相关论文: Solutions to the Boltzmann equation in the Boussin…
We report a study of the homogeneous isotropic Boltzmann equation for an open system. We seek for nonequilibrium steady solutions in presence of forcing and dissipation. Using the language of weak turbulence theory, we analyze the…
Bose-Einstein condensation (BEC) of an ideal gas is investigated, beyond the thermodynamic limit, for a finite number $N$ of particles trapped in a generic three-dimensional power-law potential. We derive an analytical expression for the…
A study of convection in a circular two dimensional cell is presented. The system is heated and cooled at two diametrically opposed points on the edge of the circle, which are parallel or anti-parallel to gravity. The latter's role in the…
Natural convection is ubiquitous throughout the physical sciences and engineering, yet many of its important properties remain elusive. To study convection in a novel context, we derive and solve a quasilinear form of the Rayleigh-B\'enard…
The solutions of the one-dimensional homogeneous nonlinear Boltzmann equation are studied in the QE-limit (Quasi-Elastic; infinitesimal dissipation) by a combination of analytical and numerical techniques. Their behavior at large velocities…
We consider an initial boundary value problem of the multi-dimensional Boussinesq equations in the absence of thermal diffusion with velocity damping or velocity diffusion under the stress free boundary condition in horizontally periodic…
A kinetic equation for a dilute gas of hard spheres confined between two parallel plates separated a distance smaller than two particle dimeters is derived. It is a Boltzmann-like equation, which incorporates the effect of the confinement…
The time evolution of moderately dense gas evolving in vacuum described by the Boltzmann-Enskog equation is studied. The associated stochastic process, the Boltzmann-Enskog process, was constructed by Albeverio, R\"udiger and Sundar (2017)…
Ab initio thermodynamics is a widespread, computationally efficient approach to predict the stable configuration of a surface in contact with a surrounding (gas or liquid) environment. In a prevalent realization of this approach, this…
A kinetic model for the Boltzmann equation is proposed and explored as a practical means to investigate the properties of a dilute granular gas. It is shown that all spatially homogeneous initial distributions approach a universal…
In this article we study the well-posedness of the Boltzmann equation near its hydrodynamic limit on a bounded domain. We consider two types of domains, namely $C^2$ domains with Maxwell boundary conditions where the accommodation…
We present hydrodynamic equations of compressible fluids in gravity as a generalization of those in the Boussinesq approximation used for nearly incompressible fluids. They account for adiabatic processes taking place throughout the cell…
In this article we consider the asymptotic stability of the two-dimensional Boussinesq equations with partial dissipation near a combination of Couette flow and temperature profiles $T(y)$. As a first main result we show that if $T'$ is of…
Slow flows of a slightly rarefied gas under high thermal stresses are considered. The correct fluid-dynamic description of this class of flows is based on the Kogan--Galkin--Friedlander equations, containing some non-Navier--Stokes terms in…
We consider the non-relativistic quantum Boltzmann equation for fermions and bosons. Using the nonlinear energy method and mild formulation, we justify the global well-posedness when the density function is near the global Maxwellian and…
We study steady Boltzmann equation in half-space, which arises in the Knudsen boundary layer problem, with diffusive reflection boundary conditions. Under certain admissible conditions and the source term decaying exponentially, we…
The departure of a granular gas in the instable region of parameters from the initial homogeneous cooling state is studied. Results from Molecular Dynamics and from Direct Monte Carlo simulation of the Boltzmann equation are compared. It is…
We derive a general energy balance equation for a self-interacting boson gas at vanishing temperature in a curved spacetime. This represents a first step towards a formulation of the first law of thermodynamics for a scalar field in general…
We discuss the phenomenon of Bose-Einstein condensation of an ideal non-relativistic Bose gas in an arbitrarily shaped cavity. The influence of the finite extension of the cavity on all thermodynamical quantities, especially on the critical…
We present a mathematical theory of dynamical fluctuations for the hard sphere gas in the Boltzmann-Grad limit. We prove that: (1) fluctuations of the empirical measure from the solution of the Boltzmann equation, scaled with the square…