Fluctuation-regularized front propagation up a reaction-rate gradient
Seminar Room 1, Newton Institute
We introduce and study a new class of fronts in finite particle number reaction-diffusion systems, corresponding to propagating up a reaction rate gradient. We show that these systems have no traditional mean-field limit, as the nature of the long-time front solution in the stochastic process differs essentially from that obtained by solving the mean-field deterministic reaction-diffusion equations. Instead, one can incorporate some aspects of the fluctuations via introducing a density cutoff. Using this method, we derive analytic expressions for the front velocity dependence on bulk particle density and show self-consistently why this cutoff approach can get the correct leading-order physics.
* http://xxx.arxiv.org/abs/cond-mat/0406336 - Fluctuation-regularized Front Propagation Dynamics
* http://xxx.arxiv.org/abs/q-bio.PE/0410015 - Recombination dramatically speeds up evolution of finite populations
* http://xxx.arxiv.org/abs/cond-mat/0508128 - Front Propagation Dynamics with Exponentially-Distributed Hopping
* http://xxx.arxiv.org/abs/cond-mat/0508663 - Front Propagation up a Reaction Rate Gradient