Kim, E-J, Jacquet, Q and Hollerbach, R (2019) Information geometry in a reduced model of self-organised shear flows without the uniform coloured noise approximation. Journal of Statistical Mechanics: Theory and Experiment, 2019 (2). 023204. ISSN 1742-5468
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 γ⁻¹ of a stochastic forcing f . We calculate time-dependent probability density functions (PDFs) for different values of the correlation time γ⁻¹ 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 γ⁻¹ and D. We map out attractor structure associated with unimodal and bimodal PDFs of x by measuring the total information length L∞ = L(t → ∞) against the location x₀ of a narrow initial PDF of x. Here L(t) 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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2019 IOP Publishing Ltd and SISSA Medialab srl. This is an author produced version of a paper published in Journal of Statistical Mechanics: Theory and Experiment. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | stochastic processes; fluctuation phenomena |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 14 Jan 2019 12:20 |
Last Modified: | 20 Feb 2020 01:38 |
Status: | Published |
Publisher: | IOP Publishing |
Identification Number: | 10.1088/1742-5468/ab00dd |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:140647 |