Gene Lamm and Klaus Schulten.
Extended Brownian dynamics: II. Reactive, nonlinear diffusion.
Journal of Chemical Physics, 78:2713-2734, 1983.
LAMM83
An improved version of the "extended Brownian dynamics" algorithm recently proposed by the authors [J. Chem. Phys. 75, 365 (1981)] is given. This Monte Carlo procedure for solving the one-dimensional Smoluchowski diffusion equation is statistically exact near a boundary for a constant force and approximately correct for a linear force. The improved algorithm is both more accurate and simpler than the earlier version. In addition, the algorithm is extended to include diffusion near a reactive boundary or in a reactive optical potential. The treatment of diffusion for nonlinear forces is conveniently handled by choosing the time for a single diffusive jump locally. The algorithm converges as this jump time approaches zero. The appropriate modifications necessary to treat diffusion between two (possibly reactive) boundaries or diffusion with a spatially varying diffusion coefficient are also given. Finally, it is shown how multidimensional diffusion in a spherically symmetric force field may be treated by the one-dimensional algorithm described here. As in the earlier paper, numerical results are presented and compared with analytical and numerical descriptions of the diffusion process to demonstrate the validity of the algorithm.
Download Full Text
The manuscripts available on our site are provided for your personal
use only and may not be retransmitted or redistributed without written
permissions from the paper's publisher and author. You may not upload any
of this site's material to any public server, on-line service, network, or
bulletin board without prior written permission from the publisher and
author. You may not make copies for any commercial purpose. Reproduction
or storage of materials retrieved from this web site is subject to the
U.S. Copyright Act of 1976, Title 17 U.S.C.