Dresden 2011 – scientific programme

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BP: Fachverband Biologische Physik

BP 7: Posters: Statistical Physics in Biological Systems

BP 7.23: Poster

Monday, March 14, 2011, 17:15–20:00, P3

Traveling Waves in Strong-Noise Reaction-Superdiffusion Systems — •Marc Szabo and Oskar Hallatschek — Biophysics & Evolutionary Dynamics Group, MPI for Dynamics and Self-Organization, Göttingen, Germany

Traveling waves resulting from reaction and diffusion of particles describe a wide range of phenomena like epidemic waves, range expansions of populations or the dispersal of a chemical concentration. In systems of discrete particles, number fluctuations are inevitable and significantly affect the velocity and shape of such traveling waves. Here we investigate the effect of anomalous diffusion on noisy traveling wave solutions of the Fisher- Kolmogorov equation. Instead of a regular random walk, particles perform scale free Lévy Flights leading to long-range migration. Latter concept has proven to successfully describe the dynamics of human travel [1] and can also be applied to expanding populations in the context of biological evolution. While this problem has already been studied in the regime where number fluctuations are small [2], we discuss here the case of strong noise. We analyze the dependence of the wave velocity on the Lévy exponent and noise strength. Our results show considerable differences to the weak noise regime. We confirm our analytical results with detailed simulations.

[1] D.Brockmann, L.Hufnagel, T. Geisel, Nature 439, 462-465 (2006). [2] D.Brockmann and L.Hufnagel, Phys. Rev. Lett. 98 178301 (2007).