completely integrable. The Lax pair, the first conserved quantities as well as the symmetries are exhibited. Theoretical and numerical studies reveal that it supports periodic progressive Stokes waves which peak and break in finite time. Comparison between the limiting wave solution of the asymptotic model and classical irrotational results is performed.
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.
Generalized chaotic synchronization in coupled Ginzburg-Landau equations
Koronovskii, A. A., E-mail: alkor@nonlin.sgu.ru; Popov, P. V., E-mail: popovpv@nonlin.sgu.ru; Hramov, A. E. [Saratov State University (Russian Federation)], E-mail: aeh@nonlin.sgu.ru
2006-10-15T23:59:59.000Z
Generalized synchronization is analyzed in unidirectionally coupled oscillatory systems exhibiting spatiotemporal chaotic behavior described by Ginzburg-Landau equations. Several types of coupling between the systems are analyzed. The largest spatial Lyapunov exponent is proposed as a new characteristic of the state of a distributed system, and its calculation is described for a distributed oscillatory system. Partial generalized synchronization is introduced as a new type of chaotic synchronization in spatially nonuniform distributed systems. The physical mechanisms responsible for the onset of generalized chaotic synchronization in spatially distributed oscillatory systems are elucidated. It is shown that the onset of generalized chaotic synchronization is described by a modified Ginzburg-Landau equation with additional dissipation irrespective of the type of coupling. The effect of noise on the onset of a generalized synchronization regime in coupled distributed systems is analyzed.
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}.
Bains, Amrit Anoop Singh
2010-10-12T23:59:59.000Z
One of the primary reasons of the escalating rates of injuries and fatalities in the construction industry is the ever so complex, dynamic and continually changing nature of construction work. Use of cranes has become imperative to overcome...
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
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...
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.
Approximation of linear partial differential equations on spheres
Le Gia, Quoc Thong
2004-09-30T23:59:59.000Z
Subject: Mathematics iii ABSTRACT Approximation of Linear Partial Di®erential Equations on Spheres. (August 2003) Quoc Thong Le Gia, B.S., University of New South Wales; M.S., Texas A&M University Co{Chairs of Advisory Committee: Dr. Joseph D. Ward Dr... . . . . . . . . . . . . . . . . . 15 II INTERPOLATION ON SPHERES BY DILATED SBFs : : : : 16 A. Approximation theorems . . . . . . . . . . . . . . . . . . . 16 B. Locally supported basis functions on Rn+1 and Sn . . . . . 18 1. Compactly supported strictly positive de¯nite func- tions...
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.
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.
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.
Solving Chemical Master Equations by an Adaptive Wavelet Method
Jahnke, Tobias; Galan, Steffen [Universitaet Karlsruhe - TH, Fakultaet fuer Mathematik, Institut fuer Angewandte und Numerische Mathematik, Englerstr. 2, D-76128 Karlsruhe (Germany)
2008-09-01T23:59:59.000Z
Solving chemical master equations is notoriously difficult due to the tremendous number of degrees of freedom. We present a new numerical method which efficiently reduces the size of the problem in an adaptive way. The method is based on a sparse wavelet representation and an algorithm which, in each time step, detects the essential degrees of freedom required to approximate the solution up to the desired accuracy.
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.
Boundary Integral Equations and the Method of Boundary Elements
Tsynkov, Semyon V.
to consider the interior and exterior Dirichlet and Neumann boundary value problems for the Laplace equation: u 2u x2 1 + 2u x2 2 + 2u x2 3 = 0. Let be a bounded domain of the three-dimensional space R3 and exterior Dirichlet problems, respectively, and problems (13.1b) and (13.1d) are the interior and exterior
On nonlinearity implications and wind forcing in Hasselmann equation
Andrei, Pushkarev
2015-01-01T23:59:59.000Z
We discuss several experimental and theoretical techniques historically used for Hasselmann equation wind input terms derivation. We show that recently developed ZRP technique in conjunction with high-frequency damping without spectral peak dissipation allows to reproduce more than a dozen of fetch-limited field experiments. Numerical simulation of the same Cauchy problem for different wind input terms has been performed to discuss nonlinearity implications as well as correspondence to theoretical predictions.
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.
Notes 01. The fundamental assumptions and equations of lubrication theory
San Andres, Luis
2009-01-01T23:59:59.000Z
for unsteady or transient motions ? Journal angular speed (rad/s) NOTES 1. THE FUNDAMENTAL ASSUMPTIONS IN HYDRODYNAMIC LUBRICATION ? Dr. Luis San Andr?s (2009) 2 Fluid flow in a general physical domain is governed by the principles of: a) conservation... of the runner surface. For example, in journal bearings U * =?R J where ? is the journal angular speed in rad/s. Substitution of the dimensionless variables into the continuity equation (1) renders the following expression 0...
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.
Wave equation analysis of pile driving in gravel
Lawson, William Dieterich
1984-01-01T23:59:59.000Z
and gravel. The fundamental analysis procedure involves varying the soil damping parameter J to match measured static soil resistance and blowcount records. The analysis uses quake values determined by drawing a secant through a point corresponding to 25X... of the ultimate load on the load-deflection curves. For each selected pile, the J value that best correlates ultimate static resistance of the time of driving (calculated by the wave equation) and the measured ultimate static resistance from the load tests...
The Yamabe equation on complete manifolds with finite volume
Große, Nadine
2011-01-01T23:59:59.000Z
We prove the existence of a solution of the Yamabe equation on complete manifolds with finite volume and positive Yamabe invariant. In order to circumvent the standard methods on closed manifolds which heavily rely on global (compact) Sobolev embeddings we approximate the solution by eigenfunctions of certain conformal complete metrics. This also gives rise to a new proof of the well-known result for closed manifolds and positive Yamabe invariant.
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.
Physical interpretation of stochastic Schroedinger equations in cavity QED
Tarso B. L. Kist; M. Orszag; T. A. Brun; L. Davidovich
1998-05-11T23:59:59.000Z
We propose physical interpretations for stochastic methods which have been developed recently to describe the evolution of a quantum system interacting with a reservoir. As opposed to the usual reduced density operator approach, which refers to ensemble averages, these methods deal with the dynamics of single realizations, and involve the solution of stochastic Schr\\"odinger equations. These procedures have been shown to be completely equivalent to the master equation approach when ensemble averages are taken over many realizations. We show that these techniques are not only convenient mathematical tools for dissipative systems, but may actually correspond to concrete physical processes, for any temperature of the reservoir. We consider a mode of the electromagnetic field in a cavity interacting with a beam of two- or three-level atoms, the field mode playing the role of a small system and the atomic beam standing for a reservoir at finite temperature, the interaction between them being given by the Jaynes-Cummings model. We show that the evolution of the field states, under continuous monitoring of the state of the atoms which leave the cavity, can be described in terms of either the Monte Carlo Wave-Function (quantum jump) method or a stochastic Schr\\"odinger equation, depending on the system configuration. We also show that the Monte Carlo Wave-Function approach leads, for finite temperatures, to localization into jumping Fock states, while the diffusion equation method leads to localization into states with a diffusing average photon number, which for sufficiently small temperatures are close approximations to mildly squeezed states.
A new iterative approach to solving the transport equation
Maslowski Olivares, Alexander Enrique
2009-05-15T23:59:59.000Z
and Dr. Ed Larsen for their insightful discussions on slab geometry Caseology and its extension to multiple dimensions. The final stage of this research was completed at Lawrence Livermore National Laboratory. I thank Dr. Patrick Brantley and AX... arrowrightnosp . Although this model has few physical applications in itself, it is consistent with the transport equation for a single group belonging to the multi-group discretization (Lewis and Miller.) Thus, an algorithm that is scalable in space an angle...
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.
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.
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.
Algebraic multigrid for stabilized finite element discretizations of the Navier Stokes equation
Okusanya, Tolulope Olawale, 1972 -
2002-01-01T23:59:59.000Z
A multilevel method for the solution of systems of equations generated by stabilized Finite Element discretizations of the Euler and Navier Stokes equations on generalized unstructured grids is described. The method is ...
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.
mKdV equation approach to zero energy states of graphene
C. -L. Ho; P. Roy
2015-07-15T23:59:59.000Z
We utilize the relation between soliton solutions of the mKdV and the combined mKdV-KdV equation and the Dirac equation to construct electrostatic fields which yield exact zero energy states of graphene.
1 MA 15200 Lesson 17 Section 1.6 I Solving Polynomial Equations ...
charlotb
2011-02-18T23:59:59.000Z
Power Property for equations: When both sides of an equation are raised to .... Ex 14: For each planet in our solar system, its year is the time it takes the planet to.
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
Volume-averaged macroscopic equation for fluid flow in moving porous media
Wang, Liang; Guo, Zhaoli; Mi, Jianchun
2014-01-01T23:59:59.000Z
Darcy's law and the Brinkman equation are two main models used for creeping fluid flows inside moving permeable particles. For these two models, the time derivative and the nonlinear convective terms of fluid velocity are neglected in the momentum equation. In this paper, a new momentum equation including these two terms are rigorously derived from the pore-scale microscopic equations by the volume-averaging method, which can reduces to Darcy's law and the Brinkman equation under creeping flow conditions. Using the lattice Boltzmann equation method, the macroscopic equations are solved for the problem of a porous circular cylinder moving along the centerline of a channel. Galilean invariance of the equations are investigated both with the intrinsic phase averaged velocity and the phase averaged velocity. The results demonstrate that the commonly used phase averaged velocity cannot serve as the superficial velocity, while the intrinsic phase averaged velocity should be chosen for porous particulate systems.
Royden, Leigh H.
Erosion by bedrock river channels is commonly modeled with the stream power equation. We present a two-part approach to solving this nonlinear equation analytically and explore the implications for evolving river profiles. ...
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.
On the applicability of Sato's equation to capacitative radio frequency sheaths
J. Balakrishnan; G. R. Nagabhushana
2003-10-08T23:59:59.000Z
We show that the time dependent version of Sato's equation, when applied to capacitative rf sheaths is no longer independent of the electric field of the space charge, and discuss the use of the equation for a specific sheath model.
Global Solution to Enskog Equation with External Force in Infinite Vacuum
Zhenglu Jiang
2008-05-31T23:59:59.000Z
We first give hypotheses of the bicharacteristic equations corresponding to the Enskog equation with an external force. Since the collision operator of the Enskog equation is more complicated than that of the Boltzmann equation, these hypotheses are more complicated than those given by Duan et al. for the Boltzmann equation. The hypotheses are very related to collision of particles of moderately or highly dense gases along the bicharacteristic curves and they can be used to make the estimation of the so-called gain and loss integrals of the Enskog integral equation. Then, by controlling these integrals, we show the existence and uniqueness of the global mild solution to the Enskog equation in an infinite vacuum for moderately or highly dense gases. Finally, we make some remarks on the locally Lipschitz assumption of the collision factors in the Enskog equation.
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.
A Block-Based Parallel Adaptive Scheme for Solving the 4D Vlasov Equation
Genaud, Stéphane
such as controlled thermonuclear fusion. This equation is defined in the phase space, i.e., the position and velocity
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
Longtime asymptotics of the NavierStokes and vorticity equations on R 3
Gallay, Thierry
LongÂtime asymptotics of the NavierÂStokes and vorticity equations on R 3 Thierry Gallay Universit
Xueke Pu; Boling Guo
2015-04-21T23:59:59.000Z
The hydrodynamic equations with quantum effects are studied in this paper. First we establish the global existence of smooth solutions with small initial data and then in the second part, we establish the convergence of the solutions of the quantum hydrodynamic equations to those of the classical hydrodynamic equations. The energy equation is considered in this paper, which added new difficulties to the energy estimates, especially to the selection of the appropriate Sobolev spaces.
On rotating star solutions to non-isentropic Euler-Poisson equations
Yilun Wu
2014-11-04T23:59:59.000Z
This paper investigates rotating star solutions to the Euler-Poisson equations with a non-isentropic equation of state. As a first step, the equation for gas density with a prescribed entropy and angular velocity distribution is studied. The resulting elliptic equation is solved either by the method of sub and supersolutions or by a variational method, depending on the value of the adiabatic index. The reverse problem of determining angular velocity from gas density is also considered.
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
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 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
A wideband fast multipole method for the Helmholtz equation in three dimensions
Martinsson, Gunnar
A wideband fast multipole method for the Helmholtz equation in three dimensions Hongwei Cheng of the Fast Multipole Method for the Helmholtz equation in three dimensions. It uni- fies previously existing Inc. All rights reserved. MSC: 65R99; 78A45 Keywords: Helmholtz equation; Fast multipole method
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
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
FIRST-ORDER ENTROPIES FOR THE DERRIDA-LEBOWITZ-SPEER-SPOHN EQUATION
Jüngel, Ansgar
FIRST-ORDER ENTROPIES FOR THE DERRIDA-LEBOWITZ-SPEER-SPOHN EQUATION ANSGAR J¨UNGEL AND INGRID first derived by Derrida, Lebowitz, Speer, and Spohn [8, 9], and we shall therefore refer to (1) as the Derrida-Lebowitz-Speer-Spohn equation or simply the DLSS equation. Derrida et al. studied in [8, 9
THE DERRIDA-LEBOWITZ-SPEER-SPOHN EQUATION: EXISTENCE, NON-UNIQUENESS, AND DECAY RATES OF THE
THE DERRIDA-LEBOWITZ-SPEER-SPOHN EQUATION: EXISTENCE, NON-UNIQUENESS, AND DECAY RATES,j=1 2 ij (u2 ij log u) = 0, u(0, ·) = u0, called the Derrida-Lebowitz-Speer-Spohn equation, Speer, and Spohn [11, 12], and we shall therefore refer to (1.1) as the DLSS equation. Derrida et al
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
Volume equations for New Mexico's pinyon-juniper dryland forests. Forest Service research paper
Chojnacky, D.C.
1994-01-01T23:59:59.000Z
Volume equations were developed to predict cubic volume for New Mexico's pinyon-juniper species. The volume equations estimate wood and bark of all aboveground bole, stem, and branch material with diameter 3.8 cm (1.5 inches) and larger. Use of the equations require diameter and height measurements.
COUPLING OF DARCY-FORCHHEIMER AND COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH HEAT TRANSFER
Paris-Sud XI, Université de
COUPLING OF DARCY-FORCHHEIMER AND COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH HEAT TRANSFER M. AMARA are respectively described by the Darcy-Forchheimer and the compressible Navier-Stokes equations, together coordinates and consisting of the Darcy- Forchheimer equation coupled with an exhaustive energy balance, has
Equal-order finite elements with local projection stabilization for the Darcy-Brinkman equations
Schieweck, Friedhelm
Equal-order finite elements with local projection stabilization for the Darcy-Brinkman equations M. Braack and F. Schieweck Mai 2010 Abstract For the Darcy-Brinkman equations, which model porous media: Porous media flow, Darcy-Brinkman equations, Stokes, equal-order finite elements, local projection
Cirpka, Olaf Arie
-flow region): Mass balance (porous medium, given by Darcy`s law): Transport equation, Lagrange multiplierCoupling concept based on thermodynamic equilibrium using the mortar method: Stokes equation (free-Laplace equation is used to determine which tubes are filled with water: Coupling concept for the one-phase micro
Improved approximation of the Brinkman equation using a lattice Boltzmann method
Bentz, Dale P.
conditions. The Brinkman equation3 is a generalization of Darcy's law that facilitates the matchingImproved approximation of the Brinkman equation using a lattice Boltzmann method by Nicos S. Martys;Improved approximation of the Brinkman equation using a lattice Boltzmann method Nicos S. Martys Building
A mechanical picture of fractional-order Darcy equation Luca Deseri a,b,c,d
Deseri, Luca
A mechanical picture of fractional-order Darcy equation Luca Deseri a,b,c,d , Massimiliano Zingales: Anomalous diffusion Porous media Darcy equation Fractional derivatives Anomalous scaling a b s t r a c of the particle flow. The transport equation, formally analogous to the Fick relation is the so-called Darcy
Eindhoven, Technische Universiteit
. Here u denotes the water saturation. Equation (1.6) follows by combining Darcy's law, the massNumerical schemes for a pseudo-parabolic Burgers equation: discontinuous data and long Burgers'type equation that is extended with a third-order term containing mixed derivatives in space
Mortar finite element discretization of a model coupling Darcy and Stokes equations
Boyer, Edmond
Mortar finite element discretization of a model coupling Darcy and Stokes equations by C. Bernardi1 flowing on a homogeneous porous ground, we consider a system where the Darcy and Stokes equations´erons un syst`eme o`u les ´equations de Darcy et de Stokes sont coupl´ees par des conditions de raccord
A priori and a posteriori analysis of finite volume discretizations of Darcy's equations
Achdou, Yves
A priori and a posteriori analysis of finite volume discretizations of Darcy's equations by Y of some finite volume disÂ cretizations of Darcy's equations. We propose two finite volume schemesâ??eÂ tisation par volumes finis des â??equations de Darcy. Nous proposons deux schâ??emas de volÂ umes finis sur des
Mortar finite element discretization of the time dependent nonlinear Darcy's equations
Paris-Sud XI, Université de
Mortar finite element discretization of the time dependent nonlinear Darcy's equations by Karima variations have been handled in [1] and [6], while time-dependent Darcy's equations have been studied in [5 equations model the flow in a porous medium, but underground porous media are most often nonhomogeneous
A SYMMETRIC NODAL CONSERVATIVE FINITE ELEMENT METHOD FOR THE DARCY EQUATION
Mottram, Nigel
A SYMMETRIC NODAL CONSERVATIVE FINITE ELEMENT METHOD FOR THE DARCY EQUATION GABRIEL R. BARRENECHEA results. 1. Introduction The Darcy equation arising in a porous media field belongs to the family of mixed element methods [23, 21, 13, 9, 10] the range of possibilities to tackle the Darcy equation has increased
J. Differential Equations 245 (2008) 18191837 www.elsevier.com/locate/jde
Daripa, Prabir
2008-01-01T23:59:59.000Z
are governed by linear field equations, namely Darcy's law and incompressibility condition. In two for saturation (the volume fraction of water in oil at the microscopic level). This is a nonlinear equation which. The nonlinear field equations of immisci- ble displacement of oil by water in porous media admit soluti
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
Lie group classifications and exact solutions for time-fractional Burgers equation
Guo-cheng Wu
2010-11-16T23:59:59.000Z
Lie group method provides an efficient tool to solve nonlinear partial differential equations. This paper suggests a fractional Lie group method for fractional partial differential equations. A time-fractional Burgers equation is used as an example to illustrate the effectiveness of the Lie group method and some classes of exact solutions are obtained.
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.
On the Interior Boundary-Value Problem for the Stationary Povzner Equation with Hard
Panferov, Vladislav
oteborg University, S-412 96 Goteborg, Sweden current address: Department of Mathematics and Statistics, University the `natural' a priori bounds for solutions and the structure of the equation. More speci#12;cally equation for a dense gas of hard spheres [3, 32, 33]. The Povzner equation is another closely related model
On the Interior Boundary-Value Problem for the Stationary Povzner Equation with Hard
Panferov, Vladislav
¨oteborg University, S-412 96 G¨oteborg, Sweden current address: Department of Mathematics and Statistics, University to that equation arise because of the discrepancy between the `natural' a priori bounds for solutions. One such model is the Enskog equation for a dense gas of hard spheres [3,32,33]. The Povzner equation
Fractional advection-dispersion equations for1 modeling transport at the Earth surface2
Bäumer, Boris
Fractional advection-dispersion equations for1 modeling transport at the Earth surface2 Rina partial differential equations such as the advection-dispersion equation12 (ADE) begin with assumptions biomechanical transport and mixing29 by bioturbation, and the transport of sediment particles and sediment
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
Three regularization models of the Navier-Stokes equations
J. Pietarila Graham; Darryl Holm; Pablo Mininni; Annick Pouquet
2008-01-11T23:59:59.000Z
We determine how the differences in the treatment of the subfilter-scale physics affect the properties of the flow for three closely related regularizations of Navier-Stokes. The consequences on the applicability of the regularizations as SGS models are also shown by examining their effects on superfilter-scale properties. Numerical solutions of the Clark-alpha model are compared to two previously employed regularizations, LANS-alpha and Leray-alpha (at Re ~ 3300, Taylor Re ~ 790) and to a DNS. We derive the Karman-Howarth equation for both the Clark-alpha and Leray-alpha models. We confirm one of two possible scalings resulting from this equation for Clark as well as its associated k^(-1) energy spectrum. At sub-filter scales, Clark-alpha possesses similar total dissipation and characteristic time to reach a statistical turbulent steady-state as Navier-Stokes, but exhibits greater intermittency. As a SGS model, Clark reproduces the energy spectrum and intermittency properties of the DNS. For the Leray model, increasing the filter width decreases the nonlinearity and the effective Re is substantially decreased. Even for the smallest value of alpha studied, Leray-alpha was inadequate as a SGS model. The LANS energy spectrum k^1, consistent with its so-called "rigid bodies," precludes a reproduction of the large-scale energy spectrum of the DNS at high Re while achieving a large reduction in resolution. However, that this same feature reduces its intermittency compared to Clark-alpha (which shares a similar Karman-Howarth equation). Clark is found to be the best approximation for reproducing the total dissipation rate and the energy spectrum at scales larger than alpha, whereas high-order intermittency properties for larger values of alpha are best reproduced by LANS-alpha.
The Runge-Kutta equations through the eighth order
Smitherman, John Alvis
1966-01-01T23:59:59.000Z
where, thus far, R. , a. and b, . are arbitrary. We must determine 1 1 i, j their values such that a sum of n terms on the right hand side of (2. 11) should agree with the Taylor's expansion (2. 7) up to and n including the term of order h . We begin... of Differential Equations A Fourth Order System by Conventional Methods III. DISCUSSION OF BUTCHER'S METHOD Elementary Differentials Elementary Weights 8 11 BIBLIOGRAPHY APPENDIX A 17 Summation Formulas APPENDIX B 36 Seventh Order Explicit Formulas...
A first order iteration process for simultaneous equations
Stewart, Wallace Franklin
1966-01-01T23:59:59.000Z
let n n n (5a) g . (X) = (d(X) /Sp(J (X) J(X) I ] I f . (X) f . (E) Ri Rj t and let (3b) G(X) = [g (X) ], 1& i, j &n Then clearly (see (4)) X ? Y ? H(K) = (I ? G(X))(X - Y) The only use we want of the above in the present section is to show...A FIRST ORDER INTERATION PROCESS FOR SIMULTANEOUS EQUATIONS A Thesis WALLACE FRANKLIN STEWART Approved as to style and content by; (Chairman of Committee) F. c (Head of Depart n (Mem er) Q D~ (Member) May, 1966 4 5 7 2 8 0...
Numerical studies of the stochastic Korteweg-de Vries equation
Lin Guang [Division of Applied Mathematics, Brown University, 182 George Street, Box F, Providence, RI 02912 (United States); Grinberg, Leopold [Division of Applied Mathematics, Brown University, 182 George Street, Box F, Providence, RI 02912 (United States); Karniadakis, George Em [Division of Applied Mathematics, Brown University, 182 George Street, Box F, Providence, RI 02912 (United States)]. E-mail: gk@dam.brown.edu
2006-04-10T23:59:59.000Z
We present numerical solutions of the stochastic Korteweg-de Vries equation for three cases corresponding to additive time-dependent noise, multiplicative space-dependent noise and a combination of the two. We employ polynomial chaos for discretization in random space, and discontinuous Galerkin and finite difference for discretization in physical space. The accuracy of the stochastic solutions is investigated by comparing the first two moments against analytical and Monte Carlo simulation results. Of particular interest is the interplay of spatial discretization error with the stochastic approximation error, which is examined for different orders of spatial and stochastic approximation.
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.
Parametrization of the equation of state and the expanding universe
W. F. Kao
2006-07-10T23:59:59.000Z
The structure of the equation of state $\\omega$ could be very complicate in nature while a few linear models have been successful in cosmological predictions. Linear models are treated as leading approximation of a complete Taylor series in this paper. If the power series converges quickly, one can freely truncate the series order by order. Detailed convergent analysis on the choices of the expansion parameters is presented in this paper. The related power series for the energy density function, the Hubble parameter and related physical quantities of interest are also computed in this paper.
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.
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.
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.
Bootstrap and momentum transfer dependence in small x evolution equations
G. Chachamis; A. Sabio Vera; C. Salas
2012-11-27T23:59:59.000Z
Using Monte Carlo integration techniques, we investigate running coupling effects compatible with the high energy bootstrap condition to all orders in the strong coupling in evolution equations valid at small values of Bjorken x in deep inelastic scattering. A model for the running of the coupling with analytic behavior in the infrared region and compatible with power corrections to jet observables is used. As a difference to the fixed coupling case, where the momentum transfer acts as an effective strong cut-off of the diffusion to infrared scales, in our running coupling study the dependence on the momentum transfer is much milder.
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...
Solution of One-dimensional Dirac Equation via Poincare Map
Hocine Bahlouli; El Bouazzaoui Choubabi; Ahmed Jellal
2011-05-24T23:59:59.000Z
We solve the general one-dimensional Dirac equation using a "Poincare Map" approach which avoids any approximation to the spacial derivatives and reduces the problem to a simple recursive relation which is very practical from the numerical implementation point of view. To test the efficiency and rapid convergence of this approach we apply it to a vector coupling Woods--Saxon potential, which is exactly solvable. Comparison with available analytical results is impressive and hence validates the accuracy and efficiency of this method.
Factorization of Dirac Equation and Graphene Quantum Dot
Youness Zahidi; Ahmed Jellal; Hocine Bahlouli; Mohammed El Bouziani
2014-05-14T23:59:59.000Z
We consider a quantum dot described by a cylindrically symmetric 2D Dirac equation. The potentials representing the quantum dot are taken to be of different types of potential configuration, scalar, vector and pseudo-scalar to enable us to enrich our study. Using various potential configurations, we found that in the presence of a mass term an electrostatically confined quantum dot can accommodate true bound states, which is in agreement with previous work. The differential cross section associated with one specific potential configuration has been computed and discussed as function of the various potential parameters.