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Related papers: On the Solvability of Maxwell's Equations

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An explanation of polarization entanglement is presented using Maxwells classical electromagnetic theory.Two key features are required to understand these classical origins.The first is that all waves diffract and weakly diffracting…

General Physics · Physics 2015-11-20 John E. Carroll

The time-dependent Maxwell system describing electromagnetic wave propagation in inhomogeneous isotropic media in the one-dimensional case reduces to a Vekua-type equation for bicomplex-valued functions of a hyperbolic variable (see…

Analysis of PDEs · Mathematics 2016-05-23 Kira V. Khmelnytskaya , Vladislav V. Kravchenko , Sergii M. Torba

In the recent work~\cite{Wang:2021p2}, the author proposed the expanded Maxwell's equations for moving charged media system, which seems subtle. Considering a very short time, we can approximately define the inertial frame of reference. If…

Classical Physics · Physics 2022-02-15 Chuang Li , Junle Pei , Tianjun Li

From electromagnetic wave equations, it is first found that, mathematically, any current density that emits an electromagnetic wave into the far-field region has to be differentiable in time infinitely, and that while the odd-order time…

Classical Physics · Physics 2021-08-10 Wei Guo

The classification of exact solutions of Maxwell vacuum equations for the case when the electromagnetic fields and metrics of homogeneous spaces are invariant with respect to the motion group G(VII) is completed. All non-equivalent exact…

Mathematical Physics · Physics 2022-12-27 V. V. Obukhov

In this paper we are concerned with the plane wave method for the discretization of time-harmonic Maxwell's equations in three dimensions. As pointed out in [6], it is difficult to derive a satisfactory L2 error estimate of the standard…

Numerical Analysis · Mathematics 2018-01-01 Qiya Hu , Rongrong Song

This paper presents a thorough investigation into nonradiating sources of Maxwell's equations. Various characterizations are developed to clarify the properties of nonradiating sources, considering their varying degrees of regularity.…

Analysis of PDEs · Mathematics 2024-02-19 Peijun Li , Jue Wang

A thoughtless treatment of Maxwell's equations can lead to the interpretation of the existence of a causal relationship between their different terms and, therefore, that an electric field that varies in time generates a magnetic one and…

Physics Education · Physics 2025-01-14 Alvaro Suarez , Arturo C. Marti , Kristina Zuza , Jenaro Guisasola

Maxwell's equations and the Dirac equation are the first-order differential relativistic wave equation for electromagnetic waves and electronic waves respectively. Hence, there is a notable similarity between these two wave equations, which…

Quantum Physics · Physics 2023-08-04 Mingjie Li , S. A. R. Horsley

We show that the Maxwell equations describing an electromagnetic wave are a mathematical consequence of the Einstein equations for the same wave. This fact is significant for the problem of the Einsteinian metrics corresponding to the…

General Physics · Physics 2011-06-14 A. Loinger , T. Marsico

We present a new method for the analysis of electromagnetic scattering from homogeneous penetrable bodies. Our approach is based on a reformulation of the governing Maxwell equations in terms of two uncoupled vector Helmholtz systems: one…

Mathematical Physics · Physics 2017-04-25 Felipe Vico , Leslie Greengard , Miguel Ferrando

This paper is concerned with an inverse random source problem for the three-dimensional time-harmonic Maxwell equations. The source is assumed to be a centered complex-valued Gaussian vector field with correlated components, and its…

Analysis of PDEs · Mathematics 2020-02-21 Peijun Li , Xu Wang

The three electromagnetic properties appearing in Maxwell's equations are dielectric permittivity, electrical conductivity and magnetic permeability. The study of point diffractors in a homogeneous, isotropic, linear medium suggests the use…

Geophysics · Physics 2013-06-10 Albane Saintenoy , A. Tarantola

Plasmon and polariton modes are derived for an ideal semi-infinite (half-space) plasma and an ideal plasma slab by using a general, unifying procedure, based on equations of motion, Maxwell's equations and suitable boundary conditions.…

Optics · Physics 2015-05-13 M. Apostol , G. Vaman

A simple method is presented which enables us to construct scalar field solutions from any given Einstein-Maxwell solution in colliding plane waves. As an application we give scalar field extensions of the solution found by Hogan, Barrabes…

General Relativity and Quantum Cosmology · Physics 2007-05-23 M. Halilsoy , I. Sakalli

One can interpret the Dirac equation either as giving the dynamics for a classical field or a quantum wave function. Here I examine whether Maxwell's equations, which are standardly interpreted as giving the dynamics for the classical…

Quantum Physics · Physics 2019-05-30 Charles T. Sebens

The coupled Maxwell-Lorentz system describes feed-back action of electromagnetic fields in classical electrodynamics. When applied to point-charge sources (viewed as limiting cases of charged fluids) the resulting nonlinear weakly…

Analysis of PDEs · Mathematics 2007-05-23 Guenther Hoermann , Michael Kunzinger

We analyze the stability of Maxwell equations in bounded domains taking into account electric and magnetization effects. Well-posedness of the model is obtained by means of semigroup theory. A passitivity assumption guarantees the…

Analysis of PDEs · Mathematics 2020-04-22 Serge Nicaise , Cristina Pignotti

We present numerical results concerning the solution of the time-harmonic Maxwell's equations discretized by discontinuous Galerkin methods. In particular, a numerical study of the convergence, which compares different strategies proposed…

Numerical Analysis · Mathematics 2007-05-23 Victorita Dolean , Hugo Fol , Stephane Lanteri , Ronan Perrussel

The purpose of this article is twofold. On one hand, we rigorously derive the Newton--Maxwell equation in the Coulomb gauge from first principles of quantum electrodynamics in agreement with the formal Bohr's correspondence principle of…

Analysis of PDEs · Mathematics 2022-04-08 Zied Ammari , Marco Falconi , Fumio Hiroshima