Math. Model. Nat. Phenom.
Volume 11, Number 3, 2016Anomalous diffusion
|Page(s)||107 - 127|
|Published online||21 June 2016|
Reaction Spreading in Systems With Anomalous Diffusion
1 CNR - Istituto dei Sistemi Complessi,
Via dei Taurini 19, I-00185
2 CNR - Istituto Applicazioni del Calcolo Via dei Taurini 19, I-00185 Rome, Italy
3 Università di Roma “Sapienza”, Piazzale A. Moro 5, I-00185 Rome, Italy.
⋆ Corresponding author. E-mail: firstname.lastname@example.org
We briefly review some aspects of the anomalous diffusion, and its relevance in reactive systems. In particular we consider strong anomalous diffusion characterized by the moment behaviour ⟨x(t)q⟩ ∼ tqν(q), where ν(q) is a non constant function, and we discuss its consequences. Even in the apparently simple case ν(2) = 1 / 2, strong anomalous diffusion may correspond to non trivial features, such as non Gaussian probability distribution and peculiar scaling of large order moments. When a reactive term is added to a normal diffusion process, one has a propagating front with a constant velocity. The presence of anomalous diffusion by itself does not guarantee a changing in the front propagation scenario; a key factor to select linear in time or faster front propagation has been identified in the shape of the probability distribution tail in absence of reaction. In addition, we discuss the reaction spreading on graphs, underlying the major role of the connectivity properties of these structures, characterized by the connectivity dimension.
Mathematics Subject Classification: 35K57 / 60J60 / 60J70 / 05C81
Key words: anomalous transport / reaction spreading / front Propagation
© EDP Sciences, 2016
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.