Exact dimensional reduction of linear dynamics

Application to confined diffusion

Pavol Kalinay, Jerome Percus

Research output: Contribution to journalArticle

Abstract

In their stochastic versions, dynamical systems take the form of the linear dynamics of a probability distribution. We show that exact dimensional reduction of such systems can be carried out, and is physically relevant when the dimensions to be eliminated can be identified with those that represent transient behavior, disappearing under typical coarse graining. Application is made to non-uniform quasi-low dimensional diffusion, resulting in a systematic extension of the "classical" Fick-Jacobs approximate reduction to an exact subdynamics.

Original languageEnglish (US)
Pages (from-to)1059-1069
Number of pages11
JournalJournal of Statistical Physics
Volume123
Issue number5
DOIs
StatePublished - Jun 2006

Fingerprint

Dimensional Reduction
Coarse-graining
Transient Behavior
dynamical systems
Probability Distribution
Dynamical system
Form

Keywords

  • Diffusion
  • Dimensional reduction
  • Fick-Jacobs equation
  • Mapping

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Exact dimensional reduction of linear dynamics : Application to confined diffusion. / Kalinay, Pavol; Percus, Jerome.

In: Journal of Statistical Physics, Vol. 123, No. 5, 06.2006, p. 1059-1069.

Research output: Contribution to journalArticle

Kalinay, Pavol ; Percus, Jerome. / Exact dimensional reduction of linear dynamics : Application to confined diffusion. In: Journal of Statistical Physics. 2006 ; Vol. 123, No. 5. pp. 1059-1069.
@article{1d8289bc8cbd4081a4fd3e59a788a6e3,
title = "Exact dimensional reduction of linear dynamics: Application to confined diffusion",
abstract = "In their stochastic versions, dynamical systems take the form of the linear dynamics of a probability distribution. We show that exact dimensional reduction of such systems can be carried out, and is physically relevant when the dimensions to be eliminated can be identified with those that represent transient behavior, disappearing under typical coarse graining. Application is made to non-uniform quasi-low dimensional diffusion, resulting in a systematic extension of the {"}classical{"} Fick-Jacobs approximate reduction to an exact subdynamics.",
keywords = "Diffusion, Dimensional reduction, Fick-Jacobs equation, Mapping",
author = "Pavol Kalinay and Jerome Percus",
year = "2006",
month = "6",
doi = "10.1007/s10955-006-9081-3",
language = "English (US)",
volume = "123",
pages = "1059--1069",
journal = "Journal of Statistical Physics",
issn = "0022-4715",
publisher = "Springer New York",
number = "5",

}

TY - JOUR

T1 - Exact dimensional reduction of linear dynamics

T2 - Application to confined diffusion

AU - Kalinay, Pavol

AU - Percus, Jerome

PY - 2006/6

Y1 - 2006/6

N2 - In their stochastic versions, dynamical systems take the form of the linear dynamics of a probability distribution. We show that exact dimensional reduction of such systems can be carried out, and is physically relevant when the dimensions to be eliminated can be identified with those that represent transient behavior, disappearing under typical coarse graining. Application is made to non-uniform quasi-low dimensional diffusion, resulting in a systematic extension of the "classical" Fick-Jacobs approximate reduction to an exact subdynamics.

AB - In their stochastic versions, dynamical systems take the form of the linear dynamics of a probability distribution. We show that exact dimensional reduction of such systems can be carried out, and is physically relevant when the dimensions to be eliminated can be identified with those that represent transient behavior, disappearing under typical coarse graining. Application is made to non-uniform quasi-low dimensional diffusion, resulting in a systematic extension of the "classical" Fick-Jacobs approximate reduction to an exact subdynamics.

KW - Diffusion

KW - Dimensional reduction

KW - Fick-Jacobs equation

KW - Mapping

UR - http://www.scopus.com/inward/record.url?scp=33746931214&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33746931214&partnerID=8YFLogxK

U2 - 10.1007/s10955-006-9081-3

DO - 10.1007/s10955-006-9081-3

M3 - Article

VL - 123

SP - 1059

EP - 1069

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 5

ER -