We present a general approach for obtaining the generalized transport equations weakly nonequilibrium processes with fractional derivatives by using Liouville equation system of classical particles and Zubarev statistical operator method. A diffusion in is obtained processes. Based on non-Markov equation, taking into account spatial nonlocality modeling coefficient particle Dαα′(r,r′;t,t′)=W(t,...

A new relativistic description of quantum electrodynamics is presented. Guideline of the theory is the Klein-Gordon equation, which is reformulated to consider spin effects. This is achieved by a representation of relativistic vectors with a space-time algebra made up of Pauli matrices and hyperbolic numbers. The algebra is used to construct the differential operator of the electron as well as ...

We introduce an analog of the Dirichlet-to-Neumann map for Maxwell equation in a bounded domain. show that it can be approximated by pseudodifferential operator on boundary with matrix-valued symbol and we compute principal symbol. As application, obtain parabolic region free transmission eigenvalues associated equation.

2014 From the exact numerical resolution of the discretized semi-classical equations of the anomalous skin effect theory, we prove that E.M. electron-electron coupling vanishes in the limit of short wavelengths (03BB typically shorter than 2 03BCm for noble metals). That leads to substantial simplification of the algorithms allowing the calculation of the surface impedance. In addition, numeric...

In this paper we study the large-time behavior of classical solutions to the two-species Vlasov-Maxwell-Boltzmann system in the whole space R. The existence of global in time nearby Maxwellian solutions is known from [37] in 2006. However the asymptotic behavior of these solutions has been a challenging open problem. Building on our previous work [12] on time decay for the simpler Vlasov-Poisso...

This paper investigates the axial unsteady flow of a generalized Burgers’ fluid with fractional constitutive equation in a circular micro-tube, in presence of a time-dependent pressure gradient and an electric field parallel to flow direction and a magnetic field perpendicular on the flow direction. The mathematical model used in this work is based on a time-nonlocal constitutive equation for s...

Selfand binary Maxwell-Stefan diffusion coefficients were determined by equilibrium molecular dynamics simulations with the Green-Kubo method. This study covers selfdiffusion coefficients at liquid states for eight pure fluids, i.e. F2, N2, CO2, CS2, C2H6, C2H4, C2H2 and SF6 as well as Maxwell-Stefan diffusion coefficients for three binary mixtures N2+CO2, N2+C2H6 and CO2+C2H6. The fluids were ...

We introduce and discuss spatially homogeneous Maxwell-type models of the nonlinear Boltzmann equation undergoing binary collisions with a random component. The random contribution to collisions is such that the usual collisional invariants of mass, momentum and energy do not hold pointwise, even if they all hold in the mean. Under this assumption it is shown that, while the Boltzmann equation ...

Spectrally and spatially resolved x rays are widely used diagnostics for high-temperature plasmas in laser-driven experiments. The relatively small time scales and small optical depths that occur often require a non-LTE (local thermodynamic equilibrium) analysis of atomic phenomena, and the relatively long mean free path of the most energetic electrons can make non-Maxwellian electron energy di...