/ #Stochastic Differential Equations #Fisher 

Macroscopic Response to Microscopic Intrinsic Noise in Three-Dimensional Fisher Fronts

Authors:Svetozar Nesic, Rodolfo Cuerno, and Esteban Moro
Journal: Physical Review Letters 113, 180602 (2014) LINK

Summary We study the dynamics of three-dimensional Fisher fronts in the presence of density fluctuations. To this end we simulate the Fisher equation subject to stochastic internal noise, and study how the front moves and roughens as a function of the number of particles in the system, N. Our results suggest that the macroscopic behaviour of the system is driven by the microscopic dynamics at its leading edge where number fluctuations are dominated by rare events. Contrary to naive expectations, the strength of front fluctuations decays extremely slowly as 1 / log N, inducing large-scale fluctuations which we find belong to the one-dimensional Kardar-Parisi-Zhang universality class of kinetically rough interfaces. Hence, we find that there is no weak-noise regime for Fisher fronts, even for realistic numbers of particles in macroscopic systems.

Author

Esteban Moro

Professor at Universidad Carlos III de Madrid and MIT Medialab. Working on Complex Systems, Social Networks and Urban Science.