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Stochastic reaction, stochastic diffusion

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Abstract

This work explains the stochastic simulation of reaction, diffusion, and combined reaction-diffusion using algorithms and examples of generic cases in 1D and 2D geometries. It explains the Gillespie method for the simulation of chemical reactions and extends it to the simulation of diffusion, including a new improvement on the use of multiple molecule transfers. This work is useful for undergraduate students interested in reactions and transport phenomena at the small scale and for graduate students undertaking a simulation.

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Notes

  1. A literal application of Eq. (20) is not practical because of its factorial terms; hence, the values of \({\mathcal {P}}_{{\mathrm {acum}}}\) are calculated numerically through the incomplete beta function

    $$\begin{aligned} {\mathcal {P}}_{{\mathrm {acum}}}\left( M,m,p_\mathrm{T}\right) =I_{p_\mathrm{T}}\left( m,M-m+1\right), \end{aligned}$$

    which is incorporated in many modern programming languages and is included in Numerical Recipes [45].

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Acknowledgements

Supported by Grant 38600 from DIMA-Manizales.

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Authors and Affiliations

  1. Departamento de Ingeniería Química, Universidad Nacional de Colombia, sede Manizales. (Chemical Engineering Department, Colombia’s National University at Manizales) Campus La Nubia, Manizales, 170005, Caldas, Colombia

    J. I. Carrero

  2. Departamento de Ingeniería Química, Universidad Nacional de Colombia, sede Manizales, Manizales, Colombia

    J. S. Loaiza

  3. Departamento de Ingeniería Física, Universidad Nacional de Colombia, sede Manizales (Physics Engineering Department, Colombia’s National University at Manizales) Campus La Nubia, Manizales, 170005, Caldas, Colombia

    A. Serna

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  1. J. I. Carrero
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  2. J. S. Loaiza
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  3. A. Serna
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Correspondence to J. I. Carrero.

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Carrero, J.I., Loaiza, J.S. & Serna, A. Stochastic reaction, stochastic diffusion. ChemTexts 6, 14 (2020). https://doi.org/10.1007/s40828-020-0108-1

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