共查询到20条相似文献,搜索用时 15 毫秒
1.
Nataliya Sakhnenko Alexander Nerukh Trevor Benson Phillip Sewell 《Optical and Quantum Electronics》2007,39(10-11):825-836
The resolvent method approach is proposed for analytically solving the time domain Volterra integral equation (TDVIE) which describes the electromagnetic fields in 2-D cylindrical structures with time changes in the permittivity. It is shown that the approach allows investigation of the electromagnetic field transformation due to an abrupt time change in dielectric permittivity inside a circular cylinder as well as the construction of the Green’s function for an initial-boundary value problem. Key mechanisms of electromagnetic field transformation are investigated and a qualitative distinction of the processes is shown that depends on an initial field configuration. 相似文献
2.
线性瞬态涡流电磁场定解问题的主要特点是边界条件使用磁感应强度的法向分量边界条件代替了电场强度的切向分量边界条件,约束方程中忽略了位移电流.这种具有特殊性的定解问题的解是否唯一和稳定对于求解瞬态涡流电磁场而言是一个基本问题.本文在非涡流区引入标量位函数,证明了在推导过程中起重要作用的辅助函数的存在性.通过推导线性瞬态涡流电磁场定解问题的能量估计式,证明了该定解问题的解是唯一的,并且关于初始条件和外源项是稳定的.本结果对于线性瞬态涡流电磁场的求解有一定的指导意义.作为应用,给出了通有单脉冲电流的单匝圆环线圈与球形导体共轴的涡流问题的解析解.
关键词:
瞬态涡流电磁场
能量估计式
唯一性
稳定性 相似文献
3.
《Physics letters. A》2020,384(13):126258
We discuss implications of the seaward boundary conditions used in initial-boundary value problem formulation of nonlinear shallow-water wave propagation over a linear slope. We first demonstrate the reflection of wave velocity in the case of Dirichlet condition and that of water elevation in the case of Neumann condition. We then show that linear superposition of the two boundary conditions results in much less reflection at the artificial boundary. We also propose a new boundary condition of mixed type and compare its results with that of the aforementioned conditions. 相似文献
4.
《Journal of Nonlinear Mathematical Physics》2013,20(4):445-452
There exists a particular class of boundary value problems for integrable nonlinear evolution equations formulated on the half-line, called linearizable. For this class of boundary value problems, the Fokas method yields a formalism for the solution of the associated initial-boundary value problem, which is as efficient as the analogous formalism for the Cauchy problem. Here, we employ this formalism for the analysis of several concrete initial-boundary value problems for the nonlinear Schrödinger equation. This includes problems involving initial conditions of a hump type coupled with boundary conditions of Robin type. 相似文献
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6.
Jeffrey Winicour 《General Relativity and Gravitation》2011,43(12):3269-3288
I treat the worldtube constraints which arise in the null-timelike initial-boundary value problem for the Bondi-Sachs formulation
of Einstein’s equations. Boundary data on a worldtube and initial data on an outgoing null hypersurface determine the exterior
spacetime by integration along the outgoing null geodsics. The worldtube constraints are a set of conservation laws which
impose conditions on the integration constants. I show how these constraints lead to a well-posed initial value problem governing
the extrinsic curvature of the worldtube, whose components are related to the integration constants. Possible applications
to gravitational waveform extraction and to the well-posedness of the null-timelike initial-boundary value problem are discussed. 相似文献
7.
Vincent Caudrelier 《Communications in Mathematical Physics》2015,338(2):893-917
We present a framework to solve the open problem of formulating the inverse scattering method (ISM) for an integrable PDE on a star-graph. The idea is to map the problem on the graph to a matrix initial-boundary value (IBV) problem and then to extend the unified method of Fokas to such a matrix IBV problem. The nonlinear Schrödinger equation is chosen to illustrate the method. The framework unifies all previously known examples which are recovered as particular cases. The case of general Robin conditions at the vertex is discussed: the notion of linearizable initial-boundary conditions is introduced. For such conditions, the method is shown to be as efficient as the ISM on the full-line. 相似文献
8.
This article presents the theory of thermopiezoelectricity in which the second displacement gradient and the second electric potential gradient are included in the set of independent constitutive variables. This is achieved by using the entropy production inequality proposed by Green and Laws. At first, appropriate thermodynamic restrictions and constitutive equations are obtained, using the well-established Coleman and Noll procedure. Then, the balance equations and the constitutive equations of linear theory are derived, and the mixed initial-boundary value problem is set. For this problem a uniqueness result is established. Next, the basic equations for the isotropic case are derived. Finally, a set of inequalities is obtained for the constant constitutive coefficients of the isotropic case that, on the basis on the previous theorem, ensure the uniqueness of the solution of the mixed initial-boundary value problem. 相似文献
9.
CHEN Shennian Department of Electronic Engineering Huaqiao University Quanzhou China 《中国科学G辑(英文版)》2005,48(3):300-318
1 Introduction Historically, circuit theory was initially considered as a part of the electromagnetic theory. Later on, it branched out to become an independent theory. After several stages of its development, Kirchhoff’s law was commonly regarded as the fundamental law of circuits[1]. Especially after the 1960s, the completely topological formulation of Kirchhoff’s law made even more important contribution to the development of moderncircuit theory. However, it has been also known for a l… 相似文献
10.
D.H. Delphenich 《Annalen der Physik》2005,14(6):347-377
The axioms of topological electromagnetism that were given by Hehl, Obukhov, and Rubilar are refined by the use of geometrical and topological notions that are found on orientable manifolds. The central problem of defining the spacetime electromagnetic constitutive law in terms of the geometrical and topological structure of the spacetime manifold is elaborated upon in the linear and nonlinear cases. The manner by which the spacetime metric might follow from the electromagnetic constitutive law is examined in the linear case. The possibility that the intersection form of the spacetime manifold might play a role in defining a topological basis for a nonlinear electromagnetic constitutive law is explored. The manner by which electromagnetic wave motion relates to the geometric structure is also discussed. 相似文献
11.
J.C. Murray 《Physics letters. A》1974,47(1):59-60
A uniqueness theorem is established for a linear initial-boundary value problem associated with the equations of telegraphy, neutron diffusion, heat conduction, classical wave propagation, wave propagation in a porous medium, together with the Klein-Gordon and Schrödinger equations. 相似文献
12.
A fundamental problem in general relativity is the determination of the field produced by a source configuration consisting of a time-varying charge. By employing a generalized form for the electromagnetic energy-momentum tensor, it is possible to obtain an exact solution of the Einstein field equations for this distribution, without postulating a null fluid. 相似文献
13.
14.
Gregory Eyink Joel L. Lebowitz Herbert Spohn 《Communications in Mathematical Physics》1991,140(1):119-131
Extending the results of a previous work, we consider a class of discrete lattice gas models in a finite interval whose bulk dynamics consists of stochastic exchanges which conserve the particle number, and with stochastic dynamics at the boundaries chosen to model infinite particle reservoirs at fixed chemical potentials. We establish here the local equilibrium structure of the stationary measures for these models. Further, we prove as a law of large numbers that the time-dependent empirical density field converges to a deterministic limit process which is the solution of the initial-boundary value problem for a nonlinear diffusion equation.Supported in part by NSF Grants DMR89-18903 and INT85-21407. G.E. and H.S. also supported by the Deutsche Forschungsgemeinschaft 相似文献
15.
Donald H. Kobe 《International Journal of Theoretical Physics》1982,21(8-9):685-702
The gauge invariance of the Dirac equation is reviewed and gauge-invariant operators are defined. The Hamiltonian is shown
to be gauge dependent, and an energy operator is defined which is gauge invariant. Gauge-invariant operators corresponding
to observables are shown to satisfy generalized Ehrenfest theorems. The time rate of change of the expectation value of the
energy operator is equal to the expectation value of the power operator. The virial theorem is proved for a relativistic electron
in a time-varying electromagnetic field. The conventional approach to probability amplitudes, using the eigenstates of the
unperturbed Hamiltonian, is shown in general to be gauge dependent. A gaugeinvariant procedure for probability amplitudes
is given, in which eigenstates of the energy operator are used. The two methods are compared by applying them to an electron
in a zero electromagnetic field in an arbitrary gauge.
Presented at the Dirac Symposium, Loyola University, New Orleans, May 1981. 相似文献
16.
A boundary problem of linear classical optics is solved in which the behavior of the electromagnetic field near the surface of a dielectric medium is studied. It is shown that including the discrete structure of a medium into the analysis has the most substantial effect on the behavior of the electromagnetic field at distances smaller than 2a 0, where a 0 is the lattice constant. This fact makes it possible to obtain numerical estimates of the size of the region where the reflected and transmitted waves are formed. 相似文献
17.
V. M. Mekhitarian 《Journal of Contemporary Physics (Armenian Academy of Sciences)》2016,51(2):108-126
The Faraday law of electromagnetic induction for an arbitrarily moving charge is generalized and the expression for the force acting on the charge in an alternating magnetic field is obtained. It is shown that besides the Lorentz force perpendicular to the velocity of the particle, the Faraday force parallel to the particle velocity and proportional to it is acting on the charge, too. The equations of motion of the charged particle and the magnetic moment are obtained in the time-varying magnetic field. The problems of induction acceleration of charged particles (betatron) and induction heating of medium (plasma, plasma betatron) are considered. 相似文献
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19.
Hitoshi Wakita 《Communications in Mathematical Physics》1976,50(1):61-68
Some integrations of the Tomonaga-Schwinger equation with a non-local interaction are studied with mathematical rigor. It is proved that the related initial value problem has a unique solution in any finite region of the space-time corresponding to each set of space-like surfaces which covers the region. Such an analysis can be extended to the case of quantum electrodynamics by the aid of a Lorentz-invariant topology introduced in the *-algebra of electromagnetic field operators. 相似文献
20.
Marian H. Rose 《International Journal of Infrared and Millimeter Waves》1986,7(2):197-235
A previously developed variational technique for finding the approximate solution to the electromagnetic field inside waveguides of varying shapes and containing non-uniform dielectric and magnetic materials is applied to the specific case of an axisymmetric waveguide containing three layers of different dielectric materials. The magnetic permeability is taken equal to unity. The method enables the problem to be reduced to a two point boundary value problem for a pair of second order, linear, ordinary differential equations. The values of the reflection and transmission coefficients obtained by this method are in good agreement with those derived from solving the partial differential equations for the field. 相似文献