Diffusion in a Half-Space: From Lord Kelvin to Path Integrals
Statistical Mechanics
2007-05-23 v1
Abstract
Many important transport phenomena are described by simple mathematical models rooted in the diffusion equation. Geometrical constraints present in such phenomena often have influence of a universal sort and manifest themselves in scaling relations and stable distribution functions. In this paper, I present a treatment of a random walk confined to a half--space using a number of different approaches: diffusion equations, lattice walks and path integrals. Potential generalizations are discussed critically.
Cite
@article{arxiv.cond-mat/0406613,
title = {Diffusion in a Half-Space: From Lord Kelvin to Path Integrals},
author = {Michael Slutsky},
journal= {arXiv preprint arXiv:cond-mat/0406613},
year = {2007}
}