相关论文: Notes on diffusion in collisionless medium
The velocity distribution in a homogeneously cooling granular gas has been studied in the viscoelastic regime when the restitution coefficient of colliding particles depends on the impact velocity. We show that for viscoelastic particles…
The weak noise limit of dissipative dynamical systems is often the most fascinating one. In such a case fluctuations can interact with a rich complexity frequently hidden in deterministic systems to give rise of completely new phenomena…
In most of the literature on granular gases it is assumed that the restitution coefficient \epsilon, which quantifies the loss of kinetic energy upon a collision is independent on the impact velocity. Experiments as well as theoretical…
Since microscopic velocity diffusion can be incorporated into general relativity in a consistent way, we study cosmological background solutions when the diffusion phenomena takes place in an expanding universe. Our focus here relies on the…
An impact of particles' roughness on the self-diffusion coefficient in granular gases is investigated. For a simplified collision model where the normal and tangential restitution coefficients are assumed to be constant we develop an…
We investigate the diffusive properties of energy fluctuations in a one-dimensional diatomic chain of hard-point particles interacting through a square--well potential. The evolution of initially localized infinitesimal and finite…
Since the dawn of the space age, observations of energetic particles in planetary radiation belts have been interpreted within a diffusive transport framework, even though the processes that populate and deplete these belts produce highly…
We consider a spatially homogeneous advection-diffusion equation in which the diffusion tensor and drift velocity are time-independent, but otherwise general. We derive asymptotic expressions, valid at large distances from a steady point…
The similarity between the energy spectra of relativistic particles and that of quasi-particles in super-conductivity BCS theory makes us conjecture that the relativistic physical vacuum medium as the ground state of the background field is…
We report on recent progress in the study of nonlinear diffusion equations involving nonlocal, long-range diffusion effects. Our main concern is the so-called fractional porous medium equation, $\partial_t u +(-\Delta)^{s}(u^m)=0$, and some…
A heuristic approach for collisionless perpendicular diffusion of energetic particles is presented. Analytic forms for the corresponding diffusion coefficient are derived. The heuristic approach presented here explains the parameter $a^2$…
We study diffusion of charged particles in stationary stochastic magnetic field ${\bf B}$ with zero mean, $\langle {\bf B} \rangle = 0 $. In the case when electric current is carried by electrons, the field is force-free, $\mathrm{curl}…
We consider the physical conditions of the neutral medium within, and in the environments of, galaxies. The basic physical and morphological properties of the neutral medium within galaxy disks are now quite well-constrained. Systematic…
We consider the dynamics of diffusing particles in one space dimension with annihilation on collision and nucleation (creation of particles) with constant probability per unit time and length. The cases of nucleation of single particles and…
The primordial velocity dispersion of dark matter is small compared to the velocities attained during structure formation. The initial density distribution is close to uniform and it occupies an initial sheet in phase space that is single…
We present experimental observations of the velocity and spatial distribution of inertial particles dispersed in the turbulent downward flow through a vertical channel at $Re_{\tau} = 235$ and $335$. The working fluid is air laden with…
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 investigate the long time behavior of a passive particle evolving in a one-dimensional diffusive random environment, with diffusion constant $D$. We consider two cases: (a) The particle is pulled forward by a small external constant…
We consider a class of nonlinear Boltzmann equations describing return to thermal equilibrium in a gas of colliding particles suspended in a thermal medium. We study solutions in the space $L^{1}(\mathbb{R}^{3}\times \mathbb{T}^3).$ Special…
We consider the distribution of free path lengths, or the distance between consecutive bounces of random particles, in an n-dimensional rectangular box. If each particle travels a distance R, then, as R tends to infinity the free path…