We study the frequency form, popular in physics, of Maxwell equations for nonlinear spatially inhomogeneous dielectric media. Using wavepackets based on eigenmodes of the underlying linear dielectric medium we develop a mathematically consistent interpretation of the frequency form of nonlinear Maxwell operators. In particular, we construct the operator of nonlinear polarization based on freque...

In 1948, Feynman showed Dyson how the Lorentz force law and homogeneous Maxwell equations could be derived from commutation relations among Euclidean coordinates and velocities, without reference to an action or variational principle. When Dyson published the work in 1990, several authors noted that the derived equations have only Galilean symmetry and so are not actually the Maxwell theory. In...

We derive higher-order macroscopic transport models for semiconductor device simulation from Boltzmann’s transport equation using the method of moments. To obtain a tractable equation set suitable for numerical implementation the validity of the diffusion limit will be assumed which removes the convective terms from the equation system. The infinite hierarchy of equations is then truncated at t...

The long-time asymptotics is analyzed for all finite energy solutions to a model U(1)-invariant nonlinear KleinGordon equation in one dimension, with the nonlinearity concentrated at a single point: each finite energy solution converges as t →±∞ to the set of all “nonlinear eigenfunctions” of the form ψ(x)e−iωt . The global attraction is caused by the nonlinear energy transfer from lower harmon...

In this article a new approach is considered for implementing operator splitting methods for transport problems, influenced by electric fields. Our motivation came to model PE-CVD (plasma-enhanced chemical vapor deposition) processes, means the flow of species to a gasphase, which are influenced by an electric field. Such a field we can model by wave equations. The main contributions are to imp...

A lattice Boltzmann model for binary mixtures is formally derived from a two-fluid kinetic model for Maxwell molecules by discretizing the Boltzmann equation. In this model, collisions among the same and different species are treated separately, as non-linear BGK terms, enabling the independent management of the species viscosities and thermal conductivities from the binary diffusion coefficien...

We show that when correctly formulated the equation ∇ × a = κa does not exhibit some inconsistencies atributed to it, so that its solutions can represent physical fields. We want to look for solutions of Maxwell equations which describe stationary electromagnetic configurations – in the sense that the energy of the field does not propagate. In order to obtain one such stationary solution it is ...

We describe an explicit connection between solutions to equations Df = 0 (the Generalized Cauchy-Riemann equation) and (D+M)f = 0, where operators D and M commute. The described connection allows to construct a “function theory” (the Cauchy theorem, the Cauchy integral, the Taylor and Laurent series etc.) for solutions of the second equation from the known function theory for solution of the fi...

We consider the coupled Maxwell{Lorentz equations for a single charge with a rigid charge distribution subject to slowly varying external potentials. In the adiabatic limit, to lowest order, the motion of the charge is governed by an eeective Hamiltonian. In the next order we obtain, as a small correction, the radiation reaction containing q {terms. This equation has a stable center manifold an...

Part 1: (LL, PB) Foundations: (11 lectures) History of thermodynamics, kinetic theory and equilibrium statistical mechanics. Axioms of equilibrium statistical physics, Master equation, Liouville equation. Equilibrium conditions, Boltzmann weights and partition functions. Free energies and relation to partition functions. Survey of many particle, spin and field systems: the case of classical par...