Kreczak, H, Sturman, R and Wilson, M orcid.org/0000-0002-1058-2003 (2017) Deceleration of one-dimensional mixing by discontinuous mappings. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 96 (5). 053112. ISSN 1539-3755
Abstract
We present a computational study of a simple one-dimensional map with dynamics composed of stretching, permutations of equal sized cells, and diffusion. We observe that the combination of the aforementioned dynamics results in eigenmodes with long-time exponential decay rates. The decay rate of the eigenmodes is shown to be dependent on the choice of permutation and changes non-monotonically with the diffusion coefficient for many of the permutations. The global mixing rate of the map M in the limit of vanishing diffusivity approximates well the decay rates of the eigenmodes for small diffusivity, however this global mixing rate does not bound the rates for all values of the diffusion coefficient. This counter-intuitively predicts a deceleration in the asymptotic mixing rate with increasing diffusivity rate. The implication of the results on finite time mixing are discussed.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | ©2017 American Physical Society. This is an author produced version of a paper published in Physical Review E. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Dynamical Systems; Fluid Dynamics; Mixing |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mechanical Engineering (Leeds) > Institute of Engineering Thermofluids, Surfaces & Interfaces (iETSI) (Leeds) The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 10 Nov 2017 12:33 |
Last Modified: | 15 Jan 2018 14:46 |
Status: | Published |
Publisher: | American Physical Society |
Identification Number: | 10.1103/PhysRevE.96.053112 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:123760 |