Reaction spreading on graphs (Articolo in rivista)

Type
Label
  • Reaction spreading on graphs (Articolo in rivista) (literal)
Anno
  • 2012-01-01T00:00:00+01:00 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
  • 10.1103/PhysRevE.86.055101 (literal)
Alternative label
  • Burioni R., Chibbaro S., Vergni D., Vulpiani A. (2012)
    Reaction spreading on graphs
    in Physical review. E, Statistical, nonlinear, and soft matter physics (Print)
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • Burioni R., Chibbaro S., Vergni D., Vulpiani A. (literal)
Pagina inizio
  • 1 (literal)
Pagina fine
  • 4 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
  • 86 (literal)
Rivista
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#pagineTotali
  • 4 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroFascicolo
  • 055101 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • Raffaella Burioni Dipartimento di Fisica and INFN, Universita' di Parma,Parco Area delle Scienze 7/A, 43100 Parma, Italy Sergio Chibbaro Institut D'Alembert University Pierre et Marie Curie, 4, place jussieu 75252 Paris Cedex 05 Angelo Vulpiani Dipartimento di Fisica, Universita' La Sapienza'' and ISC-CNR, Piazzale Aldo Moro 2, I-00185 Roma, Italy (literal)
Titolo
  • Reaction spreading on graphs (literal)
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, $d_s$, for reaction spreading the important quantity 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 $M(t) \sim t^{d_l}$. In the case of Erd\"{o}s-Renyi random graphs, the reaction-product is characterized by an exponential growth $M(t) \sim e^{\alpha t}$ with $\alpha$ proportional to $\ln \lra{k}$, where $\lra{k}$ is the average degree of the graph. (literal)
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