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...
Approximation Methods for Pricing Problems under the Nested Logit Model with Price Bounds
Rusmevichientong, Paat
Approximation Methods for Pricing Problems under the Nested Logit Model with Price Bounds W@orie.cornell.edu September 5, 2013 Abstract We consider two variants of a pricing problem under the nested logit model. In the first variant, the set of products offered to customers is fixed and we want to determine the prices
Estimating long-term world coal production with logit and probit transforms David Rutledge
Low, Steven H.
Estimating 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 Coal resources Coal production estimates IPCC Logistic model Cumulative normal model An estimate
Phung, Kim-dang.- Le Laboratoire de MathÃ©matiques
I: Heat equation II: SchrÃ¶dinger equation III: Wave equation IV: Radiative transfer equation;I: Heat equation II: SchrÃ¶dinger equation III: Wave equation IV: Radiative transfer equation QUCP: Heat equation II: SchrÃ¶dinger equation III: Wave equation IV: Radiative transfer equation QUCP
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
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.
Separable Differential Equations
PRETEX (Halifax NS) #1 1054 1999 Mar 05 10:59:16
2010-01-20T23:59:59.000Z
Feb 16, 2007 ... preceding differential equation and several mem- bers of the given family of curves. Describe the family of orthogonal trajectories. 34. Consider ...
First order differential equations
Samy Tindel
2015-09-29T23:59:59.000Z
Chemical pollution example (2). Notation: Q(t) ? quantity of ... Initial velocity v0, upward. Air resistance negligible ... Air resistance neglected. Equation: v = ?g.
Integrating the Jacobian equation
Airton von Sohsten de Medeiros; Ráderson Rodrigues da Silva
2014-09-16T23:59:59.000Z
We show essentially that the differential equation $\\frac{\\partial (P,Q)}{\\partial (x,y)} =c \\in {\\mathbb C}$, for $P,\\,Q \\in {\\mathbb C}[x,y]$, may be "integrated", in the sense that it is equivalent to an algebraic system of equations involving the homogeneous components of $P$ and $Q$. Furthermore, the first equations in this system give explicitly the homogeneous components of $Q$ in terms of those of $P$. The remaining equations involve only the homogeneous components of $P$.
Sergei Kuksin; Alberto Maiocchi
2015-01-17T23:59:59.000Z
In this chapter we present a general method of constructing the effective equation which describes the behaviour of small-amplitude solutions for a nonlinear PDE in finite volume, provided that the linear part of the equation is a hamiltonian system with a pure imaginary discrete spectrum. The effective equation is obtained by retaining only the resonant terms of the nonlinearity (which may be hamiltonian, or may be not); the assertion that it describes the limiting behaviour of small-amplitude solutions is a rigorous mathematical theorem. In particular, the method applies to the three-- and four--wave systems. We demonstrate that different possible types of energy transport are covered by this method, depending on whether the set of resonances splits into finite clusters (this happens, e.g. in case of the Charney-Hasegawa-Mima equation), or is connected (this happens, e.g. in the case of the NLS equation if the space-dimension is at least two). For equations of the first type the energy transition to high frequencies does not hold, while for equations of the second type it may take place. In the case of the NLS equation we use next some heuristic approximation from the arsenal of wave turbulence to show that under the iterated limit "the volume goes to infinity", taken after the limit "the amplitude of oscillations goes to zero", the energy spectrum of solutions for the effective equation is described by a Zakharov-type kinetic equation. Evoking the Zakharov ansatz we show that stationary in time and homogeneous in space solutions for the latter equation have a power law form. Our method applies to various weakly nonlinear wave systems, appearing in plasma, meteorology and oceanology.
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.
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 ...
Differential Equations of Mathematical Physics
Max Lein
2015-08-16T23:59:59.000Z
These lecture notes for the course APM 351 at the University of Toronto are aimed at mathematicians and physicists alike. It is not meant as an introductory course to PDEs, but rather gives an overview of how to view and solve differential equations that are common in physics. Among others, I cover Hamilton's equations, variations of the Schr\\"odinger equation, the heat equation, the wave equation and Maxwells equations.
Deviation differential equations. Jacobi fields
G. Sardanashvily
2013-04-02T23:59:59.000Z
Given a differential equation on a smooth fibre bundle Y, we consider its canonical vertical extension to that, called the deviation equation, on the vertical tangent bundle VY of Y. Its solutions are Jacobi fields treated in a very general setting. In particular, the deviation of Euler--Lagrange equations of a Lagrangian L on a fibre bundle Y are the Euler-Lagrange equations of the canonical vertical extension of L onto VY. Similarly, covariant Hamilton equations of a Hamiltonian form H are the Hamilton equations of the vertical extension VH of H onto VY.
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.
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...
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.
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.
On the generalized Jacobi equation
Volker Perlick
2007-10-14T23:59:59.000Z
The standard text-book Jacobi equation (equation of geodesic deviation) arises by linearizing the geodesic equation around some chosen geodesic, where the linearization is done with respect to the coordinates and the velocities. The generalized Jacobi equation, introduced by Hodgkinson in 1972 and further developed by Mashhoon and others, arises if the linearization is done only with respect to the coordinates, but not with respect to the velocities. The resulting equation has been studied by several authors in some detail for timelike geodesics in a Lorentzian manifold. Here we begin by briefly considering the generalized Jacobi equation on affine manifolds, without a metric; then we specify to lightlike geodesics in a Lorentzian manifold. We illustrate the latter case by considering particular lightlike geodesics (a) in Schwarzschild spacetime and (b) in a plane-wave spacetime.
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.
Schroeder's Equation in Several Variables
1910-10-20T23:59:59.000Z
2000 Mathematics Subject Classification: Primary: 32H50. Secondary: 30D05, 39B32, 47B33. Keywords: Schroeder's functional equation, iteration, composition
TRANSFORMING THE HEUN EQUATION TO THE HYPERGEOMETRIC EQUATION
TRANSFORMING THE HEUN EQUATION TO THE HYPERGEOMETRIC EQUATION: I. POLYNOMIAL TRANSFORMATIONS ROBERT by rational changes of its in dependent variable are classified. Heuntohypergeometric transformationstohypergeometric transformations) of Goursat. However, a transformation is possible only if the singular point location parameter
TRANSFORMING THE HEUN EQUATION TO THE HYPERGEOMETRIC EQUATION
Maier, Robert S.
TRANSFORMING THE HEUN EQUATION TO THE HYPERGEOMETRIC EQUATION: I. POLYNOMIAL TRANSFORMATIONS ROBERT by rational changes of its independent variable are classi#12;ed. Heun-to-hypergeometric transformations-to-hypergeometric transforma- tions) of Goursat. However, a transformation is possible only if the singular point location
TRANSFORMING THE HEUN EQUATION TO THE HYPERGEOMETRIC EQUATION
Maier, Robert S.
TRANSFORMING THE HEUN EQUATION TO THE HYPERGEOMETRIC EQUATION: I. POLYNOMIAL TRANSFORMATIONS ROBERT changes of its in- dependent variable are classified. Heun-to-hypergeometric transformations are analogous to the classical hypergeo- metric identities (i.e., hypergeometric-to-hypergeometric transformations) of Goursat
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
A Grassmann integral equation K. Scharnhorst a)
Scharnhorst, Klaus
A Grassmann integral equation K. Scharnhorst a) HumboldtÂUniversita Ë? t zu Berlin, Institut fu Ë? r Grassmann integral equation in analogy to integral equations studied in real analysis. A Grassmann integral equation is an equation which involves Grassmann #Berezin# integrations and which is to be obeyed
A Grassmann integral equation K. Scharnhorsta)
Scharnhorst, Klaus
A Grassmann integral equation K. Scharnhorsta) Humboldt-UniversitaÂ¨t zu Berlin, Institut fu Grassmann integral equation in analogy to integral equations studied in real analysis. A Grassmann integral equation is an equation which involves Grassmann Berezin integrations and which is to be obeyed
Logit Models for Estimating Urban Area Through Travel
Talbot, Eric
2011-10-21T23:59:59.000Z
the greatest data collection efforts. All three of the models performed reasonably well for external stations with high traffic volumes, but performed erratically for external stations with low traffic volumes (Chatterjee and Raja 1989). Reeder tested...
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.
Entropic corrections to Einstein equations
Hendi, S. H. [Physics Department, College of Sciences, Yasouj University, Yasouj 75914 (Iran, Islamic Republic of); Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Maragha (Iran, Islamic Republic of); Sheykhi, A. [Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Maragha (Iran, Islamic Republic of); Department of Physics, Shahid Bahonar University, P.O. Box 76175-132, Kerman (Iran, Islamic Republic of)
2011-04-15T23:59:59.000Z
Considering the general quantum corrections to the area law of black hole entropy and adopting the viewpoint that gravity interprets as an entropic force, we derive the modified forms of Modified Newtonian dynamics (MOND) theory of gravitation and Einstein field equations. As two special cases we study the logarithmic and power-law corrections to entropy and find the explicit form of the obtained modified equations.
Schroedinger equation and classical physics
Milos V. Lokajicek
2012-05-30T23:59:59.000Z
Any time-dependent solution of Schr\\"{o}dinger equation may be always correlated to a solution of Hamilton equations or to a statistical combination of their solutions; only the set of corresponding solutions is somewhat smaller (due to existence of quantization). There is not any reason to the physical interpretation according to Copenhagen alternative as Bell's inequalities are valid in the classical physics only (and not in any alternative based on Schr\\"{o}dinger equation). The advantage of Schr\\"{o}dinger equation consists then in that it enables to represent directly the time evolution of a statistical distribution of classical initial states (which is usual in collision experiments). The Schr\\"{o}dinger equation (without assumptions added by Bohr) may then represent the common physical theory for microscopic as well as macroscopic physical systems. However, together with the last possibility the solutions of Schr\\"{o}dinger equation may be helpful also in analyzing the influence of other statistically distributed properties (e.g., spin orientations or space structures) of individual matter objects forming a corresponding physical system, which goes in principle beyond the classical physics. In any case, the contemporary quantum theory represents the phenomenological approximative description of some matter characteristics only, without providing any insight into quantum mechanism emergence. In such a case it is necessary to take into account more detailed properties at least of some involved objects.
4.3 Boundary integral equations
2010-10-18T23:59:59.000Z
62. CHAPTER 4. OBSTACLE SCATTERING. 4.3 Boundary integral equations. We introduce the equivalent sources for the Helmholtz equation and establish ...
A connection between the shallow-water equations and the Euler-Poincaré equations
Roberto Camassa; Long Lee
2014-04-18T23:59:59.000Z
The Euler-Poincar\\'e differential (EPDiff) equations and the shallow water (SW) equations share similar wave characteristics. Using the Hamiltonian structure of the SW equations with flat bottom topography, we establish a connection between the EPDiff equations and the SW equations in one and multi-dimensions. Additionally, we show that the EPDiff equations can be recast in a curl formulation.
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.
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
2. System boundaries; Balance equations
Zevenhoven, Ron
") Introduction to Process Engineering v.2014 Åbo Akademi University | Thermal and Flow Engineering | 20500 Turku | Finland 2/28 2.1 System boundaries Åbo Akademi University | Thermal and Flow Engineering | 20500 Turku equations: Mass balances, other balances Åbo Akademi University | Thermal and Flow Engineering | 20500 Turku
Energy stories, equations and transition
Ernst, Damien
, . . . , T 1}, Bt = 1 r e (t t0) 1 + e (t t0) 2 #12;· Set of renewable energy production technologies Sustainable Energy April 28th, 2015 Raphael Fonteneau, University of Liège, Belgium @R_Fonteneau #12;Energy% - Renewable Non renewable The challenge #12;Equations and Transition #12;ERoEI · ERoEI for « Energy
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.
Blink, J.A.
1983-09-01T23:59:59.000Z
In 1977, Dave Young published an equation-of-state (EOS) for lithium. This EOS was used by Lew Glenn in his AFTON calculations of the HYLIFE inertial-fusion-reactor hydrodynamics. In this paper, I summarize Young's development of the EOS and demonstrate a computer program (MATHSY) that plots isotherms, isentropes and constant energy lines on a P-V diagram.
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.
Use of Regression Equations 1 Running head: Equations from summary data
Crawford, John R.
Use of Regression Equations 1 Running head: Equations from summary data Neuropsychology, in press the final version published in the APA journal. It is not the copy of record Using regression equations.crawford@abdn.ac.uk #12;Use of Regression Equations 2 Abstract Regression equations have many useful roles
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.
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...
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.
Mahouton Norbert Hounkonnou; André Ronveaux
2013-06-20T23:59:59.000Z
This paper addresses a general method of polynomial transformation of hypergeometric equations. Examples of some classical special equations of mathematical physics are generated. Heun's equation and exceptional Jacobi polynomials are also treated.
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.
On Process Equivalence = Equation Solving in CCS
Bundy, Alan; Monroy, Raul; Green, Ian
Unique Fixpoint Induction (UFI) is the chief inference rule to prove the equivalence of recursive processes in the Calculus of Communicating Systems (CCS) (Milner 1989). It plays a major role in the equational approach to verification. Equational...
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 ...
Deriving Mathisson - Papapetrou equations from relativistic pseudomechanics
R. R. Lompay
2005-03-12T23:59:59.000Z
It is shown that the equations of motion of a test point particle with spin in a given gravitational field, so called Mathisson - Papapetrou equations, can be derived from Euler - Lagrange equations of the relativistic pseudomechanics -- relativistic mechanics, which side by side uses the conventional (commuting) and Grassmannian (anticommuting) variables. In this approach the known difficulties of the Mathisson - Papapetrou equations, namely, the problem of the choice of supplementary conditions and the problem of higher derivatives are not appear.
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 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.
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.
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.
Some generalizations of the Raychaudhuri equation
Abreu, Gabriel
2010-01-01T23:59:59.000Z
The Raychaudhuri equation has seen extensive use in general relativity, most notably in the development of various singularity theorems. In this rather technical article we shall generalize the Raychaudhuri equation in several ways. First an improved version of the standard timelike Raychaudhuri equation is developed, where several key terms are lumped together as a divergence. This already has a number of interesting applications, both within the ADM formalism and elsewhere. Second, a spacelike version of the Raychaudhuri equation is briefly discussed. Third, a version of the Raychaudhuri equation is developed that does not depend on the use of normalized congruences. This leads to useful formulae for the "diagonal" part of the Ricci tensor. Fourth, a "two vector" version of the Raychaudhuri equation is developed that uses two congruences to effectively extract "off diagonal" information concerning the Ricci tensor.
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.
Electromagnetic Media with no Dispersion Equation
Ismo V. Lindell; Alberto Favaro
2013-03-25T23:59:59.000Z
It has been known through some examples that parameters of an electromagnetic medium can be so defined that there is no dispersion equation (Fresnel equation) to restrict the choice of the wave vector of a plane wave in such a medium, i.e., that the dispersion equation is satisfied identically for any wave vector. In the present paper, a more systematic study to define classes of media with no dispersion equation is attempted. The analysis makes use of coordinate-free four-dimensional formalism in terms of multivectors, multiforms and dyadics.
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.
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{\
Comment on ``Discrete Boltzmann Equation for Microfluidics''
Luo, Li-Shi
Comment on ``Discrete Boltzmann Equation for Microfluidics'' In a recent Letter [1], Li and Kwok use a lattice Boltzmann equation (LBE) for microfluidics. Their main claim is that an LBE model for microfluidics can be constructed based on the ``Bhatnagar-Gross-Kooky [sic]'' model by including ``the
The Papapetrou equations and supplementary conditions
O. B. Karpov
2004-06-02T23:59:59.000Z
On the bases of the Papapetrou equations with various supplementary conditions and other approaches a comparative analysis of the equations of motion of rotating bodies in general relativity is made. The motion of a body with vertical spin in a circular orbit is considered. An expression for the spin-orbit force in a post-Newtonian approximation is investigated.
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.
Nonlocal kinetic equation: integrable hydrodynamic reductions, symmetries
, Troitsk, Moscow Region, Russia Lebedev Physical Institute, Russian Academy of Sciences, Moscow Â§ SISSA, Ekaterinburg, Russia We study a new class of nonlinear kinetic equations recently derived in the context for the Whitham modulation systems for soliton equations. We prove that the N-component `cold-gas' hydro- dynamic
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.
NOTE / NOTE Allometric equations for young northern
Battles, John
. Vadeboncoeur, Mary A. Arthur, Russell D. Briggs, and Carrie R. Levine Abstract: Estimates of aboveground-specific equations for estimating aboveground biomass Farrah R. Fatemi, Ruth D. Yanai, Steven P. Hamburg, Matthew A relationships. Despite the widespread use of this approach, there is little information about whether equations
Elementary Differential Equations with Boundary Value Problems
William F. Trench
2014-02-24T23:59:59.000Z
Dec 1, 2013 ... In Sections 12.1 (The Heat Equation) and 12.2 (The Wave Equation) I devote .... Figure 1.1.1 shows typical graphs of P versus t for various values of P0. ...... Suppose a space vehicle is launched vertically and its fuel is ...
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
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.
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.
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.
Integral equations of scattering in one dimension
Vania E. Barlette; Marcelo M. Leite; Sadhan K. Adhikari
2001-03-05T23:59:59.000Z
A self-contained discussion of integral equations of scattering is presented in the case of centrally-symmetric potentials in one dimension, which will facilitate the understanding of more complex scattering integral equations in two and three dimensions. The present discussion illustrates in a simple fashion the concept of partial-wave decomposition, Green's function, Lippmann-Schwinger integral equations of scattering for wave function and transition operator, optical theorem and unitarity relation. We illustrate the present approach with a Dirac delta potential.
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.
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
On the solutions to the string equation
A. Schwarz
1991-09-10T23:59:59.000Z
The set of solutions to the string equation $[P,Q]=1$ where $P$ and $Q$ are differential operators is described.It is shown that there exists one-to-one correspondence between this set and the set of pairs of commuting differential operators.This fact permits us to describe the set of solutions to the string equation in terms of moduli spa- ces of algebraic curves,however the direct description is much simpler. Some results are obtained for the superanalog to the string equation where $P$ and $Q$ are considered as superdifferential operators. It is proved that this equation is invariant with respect to Manin-Radul, Mulase-Rabin and Kac-van de Leur KP-hierarchies.
Electric-Magnetic Duality and WDVV Equations
B. de Wit; A. Marshakov
2001-06-11T23:59:59.000Z
We consider the associativity (or WDVV) equations in the form they appear in Seiberg-Witten theory and prove that they are covariant under generic electric-magnetic duality transformations. We discuss the consequences of this covariance from various perspectives.
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 ...
Atilhan, Mert
2004-09-30T23:59:59.000Z
and thermophysical properties of natural gas for practical engineering applications. This thesis presents a new cubic EOS for pure argon. In this work, a theoretically based EOS represents the PVT behavior of pure fluids. The new equation has its basis...
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.
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.
Integral equations, fractional calculus and shift operator
D. Babusci; G. Dattoli; D. Sacchetti
2010-07-29T23:59:59.000Z
We present an extension of a previously developed method employing the formalism of the fractional derivatives to solve new classes of integral equations. This method uses different forms of integral operators that generalizes the exponential shift operator.
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.
Inverse Problems for Fractional Diffusion Equations
Zuo, Lihua
2013-06-21T23:59:59.000Z
; t > 0; (1.13) combined with the initial condition u(x; 0) = f(x); ?1 : u^t = ?s2u^; t > 0; u^(s; 0) = f^(s): Solving the above equation, we obtain u...
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 ...
MATH 411 SPRING 2001 Ordinary Differential Equations
Alekseenko, Alexander
MATH 411 SPRING 2001 Ordinary Differential Equations Schedule # 749025 TR 01:00-02:15 316 Boucke Instructor: Alexander Alekseenko, 328 McAllister, 865-1984, alekseen@math.psu.edu The course
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.
Conformally Invariant Spinorial Equations in Six Dimensions
Carlos Batista
2015-06-04T23:59:59.000Z
This work deals with the conformal transformations in six-dimensional spinorial formalism. Several conformally invariant equations are obtained and their geometrical interpretation are worked out. Finally, the integrability conditions for some of these equations are established. Moreover, in the course of the article, some useful identities involving the curvature of the spinorial connection are attained and a digression about harmonic forms and more general massless fields is made.
Symmetric Instantons and Discrete Hitchin Equations
Ward, R S
2015-01-01T23:59:59.000Z
Self-dual Yang-Mills instantons on $R^4$ correspond to algebraic ADHM data. This paper describes how to specialize such ADHM data so that the instantons have a $T^2$ symmetry, and this in turn motivates an integrable discrete version of the 2-dimensional Hitchin equations. It is analogous to the way in which the ADHM data for $S^1$-symmetric instantons, or hyperbolic BPS monopoles, may be viewed as a discretization of the Nahm equations.
Painleve VI, Rigid Tops and Reflection Equation
A. Levin; M. Olshanetsky; A. Zotov
2006-06-01T23:59:59.000Z
We show that the Painlev{\\'e} VI equation has an equivalent form of the non-autonomous Zhukovsky-Volterra gyrostat. This system is a generalization of the Euler top in $C^3$ and include the additional constant gyrostat momentum. The quantization of its autonomous version is achieved by the reflection equation. The corresponding quadratic algebra generalizes the Sklyanin algebra. As by product we define integrable XYZ spin chain on a finite lattice with new boundary conditions.
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.
Lagrangian submanifolds and Hamilton-Jacobi equation
M. Barbero-Liñán; M. de León; D. Martín de Diego
2012-09-04T23:59:59.000Z
Lagrangian submanifolds are becoming a very essential tool to generalize and geometrically understand results and procedures in the area of mathematical physics. Here we use general Lagrangian submanifolds to provide a geometric version of the Hamilton-Jacobi equation. This interpretation allows us to study some interesting applications of Hamilton-Jacobi equation in holonomic, nonholonomic and time-dependent dynamics from a geometrical point of view.
Integration Rules for Loop Scattering Equations
Baadsgaard, Christian; Bourjaily, Jacob L; Damgaard, Poul H; Feng, Bo
2015-01-01T23:59:59.000Z
We formulate new integration rules for one-loop scattering equations analogous to those at tree-level, and test them in a number of non-trivial cases for amplitudes in scalar $\\phi^3$-theory. This formalism greatly facilitates the evaluation of amplitudes in the CHY representation at one-loop order, without the need to explicitly sum over the solutions to the loop-level scattering equations.
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.
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...
Charging Capacitors According to Maxwell's Equations: Impossible
Daniele Funaro
2014-11-02T23:59:59.000Z
The charge of an ideal parallel capacitor leads to the resolution of the wave equation for the electric field with prescribed initial conditions and boundary constraints. Independently of the capacitor's shape and the applied voltage, none of the corresponding solutions is compatible with the full set of Maxwell's equations. The paradoxical situation persists even by weakening boundary conditions, resulting in the impossibility to describe a trivial phenomenon such as the capacitor's charging process, by means of the standard Maxwellian theory.
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.
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.
Active-space completely-renormalized equation-of-motioncoupled...
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
equation-of-motion coupled-clusterformalism: Excited-state studies of green fluorescent Active-space completely-renormalized equation-of-motion...
From the Boltzmann equation to fluid mechanics on a manifold
Peter J. Love; Donato Cianci
2012-08-27T23:59:59.000Z
We apply the Chapman-Enskog procedure to derive hydrodynamic equations on an arbitrary surface from the Boltzmann equation on the surface.
1.12 Basic Theory of Differential Equations
PRETEX (Halifax NS) #1 1054 1999 Mar 05 10:59:16
2010-01-20T23:59:59.000Z
Feb 16, 2007 ... 1.12. Chapter Review. Basic Theory of Differential Equations. This chapter has provided an introduction to the theory of differential equations. A.
Hyperinstantons, the Beltrami Equation, and Triholomorphic Maps
Fré, P; Sorin, A S
2015-01-01T23:59:59.000Z
We consider the Beltrami equation for hydrodynamics and we show that its solutions can be viewed as instanton solutions of a more general system of equations. The latter are the equations of motion for an ${\\cal N}=2$ sigma model on 4-dimensional worldvolume (which is taken locally HyperK\\"ahler) with a 4-dimensional HyperK\\"ahler target space. By means of the 4D twisting procedure originally introduced by Witten for gauge theories and later generalized to 4D sigma-models by Anselmi and Fr\\'e, we show that the equations of motion describe triholomophic maps between the worldvolume and the target space. Therefore, the classification of the solutions to the 3-dimensional Beltrami equation can be performed by counting the triholomorphic maps. The counting is easily obtained by using several discrete symmetries. Finally, the similarity with holomorphic maps for ${\\cal N}=2$ sigma on Calabi-Yau space prompts us to reformulate the problem of the enumeration of triholomorphic maps in terms of a topological sigma mod...
Electromagnetic field with constraints and Papapetrou equation
Z. Ya. Turakulov; A. T. Muminov
2006-01-12T23:59:59.000Z
It is shown that geometric optical description of electromagnetic wave with account of its polarization in curved space-time can be obtained straightforwardly from the classical variational principle for electromagnetic field. For this end the entire functional space of electromagnetic fields must be reduced to its subspace of locally plane monochromatic waves. We have formulated the constraints under which the entire functional space of electromagnetic fields reduces to its subspace of locally plane monochromatic waves. These constraints introduce variables of another kind which specify a field of local frames associated to the wave and contain some congruence of null-curves. The Lagrangian for constrained electromagnetic field contains variables of two kinds, namely, a congruence of null-curves and the field itself. This yields two kinds of Euler-Lagrange equations. Equations of first kind are trivial due to the constraints imposed. Variation of the curves yields the Papapetrou equations for a classical massless particle with helicity 1.
Some Wave Equations for Electromagnetism and Gravitation
Zi-Hua Weng
2010-08-11T23:59:59.000Z
The paper studies the inferences of wave equations for electromagnetic fields when there are gravitational fields at the same time. In the description with the algebra of octonions, the inferences of wave equations are identical with that in conventional electromagnetic theory with vector terminology. By means of the octonion exponential function, we can draw out that the electromagnetic waves are transverse waves in a vacuum, and rephrase the law of reflection, Snell's law, Fresnel formula, and total internal reflection etc. The study claims that the theoretical results of wave equations for electromagnetic strength keep unchanged in the case for coexistence of gravitational and electromagnetic fields. Meanwhile the electric and magnetic components of electromagnetic waves can not be determined simultaneously in electromagnetic fields.
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.
Chemical potential and the gap equation
Huan Chen; Wei Yuan; Lei Chang; Yu-Xin Liu; Thomas Klahn; Craig D. Roberts
2008-07-17T23:59:59.000Z
In general the kernel of QCD's gap equation possesses a domain of analyticity upon which the equation's solution at nonzero chemical potential is simply obtained from the in-vacuum result through analytic continuation. On this domain the single-quark number- and scalar-density distribution functions are mu-independent. This is illustrated via two models for the gap equation's kernel. The models are alike in concentrating support in the infrared. They differ in the form of the vertex but qualitatively the results are largely insensitive to the Ansatz. In vacuum both models realise chiral symmetry in the Nambu-Goldstone mode and in the chiral limit, with increasing chemical potential, exhibit a first-order chiral symmetry restoring transition at mu~M(0), where M(p^2) is the dressed-quark mass function. There is evidence to suggest that any associated deconfinement transition is coincident and also of first-order.
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...
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
Differential Equations I Lab #8: Differential Equations and Linear Algebra with Mathematica
Peckham, Bruce B.
and NDSolve for differential equations, and LinearSolve, Eigenvector, Eigen- value, NullSpace, Inverse/instructor each output line generated by Mathematica. If you elect to write a report, your report should include an analytical solution to y + 3y + 2y = 3e4t. #12;2. The logistic differential equation (again). Consider
Interplay of Boltzmann equation and continuity equation for accelerated electrons in solar flares
Codispoti, Anna
2015-01-01T23:59:59.000Z
During solar flares a large amount of electrons are accelerated within the plasma present in the solar atmosphere. Accurate measurements of the motion of these electrons start becoming available from the analysis of hard X-ray imaging-spectroscopy observations. In this paper, we discuss the linearized perturbations of the Boltzmann kinetic equation describing an ensemble of electrons accelerated by the energy release occurring during solar flares. Either in the limit of high energy or at vanishing background temperature such an equation reduces to a continuity equation equipped with an extra force of stochastic nature. This stochastic force is actually described by the well known energy loss rate due to Coulomb collision with ambient particles, but, in order to match the collision kernel in the linearized Boltzmann equation it needs to be treated in a very specific manner. In the second part of the paper the derived continuity equation is solved with some hyperbolic techniques, and the obtained solution is wr...
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.
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.
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.
Principle of Least Squares Regression Equations Residuals Correlation and Regression
Watkins, Joseph C.
Principle of Least Squares Regression Equations Residuals Topic 3 Correlation and Regression Linear Regression I 1 / 15 #12;Principle of Least Squares Regression Equations Residuals Outline Principle of Least Squares Regression Equations Residuals 2 / 15 #12;Principle of Least Squares Regression Equations
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...
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...
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.
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.
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
MULTIVARIATE PUBLIC KEY CRYPTOSYSTEMS FROM DIOPHANTINE EQUATIONS
Gao, Shuhong
MULTIVARIATE PUBLIC KEY CRYPTOSYSTEMS FROM DIOPHANTINE EQUATIONS SHUHONG GAO AND RAYMOND HEINDL for multivariate public key cryptosystems, which combines ideas from both triangular and oil-vinegar schemes. We the framework. 1. Introduction 1.1. Multivariate Public Key Cryptography. Public key cryptography plays
Partial Differential Equations of Electrostatic MEMS
Fournier, John J.F.
) The University of British Columbia July 2007 c Yujin Guo 2007 #12;Abstract Micro-Electromechanical Systems (MEMSPartial Differential Equations of Electrostatic MEMS by Yujin Guo B.Sc., China Three Gorges their initial development in the 1980s, MEMS has revolutionized numerous branches of science and industry
Optimal polarisation equations in FLRW universes
Tram, Thomas; Lesgourgues, Julien, E-mail: thomas.tram@epfl.ch, E-mail: Julien.Lesgourgues@cern.ch [Institut de Théorie des Phénomènes Physiques, École Polytechnique Fédérale de Lausanne, CH-1015, Lausanne (Switzerland)
2013-10-01T23:59:59.000Z
This paper presents the linearised Boltzmann equation for photons for scalar, vector and tensor perturbations in flat, open and closed FLRW cosmologies. We show that E- and B-mode polarisation for all types can be computed using only a single hierarchy. This was previously shown explicitly for tensor modes in flat cosmologies but not for vectors, and not for non-flat cosmologies.
NOTES ON THE JACOBI EQUATION ALEXANDER LYTCHAK
Lytchak, Alexander
NOTES ON THE JACOBI EQUATION ALEXANDER LYTCHAK Abstract. We discuss some properties of Jacobi spaces of Jacobi fields and give some applica- tions to Riemannian geometry. 1. Introduction This note is essentially a collection of results about conjugate points of Jacobi fields for which we could not find
DIFFERENTIAL EQUATIONS FOR FLOW IN RESERVOIRS By ...
2008-08-23T23:59:59.000Z
where Ap is the applied pressure drop across the sample, 1.1 is the viscosity of .... When this is done we have, in theory, all the information necessary to solve ..... The simplicity of this equation indicates the fundamental role that total ve-.
Cubic Nonlinear Schrodinger Equation with vorticity
Caliari, Marco
) Equation, plays a fundamental role in describing the hydrodynamics of a BoseEinstein condensate [4] (see Bose particles, as recently described within Stochastic Quantization by Lagrangian Variational the general one-particle Bose dynamics out of dynamical equilibrium. We observe that in the most simple
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...
Conservation of Energy Thermodynamic Energy Equation
Hennon, Christopher C.
, is derived beginning with an alternative form of the 1st Law of Thermodynamics, the internal energy formConservation of Energy Thermodynamic Energy Equation The previous two sections dealt addresses the conservation of energy. The first law of thermodynamics, of which you should be very familiar
Construction of tree volume tables from integration of taper equations
Coffman, Jerry Gale
1973-01-01T23:59:59.000Z
) were used as a basis for comparison. The integrated taper equation appears to be as accurate as the tradi- 2 tional volume equation V a + bD H, but somewhat less accurate than volume equations involving form class measurements. A computer program... and help throughout my graduate career. TABLE OF CONTENTS CHAPTER Page I INTRODUCTION AND OBJECTIVES II REVIEW OF LITERATURE III METHODS Sample Data Procedure Analysis 1 Analysis 2 13 Integration of Taper Equations to Volume Equations Tests...
The Semiclassical Einstein Equation on Cosmological Spacetimes
Daniel Siemssen
2015-03-06T23:59:59.000Z
The subject of this thesis is the coupling of quantum fields to a classical gravitational background in a semiclassical fashion. It contains a thorough introduction into quantum field theory on curved spacetime with a focus on the stress-energy tensor and the semiclassical Einstein equation. Basic notions of differential geometry, topology, functional and microlocal analysis, causality and general relativity will be summarised, and the algebraic approach to QFT on curved spacetime will be reviewed. Apart from these foundations, the original research of the author and his collaborators will be presented: Together with Fewster, the author studied the up and down structure of permutations using their decomposition into so-called atomic permutations. The relevance of these results to this thesis is their application in the calculation of the moments of quadratic quantum fields. In a work with Pinamonti, the author showed the local and global existence of solutions to the semiclassical Einstein equation in flat cosmological spacetimes coupled to a scalar field by solving simultaneously for the quantum state and the Hubble function in an integral-functional equation. The theorem is proved with a fixed-point theorem using the continuous functional differentiability and boundedness of the integral kernel of the integral-functional equation. In another work with Pinamonti the author proposed an extension of the semiclassical Einstein equations which couples the moments of a stochastic Einstein tensor to the moments of the quantum stress-energy tensor. In a toy model of a Newtonianly perturbed exponentially expanding spacetime it is shown that the quantum fluctuations of the stress-energy tensor induce an almost scale-invariant power spectrum for the perturbation potential and that non-Gaussianties arise naturally.
Kovalyov, Mikhail [Department of Mathematics, University of Alberta, Edmonton, Alberta, T6G 2G1 (Canada)
2010-06-15T23:59:59.000Z
In this article the sets of solutions of the sine-Gordon equation and its linearization the Klein-Gordon equation are discussed and compared. It is shown that the set of solutions of the sine-Gordon equation possesses a richer structure which partly disappears during linearization. Just like the solutions of the Klein-Gordon equation satisfy the linear superposition principle, the solutions of the sine-Gordon equation satisfy a nonlinear superposition principle.
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.
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.
Fundamental Equation of State for Deuterium
Richardson, I. A.; Leachman, J. W., E-mail: jacob.leachman@wsu.edu [HYdrogen Properties for Energy Research (HYPER) Laboratory, School of Mechanical and Materials Engineering, Washington State University, P.O. Box 642920, Pullman, Washington 99164 (United States); Lemmon, E. W. [Applied Chemicals and Materials Division, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305 (United States)] [Applied Chemicals and Materials Division, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305 (United States)
2014-03-15T23:59:59.000Z
World utilization of deuterium is anticipated to increase with the rise of fusion-energy machines such as ITER and NIF. We present a new fundamental equation of state for the thermodynamic properties of fluid deuterium. Differences between thermodynamic properties of orthodeuterium, normal deuterium, and paradeuterium are described. Separate ideal-gas functions were fitted for these separable forms together with a single real-fluid residual function. The equation of state is valid from the melting line to a maximum pressure of 2000 MPa and an upper temperature limit of 600 K, corresponding to available experimental measurements. The uncertainty in predicted density is 0.5% over the valid temperature range and pressures up to 300 MPa. The uncertainties of vapor pressures and saturated liquid densities are 2% and 3%, respectively, while speed-of-sound values are accurate to within 1% in the liquid phase.
Ultrarelativistic Decoupling Transformation for Generalized Dirac Equations
Noble, J H
2015-01-01T23:59:59.000Z
The Foldy--Wouthuysen transformation is known to uncover the nonrelativistic limit of a generalized Dirac Hamiltonian, lending an intuitive physical interpretation to the effective operators within Schr\\"{o}dinger--Pauli theory. We here discuss the opposite, ultrarelativistic limit which requires the use of a fundamentally different expansion where the leading kinetic term in the Dirac equation is perturbed by the mass of the particle and other interaction (potential) terms, rather than vice versa. The ultrarelativistic decoupling transformation is applied to free Dirac particles (in the Weyl basis) and to high-energy tachyons, which are faster-than-light particles described by a fully Lorentz-covariant equation. The effective gravitational interactions are found. For tachyons, the dominant gravitational interaction term in the high-energy limit is shown to be attractive, and equal to the leading term for subluminal Dirac particles (tardyons) in the high-energy limit.
Ultrarelativistic Decoupling Transformation for Generalized Dirac Equations
J. H. Noble; U. D. Jentschura
2015-06-05T23:59:59.000Z
The Foldy--Wouthuysen transformation is known to uncover the nonrelativistic limit of a generalized Dirac Hamiltonian, lending an intuitive physical interpretation to the effective operators within Schr\\"{o}dinger--Pauli theory. We here discuss the opposite, ultrarelativistic limit which requires the use of a fundamentally different expansion where the leading kinetic term in the Dirac equation is perturbed by the mass of the particle and other interaction (potential) terms, rather than vice versa. The ultrarelativistic decoupling transformation is applied to free Dirac particles (in the Weyl basis) and to high-energy tachyons, which are faster-than-light particles described by a fully Lorentz-covariant equation. The effective gravitational interactions are found. For tachyons, the dominant gravitational interaction term in the high-energy limit is shown to be attractive, and equal to the leading term for subluminal Dirac particles (tardyons) in the high-energy limit.
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.
Quantum Potential Via General Hamilton - Jacobi Equation
Maedeh Mollai; Mohammad Razavi; Safa Jami; Ali Ahanj
2011-10-29T23:59:59.000Z
In this paper, we sketch and emphasize the automatic emergence of a quantum potential (QP) in general Hamilton-Jacobi equation via commuting relations, quantum canonical transformations and without the straight effect of wave function. The interpretation of QP in terms of independent entity is discussed along with the introduction of quantum kinetic energy. The method has been extended to relativistic regime, and same results have been concluded.
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.
Wave equation prediction of pile bearing capacity
Bartoskewitz, Richard Edward
1970-01-01T23:59:59.000Z
are predicted by using a numerical method for solving the one-dimensional wave equation. The predicted capac- ities are compared with field data from static load tests. The results obtained by using currently accepted soil parameters, which characterize... the dynamic response of a soil to impact loading, are compared to those attained by using soil parameters which were recently developed from model pile tests . A study is made to determine the qualitative affects that the soil parameters have...
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.
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.
Weakly nonlocal fluid mechanics - the Schrodinger equation
P. Van; T. Fulop
2004-06-09T23:59:59.000Z
A weakly nonlocal extension of ideal fluid dynamics is derived from the Second Law of thermodynamics. It is proved that in the reversible limit the additional pressure term can be derived from a potential. The requirement of the additivity of the specific entropy function determines the quantum potential uniquely. The relation to other known derivations of Schr\\"odinger equation (stochastic, Fisher information, exact uncertainty) is clarified.
Towards a characteristic equation for permeability
Siddiqui, Adil Ahmed
2008-10-10T23:59:59.000Z
FOR PERMEABILITY A Thesis by ADIL AHMED SIDDIQUI 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 2008... Major Subject: Petroleum Engineering TOWARDS A CHARACTERISTIC EQUATION FOR PERMEABILITY A Thesis by ADIL AHMED SIDDIQUI Submitted to the Office of Graduate Studies of Texas A&M University in partial fulfillment...
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.
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.
Total Operators and Inhomogeneous Proper Values Equations
Jose G. Vargas
2015-07-09T23:59:59.000Z
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.
Guiding center equations for ideal magnetohydrodynamic modes
White, R. B. [Plasma Physics Laboratory, Princeton University, P.O. Box 451, Princeton, New Jersey 08543 (United States)
2013-04-15T23:59:59.000Z
Guiding center simulations are routinely used for the discovery of mode-particle resonances in tokamaks, for both resistive and ideal instabilities and to find modifications of particle distributions caused by a given spectrum of modes, including large scale avalanches during events with a number of large amplitude modes. One of the most fundamental properties of ideal magnetohydrodynamics is the condition that plasma motion cannot change magnetic topology. The conventional representation of ideal magnetohydrodynamic modes by perturbing a toroidal equilibrium field through {delta}B-vector={nabla} Multiplication-Sign ({xi}-vector Multiplication-Sign B-vector), however, perturbs the magnetic topology, introducing extraneous magnetic islands in the field. A proper treatment of an ideal perturbation involves a full Lagrangian displacement of the field due to the perturbation and conserves magnetic topology as it should. In order to examine the effect of ideal magnetohydrodynamic modes on particle trajectories, the guiding center equations should include a correct Lagrangian treatment. Guiding center equations for an ideal displacement {xi}-vector are derived which preserve the magnetic topology and are used to examine mode particle resonances in toroidal confinement devices. These simulations are compared to others which are identical in all respects except that they use the linear representation for the field. Unlike the case for the magnetic field, the use of the linear field perturbation in the guiding center equations does not result in extraneous mode particle resonances.
Nonholonomic Hamilton-Jacobi equation and Integrability
Tomoki Ohsawa; Anthony M. Bloch
2009-12-18T23:59:59.000Z
We discuss an extension of the Hamilton-Jacobi theory to nonholonomic mechanics with a particular interest in its application to exactly integrating the equations of motion. We give an intrinsic proof of a nonholonomic analogue of the Hamilton--Jacobi theorem. Our intrinsic proof clarifies the difference from the conventional Hamilton-Jacobi theory for unconstrained systems. The proof also helps us identify a geometric meaning of the conditions on the solutions of the Hamilton-Jacobi equation that arise from nonholonomic constraints. The major advantage of our result is that it provides us with a method of integrating the equations of motion just as the unconstrained Hamilton--Jacobi theory does. In particular, we build on the work by Iglesias-Ponte, de Leon, and Martin de Diego so that the conventional method of separation of variables applies to some nonholonomic mechanical systems. We also show a way to apply our result to systems to which separation of variables does not apply.
Guiding Center Equations for Ideal Magnetohydrodynamic Modes
Roscoe B. White
2013-02-21T23:59:59.000Z
Guiding center simulations are routinely used for the discovery of mode-particle resonances in tokamaks, for both resistive and ideal instabilities and to find modifications of particle distributions caused by a given spectrum of modes, including large scale avalanches during events with a number of large amplitude modes. One of the most fundamental properties of ideal magnetohydrodynamics is the condition that plasma motion cannot change magnetic topology. The conventional representation of ideal magnetohydrodynamic modes by perturbing a toroidal equilibrium field through ?~B = ? X (? X B) however perturbs the magnetic topology, introducing extraneous magnetic islands in the field. A proper treatment of an ideal perturbation involves a full Lagrangian displacement of the field due to the perturbation and conserves magnetic topology as it should. In order to examine the effect of ideal magnetohydrodynamic modes on particle trajectories the guiding center equations should include a correct Lagrangian treatment. Guiding center equations for an ideal displacement ? are derived which perserve the magnetic topology and are used to examine mode particle resonances in toroidal confinement devices. These simulations are compared to others which are identical in all respects except that they use the linear representation for the field. Unlike the case for the magnetic field, the use of the linear field perturbation in the guiding center equations does not result in extraneous mode particle resonances.
Measuring the dark matter equation of state
Ana Laura Serra; Mariano Javier de León Domínguez Romero
2011-05-30T23:59:59.000Z
The nature of the dominant component of galaxies and clusters remains unknown. While the astrophysics community 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 that combines kinematic and gravitational lensing data to test the widely adopted assumption of pressureless dark matter. Following 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 because typically the masses determined with lensing are larger than those obtained through kinematic methods. We have tested our techniques using simulations and we have also analyzed possible sources of error that could invalidate or mimic our results. In the light of this result, we can now suggest that the understanding of the nature of dark matter requires a complete general relativistic analysis.
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.
Stochastic partial differential equations with singular terminal condition
Popier, Alexandre
Stochastic partial differential equations with singular terminal condition A Matoussi, Lambert Piozin, A Popier To cite this version: A Matoussi, Lambert Piozin, A Popier. Stochastic partial differential equations with singular terminal condition. 2015. HAL Id: hal-01152687 https
Pad\\'e interpolation for elliptic Painlev\\'e equation
Noumi, Masatoshi; Yamada, Yasuhiko
2012-01-01T23:59:59.000Z
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.
Outline for Linear Equations and Inequalities of 2 variables
charlotb
2010-04-15T23:59:59.000Z
Outline for Linear Equations and Inequalities of 2 variables. A. 1. Substitute any value for x in the equation and solve for y. This results in a point (x, y). OR.
EFFECTIVE MACROSCOPIC DYNAMICS OF STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS IN PERFORATED
Duan, Jinqiao
EFFECTIVE MACROSCOPIC DYNAMICS OF STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS IN PERFORATED DOMAINS equation defined on a domain perforated with small holes or heterogeneities. The homogenized effective, effective macroscopic model, stochastic homogenization, white noise, probability distribution, perforated
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
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.
Derivation of the Camassa-Holm equations for elastic waves
H. A. Erbay; S. Erbay; A. Erkip
2015-02-10T23:59:59.000Z
In this paper we provide a formal derivation of both the Camassa-Holm equation and the fractional Camassa-Holm equation for the propagation of small-but-finite amplitude long waves in a nonlocally and nonlinearly elastic medium. We first show that the equation of motion for the nonlocally and nonlinearly elastic medium reduces to the improved Boussinesq equation for a particular choice of the kernel function appearing in the integral-type constitutive relation. We then derive the Camassa-Holm equation from the improved Boussinesq equation using an asymptotic expansion valid as nonlinearity and dispersion parameters tend to zero independently. Our approach follows mainly the standard techniques used widely in the literature to derive the Camassa-Holm equation for shallow water waves. The case where the Fourier transform of the kernel function has fractional powers is also considered and the fractional Camassa-Holm equation is derived using the asymptotic expansion technique.
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.
A characterization of causal automorphisms by wave equations
Do-Hyung Kim
2011-11-07T23:59:59.000Z
A characterization of causal automorphism on Minkowski spacetime is given by use of wave equation. The result shows that causal analysis of spacetime may be replaced by studies of wave equation on manifolds.
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
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
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.
Nonlinear Integral Equations for the Inverse Problem in Corrosion ...
2012-06-15T23:59:59.000Z
Nonlinear Integral Equations for the Inverse. Problem in Corrosion Detection from Partial. Cauchy Data. Fioralba Cakoni. Department of Mathematical Sciences, ...
Theory Revision in Equation Discovery Ljupco Todorovski and Saso Dzeroski
Dzeroski, Saso
.Dzeroski@ijs.si Abstract. State of the art equation discovery systems start the discov- ery process from scratch, rather the accuracy of the model. 1 Introduction Most of the existing equation discovery systems make use of a very neglected by the equation discovery systems are the existing models in the domain. Rather than starting
Reasoning About Systems of Physics Equations Chun Wai Liew1
Liew, Chun Wai
Reasoning About Systems of Physics Equations Chun Wai Liew1 and Donald E. Smith2 1 Department Physics require the student to enter a system of algebraic equations as the answer. Tutoring systems must presents an approach that accepts from the student a system of equations describing the physics
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
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.
Lagrangian Reduction, the EulerPoincare Equations, and Semidirect Products
Marsden, Jerrold
reduction for semidirect products, which applies to examples such as the heavy top, com- pressible fluids equations for a fluid or a rigid body, namely Lie-Poisson systems on the dual of a Lie algebra and their Lagrangian counterpart, the "pure" Euler-Poincar´e equations on a Lie algebra. The Lie-Poisson Equations
EXISTENCE OF INSENSITIZING CONTROLS FOR A SEMILINEAR HEAT EQUATION WITH
González Burgos, Manuel
EXISTENCE OF INSENSITIZING CONTROLS FOR A SEMILINEAR HEAT EQUATION WITH A SUPERLINEAR NONLINEARITY system of heat equations, the first one of semilinear type. In addition, the control enters on the second by D.G.E.S. (Spain), Grant PB981134. Abstract In this paper we consider a semilinear heat equation (in
Partitioning Multivariate Polynomial Equations via Vertex Separators for Algebraic Cryptanal-
International Association for Cryptologic Research (IACR)
Partitioning Multivariate Polynomial Equations via Vertex Separators for Algebraic Cryptanal- ysis. In this paper, we apply similar graph theory techniques to systems of multivariate polynomial equations to a system of multivariate polynomial equations is an NP-complete problem [7, Ch. 3.9]. A variety of solution
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.
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
Long-wave instabilities and saturation in thin film equations
Pugh, Mary
to shorter wavelengths which then dissipate the energy. The nonlinearity in the KS equation is advective.2) The equation arises as an interface model in bio-fluids [15], solar convec- tion [19], and binary alloys [48Long-wave instabilities and saturation in thin film equations A. L. Bertozzi Department
Longwave instabilities and saturation in thin film equations
Pugh, Mary
then dissipate the energy. The nonlinearity in the KS equation is advective, and a#ects the dyÂ namics di.2) The equation arises as an interface model in bioÂfluids [15], solar convecÂ tion [19], and binary alloys [48LongÂwave instabilities and saturation in thin film equations A. L. Bertozzi Department
UNCONDITIONALLY STABLE METHODS FOR HAMILTON-JACOBI EQUATIONS
UNCONDITIONALLY STABLE METHODS FOR HAMILTON-JACOBI EQUATIONS KENNETH HVISTENDAHL KARLSEN AND NILS to the Cauchy problem for Hamilton-Jacobi equations of the form u t + H(Dxu) = 0. The methods are based stable numerical methods for the Cauchy problem for multi-dimensional Hamilton-Jacobi equations ( u t +H
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
Radon transform and kinetic equations in tomographic representation
V. N. Chernega; V. I. Man'ko; B. I. Sadovnikov
2009-11-01T23:59:59.000Z
Statistical properties of classical random process are considered in tomographic representation. The Radon integral transform is used to construct the tomographic form of kinetic equations. Relation of probability density on phase space for classical systems with tomographic probability distributions is elucidated. Examples of simple kinetic equations like Liouville equations for one and many particles are studied in detail.
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
Two-component equations modelling water waves with constant vorticity
Joachim Escher; David Henry; Boris Kolev; Tony Lyons
2014-09-30T23:59:59.000Z
In this paper we derive a two-component system of nonlinear equations which model two-dimensional shallow water waves with constant vorticity. Then we prove well-posedness of this equation using a geometrical framework which allows us to recast this equation as a geodesic flow on an infinite dimensional manifold. Finally, we provide a criteria for global existence.
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.
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
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.
Noncommutative Algebraic Equations and Noncommutative Eigenvalue Problem
Albert Schwarz
2000-04-27T23:59:59.000Z
We analyze the perturbation series for noncommutative eigenvalue problem $AX=X\\lambda$ where $\\lambda$ is an element of a noncommutative ring, $ A$ is a matrix and $X$ is a column vector with entries from this ring. As a corollary we obtain a theorem about the structure of perturbation series for Tr $x^r$ where $x$ is a solution of noncommutative algebraic equation (for $r=1$ this theorem was proved by Aschieri, Brace, Morariu, and Zumino, hep-th/0003228, and used to study Born-Infeld lagrangian for the gauge group $U(1)^k$).
Generalized Ideal Gas Equations for Structureful Universe
Shahid N. Afridi; Khalid Khan
2006-09-04T23:59:59.000Z
We have derived generalized ideal gas equations for a structureful universe consisting of all forms of matters. We have assumed a universe that contains superclusters. Superclusters are then made of clusters. Each cluster can be further divided into smaller ones and so on. We have derived an expression for the entropy of such a universe. Our model is rather independent of the geometry of the intermediate clusters. Our calculations are valid for a non-interacting universe within non-relativistic limits. We suggest that structure formation can reduce the expansion rate of the universe.
The Schrodinger Equation as a Volterra Problem
Mera, Fernando Daniel
2011-08-08T23:59:59.000Z
is obtained from Chapter IV of Lawrence C. Evans?s book on partial di erential equations [5]. Let y = x+ z, where 2 = 2~tm ; then we can rewrite the Poisson integral as u(x; t) = 1 i n=2 Z Rn eijzj 2 f(x+ z) dz (II.18) where jzj = jx yj . Let... implies that 8 > 0 9 > 0 such that 8x 2 Rn with jx yj 0, then there exists a t so small such that jf(x + z) f(x)j < for all z...
An Interesting Class of Partial Differential Equations
Wen-an Yong
2007-08-28T23:59:59.000Z
This paper presents an observation that under reasonable conditions, many partial differential equations from mathematical physics possess three structural properties. One of them can be understand as a variant of the celebrated Onsager reciprocal relation in Modern Thermodynamics. It displays a direct relation of irreversible processes to the entropy change. We show that the properties imply various entropy dissipation conditions for hyperbolic relaxation problems. As an application of the observation, we propose an approximation method to solve relaxation problems. Moreover, the observation is interpreted physically and verified with eight (sets of) systems from different fields.
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.
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.
On the multivariate Burgers equation and the incompressible Navier-Stokes equation (Part I)
Joerg Kampen
2011-03-14T23:59:59.000Z
We provide a constructive global existence proof for the multivariate viscous Burgers equation system defined on the whole space or on a domain isomorphic to the n-torus and with time horizon up to infinity and C^{\\infty}- data (satisfying some growth conditions if the problem is posed on the whole space). The proof is by a time discretized semiexplicit perturbative expansion in transformed coordinates where the convergence is guaranteed by certain a priori estimates. The scheme is useful in order to define computation for related equation systems of fluid dynamics.
Calculating work in weakly driving quantum master equations: backward and forward equations
Fei Liu
2015-06-28T23:59:59.000Z
We present a technical report that the two methods of calculating characteristic functions for the work distribution in the weakly driven quantum master equations are equivalent. One is obtained by the notion of quantum jump trajectory [Phys. Rev. E 89, 042122 (2014)], while the other is based on the two time energy measurements on the combined system and reservoir [Silaev, et al., Phys. Rev. E 90, 022103 (2014)]. They are indeed the backward and forward methods, respectively, which is very similar to the case of the Kolmogorov backward and forward equations in classical stochastic theory. The microscopic basis of the former method is also clarified.
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.
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.
Topography influence on the Lake equations in bounded domains
Christophe Lacave; Toan T. Nguyen; Benoit Pausader
2013-06-10T23:59:59.000Z
We investigate the influence of the topography on the lake equations which describe the two-dimensional horizontal velocity of a three-dimensional incompressible flow. We show that the lake equations are structurally stable under Hausdorff approximations of the fluid domain and $L^p$ perturbations of the depth. As a byproduct, we obtain the existence of a weak solution to the lake equations in the case of singular domains and rough bottoms. Our result thus extends earlier works by Bresch and M\\'etivier treating the lake equations with a fixed topography and by G\\'erard-Varet and Lacave treating the Euler equations in singular domains.
Integral equations for the H- X- and Y-functions
B. Rutily; L. Chevallier; J. Bergeat
2006-01-16T23:59:59.000Z
We come back to a non linear integral equation satisfied by the function H, which is distinct from the classical H-equation. Established for the first time by Busbridge (1955), it appeared occasionally in the literature since then. First of all, this equation is generalized over the whole complex plane using the method of residues. Then its counterpart in a finite slab is derived; it consists in two series of integral equations for the X- and Y-functions. These integral equations are finally applied to the solution of the albedo problem in a slab.
Integer Algorithms to Solver Diophantine Linear Equations and Systems
Florentin Smarandache
2007-11-28T23:59:59.000Z
The present work includes some of the author's original researches on integer solutions of Diophantine liner equations and systems. The notion of "general integer solution" of a Diophantine linear equation with two unknowns is extended to Diophantine linear equations with $n$ unknowns and then to Diophantine linear systems. The proprieties of the general integer solution are determined (both for a Diophantine linear equation and for a Diophantine linear system). Seven original integer algorithms (two for Diophantine linear equations, and five for Diophantine linear systems) are exposed. The algorithms are strictly proved and an example for each of them is given. These algorithms can be easily implemented on the computer.
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.
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.
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.
Multiscale functions, Scale dynamics and Applications to partial differential equations
Jacky Cresson; Frédéric Pierret
2015-09-03T23:59:59.000Z
Modeling phenomena from experimental data, always begin with a \\emph{choice of hypothesis} on the observed dynamics such as \\emph{determinism}, \\emph{randomness}, \\emph{derivability} etc. Depending on these choices, different behaviors can be observed. The natural question associated to the modeling problem is the following : \\emph{"With a finite set of data concerning a phenomenon, can we recover its underlying nature ?} From this problem, we introduce in this paper the definition of \\emph{multi-scale functions}, \\emph{scale calculus} and \\emph{scale dynamics} based on the \\emph{time-scale calculus} (see \\cite{bohn}). These definitions will be illustrated on the \\emph{multi-scale Okamoto's functions}. The introduced formalism explains why there exists different continuous models associated to an equation with different \\emph{scale regimes} whereas the equation is \\emph{scale invariant}. A typical example of such an equation, is the \\emph{Euler-Lagrange equation} and particularly the \\emph{Newton's equation} which will be discussed. Notably, we obtain a \\emph{non-linear diffusion equation} via the \\emph{scale Newton's equation} and also the \\emph{non-linear Schr\\"odinger equation} via the \\emph{scale Newton's equation}. Under special assumptions, we recover the classical \\emph{diffusion} equation and the \\emph{Schr\\"odinger equation}.
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.
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.
Jimack, Peter
-Stokes equations Ren´e Schneider1, and Peter K. Jimack1 1 School of Computing, University of Leeds, LS2 9JT, UK: rschneid@comp.leeds.ac.uk #12;PRECOND. DISCR. ADJOINT INCOMP. NAVIER-STOKES EQS. 1 of the steady state size parameter h. We briefly review some of the most important issues associated with the application
Stochastic evolution equations with random generators
Leon, Jorge A.; Nualart, David
1998-05-01T23:59:59.000Z
; × #26;#17;L 2 #3;U#7;H#4;#4; for some constant M> 0. The Sobolev spaces D k#7;2 #3;L#3;H#7;G#4;#4; for any integer k ? 1 are defined as in Definition 2.1, replacingU byU ?k andD byD k in (2.2). If F ? D k#7;2 #3;L#3;H#7;G#4;#4;, and p ? 2, we define F p... [15], Theorem 2.1). Thus, we have proved that #20;X s #20; p?2 H B ? s #3;X s #4; belongs to L 1#7;2 #3;U#4;. STOCHASTIC EVOLUTION EQUATIONS 161 Notice that F ?? #3;x#4; L#3;H#7;H#4; ? p#3;p? 1#4;#20;x#20; p?2 H . Hence, taking expectations in (3...
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.
The Raychaudhuri equation in homogeneous cosmologies
Albareti, F.D. [Departamento de Física Teórica, Universidad Autónoma de Madrid, Campus de Cantoblanco, Madrid, E-28049 (Spain); Cembranos, J.A.R.; Cruz-Dombriz, A. de la; Dobado, A., E-mail: fdalbareti@ucm.es, E-mail: cembra@fis.ucm.es, E-mail: dombriz@fis.ucm.es, E-mail: dobado@fis.ucm.es [Departamento de Física Teórica I, Universidad Complutense de Madrid, Ciudad Universitaria, Madrid, E-28040 (Spain)
2014-03-01T23:59:59.000Z
In this work we address the issue of studying the conditions required to guarantee the Focusing Theorem for both null and timelike geodesic congruences by using the Raychaudhuri equation. In particular we study the case of Friedmann-Robertson-Walker as well as more general Bianchi Type I spacetimes. The fulfillment of the Focusing Theorem is mandatory in small scales since it accounts for the attractive character of gravity. However, the Focusing Theorem is not satisfied at cosmological scales due to the measured negative deceleration parameter. The study of the conditions needed for congruences convergence is not only relevant at the fundamental level but also to derive the viability conditions to be imposed on extended theories of gravity describing the different expansion regimes of the universe. We illustrate this idea for f(R) gravity theories.
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.
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.
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
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
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
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.
Exact Anisotropic Solutions of the Generalized TOV Equation
Riazi, Nematollah; Sajadi, S Naseh; Assyaee, S Shahrokh
2015-01-01T23:59:59.000Z
We explore gravitating relativistic spheres composed of an anisotropic, barotropic uid. We assume a bi-polytropic equation of state which has a linear and a power-law terms. The generalized Tolman-Oppenheimer-Volkoff (TOV) equation which describes the hydrostatic equilibrium is obtained. The full system of equations are solved for solutions which are regular at the origin and asymptotically flat. Conditions for the appearance of horizon and a basic treatment of stability are also discussed.
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.
Power-law spatial dispersion from fractional Liouville equation
Tarasov, Vasily E. [Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991 (Russian Federation)] [Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991 (Russian Federation)
2013-10-15T23:59:59.000Z
A microscopic model in the framework of fractional kinetics to describe spatial dispersion of power-law type is suggested. The Liouville equation with the Caputo fractional derivatives is used to obtain the power-law dependence of the absolute permittivity on the wave vector. The fractional differential equations for electrostatic potential in the media with power-law spatial dispersion are derived. The particular solutions of these equations for the electric potential of point charge in this media are considered.
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.
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.
Probing the softest region of the nuclear equation of state
Li, Ba; Ko, Che Ming.
1998-01-01T23:59:59.000Z
of the compressed matter. In particular, the transverse flow changes its direction as the colliding system passes through the softest region in the equation of state....
SCIENCE ON SATURDAY- "Disastrous Equations: The Role of Mathematics...
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
SCIENCE ON SATURDAY- "Disastrous Equations: The Role of Mathematics in Understanding Tsunami" Professor J. Douglas Wright, Associate Professor Department of Mathematics, Drexel...
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
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
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.
A six dimensional analysis of Maxwell's Field Equations
Ana Laura García-Perciante; Alfredo Sandoval-Villalbazo; L. S. García Colín
2002-02-08T23:59:59.000Z
A framework based on an extension of Kaluza's original idea of using a five dimensional space to unify gravity with electromagnetism is used to analyze Maxwell\\'{}s field equations. The extension consists in the use of a six dimensional space in which all equations of electromagnetism may be obtained using only Einstein's field equation. Two major advantages of this approach to electromagnetism are discussed, a full symmetric derivation for the wave equations for the potentials and a natural inclusion of magnetic monopoles without using any argument based on singularities.
Jerk, snap, and the cosmological equation of state
Matt Visser
2004-03-31T23:59:59.000Z
Taylor expanding the cosmological equation of state around the current epoch is the simplest model one can consider that does not make any a priori restrictions on the nature of the cosmological fluid. Most popular cosmological models attempt to be ``predictive'', in the sense that once somea priori equation of state is chosen the Friedmann equations are used to determine the evolution of the FRW scale factor a(t). In contrast, a retrodictive approach might usefully take observational dataconcerning the scale factor, and use the Friedmann equations to infer an observed cosmological equation of state. In particular, the value and derivatives of the scale factor determined at the current epoch place constraints on the value and derivatives of the cosmological equation of state at the current epoch. Determining the first three Taylor coefficients of the equation of state at the current epoch requires a measurement of the deceleration, jerk, and snap -- the second, third, and fourth derivatives of the scale factor with respect to time. Higher-order Taylor coefficients in the equation of state are related to higher-order time derivatives of the scale factor. Since the jerk and snap are rather difficult to measure, being related to the third and fourth terms in the Taylor series expansion of the Hubble law, it becomes clear why direct observational constraints on the cosmological equation of state are so relatively weak; and are likely to remain weak for the foreseeable future.
Massively parallel structured direct solver for equations describing ...
2011-10-17T23:59:59.000Z
need for the introduction of coupled systems of partial differential equations to lower ... complexity and interprocessor communication estimates of our algorithm.
Dirac equation in the Nonsymmetric Kaluza-Klein Theory
Kalinowski, M W
2015-01-01T23:59:59.000Z
We rederive Dirac equation in the Nonsymmetric Kaluza-Klein Theory gettig an electric dipole moment of fermion and CP violation.
Dirac equation in the Nonsymmetric Kaluza-Klein Theory
M. W. Kalinowski
2015-07-08T23:59:59.000Z
We rederive Dirac equation in the Nonsymmetric Kaluza-Klein Theory gettig an electric dipole moment of fermion and CP violation.
Software for Numerical Methods for Partial Differential Equations
Software for Numerical Methods for Partial Differential Equations. This software was developed for and by the students in CS 615, Numerical Methods for Partial
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.
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.
Andrey Akhmeteli
2015-07-13T23:59:59.000Z
Previously (A. Akhmeteli, J. Math. Phys., v. 52, p. 082303 (2011)), the Dirac equation in an arbitrary electromagnetic field was shown to be generally equivalent to a fourth-order equation for just one component of the four-component Dirac spinor function. This was done for a specific (chiral) representation of gamma-matrices and for a specific component. In the current work, the result is generalized for a general representation of gamma-matrices and a general component (satisfying some conditions). The resulting equivalent of the Dirac equation is also manifestly relativistically covariant and should be useful in applications of the Dirac equation.
FOURTH ORDER PARTIAL DIFFERENTIAL EQUATIONS ON GENERAL GEOMETRIES
FOURTH ORDER PARTIAL DIFFERENTIAL EQUATIONS ON GENERAL GEOMETRIES By John B. Greer Andrea L0436 Phone: 612/624-6066 Fax: 612/626-7370 URL: http://www.ima.umn.edu #12;Fourth Order Partial Differential (Bertalm´io, Cheng, Osher, and Sapiro 2001) to fourth order PDEs including the Cahn- Hilliard equation
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
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.
Parameter Estimation for the Heat Equation on Perforated Domains
Parameter Estimation for the Heat Equation on Perforated Domains H.T. Banks1 , D. Cioranescu2 , A: Inverse problems, parameter estimation, perforated domains, homogeniza- tion, thermal diffusion, ordinary porous samples by use of solutions of a heat equation on a randomly perforated domain. As noted
Modular Termination of Basic Narrowing and Equational Unification
Escobar, Santiago
Modular Termination of Basic Narrowing and Equational Unification MarÂ´ia Alpuente Santiago Escobar steps to a set of unblocked (or basic) positions. In this work, we study the modularity of termination termination of basic narrowing. Basic narrowing has a number of impor- tant applications including equational
Simultaneous temperature and flux controllability for heat equations with memory
Ceragioli, Francesca
Simultaneous temperature and flux controllability for heat equations with memory S. Avdonin Torino -- Italy, luciano.pandolfi@polito.it June 14, 2010 Abstract It is known that, in the case of heat equation with memory, tem- perature can be controlled to an arbitrary square integrable target provided
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...
Exact null controllability of degenerate evolution equations with scalar control
Fedorov, Vladimir E; Shklyar, Benzion
2012-12-31T23:59:59.000Z
Necessary and sufficient conditions for the exact null controllability of a degenerate linear evolution equation with scalar control are obtained. These general results are used to examine the exact null controllability of the Dzektser equation in the theory of seepage. Bibliography: 13 titles.
Geometric Integration: Numerical Solution of Differential Equations on Manifolds
Scheichl, Robert
and the solar system. Conserved quantities of a Hamiltonian system, such as energy, linear and angular momentumGeometric Integration: Numerical Solution of Differential Equations on Manifolds C.J. Budd 1 & A riches. Psalms 104:24 Since their introduction by Sir Isaac Newton, differential equations have played
Hamilton-Jacobi-Bellman Equations Analysis and Numerical Analysis
Flynn, E. Victor
Hamilton-Jacobi-Bellman Equations Analysis and Numerical Analysis Iain Smears #12;My deepest thanks at Durham University. Abstract. This work treats Hamilton-Jacobi-Bellman equations. Their relation and the inaugural papers on mean-field games. Original research on numerical methods for Hamilton-Jacobi
THE HAMILTON-JACOBI EQUATION, INTEGRABILITY, AND NONHOLONOMIC SYSTEMS
Fassò, Francesco
THE HAMILTON-JACOBI EQUATION, INTEGRABILITY, AND NONHOLONOMIC SYSTEMS LARRY BATES, FRANCESCO FASSÒ why it appears there should not be an analogue of a complete integral for the Hamilton-Jacobi equation for integrable nonholonomic systems. February 7, 2014 1. Introduction The Hamilton-Jacobi theory is at the heart
Hamilton-Jacobi equations with discontinuous source terms Nao Hamamuki
Ishii, Hitoshi
Hamilton-Jacobi equations with discontinuous source terms Nao Hamamuki We study the initial-value problem for the Hamilton-Jacobi equation of the form { tu(x, t) + H(x, xu(x, t)) = 0 in Rn × (0, T), u control problem with a semicontinuous running cost function. References [1] Y. Giga, N. Hamamuki, Hamilton-Jacobi
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
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.
The Lamb-Bateman integral equation and the fractional derivatives
D. Babusci; G. Dattoli; D. Sacchetti
2010-06-08T23:59:59.000Z
The Lamb-Bateman integral equation was introduced to study the solitary wave diffraction and its solution was written in terms of an integral transform. We prove that it is essentially the Abel integral equation and its solution can be obtained using the formalism of fractional calculus.
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
Generalized Input/Output Equations and Nonlinear Realizability
Wang, Yuan
operator satisfies a possibly high-order differential input/output equation, then it is locally realizable-9108250 and DMS-9403924 Keywords: Generating series, local realization of input/output operators, input/outputGeneralized Input/Output Equations and Nonlinear Realizability Yuan Wang Mathematics Department
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
Equisolvability of Series vs. Controller's Topology in Synchronous Language Equations
Brayton, Robert K.
Equisolvability of Series vs. Controller's Topology in Synchronous Language Equations Nina operators for abstract languages: synchronous composition, #15;, and parallel composition, #5;, and we studied the solutions of the equations defined over finite state machines (FSMs) of the type MA #15; MX
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
KH Computational Physics-2015 Basic Numerical Algorithms Ordinary differential equations
Gustafsson, Torgny
KH Computational Physics- 2015 Basic Numerical Algorithms Ordinary differential equations The set(xl) at certain points xl. Kristjan Haule, 2015 1 #12;KH Computational Physics- 2015 Basic Numerical Algorithms purpose routine · Numerov's algorithm: ¨y = f(t)y(t) ( for Schroedinger equation) · Verlet algorithm: ¨y
MATH 225 Fall 2011 Differential Equations Course Syllabus
MATH 225 Fall 2011 Differential Equations Course Syllabus Instructor Info Instructor: Phone: Office: Email: Office Hours: Section Website: Course Website: http://mcs.mines.edu/Courses/math225/ Grading sciences. Prerequisites: MATH213 or MATH223 Text Differential Equations with Boundary-Value Problems, 7th
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
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.
The modified equation for spinless particles and superalgebra
Sadeghi, J.; Rostami, M. [Department of Physics, Islamic Azad University, Ayatollah Amoli Branch, P.O. Box 678, Amol (Iran, Islamic Republic of)] [Department of Physics, Islamic Azad University, Ayatollah Amoli Branch, P.O. Box 678, Amol (Iran, Islamic Republic of); Sadeghi, Z. [Young Researchers Club, Islamic Azad University, Ayatollah Amoli Branch, Amol (Iran, Islamic Republic of)] [Young Researchers Club, Islamic Azad University, Ayatollah Amoli Branch, Amol (Iran, Islamic Republic of)
2013-09-15T23:59:59.000Z
In this paper we consider modified wave equations for spinless particles in an external magnetic field. We consider 4-potentials which guarantee Lorentz' and Coulomb's conditions. The new variable for modified wave equation leads us to consider the associated Laguerre differential equation. We take advantage of the factorization method in Laguerre differential equation and solve the modified equation. In order to obtain the wave function, energy spectrum and its quantization, we will establish conditions for the orbital quantum number. We account such orbital quantum number and obtain the raising and lowering operators. If we want to have supersymmetry partners, we need to apply the shape invariance condition. This condition for the partner potential will help us find the limit of ? as ?=±?(l)
Moment equations for chemical reactions on interstellar dust grains
Azi Lipshtat; Ofer Biham
2002-12-09T23:59:59.000Z
While most chemical reactions in the interstellar medium take place in the gas phase, those occurring on the surfaces of dust grains play an essential role. Chemical models based on rate equations including both gas phase and grain surface reactions have been used in order to simulate the formation of chemical complexity in interstellar clouds. For reactions in the gas phase and on large grains, rate equations, which are highly efficient to simulate, are an ideal tool. However, for small grains under low flux, the typical number of atoms or molecules of certain reactive species on a grain may go down to order one or less. In this case the discrete nature of the opulations of reactive species as well as the fluctuations become dominant, thus the mean-field approximation on which the rate equations are based does not apply. Recently, a master equation approach, that provides a good description of chemical reactions on interstellar dust grains, was proposed. Here we present a related approach based on moment equations that can be obtained from the master equation. These equations describe the time evolution of the moments of the distribution of the population of the various chemical species on the grain. An advantage of this approach is the fact that the production rates of molecular species are expressed directly in terms of these moments. Here we use the moment equations to calculate the rate of molecular hydrogen formation on small grains. It is shown that the moment equation approach is efficient in this case in which only a single reactive specie is involved. The set of equations for the case of two species is presented and the difficulties in implementing this approach for complex reaction networks involving multiple species are discussed.
Grossberg, Stephen
Appendix: Equations and Parameters This section describes BCS and FCS equations that incorporate data: Only a single scale is used, and hypercomplex and bipole cells in the BCS and monocular filling Simple Cells of the BCS Evensymmetric and oddsymmetric simple cell receptive fields centered
Grossberg, Stephen
Appendix: Equations and Parameters This section describes BCS and FCS equations that incorporate: Only a single scale is used, and hypercomplex and bipole cells in the BCS and monocular lling. This assures a positive response to ganzfelds. A2 Simple Cells of the BCS Even-symmetric and odd
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
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.
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.
Symmetries and exact solutions of the rotating shallow water equations
Alexander Chesnokov
2008-08-11T23:59:59.000Z
Lie symmetry analysis is applied to study the nonlinear rotating shallow water equations. The 9-dimensional Lie algebra of point symmetries admitted by the model is found. It is shown that the rotating shallow water equations are related with the classical shallow water model with the change of variables. The derived symmetries are used to generate new exact solutions of the rotating shallow equations. In particular, a new class of time-periodic solutions with quasi-closed particle trajectories is constructed and studied. The symmetry reduction method is also used to obtain some invariant solutions of the model. Examples of these solutions are presented with a brief physical interpretation.
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...
New Dirac equation from the view point of particle
Ozaydin, Fatih; Altintas, Azmi Ali; Susam, Lidya Amon; Arik, Metin; Yarman, Tolga [Okan University, Istanbul (Turkey); Istanbul University, Istanbul (Turkey); Bogazici University, Istanbul (Turkey)
2012-09-06T23:59:59.000Z
According to the classical approach, especially the Lorentz Invariant Dirac Equation, when particles are bound to each other, the interaction term appears as a quantity belonging to the 'field'. In this work, as a totally new approach, we propose to alter the rest masses of the particles due to their interaction, as much as their respective contributions to the static binding energy. Thus we re-write and solve the Dirac Equation for the hydrogen atom, and amazingly, obtain practically the same numerical results for the ground states, as those obtained from the Dirac Equation.
A new vapor pressure equation originating at the critical point
Nuckols, James William
1976-01-01T23:59:59.000Z
111 1v vi vi1 25 29 32 33 vi Table LIST OF TABLES Page 1. Hall-Eubank Coefficients for Ar, N2, and C2H6 2. HEN Equation Coefficients and Sources of Data 3. Comparison of the HEN, Frost-Kalkwarf, and Wagner Equations 17 27 vii LIST... in existence are discussed by Wagner (1973), Niiller (1964), and Reid and Sherwood (1966). These references indicate that the Frost-Kalkwarf (1953) and the Wagner (1973) equations achieve the best overall description of the coexistence curve, but they too...
Skyrme models and nuclear matter equation of state
Adam, Christoph; Wereszczynski, Andrzej
2015-01-01T23:59:59.000Z
We investigate the role of pressure in a class of generalised Skyrme models. We introduce pressure as the trace of the spatial part of the energy-momentum tensor and show that it obeys the usual thermodynamical relation. Then, we compute analytically the mean-field equation of state in the high and medium pressure regimes by applying topological bounds on compact domains. The equation of state is further investigated numerically for the charge one skyrmions. We identify which term in a generalised Skyrme model is responsible for which part in the equation of state. Further, we compare our findings with the corresponding results in the Walecka model.
Solution of the Helmholtz equation for spin-2 fields
G. F. Torres del Castillo; J. E. Rojas Marcial
2003-05-01T23:59:59.000Z
The Helmholtz equation for symmetric, traceless, second-rank tensor fields in three-dimensional flat space is solved in spherical and cylindrical coordinates by separation of variables making use of the corresponding spin-weighted harmonics. It is shown that any symmetric, traceless, divergenceless second-rank tensor field that satisfies the Helmholtz equation can be expressed in terms of two scalar potentials that satisfy the Helmholtz equation. Two such expressions are given, which are adapted to the spherical or cylindrical coordinates. The application to the linearized Einstein theory is discussed.
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
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 ...
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.
A rough analytic relation on partial differential equations
Kato, Tsuyoshi
2010-01-01T23:59:59.000Z
We introduce some analytic relations on the set of partial differential equations of two variables. It relies on a new comparison method to give rough asymptotic estimates for solutions which obey different partial differential equations. It uses a kind of scale transform called tropical geometry which connects automata with real rational dynamics. Two different solutions can be considered when their defining equations are transformed to the same automata at infinity. We have a systematic way to construct related pairs of different partial differential equations, and also construct some unrelated pairs concretely. These verify that the new relations are non trivial. We also make numerical calculations and compare the results for both related and unrelated pairs of PDEs.
An inverse problem for the transmission wave equation.
2006-11-03T23:59:59.000Z
We consider a transmission wave equation in two embedded domains in. R. 2, where the speed is a1 > 0 in the inner domain and a2 > 0 in the outer domain.
Fit Index Sensitivity in Multilevel Structural Equation Modeling
Boulton, Aaron Jacob
2011-07-29T23:59:59.000Z
Multilevel Structural Equation Modeling (MSEM) is used to estimate latent variable models in the presence of multilevel data. A key feature of MSEM is its ability to quantify the extent to which a hypothesized model fits ...
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.
M. J. Holst The Poisson-Boltzmann Equation
Holst, Michael J.
discontinuous coefficients representing material interfaces, rapid nonlinearities, and three spatial dimensions. Similar equations occur in various applications, including nuclear physics, semiconductor physics complex biomolecule lying in a solvent. We next study the theoretical properties of the linearized
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
Fast methods for static Hamilton-Jacobi Partial Differential Equations
Vladimirsky, Alexander Boris
2001-01-01T23:59:59.000Z
k y , A . , Fast Methods for the Eikonal Jacobi Equations onMethod and "lifting-to-manifold" to solve an anisotropic static H a m i l t o n - Jacobi
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.
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...
A piecewise linear finite element discretization of the diffusion equation
Bailey, Teresa S
2006-10-30T23:59:59.000Z
In this thesis, we discuss the development, implementation and testing of a piecewise linear (PWL) continuous Galerkin finite element method applied to the threedimensional diffusion equation. This discretization is particularly interesting because...
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.
Lorentz-Dirac equation in the delta-function pulse
Miroslav Pardy
2012-08-01T23:59:59.000Z
We formulate the Lorentz-Dirac equation in the plane wave and in the Dirac delta-function pulse. The discussion on the relation of the Dirac delta-function to the ultrashort laser pulse is involved.
A Note on DeMoivre's Quintic Equation
M. L. Glasser
2009-07-18T23:59:59.000Z
The quintic equation with real coefficients $$x^5+5ax^3+5a^2x+b=0$$ is solved in terms of radicals and the results used to sum a hypergeometric series for several arguments.
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.
Electrolux Gibson Air Conditioner and Equator Clothes Washer...
Broader source: Energy.gov (indexed) [DOE]
DOE testing in support of the ENERGY STAR program has revealed that an Electrolux Gibson air conditioner (model GAH105Q2T1) and an Equator clothes washer (model EZ 3720 CEE), both...
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.
MATH 411 SPRING 2001 Ordinary Di#erential Equations
Alekseenko, Alexander
MATH 411 SPRING 2001 Ordinary Di#erential Equations Schedule # 749025 TR 01:00Â02:15 316 Boucke Instructor: Alexander Alekseenko, 328 McAllister, 865Â1984, alekseen@math.psu.edu The course
A Hamiltonian functional for the linearized Einstein vacuum field equations
R. Rosas-Rodriguez
2005-07-26T23:59:59.000Z
By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form by using a conserved functional as Hamiltonian; this Hamiltonian is not the analog of the energy of the field. A Poisson bracket between functionals of the field, compatible with the constraints satisfied by the field variables, is obtained. The generator of spatial translations associated with such bracket is also obtained.
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-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.
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).
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.
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...
Integral relations for solutions of confluent Heun equations
Léa Jaccoud El-Jaick; Bartolomeu D. B. Figueiredo
2015-03-02T23:59:59.000Z
Firstly, we construct kernels of integral relations among solutions of the confluent Heun equation (CHE) and its limit, the reduced CHE (RCHE). In both cases we generate additional kernels by systematically applying substitutions of variables. Secondly, we establish integral relations between known solutions of the CHE that are power series and solutions that are series of special functions; and similarly for solutions of the RCHE. Thirdly, by using one of the integral relations as an integral transformation we obtain a new series solution of the spheroidal wave equation. From this solution we construct new solutions of the general CHE, and show that these are suitable for solving the radial part of the two-center problem in quantum mechanics. Finally, by applying a limiting process to kernels for the CHEs we obtain kernels for {two} double-confluent Heun equations. As a result, we deal with kernels of four equations of the Heun family, each equation presenting a distinct structure of singularities. In addition, we find that the known kernels for the Mathieu equation are special instances of kernels of the RCHE.
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.
Farquharson, Colin G.
Comparison of integral equation and physical scale modelling of the electromagnetic response history of EM numerical modelling in geophysics. Â· Another integral equation modelling program;Introduction: a brief history Â· Two main approaches to numerical modelling: integral equation; finite
A meshfree method for the Poisson equation with 3D wall-bounded flow application
Vasilyeva, Anna, S.M. Massachusetts Institute of Technology
2010-01-01T23:59:59.000Z
The numerical approximation of the Poisson equation can often be found as a subproblem to many more complex computations. In the case of Lagrangian approaches of flow equations, the Poisson equation often needs to be solved ...
Handbook of Industrial Engineering Equations, Formulas, and Calculations
Badiru, Adedeji B [ORNL; Omitaomu, Olufemi A [ORNL
2011-01-01T23:59:59.000Z
The first handbook to focus exclusively on industrial engineering calculations with a correlation to applications, Handbook of Industrial Engineering Equations, Formulas, and Calculations contains a general collection of the mathematical equations often used in the practice of industrial engineering. Many books cover individual areas of engineering and some cover all areas, but none covers industrial engineering specifically, nor do they highlight topics such as project management, materials, and systems engineering from an integrated viewpoint. Written by acclaimed researchers and authors, this concise reference marries theory and practice, making it a versatile and flexible resource. Succinctly formatted for functionality, the book presents: Basic Math Calculations; Engineering Math Calculations; Production Engineering Calculations; Engineering Economics Calculations; Ergonomics Calculations; Facility Layout Calculations; Production Sequencing and Scheduling Calculations; Systems Engineering Calculations; Data Engineering Calculations; Project Engineering Calculations; and Simulation and Statistical Equations. It has been said that engineers make things while industrial engineers make things better. To make something better requires an understanding of its basic characteristics and the underlying equations and calculations that facilitate that understanding. To do this, however, you do not have to be computational experts; you just have to know where to get the computational resources that are needed. This book elucidates the underlying equations that facilitate the understanding required to improve design processes, continuously improving the answer to the age-old question: What is the best way to do a job?
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.
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.
Consistency of equations of motion in conformal frames
J. R. Morris
2014-11-05T23:59:59.000Z
Four dimensional scalar-tensor theory is considered within two conformal frames, the Jordan frame (JF) and the Einstein frame (EF). The actions for the theory are equivalent and equations of motion can be obtained from each action. It is found that the JF equations of motion, expressed in terms of EF variables, translate directly into and agree with the EF equations of motion obtained from the EF action, provided that certain simple consistency conditions are satisfied, which is always the case. The implication is that a solution set obtained in one conformal frame can be reliably translated into a solution set for the other frame, and therefore the two frames are, at least, mathematically equivalent.
Fourth order gravity: equations, history, and applications to cosmology
H. -J. Schmidt
2006-03-25T23:59:59.000Z
The field equations following from a Lagrangian L(R) will be deduced and solved for special cases. If L is a non-linear function of the curvature scalar, then these equations are of fourth order in the metric. In the introduction we present the history of these equations beginning with the paper of H. Weyl from 1918, who first discussed them as alternative to Einstein's theory. In the third part, we give details about the cosmic no hair theorem, i.e., the details how within fourth order gravity with L= R + R^2 the inflationary phase of cosmic evolution turns out to be a transient attractor. Finally, the Bicknell theorem, i.e. the conformal relation from fourth order gravity to scalar-tensor theory, will be shortly presented.
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.
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
Reformulating the Schrodinger equation as a Shabat-Zakharov system
Boonserm, Petarpa
2009-01-01T23:59:59.000Z
We reformulate the second-order Schrodinger equation as a set of two coupled first order differential equations, a so-called "Shabat-Zakharov system", (sometimes called a "Zakharov-Shabat" system). There is considerable flexibility in this approach, and we emphasise the utility of introducing an "auxiliary condition" or "gauge condition" that is used to cut down the degrees of freedom. Using this formalism, we derive the explicit (but formal) general solution to the Schrodinger equation. The general solution depends on three arbitrarily chosen functions, and a path-ordered exponential matrix. If one considers path ordering to be an "elementary" process, then this represents complete quadrature, albeit formal, of the second-order linear ODE.
Generic master equations for quasi-normal frequencies
Skakala, Jozef
2010-01-01T23:59:59.000Z
Generic master equations governing the highly-damped quasi-normal frequencies [QNFs] of one-horizon, two-horizon, and even three-horizon spacetimes can be obtained through either semi-analytic or monodromy techniques. While many technical details differ, both between the semi-analytic and monodromy approaches, and quite often among various authors seeking to apply the monodromy technique, there is nevertheless widespread agreement regarding the the general form of the QNF master equations. Within this class of generic master equations we can establish some rather general results, relating the existence of "families" of QNFs of the form omega_{a,n} = (offset)_a + i n (gap) to the question of whether or not certain ratios of parameters are rational or irrational.
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
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.
The Schroedinger equation with friction from the quantum trajectory perspective
Garashchuk, Sophya; Dixit, Vaibhav; Gu Bing; Mazzuca, James [Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208 (United States)
2013-02-07T23:59:59.000Z
Similarity of equations of motion for the classical and quantum trajectories is used to introduce a friction term dependent on the wavefunction phase into the time-dependent Schroedinger equation. The term describes irreversible energy loss by the quantum system. The force of friction is proportional to the velocity of a quantum trajectory. The resulting Schroedinger equation is nonlinear, conserves wavefunction normalization, and evolves an arbitrary wavefunction into the ground state of the system (of appropriate symmetry if applicable). Decrease in energy is proportional to the average kinetic energy of the quantum trajectory ensemble. Dynamics in the high friction regime is suitable for simple models of reactions proceeding with energy transfer from the system to the environment. Examples of dynamics are given for single and symmetric and asymmetric double well potentials.
Semi-Spectral Method for the Wigner equation
Oliver Furtmaier; Sauro Succi; Miller Mendoza
2015-06-29T23:59:59.000Z
We propose a numerical method to solve the Wigner equation in quantum systems of spinless, non-relativistic particles. The method uses a spectral decomposition into $L^2(\\mathbb{R}^d)$ basis functions in momentum-space to obtain a system of first-order advection-reaction equations. The resulting equations are solved by splitting the reaction and advection steps so as to allow the combination of numerical techniques from quantum mechanics and computational fluid dynamics by identifying the skew-hermitian reaction matrix as a generator of unitary rotations. The method is validated for the case of particles subject to a one-dimensional (an-)harmonic potential using finite-differences for the advection part. Thereby, we verify the second order of convergence and observe non-classical behavior in the evolution of the Wigner function.
Semi-Spectral Method for the Wigner equation
Furtmaier, Oliver; Mendoza, Miller
2015-01-01T23:59:59.000Z
We propose a numerical method to solve the Wigner equation in quantum systems of spinless, non-relativistic particles. The method uses a spectral decomposition into $L^2(\\mathbb{R}^d)$ basis functions in momentum-space to obtain a system of first-order advection-reaction equations. The resulting equations are solved by splitting the reaction and advection steps so as to allow the combination of numerical techniques from quantum mechanics and computational fluid dynamics by identifying the skew-hermitian reaction matrix as a generator of unitary rotations. The method is validated for the case of particles subject to a one-dimensional (an-)harmonic potential using finite-differences for the advection part. Thereby, we verify the second order of convergence and observe non-classical behavior in the evolution of the Wigner function.
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.
Invariant discretization schemes for the shallow-water equations
Alexander Bihlo; Roman O. Popovych
2013-01-03T23:59:59.000Z
Invariant discretization schemes are derived for the one- and two-dimensional shallow-water equations with periodic boundary conditions. While originally designed for constructing invariant finite difference schemes, we extend the usage of difference invariants to allow constructing of invariant finite volume methods as well. It is found that the classical invariant schemes converge to the Lagrangian formulation of the shallow-water equations. These schemes require to redistribute the grid points according to the physical fluid velocity, i.e., the mesh cannot remain fixed in the course of the numerical integration. Invariant Eulerian discretization schemes are proposed for the shallow-water equations in computational coordinates. Instead of using the fluid velocity as the grid velocity, an invariant moving mesh generator is invoked in order to determine the location of the grid points at the subsequent time level. The numerical conservation of energy, mass and momentum is evaluated for both the invariant and non-invariant schemes.
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.
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.
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.
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.
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.
Equality: A tool for free-form equation editing
Cummins, Stephen; Davies, Ian; Rice, Andrew; Beresford, Alastair R.
2015-06-10T23:59:59.000Z
interface, the parser runs entirely in the web browser. This keeps the system self-contained and avoids all issues of 4http://facebook.github.io/react/ Fig. 1. The Equality equation editor. Note that the slightly jumbled symbols dropped onto the canvas have... . “Editing equations was easier because I could drag elements around With microsoft you had to put in the format (e.g. exponent) before actually putting in variables/numbers which was irritating” This reinforces our aim of providing a tool that supports...
Stable blowup for wave equations in odd space dimensions
Roland Donninger; Birgit Schörkhuber
2015-04-03T23:59:59.000Z
We consider semilinear wave equations with focusing power nonlinearities in odd space dimensions $d \\geq 5$. We prove that for every $p > \\frac{d+3}{d-1}$ there exists an open set of radial initial data in $H^{\\frac{d+1}{2}} \\times H^{\\frac{d-1}{2}}$ such that the corresponding solution exists in a backward lightcone and approaches the ODE blowup profile. The result covers the entire range of energy supercritical nonlinearities and extends our previous work for the three-dimensional radial wave equation to higher space dimensions.
Quantum optical master equation for solid-state quantum emitters
Ralf Betzholz; Juan Mauricio Torres; Marc Bienert
2014-12-15T23:59:59.000Z
We provide an elementary description of the dynamics of defect centers in crystals in terms of a quantum optical master equation which includes spontaneous decay and a simplified vibronic interaction with lattice phonons. We present the general solution of the dynamical equation by means of the eigensystem of the Liouville operator and exemplify the usage of this damping basis to calculate the dynamics of the electronic and vibrational degrees of freedom and to provide an analysis of the spectra of scattered light. The dynamics and spectral features are discussed with respect to the applicability for color centers, especially for negatively charged nitrogen-vacancy centers in diamond.
The Jacobi Equation and Poisson Geometry on R4
Rubén Flores-Espinoza
2013-06-21T23:59:59.000Z
This paper is devoted to the study of solutions of the Jacobi equation in Euclidean four dimensional space R4. Each of such solutions define a Poisson tensor. Using the elementary vector calculus operations we give explicit formulas for the main geometric objets associated to the solutions of Jacobi equation, including its characteristic foliation, their symmetries and its generators, normal forms and some useful decomposition results for the solutions. In particular we study the classes of Poisson tensors of contant rank and those preserving a volume form.
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...
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.
Electromagnetic interactions for the two-body spectator equations
J. Adam; Franz Gross; J.W. Van Orden
1997-10-01T23:59:59.000Z
This paper presents a new non-associative algebra which is used to (1) show how the spectator (or Gross) two-body equations and electromagnetic currents can be formally derived from the Bethe-Salpeter equation and currents if both are treated to all orders, (2) obtain explicit expressions for the Gross two-body electromagnetic currents valid to any order, and (3) prove that the currents so derived are exactly gauge invariant when truncated consistently to any finite order. In addition to presenting these new results, this work complements and extends previous treatments based largely on the analysis of sums of Feynman diagrams.
The modified Klein Gordon equation for neolithic population migration
M. Pelc; J. Marciak-Kozlowska; M. Kozlowski
2007-03-11T23:59:59.000Z
In this paper the model for the neolithic migration in Europe is developed. The new migration equation, the modified Klein Gordon equation is formulated and solved. It is shown that the migration process can be described as the hyperbolic diffusion with constant speed. In comparison to the existing models based on the generalization of the Fisher approach the present model describes the migration as the transport process with memory and offers the possibility to recover the initial state of migration which is the wave motion with finite velocity.
Efficiency of Carnot Cycle with Arbitrary Gas Equation of State
Tjiang, P C; Tjiang, Paulus C.; Sutanto, Sylvia H.
2006-01-01T23:59:59.000Z
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.
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.
New elliptic solutions of the Yang-Baxter equation
D. Chicherin; S. E. Derkachov; V. P. Spiridonov
2015-05-13T23:59:59.000Z
We consider finite-dimensional reductions of the most general known solution of the Yang-Baxter equation with a rank 1 symmetry algebra, which is described by an integral operator with an elliptic hypergeometric kernel. The reduced R-operators reproduce at their bottom the standard Baxter's R-matrix for the 8-vertex model and Sklyanin's L-operator. The general formula has a remarkably compact form and yields new elliptic solutions of the Yang-Baxter equation based on the finite-dimensional representations of the elliptic modular double. The same result is reproduced using the fusion formalism.
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.
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.
The random Schrödinger equation: homogenization in time-dependent potentials
Yu Gu; Lenya Ryzhik
2015-06-08T23:59:59.000Z
We analyze the solutions of the Schr\\"odinger equation with the low frequency initial data and a time-dependent weakly random potential. We prove a homogenization result for the low frequency component of the wave field. We also show that the dynamics generates a non-trivial energy in the high frequencies, which do not homogenize -- the high frequency component of the wave field remains random and the evolution of its energy is described by a kinetic equation. The transition from the homogenization of the low frequencies to the random limit of the high frequencies is illustrated by understanding the size of the small random fluctuations of the low frequency component.
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.
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
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
Development of an empirical equation to estimate the saturation exponent n of porous media
Kansal, Chaman Lal
1967-01-01T23:59:59.000Z
only the resistivity of the brine Rw, was: 31 ln n A0 + Al ln Rw (16) Coefficients of the above and the following regression equations are listed in Table 3. Equation 16 gave an average deviation of 9. 84 per cent. Similar equations of Desai... deviation of 8. 2 per cent. In Equation 19 the travel time was added to the independent variables used in Equation 18. ln n A0 + Al ln Rw + A2 ln GD + A3 ln GR + A4 ln Tc. (19) Equation 19 gave an average deviation of 7. 43 per cent The last equation...
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.
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.
GLOBAL INFINITE ENERGY SOLUTIONS FOR THE CUBIC WAVE EQUATION
Thomann, Laurent
energy) random initial data. To the best of our knowledge such a regularity is out of reachGLOBAL INFINITE ENERGY SOLUTIONS FOR THE CUBIC WAVE EQUATION by Nicolas Burq, Laurent Thomann & Nikolay Tzvetkov Abstract. -- We prove the existence of infinite energy global solutions of the cubic wave
Iterative Solution of Elliptic Equations with a Small Parameter
Segatti, Antonio
of thin structures, e.g. beams, plates and shells. All of the above examples share the characteristic. Equations of the type (1) are discretized using finite-difference or finite- element methods giving rise the properties of the operators Li and the vectors x and b describe the unknown u and the load f with respect
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.
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
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.
Parameter Estimation for the Heat Equation on Perforated Domains
Parameter Estimation for the Heat Equation on Perforated Domains H.T. Banks1 , D. Cioranescu2 , A for simulated data for heat flow in a porous medium. We consider data simulated from a model on a perforated Words: Inverse problems, parameter estimation, perforated domains, homogeniza- tion, thermal diffusion
Variations on Algebra: monadicity and generalisations of equational theories
Robinson, Edmund
Variations on Algebra: monadicity and generalisations of equational theories Edmund Robinson #3 that there was a connection between one- sorted algebraic theories and the categorical notion of monad, or more precisely toposes at the top. However, monads exist on categories other than Set, and many of the attractive
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
Generalised hydrodynamic reductions of the kinetic equation for soliton gas
Generalised hydrodynamic reductions of the kinetic equation for soliton gas Gennady A. El1 , Maxim of Russian Academy of Sciences, Moscow, 53 Leninskij Prospekt, Moscow, Russia 3 Laboratory of Geometric, Moscow, Russia 4 Institute for Nuclear Research, National Academy of Sciences of Ukraine, 47 pr. Nauky
Fast sweeping methods for eikonal equations on triangular meshes
Zhao, Hongkai
Fast sweeping methods for eikonal equations on triangular meshes Jianliang Qian1 , Yong-Tao Zhang2 , and Hong-Kai Zhao3 Abstract The original fast sweeping method, which is an efficient iterative method propose novel ordering strategies so that the fast sweeping method can be extended efficiently and easily
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.
The Geometry of First-Order DIfferential Equations
PRETEX (Halifax NS) #1 1054 1999 Mar 05 10:59:16
2010-01-20T23:59:59.000Z
“main”. 2007/2/16 page 20 i i i i i i i i. 20 CHAPTER 1. First-Order Differential Equations. 35. y = cos x, y(0) = 2, y (0) = 1. 36. y = 6x, y(0) = 1, y (0) = ?1, y (0) = 4.
Optimum Aerodynamic Design using the Navier--Stokes Equations
Pierce, Niles A.
Princeton, New Jersey 08544 USA and y Oxford University Computing Laboratory Numerical Analysis Group Oxford until an optimum solution is approached. Each design cycle requires the numerical solution of both the flow and the adjoint equations, leading to a computational cost roughly equal to the cost of two flow
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
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...
Hamilton-Jacobi equations with jumps: asymptotic stability
Amir Mahmood; Saima Parveen
2009-09-05T23:59:59.000Z
The asymptotic stability of a global solution satisfying Hamilton-Jacobi equations with jumps will be analyzed in dependence on the strong dissipativity of the jump control function and using orbits of the differentiable flows to describe the corresponding characteristic system.
On 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.
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
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
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.
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.
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
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
The generating functions of Lame equation in Weierstrass's form
Yoon Seok Choun
2014-11-07T23:59:59.000Z
Lame equation arises from deriving Laplace equation in ellipsoidal coordinates; in other words, it's called ellipsoidal harmonic equation. Lame function is applicable to diverse areas such as boundary value problems in ellipsoidal geometry, chaotic Hamiltonian systems, the theory of Bose-Einstein condensates, etc. By applying generating function into modern physics (quantum mechanics, thermodynamics, black hole, supersymmetry, special functions, etc), we are able to obtain the recursion relation, a normalization constant for the wave function and expectation values of any physical quantities. For the case of hydrogen-like atoms, generating function of associated Laguerre polynomial has been used in order to derive expectation values of position and momentum. By applying integral forms of Lame polynomial in the Weierstrass's form in which makes B_n term terminated [29], I consider generating function of it including all higher terms of A_n's. This paper is 8th out of 10 in series "Special functions and three term recurrence formula (3TRF)". See section 4 for all the papers in the series. Previous paper in series deals with the power series expansion and the integral formalism of Lame equation in the Weierstrass's form and its asymptotic behavior [29]. The next paper in the series describes analytic solution for grand confluent hypergeometric function [31].
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...
Tachyonic equations to reduce the divergent integral of QED
Z. Wang
2009-11-12T23:59:59.000Z
If the total integral including both 0
MATH 286 --FALL 2008 TEST I DIFFERENTIAL EQUATIONS PLUS
Yong, Alexander
factor correctly · 3 points for multiplying through by the integrating factor and using the reverse the logistic equation P (t) = aP - bP2 where aP is the birth rate per month and bP2 is the death rate per month
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.
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.
Topological horseshoes in travelling waves of discretized nonlinear wave equations
Chen, Yi-Chiuan, E-mail: YCChen@math.sinica.edu.tw [Institute of Mathematics, Academia Sinica, Taipei 10617, Taiwan (China)] [Institute of Mathematics, Academia Sinica, Taipei 10617, Taiwan (China); Chen, Shyan-Shiou, E-mail: sschen@ntnu.edu.tw [Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan (China)] [Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan (China); Yuan, Juan-Ming, E-mail: jmyuan@pu.edu.tw [Department of Financial and Computational Mathematics, Providence University, Shalu, Taichung 43301, Taiwan (China)] [Department of Financial and Computational Mathematics, Providence University, Shalu, Taichung 43301, Taiwan (China)
2014-04-15T23:59:59.000Z
Applying the concept of anti-integrable limit to coupled map lattices originated from space-time discretized nonlinear wave equations, we show that there exist topological horseshoes in the phase space formed by the initial states of travelling wave solutions. In particular, the coupled map lattices display spatio-temporal chaos on the horseshoes.
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
Mechanical Dynamics, the Swing Equation, Units 1.0 Preliminaries
McCalley, James D.
1 Mechanical Dynamics, the Swing Equation, Units 1.0 Preliminaries The basic requirement have mechanical speeds so as to produce the same "electrical speed." Electrical speed and mechanical speed are related as a function of the number of machine poles, p, or pole pairs, p
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
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.
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.
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
DERIVING PROGNOSTIC EQUATIONS FOR CLOUD FRACTION AND LIQUID WATER CONTENT
DERIVING PROGNOSTIC EQUATIONS FOR CLOUD FRACTION AND LIQUID WATER CONTENT Vincent E. Larson1 1 that accounts for how liquid water varies with both total water content and temperature. The variable s has- ter content, ql , and cloud fraction, C. This provides in- formation about partial cloudiness. Tiedtke
The Time-Dependent NavierStokes Equations Laminar Flows
John, Volker
Chapter 6 The Time-Dependent NavierStokes Equations Laminar Flows Remark 6.1. Motivation to distinguish between laminar and turbulent flows. It does not exist an exact definition of these terms. From the point of view of simulations, a flow is considered to be laminar, if on reasonable grids all flow
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
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.
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,
Coupling conditions for the shallow water equations on a network
Caputo, Jean-Guy; Gleyse, Bernard
2015-01-01T23:59:59.000Z
We study numerically and analytically how nonlinear shallow water waves propagate in a fork. Using a homothetic reduction procedure, conservation laws and numerical analysis in a 2D domain, we obtain angle dependent coupling conditions for the water height and the velocity. We compare these to the ones for a class of scalar nonlinear wave equations for which the angle plays no role.
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
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...
Mean field extrapolations of microscopic nuclear equations of state
Rrapaj, Ermal; Holt, Jeremy W
2015-01-01T23:59:59.000Z
We explore the use of mean field models to approximate microscopic nuclear equations of state derived from chiral effective field theory across the densities and temperatures relevant for simulating astrophysical phenomena such as core-collapse supernovae and binary neutron star mergers. We consider both relativistic mean field theory with scalar and vector meson exchange as well as energy density functionals based on Skyrme phenomenology and compare to thermodynamic equations of state derived from chiral two- and three-nucleon forces in many-body perturbation theory. Quantum Monte Carlo simulations of symmetric nuclear matter and pure neutron matter are used to determine the density regimes in which perturbation theory with chiral nuclear forces is valid. Within the theoretical uncertainties associated with the many-body methods, we find that select mean field models describe well microscopic nuclear thermodynamics. As an additional consistency requirement, we study as well the single-particle properties of ...
The State of the Dark Energy Equation of State
Alessandro Melchiorri; Laura Mersini; Carolina J. Odman; Mark Trodden
2003-04-16T23:59:59.000Z
By combining data from seven cosmic microwave background experiments (including the latest WMAP results) with large scale structure data, the Hubble parameter measurement from the Hubble Space Telescope and luminosity measurements of Type Ia supernovae we demonstrate the bounds on the dark energy equation of state $w_Q$ to be $-1.38< w_Q <-0.82$ at the 95% confidence level. Although our limit on $w_Q$ is improved with respect to previous analyses, cosmological data does not rule out the possibility that the equation of state parameter $w_Q$ of the dark energy $Q$ is less than -1. We present a tracking model that ensures $w_Q \\le -1$ at recent times and discuss the observational consequences.
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.
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.
Solution of the string equations for asymmetric potentials
Patrick Waters
2015-06-22T23:59:59.000Z
We consider the large $N$ expansion of the partition function for the Hermitian one-matrix model. It is well known that the coefficients of this expansion are generating functions $F^{(g)}$ for a certain kind of graph embedded in a Riemann surface. Other authors have made a simplifying assumption that the potential $V$ is an even function. We present a method for computing $F^{(g)}$ in the case that $V$ is not an even function. Our method is based on the string equations, and yields "valence independent" formulas which do not depend explicitly on the potential. We introduce a family of differential operators, the "string polynomials", which make clear the valence independent nature of the string equations.
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.
General Fractional Calculus, Evolution Equations, and Renewal Processes
Anatoly N. Kochubei
2011-10-08T23:59:59.000Z
We develop a kind of fractional calculus and theory of relaxation and diffusion equations associated with operators in the time variable, of the form $(Du)(t)=\\frac{d}{dt}\\int\\limits_0^tk(t-\\tau)u(\\tau)\\,d\\tau -k(t)u(0)$ where $k$ is a nonnegative locally integrable function. Our results are based on the theory of complete Bernstein functions. The solution of the Cauchy problem for the relaxation equation $Du=-\\lambda u$, $\\lambda >0$, proved to be (under some conditions upon $k$) continuous on $[(0,\\infty)$ and completely monotone, appears in the description by Meerschaert, Nane, and Vellaisamy of the process $N(E(t))$ as a renewal process. Here $N(t)$ is the Poisson process of intensity $\\lambda$, $E(t)$ is an inverse subordinator.
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.
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.
Air Shower Simulations in a Hybrid Approach using Cascade Equations
Hans-Joachim Drescher; Glennys R. Farrar
2003-05-28T23:59:59.000Z
A new hybrid approach to air shower simulations is described. At highest energies, each particle is followed individually using the traditional Monte Carlo method; this initializes a system of cascade equations which are applicable for energies such that the shower is one-dimensional. The cascade equations are solved numerically down to energies at which lateral spreading becomes significant, then their output serves as a source function for a 3-dimensional Monte Carlo simulation of the final stage of the shower. This simulation procedure reproduces the natural fluctuations in the initial stages of the shower, gives accurate lateral distribution functions, and provides detailed information about all low energy particles on an event-by-event basis. It is quite efficient in computation time.
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.
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.
Nonlocal operators, parabolic-type equations, and ultrametric random walks
Chacón-Cortes, L. F., E-mail: fchaconc@math.cinvestav.edu.mx; Zúñiga-Galindo, W. A., E-mail: wazuniga@math.cinvestav.edu.mx [Centro de Investigacion y de Estudios Avanzados del I.P.N., Departamento de Matematicas, Av. Instituto Politecnico Nacional 2508, Col. San Pedro Zacatenco, Mexico D.F., C.P. 07360 (Mexico)
2013-11-15T23:59:59.000Z
In this article, we introduce a new type of nonlocal operators and study the Cauchy problem for certain parabolic-type pseudodifferential equations naturally associated to these operators. Some of these equations are the p-adic master equations of certain models of complex systems introduced by Avetisov, V. A. and Bikulov, A. Kh., “On the ultrametricity of the fluctuation dynamicmobility of protein molecules,” Proc. Steklov Inst. Math. 265(1), 75–81 (2009) [Tr. Mat. Inst. Steklova 265, 82–89 (2009) (Izbrannye Voprosy Matematicheskoy Fiziki i p-adicheskogo Analiza) (in Russian)]; Avetisov, V. A., Bikulov, A. Kh., and Zubarev, A. P., “First passage time distribution and the number of returns for ultrametric random walks,” J. Phys. A 42(8), 085003 (2009); Avetisov, V. A., Bikulov, A. Kh., and Osipov, V. A., “p-adic models of ultrametric diffusion in the conformational dynamics of macromolecules,” Proc. Steklov Inst. Math. 245(2), 48–57 (2004) [Tr. Mat. Inst. Steklova 245, 55–64 (2004) (Izbrannye Voprosy Matematicheskoy Fiziki i p-adicheskogo Analiza) (in Russian)]; Avetisov, V. A., Bikulov, A. Kh., and Osipov, V. A., “p-adic description of characteristic relaxation in complex systems,” J. Phys. A 36(15), 4239–4246 (2003); Avetisov, V. A., Bikulov, A. H., Kozyrev, S. V., and Osipov, V. A., “p-adic models of ultrametric diffusion constrained by hierarchical energy landscapes,” J. Phys. A 35(2), 177–189 (2002); Avetisov, V. A., Bikulov, A. Kh., and Kozyrev, S. V., “Description of logarithmic relaxation by a model of a hierarchical random walk,” Dokl. Akad. Nauk 368(2), 164–167 (1999) (in Russian). The fundamental solutions of these parabolic-type equations are transition functions of random walks on the n-dimensional vector space over the field of p-adic numbers. We study some properties of these random walks, including the first passage time.
Hydrodynamic equations for an electron gas in graphene
Luigi Barletti
2015-09-16T23:59:59.000Z
In this paper we review, and extend to the non-isothermal case, the results published in [L. Barletti, J. Math. Phys. 55, 083303 (2014)], concerning the application of the maximum entropy closure technique to the derivation of hydrodynamic equations for particles with spin-orbit interaction and Fermi-Dirac statistics. In the second part of the paper we treat in more details the case of electrons on a graphene sheet and investigate various asymptotic regimes
4-space formulation of field equations for multicomponent eigenfunctions
Fanchi, J.R.
1981-04-01T23:59:59.000Z
Beginning with the assumptions employed in the development of the 4-space formulation (FSF) for spinless particles, a formalism for multicomponent eigenfunctions is constructed. The primary result is a general expression for the field equations of multicomponent eigenfunctions. The ''Relativistic Dynamics'' of Horwitz, Piron, and Reuse for spin-0 and spin- 1/2 particles is shown to be consistent with the FSF. Expectation values are defined and briefly discussed in the appendix.
Time-Periodic Solutions of the Einstein's Field Equations II
De-Xing Kong; Kefeng Liu; Ming Shen
2008-07-31T23:59:59.000Z
In this paper, we construct several kinds of new time-periodic solutions of the vacuum Einstein's field equations whose Riemann curvature tensors vanish, keep finite or take the infinity at some points in these space-times, respectively. The singularities of these new time-periodic solutions are investigated and some new physical phenomena are found. The applications of these solutions in modern cosmology and general relativity can be expected.
Resonant-state expansion Born Approximation applied to Schrodinger's Equation
Doost, M B
2015-01-01T23:59:59.000Z
The RSE Born Approximation is a new scattering formula in Physics, it allows the calculation of strong scattering via the Fourier transform of the scattering potential and Resonant-states. In this paper I apply the RSE Born Approximation to Schr\\"odinger's Equation. The resonant-states of the system can be calculated using the recently discovered RSE perturbation theory and normalised correctly to appear in spectral Green's functions via the flux volume normalisation.
The Runge-Kutta equations through the eighth order
Smitherman, John Alvis
1966-01-01T23:59:59.000Z
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... of this research is to present the formulas which will enable the user to find a Runge-Kutta process of the eighth order or lower. These formulas are listed in appendices A and B. Throughout the preparation, heavy dependence was placed on the work of Butcher [4...
The Nuclear Equation of State at high densities
Christian Fuchs
2006-10-10T23:59:59.000Z
Ab inito calculations for the nuclear many-body problem make predictions for the density and isospin dependence of the nuclear equation-of-state (EOS) far away from the saturation point of nuclear matter. I compare predictions from microscopic and phenomenological approaches. Constraints on the EOS derived from heavy ion reactions, in particular from subthreshold kaon production, as well as constraints from neutron stars are discussed.
Nuclear Shadowing and Antishadowing in a Unitarized BFKL Equation
Jianhong Ruan; Zhenqi Shen; Wei Zhu
2008-01-22T23:59:59.000Z
The nuclear shadowing and antishadowing effects are explained by a unitarized BFKL equation. The $Q^2$- and $x$-variations of the nuclear parton distributions are detailed based on the level of the unintegrated gluon distribution. In particular, the asymptotical behavior of the unintegrated gluon distribution near the saturation limit in nuclear targets is studied. Our results in the nuclear targets are insensitive to the input distributions if the parameters are fixed by the data of a free proton.
A 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...
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.
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.
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 the Bartnik conjecture for the static vacuum Einstein equations
Anderson, Michael T
2015-01-01T23:59:59.000Z
We prove that given any smooth metric $\\gamma$ and smooth positive function $H$ on $S^{2}$, there is a constant $\\lambda > 0$, depending on $(\\gamma, H)$, and an asymptotically flat solution $(M, g, u)$ of the static vacuum Einstein equations on $M = {\\mathbb R}^{3} \\setminus B^{3}$, such that the induced metric and mean curvature of $(M, g, u)$ at $\\partial M$ are given by $(\\gamma, \\lambda H)$. This gives a partial resolution of a conjecture of Bartnik.
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.
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.
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...
Probability representation of quantum evolution and energy level equations for optical tomograms
Ya. A. Korennoy; V. I. Man'ko
2011-01-13T23:59:59.000Z
The von Neumann evolution equation for density matrix and the Moyal equation for the Wigner function are mapped onto evolution equation for optical tomogram of quantum state. The connection with known evolution equation for symplectic tomogram of the quantum state is clarified. The stationary states corresponding to quantum energy levels are associated with the probability representation of the von Neumann and Moyal equations written for the optical tomograms. Classical Liouville equation for optical tomogram is obtained. Example of parametric oscillator is considered in detail.
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.
Holographic Wilson loops, Hamilton-Jacobi equation and regularizations
Pontello, Diego
2015-01-01T23:59:59.000Z
The minimal area for surfaces whose border are rectangular and circular loops are calculated using the Hamilton-Jacobi (HJ) equation. This amounts to solve the HJ equation for the value of the minimal area, without calculating the shape of the corresponding surface. This is done for bulk geometries that are asymptotically AdS. For the rectangular countour, the HJ equation, which is separable, can be solved exactly. For the circular countour an expansion in powers of the radius is implemented. The HJ approach naturally leads to a regularization which consists in locating the countour away from the border. The results are compared with other regularization which leaves the countour at the border and calculates the area of the corresponding minimal surface up to a diameter smaller than the one of the countour at the border. The results do not coincide, this is traced back to the fact that in the former case the area of a minimal surface is calculated and in the second the computed area corresponds to a fraction ...
Holographic Wilson loops, Hamilton-Jacobi equation and regularizations
Diego Pontello; Roberto Trinchero
2015-09-21T23:59:59.000Z
The minimal area for surfaces whose border are rectangular and circular loops are calculated using the Hamilton-Jacobi (HJ) equation. This amounts to solve the HJ equation for the value of the minimal area, without calculating the shape of the corresponding surface. This is done for bulk geometries that are asymptotically AdS. For the rectangular countour, the HJ equation, which is separable, can be solved exactly. For the circular countour an expansion in powers of the radius is implemented. The HJ approach naturally leads to a regularization which consists in locating the countour away from the border. The results are compared with other regularization which leaves the countour at the border and calculates the area of the corresponding minimal surface up to a diameter smaller than the one of the countour at the border. The results do not coincide, this is traced back to the fact that in the former case the area of a minimal surface is calculated and in the second the computed area corresponds to a fraction of a different minimal surface whose countour lies at the boundary.
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
Marc Briant
2015-07-11T23:59:59.000Z
We investigate the Boltzmann equation, depending on the Knudsen number, in the Navier-Stokes perturbative setting on the torus. Using hypocoercivity, we derive a new proof of existence and exponential decay for solutions close to a global equilibrium, with explicit regularity bounds and rates of convergence. These results are uniform in the Knudsen number and thus allow us to obtain a strong derivation of the incompressible Navier-Stokes equations as the Knudsen number tends to $0$. Moreover, our method is also used to deal with other kinetic models. Finally, we show that the study of the hydrodynamical limit is rather different on the torus than the one already proved in the whole space as it requires averaging in time, unless the initial layer conditions are satisfied.
Goings, Joshua J.; Li, Xiaosong, E-mail: xsli@uw.edu [Department of Chemistry, University of Washington, Seattle, Washington 98195 (United States); Caricato, Marco [Department of Chemistry, University of Kansas, Lawrence, Kansas 66045 (United States); Frisch, Michael J. [Gaussian, Inc., 340 Quinnipiac St, Bldg 40, Wallingford, Connecticut 06492 (United States)
2014-10-28T23:59:59.000Z
Methods for fast and reliable computation of electronic excitation energies are in short supply, and little is known about their systematic performance. This work reports a comparison of several low-scaling approximations to the equation of motion coupled cluster singles and doubles (EOM–CCSD) and linear-response coupled cluster singles and doubles (LR–CCSD) equations with other single reference methods for computing the vertical electronic transition energies of 11 small organic molecules. The methods, including second order equation-of-motion many-body perturbation theory (EOM–MBPT2) and its partitioned variant, are compared to several valence and Rydberg singlet states. We find that the EOM–MBPT2 method was rarely more than a tenth of an eV from EOM–CCSD calculated energies, yet demonstrates a performance gain of nearly 30%. The partitioned equation-of-motion approach, P–EOM–MBPT2, which is an order of magnitude faster than EOM–CCSD, outperforms the CIS(D) and CC2 in the description of Rydberg states. CC2, on the other hand, excels at describing valence states where P–EOM–MBPT2 does not. The difference between the CC2 and P–EOM–MBPT2 can ultimately be traced back to how each method approximates EOM–CCSD and LR–CCSD. The results suggest that CC2 and P–EOM–MBPT2 are complementary: CC2 is best suited for the description of valence states while P–EOM–MBPT2 proves to be a superior O(N{sup 5}) method for the description of Rydberg states.
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.
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 ...
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.
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.
Some new methods for Hamilton-Jacobi type nonlinear partial differential equations
Tran, Hung Vinh
2012-01-01T23:59:59.000Z
Nonlinear Adjoint Method for Hamilton–Jacobi equations 2.1compactness methods for Hamilton-Jacobi PDE”. In: Arch.NONLINEAR ADJOINT METHOD FOR HAMILTON–JACOBI EQUATIONS Lemma
Property estimation using inverse methods for elliptic and parabolic partial differential equations
Parmekar, Sandeep
1994-01-01T23:59:59.000Z
In this work we use inverse methods to estimate flow coefficients in both elliptic and parabolic partial differential equations. An algorithm is developed to solve a one layer problem for elliptic and parabolic partial differential equations...
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.
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. ...
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.
Beyond the Gross-Pitaevskii Equation: Ground State and Low Energy Excitations for Trapped Bosons
A. Polls; A. Fabrocini
2000-11-09T23:59:59.000Z
The results of a modified Gross-Pitaevskii equation for a system of Bose hard spheres trapped in a spherical harmonic potential are analyzed to study the validity regime of the standard GP equation.
Bains, Amrit Anoop Singh
2010-10-12T23:59:59.000Z
were divided into categories with respect to accident types, construction operations, degree of accident, fault, contributing factors, crane types, victim’s occupation, organs affected and load. Descriptive analysis was performed to compliment...
De Saporta, Benoîte
Renewal theorem for a system of renewal equations Th´eor`eme de renouvellement pour un syst`eme d show that the classical renewal theorems of Feller hold in the case of a system of renewal equations of renewal equations of the following type: Zi(t) = Gi(t) + p k=1 - Zk(t - u)Fik(du), t R, 1 i p, (1
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.
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
Luo Yousong, E-mail: yluo@rmit.edu.a [RMIT University, School of Mathematical and Geospatial Sciences (Australia)
2010-06-15T23:59:59.000Z
In this paper we derive a necessary optimality condition for a local optimal solution of some control problems. These optimal control problems are governed by a semi-linear Vettsel boundary value problem of a linear elliptic equation. The control is applied to the state equation via the boundary and a functional of the control together with the solution of the state equation under such a control will be minimized. A constraint on the solution of the state equation is also considered.
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
Notes on TQFT Wire Models and Coherence Equations for SU(3) Triangular Cells
Robert Coquereaux; Esteban Isasi; Gil Schieber
2010-12-28T23:59:59.000Z
After a summary of the TQFT wire model formalism we bridge the gap from Kuperberg equations for SU(3) spiders to Ocneanu coherence equations for systems of triangular cells on fusion graphs that describe modules associated with the fusion category of SU(3) at level k. We show how to solve these equations in a number of examples.
On the fourth order PI equation and coalescing phenomena of nonlinear turning points
RIMS1804 On the fourth order PI equation and coalescing phenomena of nonlinear turning points), 000--000 On the fourth order PI equation and coalescing phenomena of nonlinear turning points we present a conjecture for the fourth order PI equation with a large parameter to show its
On the fourth order PI equation and coalescing phenomena of nonlinear turning points
RIMS-1804 On the fourth order PI equation and coalescing phenomena of nonlinear turning points), 000000 On the fourth order PI equation and coalescing phenomena of nonlinear turning points Dedicated a conjecture for the fourth order PI equation with a large parameter to show its importance in the exact WKB
Soatto, Stefano
Fourth Order Partial Differential Equations on General Geometries John B. Greer Andrea L differential equations on implicit surfaces (Bertalm´io, Cheng, Osher, and Sapiro 2001) to fourth order PDEs, such as time-stepping restrictions and large stencil sizes, are shared by standard fourth order equations
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.
Numerical approximation of bang-bang controls for the heat equation: an optimal design approach
Paris-Sud XI, Université de
Numerical approximation of bang-bang controls for the heat equation: an optimal design approach computation of null controls of minimal L -norm for the linear heat equation with a bounded potential. Both and boundary controllability cases, are described within this new approach. Keywords: Linear heat equation
NUMERICAL NULL CONTROLLABILITY OF THE HEAT EQUATION THROUGH A LEAST SQUARES AND VARIATIONAL APPROACH
NUMERICAL NULL CONTROLLABILITY OF THE HEAT EQUATION THROUGH A LEAST SQUARES AND VARIATIONAL of null controls for the heat equation. The goal is to compute an approximation of controls that drives-space dimensional case. Key Words. Heat equation, Null controllability, Numerical approximation, Variational ap
Numerical approximation of bang-bang controls for the heat equation: an optimal design approach
Paris-Sud XI, Université de
Numerical approximation of bang-bang controls for the heat equation: an optimal design approach approximation of null controls of minimal L -norm for the linear heat equation with a bounded potential. Both the internal and boundary controllability problem of a linear heat equation with a bounded potential. Let us
Numerical null controllability of the 1D heat equation: dual methods
Paris-Sud XI, Université de
Numerical null controllability of the 1D heat equation: dual methods Enrique Fern for the 1D heat equation. The goal is to compute a control that drives (a numerical approximation of and efficiency. Keywords: one-dimensional heat equation, null controllability, finite element methods, dual meth
Numerical null controllability of the 1D heat equation: primal methods
Paris-Sud XI, Université de
Numerical null controllability of the 1D heat equation: primal methods Enrique Fern for the 1D heat equation, with Dirichlet boundary conditions. The goal is to compute a control that drives concerned in this work with the null controllability problem for the 1D heat PDE. The state equation
Bang-bang property for time optimal control of semilinear heat equation
Paris-Sud XI, Université de
Bang-bang property for time optimal control of semilinear heat equation Kim Dang Phung , Lijuan governed by semilinear heat equation in a bounded domain with control acting locally in a subset. Also, we present the null controllability cost for semilinear heat equation and an observability estimate from
Numerical exact controllability of the 1D heat equation: Carleman weights and duality
Numerical exact controllability of the 1D heat equation: Carleman weights and duality Enrique Fern for the 1D heat equation. The goal is to compute a control that drives (a numerical approximation of [11], where primal methods were considered. Keywords: Heat equation, null controllability, numerical
Insensitizing controls for a heat equation with a nonlinear term involving the state and the
González Burgos, Manuel
Insensitizing controls for a heat equation with a nonlinear term involving the state In this paper we present two results on the existence of insensitizing controls for a heat equation in a bounded domain of IRN . We first consider a semilinear heat equation involving gradient terms with homogeneous