Distribution of the coalescence times in a system of diffusion-aggregation of particle clusters in one dimension

We consider the stochastic dynamics of a system of diffusing clusters of particles on a finite periodic chain. A given cluster of particles can diffuse to the right or left as a whole and merge with other clusters; this process continues until all the clusters coalesce. We examine the distribution o...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2020-11, Vol.53 (50), p.505004
Main Authors: Fortin, Jean-Yves, Choi, MooYoung
Format: Article
Language:English
Subjects:
Condensed Matter
diffusion limited aggregation
diffusion reaction phenomena
Physics
Statistical Mechanics
stochastic processes
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Summary:We consider the stochastic dynamics of a system of diffusing clusters of particles on a finite periodic chain. A given cluster of particles can diffuse to the right or left as a whole and merge with other clusters; this process continues until all the clusters coalesce. We examine the distribution of the cluster numbers evolving in time, by means of a general time-dependent master equation based on a Smoluchowski equation for local coagulation and diffusion processes. Further, the limit distribution of the coalescence times is evaluated when only one cluster survives.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/abc8c5