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Internal Fluctuations Effects on Fisher Waves

Authors: Esteban Moro
Journal: Physical Review Letters 87, 238303 (2001) LINK | arXiv

Abstract: We study the diffusion-limited reaction \(A \leftrightarrow A = A\) in various spatial dimensions to observe the effect of internal fluctuations on the interface between stable and unstable phases. We find that, similar to what has been observed in d = 1 dimensions, internal fluctuations modify the mean-field predictions for this process, which is given by Fisher’s reaction-diffusion equation. In d > 1 the front displays local fluctuations perpendicular to the direction of motion which, with a proper definition of the interface, can be fully described within the Kardar-Parisi-Zhang (KPZ) universality class. This clarifies the apparent discrepancies with KPZ predictions reported recently.



Esteban Moro

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