Date:
Speaker: Sergei Fedotov, Department of Mathematics, The University of Manchester
Time : 15:00 - 16.00 CET (Rome/Paris)
Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy
YouTube : https://youtu.be/3HZnxSXuow4
Organizers : Pavan Pranjivan Mehta* (pavan.mehta@sissa.it) and Arran Fernandez** (arran.fernandez@emu.edu.tr)
* SISSA, International School of Advanced Studies, Italy
** Eastern Mediterranean University, Northern Cyprus
Keywords: anomalous transport, variable order fractional PDE’s, reaction-subduffusion
Abstract: I will start with a derivation of variable-order fractional diffusion equations from master equations corresponding to the microscopic local and barrier models. I will then discuss the asymptotic representation of the solution of the space-dependent variable-order fractional diffusion equations. Next, I will talk about how to incorporate reaction terms into heterogeneous fractional PDEs. Finally, I will demonstrate how the coarse-grained fractional reaction-subdiffusion equations are affected by the specific details of the underlying microscopic random walk models. The problem arises from the memory effects of subdiffusive transport systems. Due to these effects, the reaction can change the transport operator for the subdiffusion process. Several examples from physics and biology will be presented to illustrate these effects.
Biography: Prof. Sergei Fedotov obtained his Ph.D. (1986) from Ural Federal University. Fedotov held research positions in London (1990), Aachen (1993–1995), Wuppertal (1997), and Berlin (1998) before joining the Department of Mathematics, UMIST, in Manchester as a lecturer in 1998. Since 2005, he is a professor of applied mathematics at the Department of Mathematics, University of Manchester, UK.
Prof. Fedotov’s research focuses on random walk theory and reaction-transport systems. He has successfully applied anomalous random walk ideas to a broad range of analytical studies related to non-Markovian transport phenomena in physics, chemistry, and biology.
Bibliography
[1] Sergei Fedotov and Daniel Han. Asymptotic Behavior of the Solution of the Space Dependent Variable Order Fractional Diffusion Equation: Ultraslow Anomalous Aggregation. Phys. Rev. Lett. 123, 050602 (2019).
[2] Sergei Fedotov, Daniel Han, Andrey Yu Zubarev, Mark Johnston and Victoria J. Allan. Variable-order fractional master equation and clustering of particles: non-uniform lysosome distribution. Philos. Trans. R. Soc. Lond. A 379, 20200317 (2021).
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