Related papers: The Enskog Process
We address the problem of the so-called ``granular gases'', i.e. gases of massive particles in rapid movement undergoing inelastic collisions. We introduce a class of models of driven granular gases for which the stationary state is the…
A steady self-diffusion process in a gas of hard spheres at equilibrium is analyzed. The system exhibits a constant gradient of labeled particles. Neither the concentration of these particles nor its gradient are assumed to be small. It is…
The dynamics of the solutions to a class of conservative SPDEs are analysed from two perspectives: Firstly, a probabilistic construction of a corresponding random dynamical system is given for the first time. Secondly, the existence and…
The Nordstr\"om-Vlasov system is a Lorentz invariant model for a self-gravitating collisionless gas. We establish suitable a-priori-bounds on the solutions of this system, which together with energy estimates and the smoothing effect of…
The dynamics of multicomponent gas mixtures with vanishing barycentric velocity is described by Maxwell-Stefan equations with mass diffusion and heat conduction. The equations consist of the mass and energy balances, coupled to an algebraic…
The stochastic theory of non-relativistic quantum mechanics presented here relies heavily upon the theory of stochastic processes, with its definitions, theorems and specific vocabulary as well. Its main hypothesis states indeed that the…
We develop a rigorous formalism for the description of the kinetic evolution of many-particle systems with the dissipative interaction. The relationships of the evolution of a hard sphere system with inelastic collisions described within…
In the present paper, we give some examples of stochastic differential equations which have delicateness in the Markov and strong Markov properties, the uniqueness locally in time and globally in time, and initial conditions. Moreover, we…
We introduce a new variational characterization of Gaussian diffusion processes as minimum uncertainty states. We then define a variational method constrained by kinematics of diffusions and Schr\"{o}dinger dynamics to seek states of local…
Recently, progress has been made in the theory of turbulence, which provides a framework on how a deterministic process changes to a stochastic one owing to the change in thermodynamic states. It is well known that, in the framework of…
The solution of the Enskog equation for the one-body velocity distribution of a moderately dense, arbitrary mixture of inelastic hard spheres undergoing planar shear flow is described. A generalization of the Grad moment method, implemented…
This work focuses on the well-posedness of McKean-Vlasov stochastic differential delay equations. Under suitable lipschitz conditions on the drift and diffusion terms, along with a distribution dependent Lyapunov condition, this paper shows…
A granular gas composed of inelastic hard spheres or disks in the homogeneous cooling state is considered. Some of the particles are labeled and their number density exhibits a time-independent linear profile along a given direction. As a…
We study the kinetic Fokker-Planck equation perturbed by a stochastic Vlasov force term. When the noise intensity is not too large, we solve the Cauchy Problem in a class of well-localized (in velocity) functions. We also show that, when…
The goal of this note is to provide most of the technical details involved in the application of the Chapman-Enskog method to solve the revised Enskog equation to Navier-Stokes order. Explicit expressions for the transport coefficients and…
The existence of global solutions for a system of differential equations is proved, and some of their properties are described. The system involves a kinetic equation for quantum particles. It is a simplified version of a mathematical…
Dynamics of inelastic gases are studied within the framework of random collision processes. The corresponding Boltzmann equation with uniform collision rates is solved analytically for gases, impurities, and mixtures. Generally, the energy…
While accurate simulations of dense gas flows far from the equilibrium can be achieved by Direct Simulation adapted to the Enskog equation, the significant computational demand required for collisions appears as a major constraint. In order…
A description of many-particle systems, which is more fundamental than the fluid approach, is to consider them as a kinetic gas. In this approach the dynamical variable in which the properties of the system are encoded, is the distribution…
In this paper, we investigate a class of multiscale McKean-Vlasov stochastic systems, where the entire system depends on the distributions of both fast and slow components. First of all, by applying the Poisson equation method, we prove…