Reaction-Diffusion in random media
[ jeudi 11-04-2013 15:00
| français ]Reaction-Diffusion in random media
Institut Jean Le Rond d'Alembert, UPMC, Paris
In the first part, 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, ds, for reaction spreading the important quantity is found to be the connectivity dimension, dl. Numerical data, in agreement with analytical estimates based on the features of n independent random walkers on the graph, show that M (t) ∼ tdl. In the case of Erdo ̈s-Renyi random graphs, the reaction-product is characterized by an exponential growth M(t) ∼ exp(αt) with α proportional to ln⟨k⟩, where ⟨k⟩ is the average degree of the graph.
In the second, we show some results concerning percolation in a channel, which may be relevant for porous media.