Exact lattice calculations of dispersion coefficients in the presence of external fields and obstacles

• Published in: The European physical journal. E, Soft matter and biological physics Vol. 15; no. 1; pp. 71 - 82
• Main Authors: GAUTHIER, M. G, SLATER, G. W, DORFMAN, K. D
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer 01-09-2004
• Subjects: Algorithms; Biophysics - methods; Chemistry; Colloidal state and disperse state; Computer Simulation; Diffusion; Exact sciences and technology; General and physical chemistry; Models, Statistical; Monte Carlo Method; Physical and chemical studies. Granulometry. Electrokinetic phenomena; Particle; Monte Carlo method; Random walk model; Two dimensional system; Porous medium; Theoretical study; Percolation; Dispersion coefficient
• ISSN: 1292-8941; 1292-895X
• DOI: 10.1140/epje/i2004-10037-9

We present a study of the field-dependent dispersion coefficient of point-like particles in various 2D overdamped systems with obstructions (periodic, percolating, and trapping distributions of obstacles). These calculations profit from the synthesis of a newly proposed Monte Carlo algorithm--the first such algorithm that correctly reproduces the free dispersion coefficient in the presence of finite external fields--and an asymptotically exact calculation technique. The resulting method efficiently produces algebraic and numerical results without the need to actually perform Monte Carlo simulations. When compared to such simulations, our exact method features a negligible computational cost and exponentially small errors. Utilizing the power of this numerical method, we engage in comprehensive parametric analysis of several model systems, revealing very subtle effects that would otherwise be swamped by statistical errors or incur prohibitive computational costs. The unified framework presented here serves as a template for further applications of lattice random-walk models of biased diffusion.