anomalous diffusion

Human mobility, networks and disease dynamics on a global scale

Disease dynamics is a complex phenomenon and in order to address these questions expertises from many disciplines need to be integrated. One method that has become particularly important during the past few years is the development of computational …

Human mobility and spatial disease dynamics

The scaling laws of human travel

The dynamic spatial redistribution of individuals is a key driving force of various spatiotemporal phenomena on geographical scales. It can synchronize populations of interacting species, stabilize them, and diversify gene pools. Human travel, for …

Lévy flights in inhomogeneous media

We investigate the impact of external periodic potentials on superdiffusive random walks known as Lévy flights and show that even strongly superdiffusive transport is substantially affected by the external field. Unlike ordinary random walks, Lévy …

Lévy flights in external force fields: from models to equations

We consider different generalizations of the Fokker–Planck equation (FPE) devised to describe Lévy processes in potential force fields. We show that such generalizations can proceed along different lines. On one hand, Lévy statistics can emerge from …