Monte Carlo Simulation Methods for External Field Effects on Diffusion-Influenced Reactions

Kim, Taejun; Kim, Hyojoon

doi:10.5012/bkcs.2014.35.4.1209

Bulletin of the Korean Chemical Society

2014

DOI: 10.5012/bkcs.2014.35.4.1209

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Monte Carlo Simulation Methods for External Field Effects on Diffusion-Influenced Reactions

Taejun Kim¹,

Hyojoon Kim²

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Cited by 3 publications

References 17 publications

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Exact Fundamental Function for the One‐Dimensional Random Walk with a Perfect Mirror under the External Field

Yoon

Kim

2016

Bulletin Korean Chem Soc

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The exact analytical probability function is presented for the random walk with a perfect mirror under the constant external field in one dimension. Unlike the field-free solution, the symmetry around the boundary is broken by the external field and the fundamental function is not given by a simple form. We prove the solution by mathematical induction method and numerical simulations. Monte Carlo simulations can be replaced by the function without statistical noise. Based on this function, we also obtain the solution for the continuum diffusion-influenced reaction, which is shown to be superior to the known solution especially for the system with a strong external field.

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Exact Fundamental Function for the One‐Dimensional Random Walk with a Perfect Mirror under the External Field

Yoon

Kim

2016

Bulletin Korean Chem Soc

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Exact Fundamental Functions of the Random Walk in One‐dimensional Confined System

Yoon

Kim

2017

Bulletin Korean Chem Soc

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We have found the exact discrete solutions for the one‐dimensional confined system where two outer boundaries are either absorbing or reflecting. The solution can be easily generalized to the system where one boundary is absorbing and the other is reflecting. The exact solutions are proved by the mathematical induction method analytically and by the simulations numerically. We also prove that the exact discrete solution can be reduced to the well‐known continuum solution.

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Fundamental Function for the Random Walk Simulation under the External Field in One Dimension

Yoon¹,

Kim

2014

Bulletin of the Korean Chemical Society

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Monte Carlo Simulation Methods for External Field Effects on Diffusion-Influenced Reactions

Cited by 3 publications

References 17 publications

Exact Fundamental Function for the One‐Dimensional Random Walk with a Perfect Mirror under the External Field

Exact Fundamental Function for the One‐Dimensional Random Walk with a Perfect Mirror under the External Field

Exact Fundamental Functions of the Random Walk in One‐dimensional Confined System

Fundamental Function for the Random Walk Simulation under the External Field in One Dimension

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