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|Title:||Superdiffusion in Self-reinforcing Run-and-tumble Model with Rests|
Ivanov, A. O.
Da Silva, M. A. A.
|Publisher:||American Physical Society|
American Physical Society (APS)
|Citation:||Superdiffusion in Self-reinforcing Run-and-tumble Model with Rests / S. Fedotov, D. Han, A. O. Ivanov et al. // Physical Review E. — 2022. — Vol. 105. — Iss. 1. — 014126.|
|Abstract:||This paper introduces a run-and-tumble model with self-reinforcing directionality and rests. We derive a single governing hyperbolic partial differential equation for the probability density of random-walk position, from which we obtain the second moment in the long-time limit. We find the criteria for the transition between superdiffusion and diffusion caused by the addition of a rest state. The emergence of superdiffusion depends on both the parameter representing the strength of self-reinforcement and the ratio between mean running and resting times. The mean running time must be at least 2/3 of the mean resting time for superdiffusion to be possible. Monte Carlo simulations validate this theoretical result. This work demonstrates the possibility of extending the telegrapher's (or Cattaneo) equation by adding self-reinforcing directionality so that superdiffusion occurs even when rests are introduced. © 2022 American Physical Society.|
HYPERBOLIC PARTIAL DIFFERENTIAL EQUATION
MONTE CARLO'S SIMULATION
MONTE CARLO METHODS
MONTE CARLO METHOD
|metadata.dc.description.sponsorship:||S.F. is thankful for the support and hospitality of the Ural Mathematical Center at the Ural Federal University, Ekaterinburg. S.F. also acknowledges financial support from RSF Project No. 20-61-46013. D.H. acknowledges the support from Wellcome Trust Grant No. 215189/Z/19/Z, the Medical Research Council, as part of United Kingdom Research and Innovation (also known as UK Research and Innovation) [MC/UP/1201/21] and Churchill College, University of Cambridge. A.O.I. acknowledges financial support from the Ministry of Science and Higher Education of the Russian Federation (Ural Mathematical Center Project No. 075-02-2021-1387). D.H. and M.A.A.S acknowledge financial support from FAPESP/SPRINT Grant No. 18/15308-4. M.A.A.S acknowledges the Brazilian government's research funding agency CNPq (process no. 312667/2018-3).|
|RSCF project card:||20-61-46013|
|Appears in Collections:||Научные публикации, проиндексированные в SCOPUS и WoS CC|
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