The Solution of the Modified Helmholtz Equation in a Triangular Domain and an Application to Diffusion-Limited Coalescence

Details The Solution of the Modified Helmholtz Equation in a Triangular Domain and an Application to Diffusion-Limited Coalescence The Solution of the Modified Helmholtz Equation in a Triangular Domain and an Application to Diffusion-Limited Coalescence

2001-02-09

arxiv.org/abs/cond-mat/0102175v1

Physical Review E 64, 016114 (2001).

Physics

Condensed Matter

Statistical Mechanics

RevTeX, 7 pages, 3 figures

Scientific paper

10.1103/PhysRevE.64.016114

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.

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