Related papers: Diffusive limit for a Boltzmann-like equation with…
We derive the hydrodynamic limit of a kinetic equation where the interactions in velocity are modelled by a linear operator (Fokker-Planck or Linear Boltzmann) and the force in the Vlasov term is a stochastic process with high amplitude and…
In this paper we present a rigorous derivation of the Boltzmann equation in a compact domain with diffuse reflection boundary conditions. We consider a system of $N$ hard spheres of diameter $\epsilon$ in a box $\Lambda := [0, 1] \times…
A paradigm model is suggested for describing the diffusive limit of trajectories of two Lorentz disks moving in a finite horizon periodic configuration of smooth, strictly convex scatterers and interacting with each other via elastic…
We prove the propagation of regularity, uniformly in time, for the scaled solutions of one-dimensional dissipative Maxwell models. This result together with the weak convergence towards the stationary state proven by Pareschi and Toscani in…
In the current work we construct a multimolecule random process which leads to the Boltzmann equation in the appropriate limit, and which is different from the deterministic real gas dynamics process. We approximate the statistical…
A version of fractional diffusion on bounded domains, subject to 'homogeneous Dirichlet boundary conditions' is derived from a kinetic transport model with homogeneous inflow boundary conditions. For nonconvex domains, the result differs…
This paper is devoted to the approximation of the linear Boltzmann equation by fractional diffusion equations. Most existing results address this question when there is no external acceleration field. The goal of this paper is to…
This article is on the simultaneous diffusion approximation and homogenization of the linear Boltzmann equation when both the mean free path $\varepsilon$ and the heterogeneity length scale $\eta$ vanish. No periodicity assumption is made…
We present the arising of the Fick cross-diffusion system of equations for fluid mixtures from the multi-species Boltzmann in a rigorous manner in Sobolev spaces. To this end, we formally show that, in a diffusive scaling, the…
Unbalanced probability circulation, which yields cyclic motions in phase space, is the defining characteristics of a stationary diffusion process without detailed balance. In over-damped soft matter systems, such behavior is a hallmark of…
The Fokker-Planck equation provides complete statistical description of a particle undergoing random motion in a solvent. In the presence of Lorentz force due to an external magnetic field, the Fokker-Planck equation picks up a tensorial…
A single mechanism, endemic to the standard model of physics, is proposed to explain wavefunction collapse, classical motion, dissipation, equilibration, and the transition from pure quantum mechanics through open system decoherence to the…
The exterior domain problem is essential in fluid and kinetic equations. In this paper, we establish the validity of the diffusive expansion for the Boltzmann equations to the Navier-Stokes-Fourier system up to the critical time in an…
We study diffusive mixing in the presence of thermal fluctuations under the assumption of large Schmidt number. In this regime we obtain a limiting equation that contains a diffusive thermal drift term with diffusion coefficient obeying a…
We study a nonlinear, pseudomonotone, stochastic diffusion-convection evolution problem on a bounded spatial domain, in any space dimension, with homogeneous boundary conditions and reflection. The additive noise term is given by a…
Standard diffusion equation is based on Brownian motion of the dispersing species without considering persistence in the movement of the individuals. This description allows for the instantaneous spreading of the transported species over an…
Equation for anomalous diffusion in momentum space, recently obtained in the recent paper (S.A. Trigger, ArXiv 0907.2793 v1, [cond-matt. stat.-mech.], 16 July 2009) is solved for the stationary and non-stationary cases on basis of the…
We establish asymptotic diffusion limits of the non-classical transport equation derived in [E. W. Larsen, A generalized Boltzmann equation for non-classical particle transport, Joint international topical meeting on mathematics &…
Combining analytical and numerical methods, we study within the framework of the homogeneous non-linear Boltzmann equation, a broad class of models relevant for the dynamics of dissipative fluids, including granular gases. We use the new…
Diffusion coefficients are obtained from linear response functions and from the quantal fluctuation dissipation theorem. They are compared with the results of both the theory of hydrodynamic fluctuations by Landau and Lifschitz as well as…