相关论文: Piecewise continuous distribution function method:…

Hydrodynamic phonon transport was recently predicted as an important regime for phonon transport in graphitic materials. Many of past studies on hydrodynamic phonon transport have focused on the cases where the hydrodynamic regime…

In this paper we develop two models for the steady states and evolution of two dimensional isothermal self gravitating and rotating incompressible gas which are based on the hydrodynamic equations for stratified fluid. The first model is…

We consider the process of diffusion scattering of a wave function given on the phase space. In this process the heat diffusion is considered only along momenta. We write down the modified Kramers equation describing this situation. In this…

In this work, we study a three-wave kinetic equation with resonance broadening arising from the theory of stratified ocean flows. Unlike Gamba-Smith-Tran(On the wave turbulence theory for stratified flows in the ocean, Math. Models Methods…

We study the long-time behavior of solutions to a stochastically driven Navier-Stokes system describing the motion of a compressible viscous fluid driven by a temporal multiplicative white noise perturbation. The existence of stationary…

We derive the equations of motion for all the irreducible moments of the single-particle distribution function. We find that these moment equations of motion are highly coupled, with the dynamics of lower-rank moments always being coupled…

We analyze the transport properties of a low density ensemble of identical macroscopic particles immersed in an active fluid. The particles are modeled as inelastic hard spheres (granular gas). The non-homogeneous active fluid is modeled by…

The perturbed Korteweg--de Vries equation is considered. This equation is used for the description of one--dimensional viscous gas dynamics, nonlinear waves in a liquid with gas bubbles and nonlinear acoustic waves. The integrability of…

In this paper, we analyze a scheme for the time-dependent variable density Navier-Stokes equations. The algorithm is implicit in time, and the space approximation is based on a low-order staggered non-conforming finite element, the…

We develop numerical schemes for solving the isothermal compressible and incompressible equations of fluctuating hydrodynamics on a grid with staggered momenta. We develop a second-order accurate spatial discretization of the diffusive,…

The Bhatnagar-Gross-Krook (BGK) model, a simplification of the Boltzmann equation, in the absence of boundary effect, converges to the Euler equations when the Knudsen number is small. In practice, however, Knudsen layers emerge at the…

We study the high-energy asymptotics of the steady velocity distributions for model systems of granular media in various regimes. The main results obtained are integral estimates of solutions of the hard-sphere Boltzmann equations, which…

Driven granular media constitute model systems in out-of-equilibrium statistical physics. By assimilating the motions of granular particles to those of atoms, by analogy, one can obtain macroscopic equivalent of phase transitions. Here, we…

The Boltzmann collision operator for a dilute granular gas of inelastic rough hard spheres is much more intricate than its counterpart for inelastic smooth spheres. Now the one-body distribution function depends not only on the…

An efficient method is presented as a means of an approximate, analytic time-dependent solution of the Fokker-Planck equation (FPE) for the Langevin model subjected to additive and multiplicative noise. We have assumed that the dynamical…

The physics of settling suspensions under shear are investigated by theoretical and numerical analyses of unstable equilibrium solutions to the incompressible Navier-Stokes equations, coupled with an advection-diffusion-settling equation…

This paper considers two-dimensional stratified water waves propagating under the force of gravity over an impermeable flat bed and with a free surface. We prove the existence of a global continuum of classical solutions that are periodic…

Simulations of the discrete Boltzmann Bhatnagar-Gross-Krook (BGK) equation are an important tool for understanding fluid dynamics in non-continuum regimes. Here, we introduce a discontinuous Galerkin finite element method (DG-FEM) for…

We calculate in this work the Navier-Stokes transport coefficients from the Boltzmann equation for $d$-dimensional inelastic Maxwell models. By granular gas we mean here a low density system of identical spheres that lose a fraction of…

In this paper we derive a semiclassical hydrodynamic system for electron densities and currents in the two energy bands of a semiconductor. We use the semiclassical Wigner equation with a k.p Hamiltonian and a BGK dissipative term to…