title: Reaction spreading on graphs.
abstract: We study reaction-diffusion processes on graphs through an extension of the standard reaction-diffusion equation starting from first principles. We focus on reaction spreading, i.e., on the time evolution of the reaction product M(t). At variance with pure diffusive processes, characterized by the spectral dimension d{s}, the important quantity for reaction spreading is found to be the connectivity dimension d{l}. Numerical data, in agreement with analytical estimates based on the features of n independent random walkers on the graph, show that M(t)∼t{d{l}}. In the case of Erdös-Renyi random graphs, the reaction product is characterized by an exponential growth M(t)e{αt} with α proportional to ln(k), where (k) is the average degree of the graph.
authors.affiliation: Dipartimento di Fisica and INFN, Università di Parma, Parco Area delle Scienze 7/A, 43100 Parma, Italy.
authors.forename: Raffaella
authors.initials: R
authors.lastname: Burioni
authors.forename: Sergio
authors.initials: S
authors.lastname: Chibbaro
authors.forename: Davide
authors.initials: D
authors.lastname: Vergni
authors.forename: Angelo
authors.initials: A
authors.lastname: Vulpiani
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D004058:Diffusion; D008956:Models, Chemical; D008958:Models, Molecular; D012212:Rheology / Q000379:methods*