Levy walks and anomalous transport on scale-free networks

Prof. Sergey Fedotov, University of Manchester

Event details


Nov 30, 2017
from 02:00 PM to 03:00 PM


MAB 119

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I present a new single integro-differential wave equation for the probability density function 
of the position of a classical one-dimensional Levy walk with continuous sample paths. This 
equation involves a classical wave operator together with memory integrals describing the 
spatiotemporal coupling of the Levy walk. It generalizes the well-known telegraph or 
Cattaneo equation for the persistent random walk with the exponential switching time 
distribution. I also propose a model of superdiffusive Levy walk as an emergent nonlinear phenomenon 
in systems of interacting individuals.
I discuss 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, I show 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. 

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