相关论文: Simultaneous inference of Jefimenko's and Maxwell'…
Extended guiding-center Vlasov-Maxwell equations are derived under the assumption of time-dependent and inhomogeneous electric and magnetic fields that obey the standard guiding-center space-time-scale orderings. The guiding-center…
In the first sections of this article, we discuss two variations on Maxwell's equations that have been introduced in earlier work--a class of nonlinear Maxwell theories with well-defined Galilean limits (and correspondingly generalized…
The electric and magnetic fields of a spatio-temporally varying electric current loop are calculated using the Jefimenko equations. The radiation and the nonradiation parts of the electromagnetic fields are derived in the framework of…
Various perturbation series are factorially divergent. The behavior of their high-order terms can be found by Lipatov's method, according to which they are determined by the saddle-point configurations (instantons) of appropriate functional…
Principles of discrete time mechanics are applied to the quantisation of Maxwell's equations. Following an analysis of temporal node and link variables, we review the classical discrete time equations in the Coulomb and Lorentz gauges and…
In this paper we consider the finite element approximation of Maxwell's problem and analyse the prescription of essential boundary conditions in a weak sense using Nitsche's method. To avoid indefiniteness of the problem, the original…
Many of the new developments in machine learning are connected with gradient-based optimization methods. Recently, these methods have been studied using a variational perspective. This has opened up the possibility of introducing…
Differentiation is an important task in control, observation and fault detection. Levant's differentiator is unique, since it is able to estimate exactly and robustly the derivatives of a signal with a bounded high-order derivative.…
Maxwell's equations are formulated in arbitrary moving frames by means of tetrad fields, which are interpreted as reference frames adapted to observers in space-time. We assume the existence of a general distribution of charges and currents…
In this paper, we study an inverse problem for identifying the initial value in a space-time fractional diffusion equation from the final time data. We show the identifiability of this inverse problem by proving the existence of its unique…
We consider second-order evolution equations in an abstract setting with damping and time delay and give sufficient conditions ensuring exponential stability. Our abstract framework is then applied to the wave equation, the elasticity…
This article concerns second-order time discretization of subdiffusion equations with time-dependent diffusion coefficients. High-order differentiability and regularity estimates are established for subdiffusion equations with…
We study the Boltzmann equation near a global Maxwellian in the case of bounded domains. We consider the boundary conditions to be either specular reflections or Maxwellian diffusion. Starting from the reference work of Guo in…
The Maxwell integral equations expressing Ampere's and Faraday's laws are shown to be affected by heavy physical approximations. The usual deduction from them, moreover, of the corresponding set of differential Maxwell equations is based,…
In this paper we present a methodology for increasing the accuracy and accelerating the convergence of numerical methods for solution of Maxwell's equations in the frequency domain by taking into account the be-havior of the electromagnetic…
The Maxwell field of a charge e which experiences an impulsive acceleration or deceleration is constructed explicitly by subdividing Minkowskian space-time into two halves bounded by a future null-cone and then glueing the halves back…
The Maxwell field equations relative to a uniformly accelerated frame, and the variational principle from which they are obtained, are formulated in terms of the technique of geometrical gauge invariant potentials. They refer to the…
This paper is a review of the canonical proper-time approach to relativistic mechanics and classical electrodynamics. The purpose is to provide a physically complete classical background for a new approach to relativistic quantum theory.…
Mathematical proofs are presented concerning the existence of solutions of the Maxwell equations with suitable boundary conditions. In particular it is stated that the well known "delayed potentials" provide effective solutions of the…
A new method that enables easy and convenient discretization of partial differential equations with derivatives of arbitrary real order (so-called fractional derivatives) and delays is presented and illustrated on numerical solution of…