Noise and disorder effects on front propagation in non-linear media.

摘要

We study the dynamics of reaction-diffusion fronts under the influence of noise and static disorder. In the absence of noise mathematically rigorous results establish that fronts propagate with constant velocity. Noise affects the front propagation in two possible ways. First, intrinsic noise modeled typically by an additive thermal noise in a Langevin type equation causes a sharp crossover from ballistic to diffusive motion of the front. Second, external noise is introduced through the fluctuations of a control parameter leading to a multiplicative noise in the stochastic partial differential equation. The external noise increases the mean propagation velocity of the front. Finally, we consider the influence of static disorder of the properties of front propagation. Static disorder is found, to our surprise, to enhance the speed of propagation linearly with impurity potential and concentration strength.