Professor Fedotov will present a new single integro-differential wave equation for a classical one-dimensional Levy walk. It generalizes the well-known telegraph or Cattaneo equation for the persistent random walk with the exponential switching time distribution. Discussed will be the anomalous transport of individuals across a heterogeneous scale-free network where a few weakly connected nodes exhibit heavy-tailed residence times. Using the empirical law of the axiom of cumulative inertia and fractional analysis, it is shown that "anomalous cumulative 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.
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.