Levy walks, anomalous transport on scale-free networks and human activity

Abstract:

Levy walk is a fundamental notion in physics  and biology with numerous applications including T-cell motility in the brain and active transport within living cells. It is argued that living organisms can use Levy flights to accelerate pattern formation and to optimize searching for sparse food.

Professor Fedotov will present a new single integro-differential wave equation for a Levy walk. Discussed will be the anomalous transport of individuals across a heterogeneous scale-free network.  Using the empirical law of cumulative inertia and fractional analysis, he will show that "anomalous inertia" overpowers highly connected nodes in attracting network individuals. This fundamentally challenges the classical result that individuals tend to accumulate in high-order nodes. The derived residence time distribution has a nontrivial U shape which we encounter empirically across human residence and employment times for academic people.

Biography:

Sergei Fedotov is a Professor of Applied Mathematics in the School of Mathematics, University of Manchester. He received the M.Sc and PhD degrees from Ural State University, Ekaterinburg, Russia in 1982 and 1986. Sergei 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. He has been regularly supported by EPSRC and Royal Society research grants.