Anomalous Stochastic Transport of Particles with Self-Reinforcement and Mittag–Leffler Distributed Rest Times
We introduce a persistent random walk model for the stochastic transport of particles involving self-reinforcement and a rest state with Mittag–Leffler distributed residence times. The model involves a system of hyperbolic partial differential equations with a non-local switching term described by t...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-11-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/5/4/221 |
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| author | Daniel Han Dmitri V. Alexandrov Anna Gavrilova Sergei Fedotov |
| author_facet | Daniel Han Dmitri V. Alexandrov Anna Gavrilova Sergei Fedotov |
| author_sort | Daniel Han |
| collection | DOAJ |
| description | We introduce a persistent random walk model for the stochastic transport of particles involving self-reinforcement and a rest state with Mittag–Leffler distributed residence times. The model involves a system of hyperbolic partial differential equations with a non-local switching term described by the Riemann–Liouville derivative. From Monte Carlo simulations, we found that this model generates superdiffusion at intermediate times but reverts to subdiffusion in the long time asymptotic limit. To confirm this result, we derived the equation for the second moment and find that it is subdiffusive in the long time limit. Analyses of two simpler models are also included, which demonstrate the dominance of the Mittag–Leffler rest state leading to subdiffusion. The observation that transient superdiffusion occurs in an eventually subdiffusive system is a useful feature for applications in stochastic biological transport. |
| first_indexed | 2024-03-10T04:05:35Z |
| format | Article |
| id | doaj.art-a37ccd14b84f46eca6712082fb9a65b5 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T04:05:35Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-a37ccd14b84f46eca6712082fb9a65b52023-11-23T08:23:57ZengMDPI AGFractal and Fractional2504-31102021-11-015422110.3390/fractalfract5040221Anomalous Stochastic Transport of Particles with Self-Reinforcement and Mittag–Leffler Distributed Rest TimesDaniel Han0Dmitri V. Alexandrov1Anna Gavrilova2Sergei Fedotov3Department of Mathematics, University of Manchester, Oxford Rd, Manchester M13 9PL, UKDepartment of Theoretical and Mathematical Physics, Ural Federal University, 51 Lenin Ave., 620000 Ekaterinburg, RussiaSchool of Biological Sciences, University of Manchester, Manchester M13 9PL, UKDepartment of Mathematics, University of Manchester, Oxford Rd, Manchester M13 9PL, UKWe introduce a persistent random walk model for the stochastic transport of particles involving self-reinforcement and a rest state with Mittag–Leffler distributed residence times. The model involves a system of hyperbolic partial differential equations with a non-local switching term described by the Riemann–Liouville derivative. From Monte Carlo simulations, we found that this model generates superdiffusion at intermediate times but reverts to subdiffusion in the long time asymptotic limit. To confirm this result, we derived the equation for the second moment and find that it is subdiffusive in the long time limit. Analyses of two simpler models are also included, which demonstrate the dominance of the Mittag–Leffler rest state leading to subdiffusion. The observation that transient superdiffusion occurs in an eventually subdiffusive system is a useful feature for applications in stochastic biological transport.https://www.mdpi.com/2504-3110/5/4/221anomalous stochastic transportself-reinforcementsubdiffusionMittag–Leffler distributed rest state |
| spellingShingle | Daniel Han Dmitri V. Alexandrov Anna Gavrilova Sergei Fedotov Anomalous Stochastic Transport of Particles with Self-Reinforcement and Mittag–Leffler Distributed Rest Times Fractal and Fractional anomalous stochastic transport self-reinforcement subdiffusion Mittag–Leffler distributed rest state |
| title | Anomalous Stochastic Transport of Particles with Self-Reinforcement and Mittag–Leffler Distributed Rest Times |
| title_full | Anomalous Stochastic Transport of Particles with Self-Reinforcement and Mittag–Leffler Distributed Rest Times |
| title_fullStr | Anomalous Stochastic Transport of Particles with Self-Reinforcement and Mittag–Leffler Distributed Rest Times |
| title_full_unstemmed | Anomalous Stochastic Transport of Particles with Self-Reinforcement and Mittag–Leffler Distributed Rest Times |
| title_short | Anomalous Stochastic Transport of Particles with Self-Reinforcement and Mittag–Leffler Distributed Rest Times |
| title_sort | anomalous stochastic transport of particles with self reinforcement and mittag leffler distributed rest times |
| topic | anomalous stochastic transport self-reinforcement subdiffusion Mittag–Leffler distributed rest state |
| url | https://www.mdpi.com/2504-3110/5/4/221 |
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