On the Exact Solution of a Generalized Polya Process

On the Exact Solution of a Generalized Polya Process

There are two types of master equations in describing nonequilibrium phenomena with memory effect: (i) the memory function type and (ii) the nonstationary type. A generalized Polya process is studied within the framework of a non-stationary type master equation approach. For a transition-rate with a...

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Main Author: Hidetoshi Konno
Format: Article
Language:English
Published: Hindawi Limited 2010-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2010/504267
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spelling doaj-49f9ef9555e248caaeed8a204d7e7b122021-07-02T06:32:16ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392010-01-01201010.1155/2010/504267504267On the Exact Solution of a Generalized Polya ProcessHidetoshi Konno0Department of Risk Engineering, Faculty of Systems and Information Engineering, University of Tsukuba, Tsukuba, Ibaraki 305-8573, JapanThere are two types of master equations in describing nonequilibrium phenomena with memory effect: (i) the memory function type and (ii) the nonstationary type. A generalized Polya process is studied within the framework of a non-stationary type master equation approach. For a transition-rate with an arbitrary time-dependent relaxation function, the exact solution of a generalized Polya process is obtained. The characteristic features of temporal variation of the solution are displayed for some typical time-dependent relaxation functions reflecting memory in the systems.http://dx.doi.org/10.1155/2010/504267
collection DOAJ
language English
format Article
sources DOAJ
author Hidetoshi Konno
spellingShingle Hidetoshi Konno
On the Exact Solution of a Generalized Polya Process
Advances in Mathematical Physics
author_facet Hidetoshi Konno
author_sort Hidetoshi Konno
title On the Exact Solution of a Generalized Polya Process
title_short On the Exact Solution of a Generalized Polya Process
title_full On the Exact Solution of a Generalized Polya Process
title_fullStr On the Exact Solution of a Generalized Polya Process
title_full_unstemmed On the Exact Solution of a Generalized Polya Process
title_sort on the exact solution of a generalized polya process
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9120
1687-9139
publishDate 2010-01-01
description There are two types of master equations in describing nonequilibrium phenomena with memory effect: (i) the memory function type and (ii) the nonstationary type. A generalized Polya process is studied within the framework of a non-stationary type master equation approach. For a transition-rate with an arbitrary time-dependent relaxation function, the exact solution of a generalized Polya process is obtained. The characteristic features of temporal variation of the solution are displayed for some typical time-dependent relaxation functions reflecting memory in the systems.
url http://dx.doi.org/10.1155/2010/504267
work_keys_str_mv AT hidetoshikonno ontheexactsolutionofageneralizedpolyaprocess
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