The initial value problem for the linear Boltzmann equation describing the propagation of neutrinos in a medium composed of nuclei is rigorously solved. The structure of the equation corresponds to the Lorentz model with an angle-dependent scattering cross-section. A method yielding the rigorous...

This paper describes the results of our theoretical and numerical studies of hydrodynamic interactions in a suspension of spherical particles confined between two parallel planar walls, under creeping-flow conditions. We propose a novel algorithm for accurate evaluation of the many-particle...

We study the effective interaction in two-dimensional Coulomb systems with periodic boundary conditions. It is shown that the interaction may be identified with the electrostatic potential of the two-dimensional Wigner crystal. We derive a simple closed expression which approximates the...

The motion of a spherical colloidal particle suspended in a moving fluid near a planar hard wall or free surface is considered. The particle types include hard spheres with mixed slip-stick boundary conditions, droplets with high surface tension and porous particles. A general expression for the...

We study hindered settling in monodisperse suspensions of spherical particles in an incompressible viscous fluid. The sedimentation and self-diffusion coefficients are calculated in two-body approximation. We show that in a homogeneous and isotropic suspension in which the change of distribution...

Time-dependent equilibrium correlation functions for interacting Brownian particles are analyzed. To this end the kinetic theory method recently proposed by Bławzdziewicz and Cichocki is used. The elementary processes (i.e. single particle diffusion and many-particle interactions) contributing...

A new generalization of the Ornstein-Zernike equation for the functions describing equilibrium correlations between two groups of particles is proposed. The generalized direct correlation functions for two groups of particles are introduced, and the integral equations relating these functions to...

The evolution of the one-particle distribution for a homogeneous system of hard spheres is studied. The terms in the formal density expansion of the collision operator which correspond to the class of hard sphere dynamical events involving one binary collision, the influence of other particles...

Linear relaxation, occurring in dielectrics, viscoelastic fluids, and many other systems, is often characterized by a broad continuous spectrum. We show that the relaxation behavior may be analyzed effectively by means of N-point Padé approximants, applied in the complex plane of the square...

In view of recent theoretical results by Cichocki and Felderhof we reevaluate previously published simulation data for the mean square displacement of a particle in a hard sphere suspension without hydrodynamic interactions. This new evaluation is consistent with the theoretically predicted...