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A random walk on spheres based kinetic Monte Carlo method for simulation of the fluctuation-limited bimolecular reactions

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  • Sabelfeld, Karl K.

Abstract

To simulate spatially inhomogeneous bimolecular reactions driven by diffusion and tunneling we suggest a new stochastic algorithm which combines the well known Random Walk on Spheres (RWS) method and the kinetic Monte Carlo algorithm. This drastically decreases the computer time in the case of diffusion, and especially for low concentrations. This is the case, for instance, when the annihilation of spatially separate electrons and holes in a disordered semiconductor is studied. The method treats all kinds of reactions involved in a unified stochastic kinetic scheme. In particular, along the diffusion and tunneling, nonradiative recombinations in defect sites are taken into account. To validate the simulation algorithm, we compare our simulation results with the asymptotics of the intensity of annihilation which is known from theoretical predictions. Also, we compare the stochastic algorithms with finite-difference methods.

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  • Sabelfeld, Karl K., 2018. "A random walk on spheres based kinetic Monte Carlo method for simulation of the fluctuation-limited bimolecular reactions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 143(C), pages 46-56.
    • Handle: RePEc:eee:matcom:v:143:y:2018:i:c:p:46-56
    DOI: 10.1016/j.matcom.2016.03.011
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Sabelfeld K. & Mozartova N., 2009. "Sparsified Randomization Algorithms for large systems of linear equations and a new version of the Random Walk on Boundary method," Monte Carlo Methods and Applications, De Gruyter, vol. 15(3), pages 257-284, January.
    4. Garcia, Alejandro L. & van den Broeck, Christian & Aertsens, Marc & Serneels, Roger, 1987. "A Monte Carlo simulation of coagulation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 143(3), pages 535-546.
    5. 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.
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