Fluctuation-regularized front propagation dynamics in reaction-diffusion systems.
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.
Cohen
Elisheva
E
Department of Physics, Bar-Ilan University, Ramat-Gan, IL52900 Israel.
Kessler
David A
DA
Levine
Herbert
H
D005075:Biological Evolution; D004058:Diffusion; D008954:Models, Biological; D008956:Models, Chemical; D008962:Models, Theoretical