Related papers: A probability theory for non-equilibrium gravitati…
Many systems in nature and laboratories are far from equilibrium and exhibit significant fluctuations, invalidating the key assumptions of small fluctuations and short memory time in or near equilibrium. A full knowledge of Probability…
Distribution functions of relative velocities among particles in a vibrated bed of powder are studied both numerically and theoretically. In the solid phase where granular particles remain near their local stable states, the probability…
The stochastic theory of non-relativistic quantum mechanics presented here relies heavily upon the theory of stochastic processes, with its definitions, theorems and specific vocabulary as well. Its main hypothesis states indeed that the…
This paper discusses the possibility of constructing time-independent solutions to the collisionless Boltzmann equation which depend on quantities other than global isolating integrals such as energy and angular momentum. The key point is…
Dynamics of inelastic gases are studied within the framework of random collision processes. The corresponding Boltzmann equation with uniform collision rates is solved analytically for gases, impurities, and mixtures. Generally, the energy…
We study the dynamics of inertial particles in turbulence using datasets obtained from both direct numerical simulations and laboratory experiments of turbulent swirling flows. By analyzing time series of particle velocity increments at…
In an effort to better understand collisionless relaxation processes in gravitational systems, we investigate one-dimensional models. Taking advantage of a Hermite-Legendre expansion of relevant distribution functions, we present analytical…
The periodic Lorentz gas is a paradigmatic model to examine how macroscopic transport emerges from microscopic chaos. It consists of a triangular lattice of circular hard scatterers with a moving point particle. Recently this system became…
Time evolution of the position-velocity correlation functions (PVCF) plays a key role in a new formalism of Brownian motion. A system of differential equations, which governs PVCF, is derived for magnetic Skyrmions on a 2-dimensional…
Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal…
We present an ``equation-free'' multiscale approach to the simulation of unsteady diffusion in a random medium. The diffusivity of the medium is modeled as a random field with short correlation length, and the governing equations are cast…
Generic equilibria are derived for turbulent relaxing plasmas via an entropy-maximization procedure that accounts for the short-time conservation of certain collisionless invariants. The conservation of these collisionless invariants endows…
Turbulence is ubiquitously observed in nearly collisionless heliospheric plasmas, including the solar wind and corona and the Earth's magnetosphere. Understanding the collisionless mechanisms responsible for the energy transfer from the…
Nonequilibrium thermodynamics has shown its applicability in a wide variety of different situations pertaining to fields such as physics, chemistry, biology, and engineering. As successful as it is, however, its current formulation…
Diffusion processes are widespread in biological and chemical systems, where they play a fundamental role in the exchange of substances at the cellular level and in determining the rate of chemical reactions. Recently, the classical picture…
The global in time existence of solutions of a system describing the interaction of gravitationally attracting particles with a general diffusion term and fixed energy is proved. The presented theory covers the case of the model with…
Unbalanced probability circulation, which yields cyclic motions in phase space, is the defining characteristics of a stationary diffusion process without detailed balance. In over-damped soft matter systems, such behavior is a hallmark of…
We present an analytical and numerical study of a nonlinear diffusion model which describes density relaxation of loosely packed particles under gravity and weak random (thermal) vibration, and compare the results with Monte Carlo…
We characterize a transition from normal to ballistic diffusion in a bouncing ball dynamics. The system is composed of a particle, or an ensemble of non-interacting particles, experiencing elastic collisions with a heavy and periodically…
We investigate the effects of relatively rapid variations of the boundaries of an overmoded cavity on the stochastic properties of its interior acoustic or electromagnetic field. For quasi-static variations, this field can be represented as…