It is well-known that a conflict between Galilean relativity and Maxwell equations of electromagnetic equations was apparent by the end of the 19th century. Equally well-known is the fact that Einstein resolved the conflict by pointing out that the principle of relativity and Maxwell equations can both be correct if the notion of absolute time is abandoned. The rest is history. The purpose of t...

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...

2014 We present a new approach to the linear macroscopic behaviour of polymeric liquids and melts in terms of the macroscopic variables : velocity field, density, entropy density and strain field and we discuss how the classical Maxwell model emerges as a limiting special case. The novel approach used here, which considers the strain field as an additional macroscopic variable that relaxes on t...

A theory for lifting equations of motion for charged particle dynamics, subject to given electromagnetic like forces, up to a gauge-free system of coupled Hamiltonian Vlasov-Maxwell like equations is given. The theory provides very general expressions for the polarization and magnetization vector fields in terms of the particle dynamics description of matter. Thus, as is common in plasma physic...

Discontinuous Galerkin methods are developed for solving the Vlasov–Maxwell system, methods that are designed to be systematically as accurate as one wants with provable conservation of mass and possibly total energy. Such properties in general are hard to achieve within other numerical method frameworks for simulating the Vlasov–Maxwell system. The proposed scheme employs discontinuous Galerki...

Dvoeglazov’s paper is not trivial because we know the classical definition of any non-trivial truth: a truth is not trivial if and only if an opposite statement is not false (and vice versa, of course). So I strongly recommend his paper for a reader. But I have a few notes: 1) V. Dvoeglazov writes in his footnote number 7: ”In my opinion, equations (20,21) of ref. [1] are just another form of t...

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. In an earlier paper [1] 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 macroscopic w...