Information geometry in a reduced model of self-organised shear flows without the uniform coloured noise approximation

Eun Jin Kim, Quentin Jacquet, Rainer Hollerbach

Research output: Contribution to journalArticle

Abstract

We investigate information geometry in a toy model of self-organised shear flows, where a bimodal PDF of x with two peaks signifying the formation of mean shear gradients is induced by a finite memory time of a stochastic forcing f. We calculate time-dependent probability density functions (PDFs) for different values of the correlation time and amplitude D of the stochastic forcing, and identify the parameter space for unimodal and bimodal stationary PDFs. By comparing results with those obtained under the uniform coloured noise approximation (UCNA) in Jacquet et al (2018 Entropy 20 613), we find that UCNA tends to favor the formation of a bimodal PDF of x for given parameter values and D. We map out attractor structure associated with unimodal and bimodal PDFs of x by measuring the total information length against the location x 0 of a narrow initial PDF of x. Here represents the total number of statistically different states that a system passes through in time. We examine the validity of the UCNA from the perspective of information change and show how to fine-tune an initial joint PDF of x and f to achieve a better agreement with UCNA results.

Original languageEnglish
Article number023204
JournalJournal of Statistical Mechanics: Theory and Experiment
Volume2019
Issue number2
DOIs
Publication statusPublished - 20 Feb 2019
Externally publishedYes

Fingerprint

Information Geometry
Colored Noise
Reduced Model
Shear Flow
probability density functions
shear flow
Probability density function
Bimodal
Approximation
geometry
approximation
Forcing
Geometry
Parameter Space
Attractor
Entropy
Tend
entropy
Gradient
shear

Bibliographical note

This is an author-created, un-copyedited version of an article accepted for publication/published in Journal of Statistical Mechanics: Theory and Experiment IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://dx.doi.org/10.1088/1742-5468/ab00dd

Copyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders.

Keywords

  • fluctuation phenomena
  • stochastic processes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Information geometry in a reduced model of self-organised shear flows without the uniform coloured noise approximation. / Kim, Eun Jin; Jacquet, Quentin; Hollerbach, Rainer.

In: Journal of Statistical Mechanics: Theory and Experiment, Vol. 2019, No. 2, 023204, 20.02.2019.

Research output: Contribution to journalArticle

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