Applied Mathematics Seminar——Anomalous transport, fractional master equation and random walk of heterogeneous populations
报告人：Prof. Sergei Fedotov (University of Manchester)
时间：2024-03-19 10:15-11:15
地点：智华楼四元厅
Abstract:
We present a random walk model that incorporates random transition probabilities among a heterogeneous population of random walkers, resulting in an effectively self-reinforcing random walk. The heterogeneity of the population leads to conditional transition probabilities that increase with the number of steps taken previously (self-reinforcement). We establish the connection between random walks with a heterogeneous ensemble and those with strong memory where the transition probability depends on the entire history of steps. We employ subordination, utilizing the fractional Poisson process to count the number of steps at a given time and the discrete random walk with self-reinforcement to determine the ensemble-averaged solution of the fractional master equation. We also find the exact solution for the variance which exhibits superdiffusion even as the fractional exponent tends to 1. We discuss the applications of this random walk model for intracellular transport and stochastic endocytosis. Given that a heterogeneous population of random walkers emulates strong memory, this opens another avenue for modeling biological processes that display strong memory properties and yet are heterogeneous ensembles of inanimate objects, such as organelles and macromolecules.
Bio:
Sergei Fedotov is a Professor of Applied Mathematics in the Department of Mathematics, University of Manchester. He obtained his PhD (1986) from the Ural Federal University, Russia. Fedotov held research positions in London (1990), Aachen (1993-1995), Wuppertal (1997) and Berlin (1998) before joining the Department of Mathematics in Manchester in 1998. He held visiting professor positions at Stanford University (USA), Universitat Autonoma de Barcelona (Spain), University Lyon 1 (France), and the University of New South Wales, Sydney (Australia).
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 of non-Markovian transport phenomena.
