2001/07/31 by Mauro Mobilia, P.-A. Barès, Pierre-Antoine Bares
Mathematics · Physics and Astronomy · #Anomalous diffusion #Applied mathematics #Combinatorics #Computer science #Generalization #Interval (graph theory) #Lattice (music) #Mathematical analysis #Mathematical physics #Mathematics #Opinion Dynamics and Social Influence #Physics #Reaction–diffusion system #Similarity (geometry) #Statistical physics #Stochastic processes and statistical mechanics #String (physics) #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.64.066123
published as Phys. Rev. E 64, 066123 (2001) · 19 pages, no figure. To appear in Physical Review E (November 2001)
arxiv created 2001/09/27 · openalex publication_date 2001/11/26 · arxiv updated 2016/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this work we study, on a finite and periodic lattice, a class of one-dimensional (bimolecular and single-species) reaction-diffusion models that cannot be mapped onto free-fermion models. We extend the conventional empty-interval method, also called interparticle distribution function (IPDF) method, by introducing a string function, which is simply related to relevant physical quantities. As an illustration, we specifically consider a model that cannot be solved directly by the conventional IPDF method and that can be viewed as a generalization of the voter model and/or as an epidemic model. We also consider the reversible diffusion-coagulation model with input of particles and determine other reaction-diffusion models that can be mapped onto the latter via suitable similarity transformations. Finally we study the problem of the propagation of a wave front from an inhomogeneous initial configuration and note that the mean-field scenario predicted by Fisher's equation is not valid for the one-dimensional (microscopic) models under consideration.