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

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.

Modelling pattern formation through differential repulsion

“…In Figs. 7 (I), we show simulations of the microscopic and macroscopic models for κ AA = 4, κ BB =κ AB =κ BA = 1 for which s * ≈ 2.1 can be computed using the formula (43) (Figures (IC)). As one can observe in Fig.…”

“…We postulate that these discrepancies come from the microscopic noise due to thermal fluctuations, which gives rise to instabilities and allows the agent-based system to reach new states which are not available in the deterministic description, or produce spatial correlations which in turn dominate the macroscopic system behavior. Several works have reported these phenomena [43,38,4,14], particularly at onset for transitions from metastable or unstable phases, in which microscopic noise can be amplified to macroscopic time and length scales. The exploration of these effects will be the subject of future works.…”

Morphological stabilization and KPZ scaling by electrochemically induced co-deposition of nanostructured NiW alloy films

“… 40 , 41 ), that have been experimentally validated for one 42 – 45 and two-dimensional 46 , 47 interfaces, this class is recently focusing an enormous attention. Indeed, it is being found to encompass the scaling behavior of many fluctuating 1D systems, from classical non-linear oscillators 48 to superfluids 49 , or Fisher waves 50 . Remarkably, beyond critical exponents values, universal KPZ scaling also applies to the probability distribution of height fluctuations.…”

Spreading of nonmotile bacteria on a hard agar plate: Comparison between agent-based and stochastic simulations

“…However, these mean-field models ignore the role of population fluctuations in the system. However, recent studies have shown that population fluctuations cannot be ignored and are crucial in determining the statistics of growth front [10,37,44]. In particular, Kessler et al [43] using particle based simulation had indicated that population fluctuations can lead to destabilisation of bacterial colony front spreading by consuming nutrients.…”

“…Our approach is different than earlier studies [7,8,33,41,42] where the bacterial morphological patterns were attributed to substrate properties such as irregularities on the agar substrate [41], substrate hardness that depends on the agar concentration and local lubrication created by bacteria [42], and nutrient concentration. However, these models ignore the role of population fluctuations that have been shown [10,43,44] to play a crucial rule in determining the growth, competition and cooperation in bacterial colonies under nutrient rich conditions.…”