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

2004/04/30 by Esteban Moro · 3 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.soft #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.70.045102

published as Physical Review E 70, 045102(R) (2004) · 5 pages, 3 figures, Accepted for publication in Physical Review E as a Rapid Communication

arxiv created 2004/08/06 · openalex publication_date 2004/10/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present numerical schemes to integrate stochastic partial differential equations which describe the spatio-temporal 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. We apply the schemes to two different aspects of the Reggeon model, namely, the study of its nonequilibrium phase transition and the dynamics of fluctuating pulled fronts. In the latter case, our approach allows us to reproduce microscopic properties quantitatively within the continuum model.

Citations

• Non-equilibrium critical phenomena and phase transitions into absorbing states
• Pattern formation outside of equilibrium

Cited by

• Dense-dilute factorization for a class of stochastic processes and for high energy QCD
• Phenomenological theory giving the full statistics of the position of fluctuating pulled fronts
• Diffusive scaling and the high-energy limit of deep inelastic scattering in QCD at large