Related papers: On true relaxation statistics in gases
The Lorentz gas is one of the simplest, most widely used models to study the transport properties of rarified gases in matter. It describes the dynamics of a cloud of non-interacting point particles in an infinite array of fixed spherical…
The transport coefficients of a dilute classical gas in the presence of a drag force proportional to the velocity of the particle are determined from the Boltzmann equation. The viscous drag force could model the friction of solid particles…
Relativistic effects in the thermodynamical properties of interacting particle systems are investigated within the framework of the relativistic direct interaction theory in various forms of dynamics. In the front form of relativistic…
Theory of granular dissipative gas is discussed based on Boltzmann's equation and in view of recent experimental results in micro-gravity during few CNES and ESA campaigns [9,11]. It is recalled that the Boltzmann's distribution is a steady…
The fractional diffusion equation is rigorously derived as a scaling limit from a deterministic Rayleigh gas, where particles interact via short range potentials with support of size $\varepsilon$ and the background is distributed in space…
The head-on collision of two identical droplets is investigated based on the BGK-Boltzmann equation. Gauss-Hermite quadratures with different degree of precision are used to solve the kinetic equation, so that the continuum (solution…
The kinetics of collisionless continuous medium is studied in a bounded region on a curved manifold. We have assumed that in statistical equilibrium, the probability distribution density depends only on the total energy. It is shown that in…
The Drude-Lorentz model for the motion of electrons in a solid is a classical model in statistical mechanics, where electrons are represented as point particles bouncing on a fixed system of obstacles (the atoms in the solid). Under some…
The temporal evolution of a perturbation of the equilibrium distribution of a condensed Bose gas is investigated using the kinetic equation which describes collision between condensate and noncondensate atoms. The dynamics is studied in the…
In this paper we consider the stochastic dynamics of a finite system of particles in a finite volume (Kac-like particle system) which annihilate with probability $\alpha \in (0,1)$ or collide elastically with probability $1-\alpha$. We…
The approach of an ideal gas to equilibrium is simulated through a generalization of the Ehrenfest ball-and-box model. In the present model, the interior of each box is discretized, {\it i.e.}, balls/particles live in cells whose occupation…
We derive the exact formula for thermal-equilibrium spacing distribution of one-dimensional particle gas with repulsive potential V(r)=r^(-a) (a>0) depending on the distance r between the neighboring particles. The calculated distribution…
People are well aware that, inherently, certain small-scale nonchaotic particle movements are not governed by thermodynamics. Usually, such phenomena are studied by kinetic theory and their energy properties are considered "trivial". In…
We investigate the problem of ballistically controlled reactions where particles either annihilate upon collision with probability $p$, or undergo an elastic shock with probability $1-p$. Restricting to homogeneous systems, we provide in…
We find the probability density function $\mathcal{P}(V_{\texttt{r}})$ of the relativistic relative velocity for two colliding particles in a non-degenerate relativistic gas. The distribution reduces to Maxwell distribution for the relative…
We investigate equilibrium properties of two very different stochastic collision models: (i) the Rayleigh particle and (ii) the driven Maxwell gas. For both models the equilibrium velocity distribution is a L\'evy distribution, the Maxwell…
The stochastic scenario of relaxation in the complex systems is presented. It is based on a general probabilistic formalism of limit theorems. The nonexponential relaxation is shown to result from the asymptotic self-similar properties in…
We consider a system of $N$ interacting particles, described by SDEs driven by Poisson random measures, where the coefficients depend on the empirical measure of the system. Every particle jumps with a jump rate depending on its position.…
In a freely cooling granular material fluctuations in density and temperature cause position dependent energy loss. Due to strong local dissipation, pressure and energy drop rapidly and material moves from `hot' to `cold' regions, leading…
A simplified, but non trivial, mechanical model -- gas of $N$ particles of mass $m$ in a box partitioned by $n$ mobile adiabatic walls of mass $M$ -- interacting with two thermal baths at different temperatures, is discussed in the…