Reaction Spreading in Systems with Anomalous Diffusion

We briefly review some aspects of the anomalous diffusion, and itsrelevance in reactive systems. In particular we considerstrong anoma-lousdiffusion characterized by the moment behaviour〈x(t)q〉∼tqν(q),whereν(q) is a non constant function, and we discuss its consequences.Even in the apparently simple caseν(2) = 1/2, strong anomalous dif-fusion may correspond to non trivial features, such as non Gaussianprobability distribution and peculiar scaling of large order moments.When a reactive term is added to a normal diffusion process, onehas a propagating front with a constant velocity. The presence ofanomalous diffusion by itself does not guarantee a changing inthefront propagation scenario; a key factor to select linear intime orfaster front propagation has been identified in the shape of the prob-ability distribution tail in absence of reaction. In addition, we discussthe reaction spreading on graphs, underlying the major roleof theconnectivity properties of these structures, characterized by thecon-nectivity dimension.1