Premium
Inertial effects in the Brownian dynamics with rigid constraints
Author(s) -
Gelin Maxim F.
Publication year - 1999
Publication title -
macromolecular theory and simulations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.37
H-Index - 56
eISSN - 1521-3919
pISSN - 1022-1344
DOI - 10.1002/(sici)1521-3919(19991101)8:6<529::aid-mats529>3.0.co;2-t
Subject(s) - brownian dynamics , classical mechanics , generalized coordinates , brownian motion , inertial frame of reference , statistical physics , diffusion , fokker–planck equation , gaussian , physics , limit (mathematics) , dynamics (music) , mathematical analysis , mathematics , differential equation , quantum mechanics , acoustics
To investigate the influence of inertial effects on the dynamics of an assembly of beads subjected to rigid constraints and placed in a buffer medium, a convenient method to introduce suitable generalized coordinates is presented. Without any restriction on the nature of the soft forces involved (both stochastic and deterministic), pertinent Langevin equations are derived. Provided that the Brownian forces are Gaussian and Markovian, the corresponding Fokker‐Planck equation (FPE) is obtained in the complete phase space of generalized coordinates and momenta. The correct short time behavior for correlation functions (CFs) of generalized coordinates is established, and the diffusion equation with memory (DEM) is deduced from the FPE in the high friction limit. The DEM is invoked to perform illustrative calculations in two dimensions of the orientational CFs for once broken nonrigid rods immobilized on a surface. These calculations reveal that the CFs under certain conditions exhibit an oscillatory behavior, which is irreproducible within the standard diffusion equation. Several methods are considered for the approximate solution of the DEM, and their application to three dimensional DEMs is discussed.