Related papers: A Note on the Justification of the Eddy Current Mo…
Though sufficient for local conservation of charge, Maxwells displacement current is not necessary. An alternative to the Ampere-Maxwell equation is exhibited and the alternatives electric and magnetic fields and scalar and vector…
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…
New Lagrangians, depending on the field strengths and the electric and magnetic sources are found, which lead to the Maxwell equations. One new feature is that the equations of motion are obtained by varying the Lagrangian with respect to…
In this paper, convergence for moments of powered normal extremes is considered under an optimal choice of normalizing constants. It is shown that the rates of convergence for normalized powered normal extremes depend on the power index.…
We consider a second order linear equation with a time-dependent coefficient c(t) in front of the "elastic" operator. For these equations it is well-known that a higher space-regularity of initial data compensates a lower time-regularity of…
The self-force problem of classical electrodynamics has two closely linked facets: The ill defined dynamics of a point charge due to the divergent self field at the position of the charge, and the divergence of formally conserved…
In order to analyse classical electromagnetism in a medium at finite temperature we introduce `an optical density operator', and reformulate Maxwell's equations with the operator, starting from the Dirac-equation-like formulation of…
We derive a fundamental conservation law of operator current for master equations describing reduced quantum systems. If this law is broken, the temporal integral of the current operator of an arbitrary system observable does not yield in…
The general theory for electric current multipoles appearing at the motion of magnetic dipoles and change in these values or orientation has been suggested. Static multipoles, including an anapole, have been studied in detail.
The time at which a one-dimensional continuous strong Markov process attains a boundary point of its state space is a discontinuous path functional and it is, therefore, unclear whether the exit time can be approximated by hitting times of…
A method of solving Maxwell equations in a vicinity of a multipole particle (moving along an arbitrary trajectory) is proposed. The method is based on a geometric construction of a trajectory-adapted coordinate system, which simplifies…
We construct an analytic solution to Maxwell's equations that violates global charge conservation, by building on the possibilities demonstrated in [Foundations of Physics 49, 330 (2019)]. The construction is valid for a spacetime…
In a general class of one dimensional random differential equation the convergence of the distribution function of the solution to stationary state distribution is studied. In particular it is proved the boundedness respectively the…
The present work revisits the reduction of the nonlinear dynamics of an electromechanical system through a quasi-steady state hypothesis, discussing the fundamental aspects of this type of approach and clarifying some confusing points found…
Exact and approximate expressions are established for dissipation, the power of the shear stress at the wall and the boundary layer thickness corresponding to the motion of an Oldroyd-B fluid induced by a constantly accelerating plate. The…
Maxwell defined a true or total current in a way not widely used today. He said "... true electric current ... is not the same thing as the current of conduction but that the time-variation of the electric displacement must be taken into…
Recently Bandos, Lechner, Sorokin, and Townsend [arXiv:2007.09092] have discovered that Maxwell's electrodynamics can be generalized so that the resulting nonlinear theory preserves both conformal invariance and SO(2) duality-rotation…
This paper summarizes the motivations and results obtained so far in the frame of a particular non-linearization of Classical Electrodynamics, which was called Extended Electrodynamics. The main purpose pursued with this non-linear…
Computing the electric eddy currents in non-linear materials, such as superconductors, is \E{not straightforward}. The design of superconducting magnets and power applications needs electromagnetic computer modeling, being in many cases a…
We present examples of simple electromagnetic systems in which energy, linear momentum, and angular momentum exhibit interesting behavior. The systems are sufficiently simple to allow exact solutions of Maxwell's equations in conjunction…