相关论文: A consistent kinetic Fokker-Planck model for gas m…
General Stochastic Hybrid Systems (GSHS) have been formulated to represent various types of uncertainties in hybrid dynamical systems. In this paper, we propose computational techniques for Bayesian estimation of GSHS. In particular, the…
A generalized Fokker-Planck equation is derived to describe particle kinetics in specific situations when the probability transition function (PTF) has a long tail in momentum space. The equation is valid for an arbitrary value of the…
The relaxation to equilibrium in many systems which show strange kinetics is described by fractional Fokker-Planck equations (FFPEs). These can be considered as phenomenological equations of linear nonequilibrium theory. We show that the…
We introduce a generalization of Obukhov's model [A.M. Obukhov, Adv. Geophys. 6, 113 (1959)] for the description of the joint position-velocity statistics of a single fluid particle in fully developed turbulence. In the presented model the…
This paper is dedicated to the application of the DeGiorgi-Nash-Moser regularity theory to the kinetic Fokker-Planck equation. This equation is hypoelliptic. It is parabolic only in the velocity variable, while the Liouville transport…
The article builds on several recent advances in the Monge-Kantorovich theory of mass transport which have -- among other things -- led to new and quite natural proofs for a wide range of geometric inequalities such as the ones formulated…
We determine the Lie point symmetries of the Fokker-Planck equation and provide examples of solutions of this equation. The Fokker-Planck equation admits a conserved form, hence there is an auxiliary system associated to this equation and…
The stochastic differential equations for a model of dissipative particle dynamics, with both total energy and total momentum conservation at every time-step, are presented. The algorithm satisfies detailed balance as well as the…
We consider classical solutions to the kinetic Fokker-Planck equation on a bounded domain $\mathcal O \subset~\mathbb{R}^d$ in position, and we obtain a probabilistic representation of the solutions using the Langevin diffusion process with…
We study time averages for the norm of solutions to kinetic Fokker--Planck equations associated with general Hamiltonians. We provide fully explicit and constructive decay estimates for systems subject to a confining potential, allowing…
In this study, we investigate the phenomenon of collective motion in binary mixtures of self-propelled particles. We consider two particle species, each of which consisting of pointlike objects that propel with a velocity of constant…
An overview of recent results pertaining to the hydrodynamic description (both Newtonian and non-Newtonian) of granular gases described by the Boltzmann equation for inelastic Maxwell models is presented. The use of this mathematical model…
We model thermostatic devices using a stochastic hybrid description, and introduce an external actuation mechanism that creates random switch events in the discrete dynamics. We then conjecture the form of the Fokker-Planck equation and…
Individual constituent balance equations are often used to derive expressions for species-specific segregation velocities in flows of dense granular mixtures. We propose a semiempirical expression for the interspecies momentum exchange in…
We propose a new formulation of the fluctuating lattice Boltzmann equation that is consistent with both equilibrium statististical mechanics and fluctuating hydrodynamics. The formalism is based on a generalized lattice-gas model, with each…
We derive diffusive macroscopic equations for the particle and energy density of a system whose time evolution is described by a kinetic equation for the one particle position and velocity function f(r,v,t) that consists of a part that…
We derive, from first principle, the Fokker-Planck equation describing the non-perturbative real-time evolution of a gauge field at high temperatures on the spatial scale $(g^2T)^{-1}$ and the time scale $(g^4T)^{-1}$, where $g$ is the…
To obtain further insight on possible power law generalizations of Boltzmann equilibrium concepts, a stochastic collision model is investigated. We consider the dynamics of a tracer particle of mass $M$, undergoing elastic collisions with…
A polyatomic ideal gas with weak interaction between the translational and internal modes is considered. For the purpose of describing the behavior of such a gas, a Boltzmann equation is proposed in the form that the collision integral is a…
We consider a Navier-Stokes-Fick-Onsager-Fourier system of PDEs describing mass, energy and momentum balance in a Newtonian fluid with composite molecular structure. For the resulting parabolic-hyperbolic system, we introduce the notion of…