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Monte Carlo Methods and Applications

Managing Editor: Sabelfeld, Karl K.

Editorial Board: Binder, Kurt / Bouleau, Nicolas / Chorin, Alexandre J. / Dimov, Ivan / Dubus, Alain / Egorov, Alexander D. / Ermakov, Sergei M. / Halton, John H. / Heinrich, Stefan / Kalos, Malvin H. / Lepingle, D. / Makarov, Roman / Mascagni, Michael / Mathe, Peter / Niederreiter, Harald / Platen, Eckhard / Sawford, Brian R. / Schmid, Wolfgang Ch. / Schoenmakers, John / Simonov, Nikolai A. / Sobol, Ilya M. / Spanier, Jerry / Talay, Denis

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Volume 21, Issue 1

Issues

Stochastic simulation of fluctuation-induced reaction-diffusion kinetics governed by Smoluchowski equations

Karl K. Sabelfeld
  • Institute of Computational Mathematics and Mathematical Geophysics, Russian Academy of Sciences, Lavrentiev Prosp. 6, 630090 Novosibirsk, Russia
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/ Alexander I. Levykin
  • Institute of Computational Mathematics and Mathematical Geophysics, Russian Academy of Sciences, Lavrentiev Prosp. 6, 630090 Novosibirsk, Russia
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/ Anastasiya E. Kireeva
  • Institute of Computational Mathematics and Mathematical Geophysics, Russian Academy of Sciences, Lavrentiev Prosp. 6, 630090 Novosibirsk, Russia
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Published Online: 2015-02-08 | DOI: https://doi.org/10.1515/mcma-2014-0012

Abstract

A stochastic algorithm for simulation of fluctuation-induced reaction-diffusion kinetics is presented and further developed following our previous study [J. Math. Chem. (2015), DOI 10.1007/s10910-014-0446-6] where this method was used to describe the annihilation of spatially separate electrons and holes in a disordered semiconductor. This model is based on the spatially inhomogeneous, nonlinear Smoluchowski equations with random initial distribution density. Here we focus on the spatial distribution of the reactants, and study the segregation effect which we have found under certain reaction conditions. In addition, to extend simulations on large samples we implemented the method in the cellular-automata framework interpreted as a stochastic interacting particles system in discrete but randomly progressed time instances. We have suggested a first passage time technique to characterize the clustering of electrons and holes, which seems to be quite convenient and informative instrument also in more general processes when there is a need to analyze the segregation phenomena.

Keywords: Smoluchowski equations; fluctuation-limited reactions; reaction-diffusion kinetics; electron-hole kinetics; nonradiative recombination

MSC: 65C05; 65C20; 65C30; 60H35

About the article

Received: 2014-09-23

Accepted: 2015-01-10

Published Online: 2015-02-08

Published in Print: 2015-03-01


Funding Source: Russian Science Foundation

Award identifier / Grant number: 14-11-00083


Citation Information: Monte Carlo Methods and Applications, Volume 21, Issue 1, Pages 33–48, ISSN (Online) 1569-3961, ISSN (Print) 0929-9629, DOI: https://doi.org/10.1515/mcma-2014-0012.

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