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Reaction–diffusion system: Fate of a Gaussian probability distribution on flat potential with a sink

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  • Saravanan, Rajendran
  • Chakraborty, Aniruddha

Abstract

In this paper, we give a time domain method to solve exactly the problem of diffusion of a generic initial distribution in the presence of a sink. The diffusive motion is described by the Smoluchowski equation. The potential is taken to be flat and the sink function is taken to be a finite strength Dirac delta function. We solve this problem for the case of initial Gaussian distribution which is usually done numerically. This simple model has been an unsolved problem for some time and is of considerable importance in understanding the reaction–diffusion system. This method can be applied to solve several related problems. We verify our results numerically.

Suggested Citation

  • Saravanan, Rajendran & Chakraborty, Aniruddha, 2019. "Reaction–diffusion system: Fate of a Gaussian probability distribution on flat potential with a sink," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    • Handle: RePEc:eee:phsmap:v:536:y:2019:i:c:s0378437119305977
    DOI: 10.1016/j.physa.2019.04.225
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    References listed on IDEAS

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    1. Schulten, Klaus & Schulten, Zan & Szabo, Attila, 1980. "Reactions governed by a binomial redistribution process—The ehrenfest urn problem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 100(3), pages 599-614.
    2. Ganguly, Moumita & Chakraborty, Aniruddha, 2017. "Understanding looping kinetics of a long polymer molecule in solution. Exact solution for delta function sink model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 163-167.
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