Related papers: Stable Equilibrium Based on L\'evy Statistics: A L…
We investigate the velocity relaxation of a viscous one-dimensional granular gas, that is, one in which neither energy nor momentum is conserved in a collision. Of interest is the distribution of velocities in the gas as it cools, and the…
We discuss a relativistic diffusion in the proper time in an approach of Schay and Dudley. We derive (Langevin) stochastic differential equations in various coordinates.We show that in some coordinates the stochastic differential equations…
We study freely evolving and forced inelastic gases using the Boltzmann equation. We consider uniform collision rates and obtain analytical results valid for arbitrary spatial dimension d and arbitrary dissipation coefficient epsilon. In…
We analyze the deviations from Maxwell-Boltzmann statistics found in recent experiments studying velocity distributions in two-dimensional granular gases driven into a non-equilibrium stationary state by a strong vertical vibration. We show…
This paper presents a molecular dynamics simulation of an inelastic gas, where collisions between molecules are characterized by a coefficient of restitution less than unity. The simulation employs an event-driven algorithm to efficiently…
Statistical invariance of Wiener increments under SO(n) rotations provides a notion of gauge transformation of state-dependent Brownian motion. We show that the stochastic dynamics of non gauge-invariant systems is not unambiguously…
The L\'evy-stable distribution is the attractor of distributions which hold power laws with infinite variance. This distribution has been used in a variety of research areas, for example in economics it is used to model financial market…
Starting from the probability distribution of finite N-body systems, which maximises the Havrda--Charv\'at entropy, we build a Stein-type goodness-of-fit test. The Maxwell--Boltzmann distribution is exact only in the thermodynamic limit,…
A statistical thermodynamic approach of moving particles forming an elastic body is presented which leads to reveal molecular-mechanical properties of classical and nonextensive dynamical systems. We derive the Boltzmann-Gibbs (BG) entropy…
The particles model, the collision model, the polynomial development used for the equilibrium distribution, the time discretization and the velocity discretization are factors that let the lattice Boltzmann framework (LBM) far away from its…
On contrary to the customary thought, the well-known ``lemma'' that the distribution function of a collisionless Boltzmann gas keeps invariant along a molecule's path represents not the strength but the weakness of the standard theory. One…
We consider different generalizations of the Fokker-Planck-equation devised to describe Levy processes in potential force fields. We show that such generalizations can proceed along different lines. On one hand, Levy statistics can emerge…
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…
We study a model of rolling particles subject to stochastic fluctuations, which may be relevant in systems of nano- or micro-scale particles where rolling is an approximation for strong static friction. We consider the simplest possible…
Boltzmann equation describes the time development of the velocity distribution in the continuum fluid matter. We formulate the equation using the field theory where the {\it velocity-field} plays the central role. The matter (constituent…
In the paper we study a measure version of the evolutionary nonlinear Boltzmann-type equation in which we admit a random number of collisions of particles. We consider first a stationary model and use two methods to find its fixed points:…
We introduce a fractional Kramers equation for a particle interacting with a thermal heat bath and external non-linear force field. For the force free case the velocity damping follows the Mittag-Leffler relaxation and the diffusion is…
Hydrodynamic equations for an inelastic Maxwell model are derived from the inelastic Boltzmann equation based on a systematic Chapman-Enskog perturbative scheme. Transport coefficients appear in Navier-Stokes order have been determined as a…
We consider the single-particle velocity distribution of a one-dimensional fluid of inelastic particles. Both the freely evolving (cooling) system and the non-equilibrium stationary state obtained in the presence of random forcing are…
The inelastic Boltzmann equation for a granular gas is applied to spatially inhomogeneous states close to the uniform shear flow. A normal solution is obtained via a Chapman-Enskog-like expansion around a local shear flow distribution. The…