#Fisher #Front #Simulation #Stochastic #Stochastic Differential Equation

Numerical schemes for continuum models of reaction-diffusion systems subject to internal noise

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. ...

#Fisher #Front #Simulation #Stochastic

Hybrid method for simulating front propagation in reaction-diffusion systems

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. ...

#Fisher #Front #Monte Carlo #Simulation #Stochastic #Stochastic Differential Equation

Emergence of pulled fronts in fermionic microscopic particle models

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. ...

#Bifurcation #Convection #Simulation #Stochastic #Stochastic differential equation

Defect formation in the Swift-Hohenberg equation

Authors: Tobias Galla and Esteban Moro Journal: Phys. Rev. E, Rapid Communication 67, 035101 (2003). LINK | arXiv Abstract: We study numerically and analytically the dynamics of defect formation during a finite-time quench of the two-dimensional Swift-Hohenberg (SH) model of Rayleigh-Bénard convection. We find that the Kibble-Zurek picture of defect formation can be applied to describe the density of defects produced during the quench. Our study reveals the relevance of two factors: the effect of local variations of the striped patterns within defect-free domains and the presence of both pointlike and extended defects. ...

#Fisher #Front #Simulation #Stochastic

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. ...