Jacquet, Q, Kim, E-J and Hollerbach, R (2018) Time-Dependent Probability Density Functions and Attractor Structure in Self-Organised Shear Flows. Entropy, 20 (8). 613. ISSN 1099-4300
Abstract
We report the time-evolution of Probability Density Functions (PDFs) in a toy model of self-organised shear flows, where the formation of shear flows is induced by a finite memory time of a stochastic forcing, manifested by the emergence of a bimodal PDF with the two peaks representing non-zero mean values of a shear flow. Using theoretical analyses of limiting cases, as well as numerical solutions of the full Fokker–Planck equation, we present a thorough parameter study of PDFs for different values of the correlation time and amplitude of stochastic forcing. From time-dependent PDFs, we calculate the information length ( L ), which is the total number of statistically different states that a system passes through in time and utilise it to understand the information geometry associated with the formation of bimodal or unimodal PDFs. We identify the difference between the relaxation and build-up of the shear gradient in view of information change and discuss the total information length ( L∞=L(t→∞) ) which maps out the underlying attractor structures, highlighting a unique property of L∞ which depends on the trajectory/history of a PDF’s evolution.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). |
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: | 22 Aug 2018 15:35 |
Last Modified: | 25 Jun 2023 21:28 |
Status: | Published |
Publisher: | MDPI AG |
Identification Number: | 10.3390/e20080613 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:134709 |