The Solution of the Modified Helmholtz Equation in a Triangular Domain and an Application to Diffusion-Limited Coalescence
Statistical Mechanics
2009-11-07 v1
Abstract
A new transform method for solving boundary value problems for linear and integrable nonlinear PDEs recently introduced in the literature is used here to obtain the solution of the modified Helmholtz equation q_{xx}(x,y)+q_{yy}(x,y)-4b^2q(x,y)=0 in the triangular domain 0 < x < L-y < L, with mixed boundary conditions. This solution is applied to the problem of diffusion-limited coalescence, A + A <--> A, in the segment (-L/2,L/2), with traps at the edges.
Keywords
Cite
@article{arxiv.cond-mat/0102175,
title = {The Solution of the Modified Helmholtz Equation in a Triangular Domain and an Application to Diffusion-Limited Coalescence},
author = {Daniel ben-Avraham and Athanassios S. Fokas},
journal= {arXiv preprint arXiv:cond-mat/0102175},
year = {2009}
}
Comments
RevTeX, 7 pages, 3 figures