Berlin 2005 – wissenschaftliches Programm

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DY: Dynamik und Statistische Physik

DY 43: Einstein Symposium Brownian Motion, Diffusion and Beyond (SYBM) – Contributed Talks I

DY 43.5: Vortrag

Dienstag, 8. März 2005, 15:30–15:45, TU H2032

Topological Superdiffusion — •Dirk Brockmann and Theo Geisel — MPI für Strömungsforschung, Göttingen

Superdiffusive phenomena abound in physical, biological, economical and ecological systems. Generally these processes, also known as Lévy flights, exhibit power laws in their spatial dispersal kernels. In a number of physical systems these scale free properties have been associated with anomalous thermal properties and corresponding fractional Fokker-Planck equations were established as the canonical way to describe these phenomena. In this talk I will reveal that the description of superdiffusive phenomena is a subtle issue. In particular I will show that paradigmatic systems exist which cannot be accounted for in the canonical way, which exhibit topological Lévy-type dispersal and which are thermally inconspicuous. The description of these processes requires a novel type of fractional Fokker-Planck equation with surprising and often counterintuitive properties. Systems exhibiting topological superdiffusion are numerous, ranging from random walks on folded polymer chains, human dispersal in inhomogeneous environments, and the spread of epidemics in a globalized world.