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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. ...

Authors: Esteban Moro Journal: Physical Review E (Rapid Communication) 70, 045102 (2004). LINK | arXiv Abstract: We present numerical schemes to integrate stochastic partial differential equations which describe the spatiotemporal dynamics of reaction-diffusion problems under the effect of internal fluctuations. The schemes conserve the non-negativity of the solutions and incorporate the Poissonian nature of internal fluctuations at small densities, their performance being limited by the level of approximation of density fluctuations at small scales. ...

Authors: Esteban Moro Journal: Physical Review E, Rapid Communication 69, 060101 (2004). LINK | arXiv Abstract: We study the propagation of pulled fronts in the \(A\leftrightarrow A+A\) microscopic reaction-diffusion process using Monte Carlo simulations. In the mean field approximation the process is described by the deterministic Fisher-Kolmogorov-Petrovsky-Piscounov equation. In particular, we concentrate on the corrections to the deterministic behavior due to the number of particles per correlated volume \(\Omega\). By means of a hybrid simulation scheme, we manage to reach large macroscopic values of \(\Omega\), which allows us to show the importance in the dynamics of microscopic pulled fronts of the interplay of microscopic fluctuations and their macroscopic relaxation. ...

Authors: Esteban Moro Phys. Rev. E, Rapid Communication, 68, 025102 (2003). LINK | arXiv Abstract: We study the emergence and dynamics of pulled fronts described by the Fisher-Kolmogorov-Petrovsky-Piscounov (FKPP) equation in the microscopic reaction-diffusion process \(A\leftrightarrow A+A\) on the lattice when only a particle is allowed per site. To this end we identify the parameter that controls the strength of internal fluctuations in this model, namely, the number of particles per correlated volume. ...

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. ...