The goal of this work is to present an approach to the homogeneous Boltzmann equation for Maxwellian molecules with a physical collision kernel which allows us to construct unique solutions to the initial value problem in a space of probability measures defined via the Fourier transform. In that space, the second moment of a measure is not assumed to be finite, so infinite energy solutions are ...

Approximation theory in the context of probability density function turns out to go beyond the classical idea of orthogonal projection. Special tools have to be designed so as to respect the nonnegativity of the approximate function. We develop here and justify from the theoretical point of view an approximation procedure introduced by Levermore [Levermore, J. Stat. Phys. 83 (1996) 1021–1065] a...

In a Maxwellian view, an accelerator of charged particles converts electromagnetic field energy into mechanical energy of the particles. A conventional accelerator based on a resonant cavity emphasizes interference between the drive fields and the the spontaneous radiation fields (those fields radiated when charged particles pass through an otherwise empty cavity). In this case the interference...

In this paper we prove the existence of the high-energy tails for electron distribution function of the Boltzmann equation for semiconductors, in the stationary and homogeneous regime, in the analytic band approximation and scattering with acoustic and optical phonons and impurities. We also prove numerically that the tail is a global maxwellian in the parabolic band approximation, and in the q...

Microscopic theory of Brownian motion of a particle of mass M in a bath of molecules of mass m<<M is considered beyond lowest order in the mass ratio mM . The corresponding Langevin equation contains nonlinear corrections to the dissipative force, and the generalized Fokker-Planck equation involves derivatives of order higher than 2. These equations are derived from first principles with coeffi...

This paper is aimed at understanding what happens to the propensity functions (rates) of bimolecular chemical reactions when the volume occupied by the reactant molecules is not negligible compared to the containing volume of the system. For simplicity our analysis focuses on a one-dimensional gas of N hard-rod molecules, each of length l. Assuming these molecules are distributed randomly and u...

Plasmas in Earth's outer magnetosphere, magnetosheath, and solar wind are essentially collisionless. This means particle distributions not typically thermodynamic equilibrium deviate significantly from Maxwellian distributions. The deviations of these can be further enhanced by plasma processes, such as shocks, turbulence, magnetic reconnection. Such unstable to a wide variety kinetic instabili...