# Dresden 2006 – wissenschaftliches Programm

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# DY: Dynamik und Statistische Physik

## DY 24: Brownian Motion and Kinetic Theory I

### DY 24.1: Vortrag

### Dienstag, 28. März 2006, 14:30–14:45, H\"UL 186

**Balancing between source and target - a novel kind of fractional Fokker-Planck operator** — •Vitaly Belik, Dirk Brockmann, and Theo Geisel — MPI für Dynamik und Selbstorganisation, Göttingen

Based on the recently introduced concept of topological superdiffusion we introduce a novel kind of fractional Fokker-Planck operator for random motion in inhomogeneous environments which incorporates the relative impact of the source and target location of an underlying random walk. We show that the dynamics in weak inhomogeneities exhibits distinct regimes of attenuation and enhancement. The operator can be constructed in two ways: with non-normalized Boltzmann-like probability density (a), which corresponds to some common physical systems, such as hetero-polymers, and normalized one (b), which naturally arises in population dynamical systems. We show that in the limit of ordinary diffusion an increase in the target influence slows down the process in either case. Surspringly, a superdiffusive process may either be slowed down or enhanced with increasing target influence, in contrast with the common belief that external quenched disorder generally attenuates dispersion. As our theory obeys ordinary Gibbs-Boltzmann thermodynamics we believe that it will facilitate the understanding of a number of anomalous transport phenomena in fields such as intracellular transport and dispersal phenomena in ecological systems.