Related papers: The Maxwell-Boltzmann approximation for ion kineti…
In this paper, we are concerned with the compressible Euler-Maxwell equations with a nonconstant background density (e.g. of ions) in three dimensional space. There exist stationary solutions when the background density is a small…
We consider generalizations of kinetic granular gas models given by Boltzmann equations of Maxwell type. These type of models for non-linear elastic or inelastic interactions, have many applications in physics, dynamics of granular gases,…
We present an extension to the Poisson-Boltzmann model where the dipolar features of solvent molecules are taken explicitly into account. The formulation is derived at mean-field level and can be extended to any order in a systematic…
In this paper, we consider near cloaking for the full Maxwell equations. We extend the recent results, where the quasi-static limit case and the Helmholtz equation are considered, to electromagnetic scattering problems. We construct very…
In this paper, we are interested in the Cauchy problem for the Boltzmann-BGK model for a general class of collision frequencies. We prove that the Boltzmann-BGK model linearized around a global Maxwellian admits a unique global smooth…
Systems of Vlasov-Poisson type are kinetic models describing dilute plasma. The structure of the model differs according to whether it describes the electrons or positively charged ions in the plasma. In contrast to the electron case, where…
This paper is devoted to the approximation of the linear Boltzmann equation by fractional diffusion equations. Most existing results address this question when there is no external acceleration field. The goal of this paper is to…
Based on the analysis of biquaternion quadratic forms of field, it is shown that Maxwell equations arise as a consequence of the principle of conservation of the energy-momentum flow of field in space-time. It turns out that this principle…
In electromagnetism, the model of Maxwell's equations yields accurate and trustworthy predictions. Numerical solvers can reach electromagnetic solutions far beyond the set of analytical closed-form solutions; this is crucial in…
An eikonal expansion is developed in order to provide systematic corrections to the eikonal approximation through order 1/k^2, where k is the wave number. The expansion is applied to wave functions for the Klein-Gordon equation and for the…
We study the quantum mechanical many-body problem of $N$ nonrelativistic electrons interacting with their self-generated classical electromagnetic field and $K$ static nuclei. The system of coupled equations governing the dynamics of the…
The regularity of solutions to the Boltzmann equation is a fundamental problem in the kinetic theory. In this paper, the case with angular cut-off is investigated. It is shown that the macroscopic parts of solutions to the Boltzmann…
In [L. Liu and S. Jin, Multiscale Model. Simult., 16, 1085-1114, 2018], spectral convergence and long-time decay of the numerical solution towards the global equilibrium of the stochastic Galerkin approximation for the Boltzmann equation…
In this paper a symplectic realization for the Maxwell-Bloch equations with the rotating wave approximation is given, which also leads to a Lagrangian formulation. We show how Lie point symmetries generate a third constant of motion for the…
The origin of the Boltzmann factor is revisited. An alternative derivation from the microcanonical picture is given. The Maxwellian distribution in a mono-dimensional ideal gas is obtained by following this insight. Other possible…
We prove the orbital stability of soliton solutions for 2D Maxwell--Lorentz system with extended charged particle. The solitons corresponds to the uniform motion and rotation of the particle. We reduce the corresponding Hamilton system by…
We prove the appearance of an explicit lower bound on the solution to the full Boltzmann equation in the torus for a broad family of collision kernels including in particular long-range interaction models, under the assumption of some…
An analysis of the concept of orientation used in electrodynamics is presented. At least two different versions are encountered in the literature. Both are clearly identified and comparisons are made.
A Generalized Kinetic Theory was proposed in order to have the possibility to treat particles which obey a very general statistics. By adopting the same approach, we generalize here the Kinetic Theory of electrons and phonons. Equilibrium…
This paper's objective is to improve the existing proof of the derivation of the Rayleigh--Boltzmann equation from the nonideal Rayleigh gas [6], yielding a far faster convergence rate. This equation is a linear version of the Boltzmann…