相关论文: Propagation processes of correlations of hard sphe…
The series expansion for the evolution of the correlation functions of a finite system of hard spheres is derived from direct integration of the solution of the Liouville equation, with minimal regularity assumptions on the density of the…
The possible ways to describe the states of a system of many hard spheres are considered, in particular by means of functions describing correlations of states. It is stated an approach to the description of the evolution based on the…
The hierarchies of evolution equations of classical many-particle systems are formulated as evolution equations in functional derivatives. In particular the BBGKY hierarchy for marginal distribution functions, the dual BBGKY hierarchy for…
The kinetic theory description of a low density gas of hard spheres or disks, confined between two parallel plates separated a distance smaller than twice the diameter of the particles, is addressed starting from the Liouville equation of…
The dynamics of inelastic hard spheres is described in terms of the binary collision expansion, yielding the corresponding pseudo-Liouville equation and BBGKY hierarchy for the reduced distribution functions. Based on cluster expansion…
The rigorous approach to the description of the kinetic evolution of a many-particle system composed of a trace hard sphere and an environment of finitely many hard spheres is developed. We prove that the evolution of states of a trace hard…
The article presents the concept of a cumulant representation for distribution functions describing the states of many-particle systems with topological nearest-neighbor interaction. A solution to the Cauchy problem for the hierarchy of…
We develop a rigorous formalism for the description of the kinetic evolution of many-particle systems with the dissipative interaction. The relationships of the evolution of a hard sphere system with inelastic collisions described within…
The article deals with the challenge of the construction of solutions to hierarchies of fundamental evolution equations for many colliding particles. The method of cluster expansions of the groups of operators of the Liouville equations for…
We develop a rigorous formalism for the description of the kinetic evolution of infinitely many hard spheres. On the basis of the kinetic cluster expansions of cumulants of groups of operators of finitely many hard spheres the nonlinear…
We present a derivation of the kinetic equation describing the secular evolution of spatially inhomogeneous systems with long-range interactions, the so-called inhomogeneous Landau equation, by relying on a functional integral formalism. We…
In the gravitational evolution of a cold infinite particle distribution, two-body interactions can be predominant at early times: we show that, by treating the simple case of a Poisson particle distribution in a static universe as an…
A solution to the BBGKY hierarchy for nonequilibrium distribution functions is obtained within modified boundary conditions. The boundary conditions take into account explicitly both the nonequilibrium one-particle distribution function as…
We prove that the evolution of marginals associated to the empirical measure of a finite system of hard spheres is driven by the BBGKY hierarchical expansion. The usual hierarchy of equations for $L^1$ measures is obtained as a corollary.…
In the paper we discuss possible approaches to the problem of the rigorous derivation of quantum kinetic equations from underlying many-particle dynamics. For the description of a many-particle evolution we construct solutions of the Cauchy…
Many important properties of granular fluids can be represented by a system of hard spheres with inelastic collisions. Traditional methods of nonequilibrium statistical mechanics are effective for analysis and description of the inelastic…
The problem of statistics of molecular random walks in a classical fluid is analyzed by means of the BBGKY hierarchy of equations reformulated in terms of the Bogolyubov evolution equation for generating functional of many-particle…
We present a brief derivation of the kinetic equation describing the secular evolution of point vortices in two-dimensional hydrodynamics, by relying on a functional integral formalism. We start from Liouville's equation which describes the…
In the paper the possible approaches to the rigorous derivation of the Boltzmann kinetic equation with hard sphere collisions from underlying dynamics are considered. In particular, a formalism for the description of the evolution of…
We study the growth of correlations in systems with weak long-range interactions. Starting from the BBGKY hierarchy, we determine the evolution of the two-body correlation function by using an expansion of the solutions of the hierarchy in…