PMID: 22587063May 17, 2012Paper

Subdiffusive master equation with space-dependent anomalous exponent and structural instability

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Sergei Fedotov, Steven Falconer

Abstract

We derive the fractional master equation with space-dependent anomalous exponent. We analyze the asymptotic behavior of the corresponding lattice model both analytically and by Monte Carlo simulation. We show that the subdiffusive fractional equations with constant anomalous exponent μ in a bounded domain [0,L] are not structurally stable with respect to the nonhomogeneous variations of parameter μ. In particular, the Gibbs-Boltzmann distribution is no longer the stationary solution of the fractional Fokker-Planck equation whatever the space variation of the exponent might be. We analyze the random distribution of μ in space and find that in the long-time limit, the probability distribution is highly intermediate in space and the behavior is completely dominated by very unlikely events. We show that subdiffusive fractional equations with the nonuniform random distribution of anomalous exponent is an illustration of a "Black Swan," the low probability event of the small value of the anomalous exponent that completely dominates the long-time behavior of subdiffusive systems.

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Citations

Dec 3, 2014·Journal of Theoretical Biology·P Straka, S Fedotov
Nov 12, 2013·Biophysical Journal·Hédi SoulaHugues Berry
Nov 28, 2014·Frontiers in Physiology·Hugues Berry, Hédi A Soula
Sep 17, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·C N AngstmannT A M Langlands
Mar 18, 2017·Physical Review Letters·Sergei Fedotov, Helena Stage
Feb 20, 2019·Physical Review. E·Joseph W Baron, Tobias Galla
Jul 3, 2020·Chaos·Sean CarnaffanWladyslaw Szczotka
Aug 17, 2020·Physical Review. E·Philipp Roth, Igor M Sokolov
Jan 15, 2016·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Sergei Fedotov, Nickolay Korabel
May 3, 2019·The Journal of Chemical Physics·Xudong WangYao Chen
Jun 19, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Sergei Fedotov, Steven Falconer
Mar 4, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Sergei Fedotov, Steven Falconer
Oct 16, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Sergei Fedotov

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