Related papers: Segregation in granular binary mixtures: Thermal d…
This paper provides the first rigorous derivation of a binary-ternary Boltzmann equation describing the kinetic properties of a dense hard-spheres gas, where particles undergo either binary or ternary instantaneous interactions, while…
Inspired by a recently conjectured universal bound for thermo-electric diffusion constants in quantum critical, strongly coupled systems and relying on holographic analytical computations, we investigate the possibility of formulating…
It is proposed to consider the fast thermalization of gluons in relativistic heavy-ion collisions as a diffusion process in momentum space. Closed-form analytical solutions of a nonlinear boson diffusion equation (NBDE) with constant drift…
The homogeneous Boltzmann equation for inelastic Maxwell mixtures is considered to study the dynamics of tracer particles or impurities (solvent) immersed in a uniform granular gas (solute). The analysis is based on exact results derived…
Consider the initial-boundary value problem for the 2-speed Carleman model of the Boltzmann equation of the kinetic theory of gases set in some bounded interval with boundary conditions prescribing the density of particles entering the…
The diffusion of a bulk absorbed gas species out of spherical pebbles is studied analytically, stressing the usefulness of the time integral of the diffusion coefficient for analysis of arbitrary temperature schedule experiments. Highly…
In this paper we provide a rigorous derivation of the inelastic linear Boltzmann equation, in the Boltzmann-Grad limit, from a dissipative, random, Lorentz gas in arbitrary dimensions d $\geq$ 2. Specifically, we consider a microscopic…
We introduce a ``two-particle factorization'' condition which allows us to formulate the homogeneous Boltzmann equation for non-reversible collision kernels in terms of an entropy inequality. This formulation yields an H-Theorem. We provide…
After a brief discussion of the concepts of fractional exchange and fractional exclusion statistics, we report partly analytical and partly numerical results on thermodynamic properties of assemblies of particles obeying fractional…
We study the Boltzmann equation for a space-homogeneous gas of inelastic hard spheres, with a diffusive term representing a random background forcing. Under the assumption that the initial datum is a nonnegative $L^2$ function, with bounded…
The condition of thermal equilibrium simplifies the theoretical treatment of fluctuations as found in the celebrated Einstein's relation between mobility and diffusivity for Brownian motion. Several recent theories relax the hypothesis of…
The influence of the heating mechanism on the kinetic energy densities of the components of a vibrated granular mixture is investigated. Collisions of the particles with the vibrating wall are inelastic and characterized by two coefficients…
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…
Integro-partial differential equations occur in many contexts in mathematical physics. Typical examples include time-dependent diffusion equations containing a parameter (e.g., the temperature) that depends on integrals of the unknown…
We consider a one-dimensional exclusion dynamics in mild contact with boundary reservoirs. In the diffusive scale, the particles' density evolves as the solution of the heat equation with non-linear Robin boundary conditions. For…
When polydisperse granular systems are sheared, the transverse dynamics is characterized by the interplay of size segregation and diffusion. Segregation in nonuniform and confined shearing flows is studied using annular shear cell…
The linear intensity profile of multiply scattered light in a slab geometry extrapolates to zero at a certain distance beyond the boundary. The diffusion equation with this "extrapolated boundary condition" has been used in the literature…
This article is concerned with the dynamics of a mixture of gases. Under the assumption that all the gases are isothermal and inviscid, we show that the governing equations have an elegant conservation-dissipation structure. With the help…
We prove approach to thermal equilibrium for the fully Hamiltonian dynamics of a dynamical Lorentz gas, by which we mean an ensemble of particles moving through a $d$-dimensional array of fixed soft scatterers that each possess an internal…
We numerically examine binary-sized granular mixtures confined between two parallel walls subjected to vertical vibration using the discrete element method. For a size ratio of $3$ between large and small particles, we study the structure…