Abstract Matrix representations of the Maxwell equations are well-known. However, all these representations lack an exactness or/and are given in terms of a pair of matrix equations. We present a matrix representation of the Maxwell equation in presence of sources in a medium with varying permittivity and permeability. It is shown that such a representation necessarily requires 8×8 matrices and...

Dissipative effects in electromagnetism on macroscopic scales are examined by coarse-graining the microscopic Maxwell equations with respect to time. We illustrate a procedure to derive the dissipative effects on the macroscopic scale by using a Green-Kubo type expression in terms of the microscopic fluctuations and the correlations between them. The resulting macroscopic Maxwell equations are ...

We consider the linear dissipative Boltzmann equation describing inelastic interactions of particles with a fixed background. For the simplified model of Maxwell molecules first, we give a complete spectral analysis, and deduce from it the optimal rate of exponential convergence to equilibrium. Moreover we show the convergence to the heat equation in the diffusive limit and compute explicitely ...

We prove the existence of at least two solutions for a fourth order equation, which includes the vortex equations for the U(1) and CP (1) self-dual Maxwell-Chern-Simons models as special cases. Our method is variational, and it relies on an “asymptotic maximum principle” property for a special class of supersolutions to this fourth order equation.

We study the approximate controllability of the stochastic Maxwell equations with an abstract approach and a constructive approach using a generalization of the Hilbert uniqueness method as proposed in Kim (2004, Approximate controllability of a stochastic wave equation. Appl. Math. Optim., 49, 81–98) for the stochastic wave equation.

The two-dimensional Vlasov–Maxwell system, for a plasma with mobile, magnetised electrons and ions, is investigated numerically. A previously developed method for solving the two-dimensional electrostatic Vlasov equation, Fourier transformed in velocity space, for mobile electrons and with ions fixed in space, is generalised to the fully electromagnetic, two-dimensional Vlasov–Maxwell system fo...

In this paper we study a Landau-Lifshitz equation in ferromagnetism without exchange energy as a quasi-stationary limit of a coupled Maxwell system as dielectric permittivity approaches zero. We present a different formulation and proof of this quasi-stationary limit result. We also prove a new uniqueness and stability result for the limit Landau-Lifshitz equation.

Using systematic calculations in spinor language, we obtain simple descriptions of the second order symmetry operators for the conformal wave equation, the Dirac-Weyl equation and the Maxwell equation on a curved four dimensional Lorentzian manifold. The conditions for existence of symmetry operators for the different equations are seen to be related. Computer algebra tools have been developed ...

Based on the Vlasov-Maxwell equations describing the self-consistent nonlinear beam dynamics and collective processes, the evolution of an intense sheet beam propagating through a periodic focusing field has been studied. It has been shown that in the case of a beam with uniform phase space density the Vlasov-Maxwell equations can be replaced exactly by the hydrodynamic equations with a triple ...

We consider high order methods for the one-dimensional Helmholtz equation and frequency-Maxwell system. We demand that the scheme be higher order even when the coefficients are discontinuous. We discuss the connection between schemes for the second-order scalar Helmholtz equation and the first-order system for the electromagnetic or acoustic applications. AMS subject classifications: 65N06, 78A...