We consider the non-reactive elastic Boltzmann equation for multicomponent gaseous mixtures. We deduce, under the standard diffusive scaling, that well prepared initial conditions lead to solutions satisfying the Maxwell-Stefan diffusion equations in the vanishing Mach and Knudsen numbers limit.

We develop a numerical algorithm that computes the Green's function of Maxwell equation for a 2D finite-size photonic crystal, composed of rods of arbitrary shape. The method is based on the boundary integral equation, and a Nyström discretization is used for the numerical solution. To provide an exact solution that validates our code we derive multipole expansions for circular cylinders using ...

A model describing wave propagation in optically modulated waveguide arrays is proposed. In the weakly guided regime, a two-dimensional semidiscrete nonlinear Schrödinger equation with the addition of a bulk diffraction term and an external "optical trap" is derived from first principles, i.e., Maxwell equations. When the nonlinearity is of the defocusing type, a family of unstaggered localized...

Analytic solutions F (v, t) of the nonlinear Boltzmann equation in ddimensions are studied for a new class of dissipative models, called inelastic repulsive scatterers, interacting through pseudo-power law repulsions, characterized by a strength parameter ν, and embedding inelastic hard spheres (ν = 1) and inelastic Maxwell models (ν = 0). The systems are either freely cooling without energy in...

The Lamb shift in hydrogen spectrum is obtained here in the framework of some weak generalization of the classical Maxwell electrodynamics. It is shown that weakly generalized classical Maxwell electrodynamics can describe the intra-atomic phenomena with the same success as relativistic quantum mechanics can do. Group-theoretical grounds for the description of fermionic states by bosonic system...

In order to extend the limits of classical theory application in the microworld some weak generalization of Maxwell electrodynamics is suggested. It is shown that weakly generalized classical Maxwell electrodynamics can describe the intraatomic phenomena with the same success as relativistic quantum mechanics can do. Group-theoretical grounds for the description of fermionic states by bosonic s...

The time evolution of a collisionless plasma is modeled by the Vlasov-Maxwell system which couples Vlasov equation (the transport equation) with Maxwell equations electrodynamics. We only consider 'two-dimensional' version problem since existence global, classical solutions full three-dimensional not known. add external currents to system, in applications generated coils, control proper way. Af...

We consider the quantum nonlinear Schrödinger equation in one space and one time dimension. It is equivalent to Bose gas with delta interaction. We are interested in the non-free-fermionic case. We calculate temperature-dependent correlation functions. The determinant representation for correlation functions simplifies in the small mass limit of the Bose particle. In this limit we describe the ...

We prove global regularity, scattering and a priori bounds for the energy critical MaxwellKlein-Gordon equation relative to the Coulomb gauge on (1 + 4)-dimensional Minkowski space. The proof is based upon a modified Bahouri-Gérard profile decomposition [1] and a concentration compactness/rigidity argument by Kenig-Merle [5], following the method developed by the first author and Schlag [10] in...

The model of inelastic Maxwell particles (IMP) allows one to derive some exact results which show the strong influence of inelasticity on the nonequilibrium properties of a granular gas. The aim of this work is to propose a simple model kinetic equation that preserves the most relevant properties of the Boltzmann equation (BE) for IMP and reduces to the BGK kinetic model in the elastic limit. I...