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

S. Nesic, R. Cuerno, and E. Moro
Phys. Rev. Lett. 113, 180602 – Published 30 October 2014

Abstract

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 behavior 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/logN, 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.

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  • Received 21 July 2014

DOI:https://doi.org/10.1103/PhysRevLett.113.180602

© 2014 American Physical Society

Authors & Affiliations

S. Nesic1, R. Cuerno1, and E. Moro1,2

  • 1Departamento de Matemáticas & Grupo Interdisciplinar de Sistemas Complejos (GISC), Universidad Carlos III de Madrid, 28911 Leganés, Spain
  • 2Instituto de Ingeniería del Conocimiento, Universidad Autónoma de Madrid, 28049 Madrid, Spain

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Vol. 113, Iss. 18 — 31 October 2014

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