Regensburg 2007 – scientific programme

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BP: Fachverband Biologische Physik

BP 26: Poster Session II

BP 26.48: Poster

Thursday, March 29, 2007, 17:00–19:30, Poster B

Natural cutoff in discrete Fisher waves — •Oskar Hallatschek and David Nelson — Department of Physics, Harvard University

R.A. Fisher introduced some 70 years ago, his famous model for "the spread of an advantageous gene", that has been widely used to describe travelling waves in such diverse fields as ecology, chemistry and QCD. Effects due to the discrete nature of particles have long been ignored, until recently: Brunet and Derrida told us to introduce a cutoff in the growth rate to account for the fact that there is no growth beyond the foremost particle in the front of the wave. To leading order, the ad hoc cutoff theory explains the observed shift in the velocity of discrete Fisher and, more generally, pulled waves. Here, we show that a Hartree-like mean field theory can be fromulated that naturally takes into account the discreteness of particles without the need for an adjustable hard cutoff. For large particle numbers the discreteness correction acts like a soft cutoff in the Fisher equation. We compare this novel mean field theory with simulations and with the heuristic hard cutoff scheme proposed by Brunet and Derrida.