MODELING THE MOTION OF PARTICLES IN THE POTENTIAL FORCE FIELD WITH ALLOWANCE FOR THE RANDOM VELOCITY FLUCTUATIONS OF A MEDIUM

A study is made of the chaotic motion of particles in the potential force fi led under the infl uence of colored noise. Two fundamentally different approaches are used. In the first case, within the framework of the Eulerian approach, a closed equation is derived for the disribution density function of the random coordinate of a particle in the potential field. A conservative nonstationary equation for the probability density function in the bimodal potential is proposed. The second, i.e., the Lagrangian approach, is based on direct numerical modeling of a system of stochastic ordinary diff erential equations describing the displacement of a particle and the random velocity filed of a medium. Through the averaging of an ensemble of chaotic particle paths, the dynamics of change in the empirical probability density function in the bimodal potential is modeled. The results of modeling the dynamics of the probability density function obtained by two diff erent methods are in satisfactory agreement.

   
Author:  I. V. Derevich, A. K. Klochkov
Keywords:  probability density function, stochastic ordinary diff erential equation, conservative diff erence scheme, colored noise, bimodal potential
Page:  1089