相关论文: Simultaneous inference of Jefimenko's and Maxwell'…
A fundamental result of classical electromagnetism is that Maxwell's equations imply that electric charge is locally conserved. Here we show the converse: Local charge conservation implies the local existence of fields satisfying Maxwell's…
We present boundary-integral equations for Maxwell-type problems in a differential-form setting. Maxwell-type problems are governed by the differential equation $(\delta\mathrm{d}-k^2)\omega = 0$, where $k\in\mathbb{C}$ holds, subject to…
This simple note lays out a few observations which are well known in many ways but may not have been said in quite this way before. The basic idea is that when comparing two different Markov chains it is useful to couple them is such a way…
The perturbative approach to quantum field theory using retarded functions is extended to noncommutative theories. Unitarity as well as quantized equations of motion are studied and seen to cause problems in the case of space-time…
In the ordinary quantum Maxwell theory of a free electromagnetic field, formulated on a curved 3-manifold, we observe that magnetic and electric fluxes cannot be simultaneously measured. This uncertainty principle reflects torsion: fluxes…
We consider the Maxwell-Lorentz equations, i.e., the equation of motion of a charged dust coupled to Maxwell's equations, on an arbitrary general-relativistic spacetime. We decompose this system of equations into evolution equations and…
We analyze the convergence of piecewise collocation methods for computing periodic solutions of general retarded functional differential equations under the abstract framework recently developed in [S. Maset, Numer. Math. (2016)…
The strong convergence of Euler approximations of stochastic delay differential equations is proved under general conditions. The assumptions on drift and diffusion coefficients have been relaxed to include polynomial growth and only…
We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…
This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…
The displacement current, introduced by Maxwell, has led to persistent confusion regarding its role in generating magnetic fields. To find a new way to understand classical magnetism, in this work, the displacement current is first…
In 1948, Feynman showed Dyson how the Lorentz force and Maxwell equations could be derived from commutation relations coordinates and velocities. Several authors noted that the derived equations are not Lorentz covariant and so are not the…
In this work we study linear Maxwell equations with time- and space-dependent matrix-valued permittivity and permeability on domains with a perfectly conducting boundary. This leads to an initial boundary value problem for a first order…
We consider the problem of removing the divergences in an arbitrary gauge-field theory (possibly nonrenormalizable). We show that this can be achieved by performing, order by order in the loop expansion, a redefinition of some parameters…
Some mathematical inconsistencies in the conventional form of Maxwell's equations extended by Lorentz for a single charge system are discussed. To surmount these in framework of Maxwellian theory, a novel convection displacement current is…
In this paper we prove uniform a priori estimates for transmission problems with constant coefficients on two subdomains, with a special emphasis for the case when the ratio between these coefficients is large. In the most part of the work,…
We present a one-step algorithm that solves the Maxwell equations for systems with spatially varying permittivity and permeability by the Chebyshev method. We demonstrate that this algorithm may be orders of magnitude more efficient than…
Inverse problem to determine simultaneously a general space- and time-dependent source and an initial state in a fractional diffusion equation from an {\it a posteriori} measurement of the normal derivative of the state on a portion of a…
We consider the well-posedness of the initial value problem for Einstein-Maxwell theory modified by higher derivative effective field theory corrections. Field redefinitions can be used to bring the leading parity-symmetric 4-derivative…
Maxwell's equations are modified to incorporate a scalar field to account for the London's superconductivity. Assuming the electromagnetic field is described by the Klein-Gordon equation, London's equations of superconductivity are then…