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

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 ma...

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Bibliographic Details
Published inBulletin of the Korean Chemical Society Vol. 38; no. 3; pp. 364 - 368
Main Authors Yoon, Joung‐Hahn, Kim, Hyojoon
Format Journal Article
LanguageEnglish
Published Weinheim Wiley‐VCH Verlag GmbH & Co. KGaA 01.03.2017
대한화학회
Subjects
Confined system
Exact Functions
One Dimension
Random Walk
화학
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ISSN1229-5949
0253-2964
1229-5949
DOI10.1002/bkcs.11093

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Summary: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.
Bibliography:http://onlinelibrary.wiley.com/doi/10.1002/bkcs.11093/abstract
G704-000067.2017.38.2.033
ISSN:1229-5949
0253-2964
1229-5949
DOI:10.1002/bkcs.11093