Random walk model of subdiffusion in a system with a thin membrane

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Tadeusz Kosztołowicz

Abstract

We consider in this paper subdiffusion in a system with a thin membrane. The subdiffusion parameters are the same in both parts of the system separated by the membrane. Using the random walk model with discrete time and space variables the probabilities (Green's functions) P(x,t) describing a particle's random walk are found. The membrane, which can be asymmetrical, is characterized by the two probabilities of stopping a random walker by the membrane when it tries to pass through the membrane in both opposite directions. Green's functions are transformed to the system in which the variables are continuous, and then the membrane permeability coefficients are given by special formulas which involve the probabilities mentioned above. From the obtained Green's functions, we derive boundary conditions at the membrane. One of the conditions demands the continuity of a flux at the membrane, but the other one is rather unexpected and contains the Riemann-Liouville fractional time derivative P(x(N)(-),t)=λ(1)P(x(N)(+),t)+λ(2)∂(α/2)P(x(N)(+),t)/∂t(α/2), where λ(1),λ(2) depending on membrane permeability coefficients (λ(1)=1 for a symmetrical membrane), α is a subdiffusion parameter, and x(N) is the position of the membrane. This boundary...Continue Reading

References

Oct 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·T Kosztolowicz
Mar 14, 2001·Journal of Controlled Release : Official Journal of the Controlled Release Society·S Mitragotri
Sep 24, 2004·Journal of Controlled Release : Official Journal of the Controlled Release Society·Susanne R VeithSotiris E Pratsinis
May 21, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·T KosztołowiczSt Mrówczyński
May 21, 2005·Physical Review Letters·T KosztołowiczSt Mrówczyński
Sep 26, 2006·Journal of Controlled Release : Official Journal of the Controlled Release Society·Songmiao LiangLina Zhang
May 21, 2010·Physical Review Letters·Nickolay Korabel, Eli Barkai
Jul 7, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Nickolay Korabel, Eli Barkai
Sep 26, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Tadeusz KosztołowiczKatarzyna D Lewandowska
Oct 15, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Tadeusz Kosztołowicz, Katarzyna D Lewandowska
Nov 7, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Tadeusz Kosztołowicz

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Citations

Mar 3, 2017·The Journal of Chemical Physics·Tadeusz Kosztołowicz
Dec 14, 2016·Proceedings. Mathematical, Physical, and Engineering Sciences·E K LenziL R Evangelista
Jan 20, 2018·Physical Review. E·Tadeusz KosztołowiczKatarzyna D Lewandowska
Aug 17, 2020·Physical Review. E·Philipp Roth, Igor M Sokolov
Mar 20, 2021·Physical Review. E·Tadeusz Kosztołowicz
Apr 4, 2021·Entropy·Katarzyna GałczyńskaMichał Arabski
May 20, 2021·Physical Review. E·Tadeusz Kosztołowicz, Aldona Dutkiewicz

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