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

Author

Listed:
  • Sabelfeld Karl K.

    (Institute of Computational Mathematics and Mathematical Geophysics, Russian Academy of Sciences, Lavrentiev Prosp. 6, 630090 Novosibirsk, Russia)

  • Levykin Alexander I.

    (Institute of Computational Mathematics and Mathematical Geophysics, Russian Academy of Sciences, Lavrentiev Prosp. 6, 630090 Novosibirsk, Russia)

  • Kireeva Anastasiya E.

    (Institute of Computational Mathematics and Mathematical Geophysics, Russian Academy of Sciences, Lavrentiev Prosp. 6, 630090 Novosibirsk, Russia)

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.

Suggested Citation

  • Sabelfeld Karl K. & Levykin Alexander I. & Kireeva Anastasiya E., 2015. "Stochastic simulation of fluctuation-induced reaction-diffusion kinetics governed by Smoluchowski equations," Monte Carlo Methods and Applications, De Gruyter, vol. 21(1), pages 33-48, March.
    • Handle: RePEc:bpj:mcmeap:v:21:y:2015:i:1:p:33-48:n:6
    DOI: 10.1515/mcma-2014-0012
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    References listed on IDEAS

    as
    1. Sabelfeld K.K. & Rogasinsky S.V. & Kolodko A.A. & Levykin A.I., 1996. "Stochastic algorithms for solving Smolouchovsky coagulation equation and applications to aerosol growth simulation," Monte Carlo Methods and Applications, De Gruyter, vol. 2(1), pages 41-88, December.
    2. Kolodko, A. & Sabelfeld, K. & Wagner, W., 1999. "A stochastic method for solving Smoluchowski's coagulation equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 49(1), pages 57-79.
    3. Sabelfeld, Karl & Kolodko, Anastasia, 2003. "Stochastic Lagrangian models and algorithms for spatially inhomogeneous Smoluchowski equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 61(2), pages 115-137.
    4. Y. L. Zheng & S. L. Nie & H. Ji & Z. Hu, 2013. "Application of a Fuzzy Programming Through Stochastic Particle Swarm Optimization to Assessment of Filter Management Strategies in Fluid Power System Under Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 157(1), pages 276-286, April.
    5. Sabelfeld, K.K., 1998. "Stochastic models for coagulation of aerosol particles in intermittent turbulent flows," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 47(2), pages 85-101.
    6. Kolodko A. A. & Sabelfeld K. K., 2001. "Stochastic Lagrangian model for spatially inhomogeneous Smoluchowski equation governing coagulating and diffusing particles," Monte Carlo Methods and Applications, De Gruyter, vol. 7(3-4), pages 223-228, December.
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