Masser TO, ben-Avraham D. Method of intervals for the study of diffusion-limited annihilation, A+A-->0.
PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001;
63:066108. [PMID:
11415174 DOI:
10.1103/physreve.63.066108]
[Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/05/2001] [Indexed: 05/23/2023]
Abstract
We introduce a method of intervals for the analysis of diffusion-limited annihilation, A+A-->0, on the line. The method leads to manageable diffusion equations whose interpretation is intuitively clear. As an example, we treat the following cases: (a) annihilation in the infinite line and in infinite (discrete) chains; (b) annihilation with input of single particles, adjacent particle pairs, and particle pairs separated by a given distance; (c) annihilation, A+A-->0, along with the birth reaction A-->3A, on finite rings, with and without diffusion.
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