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Exact Fundamental Function for the One‐Dimensional Random Walk with a Perfect Mirror under the External Field
Author(s) -
Yoon JoungHahn,
Kim Hyojoon
Publication year - 2016
Publication title -
bulletin of the korean chemical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.237
H-Index - 59
ISSN - 1229-5949
DOI - 10.1002/bkcs.10921
Subject(s) - random walk , function (biology) , statistical physics , monte carlo method , field (mathematics) , dimension (graph theory) , circular symmetry , boundary value problem , mathematics , physics , mathematical analysis , classical mechanics , statistics , evolutionary biology , pure mathematics , biology
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.