Fluctuation-regularized Front Propagation Dynamics

Cohen, Elisheva; Kessler, David A.; Levine, Herbert

Fluctuation-regularized Front Propagation Dynamics

Authors

Cohen, Elisheva

Kessler, David A.

Levine, Herbert

Description

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.
4 pages, 4 figures