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This review is a kinetic theory study investigating the effects of inelasticity on the structure of the non-equilibrium states, in particular on the behavior of the velocity distribution in the high energy tails. Starting point is the…
In the first sections of this article, we discuss two variations on Maxwell's equations that have been introduced in earlier work--a class of nonlinear Maxwell theories with well-defined Galilean limits (and correspondingly generalized…
We give necessary and sufficient conditions to characterize the convergence in distribution of a sequence of arbitrary random variables to a probability distribution which is the invariant measure of a diffusion process. This class of…
We consider collisional models for granular particles and analyze the conditions under which the restitution coefficient might be a constant. We show that these conditions are not consistent with known collision laws. From the…
Following the original approach of Maxwell-Boltzmann(MB), we derive a 4-velocity distribution function for the relativistic ideal gas. This distribution function perfectly reduces to original MB distribution in the non-relativistic limit.…
In this paper, using of the rigorous statement and rigorous proof the Maxwell distribution as an example, we establish estimates of the distribution depending on the parameter $N$, the number of particles. Further, we consider the problem…
A general recipe proposed elsewhere to define, via Noether theorem, the variation of energy for a natural field theory is applied to Einstein-Maxwell theory. The electromagnetic field is analysed in the geometric framework of natural…
On transformation to the Fourier space $({\bf k}, \omega)$, the partial differential Maxwell equations simplify to algebraic equations, and the Helmholtz theorem of vector calculus reduces to vector algebraic projections. Maxwell equations…
The goal of this article is to establish general principles for high frequency dispersive estimates for Maxwell's equation in the exterior of a perfectly conducting ball. We construct entirely new generalized eigenfunctions for the…
To address the observation of Max Born (M. Born 1969) that the Newton's second law can emerge from a purely statistical perspective, we derive the evolution equation about the statistical distribution for dilute gas based solely on…
We study the velocity distribution function for inelastic Maxwell models, characterized by a Boltzmann equation with constant collision rate, independent of the energy of the colliding particles. By means of a nonlinear analysis of the…
We look at the equilibrium of a Brownian particle in an inhomogeneous space following the alternative approach proposed in ref.[1]. We consider a coordinate dependent damping that makes the stochastic dynamics the one with multiplicative…
Boltzmann's Principle S = k ln W was repeatedly criticized by Einstein since it lacked a proper dynamical foundation in view of the thermal motion of the particles, out of which a physical system consists. This suggests, in particular, that…
This paper uses dynamical invariants to describe the evolution of collisionless systems subject to time-dependent gravitational forces without resorting to maximum-entropy probabilities. We show that collisionless relaxation can be viewed…
We provide the first and rigorous confirmations of the hypotheses by Ludwig Boltzmann in his seminal paper \cite{Boltzmann} within the context of the Landau equation in the presence of a harmonic potential. We prove that (i) Each {\it…
Paper in honour of Freeman Dyson on the occasion of his 80th birthday. Normal N-body systems relax to equilibrium distributions in which classical kinetic energy components are 1/2 kT, but, when inter-particle forces are an inverse cubic…
Nonthermal velocity distributions with much greater tails than the Maxwellian have been observed for radical atoms in plasmas for a long time. Historically, such velocity distributions have been modeled by a two-temperature Maxwell…
We give a geometric formulation of the Fokker-Planck-Kramer equations for a particle moving on a Lie algebra under the influence of a dissipative and a random force. Special cases of interest are fluid mechanics, the Stochastic Loewner…
The theory of equidistribution is about hundred years old, and has been developed primarily by number theorists and theoretical computer scientists. A motivated uninitiated peer could encounter difficulties perusing the literature, due to…
On the basis of new, concise foundations, this paper establishes the four laws of thermodynamics, the Maxwell relations, and the stability requirements for response functions, in a form applicable to global (homogeneous), local…