A new set of Monte Carlo moves for lattice random-walk models of biased diffusion

Michel G. Gauthier and Gary W. Slater

Physica A: Statistical Mechanics and its Applications, 2005, vol. 355, issue 2, 283-296

Abstract: We recently demonstrated that standard fixed-time lattice random-walk models cannot be modified to represent properly the biased diffusion processes in more than two dimensions. The origin of this fundamental limitation appears to be the fact that traditional Monte Carlo moves do not allow for simultaneous jumps along each spatial direction. We thus propose a new algorithm to transform biased diffusion problems into lattice random walks such that we recover the proper dynamics for any number of spatial dimensions and for arbitrary values of the external field. Using a hypercubic lattice, we redefine the basic Monte Carlo moves, including the transition probabilities and the corresponding time durations, in order to allow simultaneous jumps along all Cartesian axes. We show that our new algorithm can be used both with computer simulations and with exact numerical methods to obtain the mean velocity and the diffusion coefficient of point-like particles in any dimension and in the presence of obstacles.

Keywords: Diffusion coefficient; Biased random walk; Monte Carlo algorithm (search for similar items in EconPapers)
Date: 2005
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437105001500
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:355:y:2005:i:2:p:283-296

DOI: 10.1016/j.physa.2005.02.015

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().