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Semi adiabatic theory of seasonal Markov processes

Abstract

The dynamics of many natural and technical systems are essentially influenced by a periodic forcing. Analytic solutions of the equations of motion for periodically driven systems are generally not known. Simulations, numerical solutions or in some limiting cases approximate analytic solutions represent the known approaches to study the dynamics of such systems. Besides the regime of weak periodic forces where linear response theory works, the limit of a slow driving force can often be treated analytically using an adiabatic approximation. For this approximation to hold all intrinsic processes must be fast on the time-scale of a period of the external driving force. We developed a perturbation theory for periodically driven Markovian systems that covers the adiabatic regime but also works if the system has a single slow mode that may even be slower than the driving force. We call it the semi adiabatic approximation. Some results of this approximation for a system exhibiting stochastic resonance which usually takes place within the semi adiabatic regime are indicated. (author) 1 fig., 8 refs.
Authors:
Talkner, P [1] 
  1. Paul Scherrer Inst. (PSI), Villigen (Switzerland)
Publication Date:
Aug 01, 1999
Product Type:
Technical Report
Report Number:
ETDE-CH-9901
Reference Number:
SCA: 661300; PA: CH-99:0E0048; EDB-99:094455; SN: 99002111490
Resource Relation:
Other Information: PBD: 1999; Related Information: Is Part Of Paul Scherrer Institute Scientific Report 1998. Volume V: General Energy; Daum, C.; Leuenberger, J. [eds.]; PB: 121 p.
Subject:
66 PHYSICS; MARKOV PROCESS; NUMERICAL DATA; PERTURBATION THEORY; PROGRESS REPORT
OSTI ID:
685705
Research Organizations:
Paul Scherrer Inst. (PSI), Villigen (Switzerland)
Country of Origin:
Switzerland
Language:
English
Other Identifying Numbers:
Journal ID: ISSN 1423-7342; Other: ON: DE99754426; TRN: CH99E0048
Availability:
OSTI as DE99754426
Submitting Site:
CH
Size:
pp. 94-95
Announcement Date:

Citation Formats

Talkner, P. Semi adiabatic theory of seasonal Markov processes. Switzerland: N. p., 1999. Web.
Talkner, P. Semi adiabatic theory of seasonal Markov processes. Switzerland.
Talkner, P. 1999. "Semi adiabatic theory of seasonal Markov processes." Switzerland.
@misc{etde_685705,
title = {Semi adiabatic theory of seasonal Markov processes}
author = {Talkner, P}
abstractNote = {The dynamics of many natural and technical systems are essentially influenced by a periodic forcing. Analytic solutions of the equations of motion for periodically driven systems are generally not known. Simulations, numerical solutions or in some limiting cases approximate analytic solutions represent the known approaches to study the dynamics of such systems. Besides the regime of weak periodic forces where linear response theory works, the limit of a slow driving force can often be treated analytically using an adiabatic approximation. For this approximation to hold all intrinsic processes must be fast on the time-scale of a period of the external driving force. We developed a perturbation theory for periodically driven Markovian systems that covers the adiabatic regime but also works if the system has a single slow mode that may even be slower than the driving force. We call it the semi adiabatic approximation. Some results of this approximation for a system exhibiting stochastic resonance which usually takes place within the semi adiabatic regime are indicated. (author) 1 fig., 8 refs.}
place = {Switzerland}
year = {1999}
month = {Aug}
}