J. Phys. France 51, 1387-1402 (1990)
DOI: 10.1051/jphys:0199000510130138700
Anomalous diffusion in presence of boundary conditions
A. Giacometti1 et A. Maritan21 Dipartimento di Scienze Ambientali, Universitá di Venezia, Calle Larga S. Marta, 30124 Venezia, Italy
2 Dipartimento di Fisica dell'Universitá di Bari e I.N.F.N., Sezione di Bari, Italy
Abstract
Anomalous diffusion in presence of a (fractal) boundary is investigated. Asymptotic behaviour of the survival probability and current through an absorbing boundary are exactly calculated in specific examples. They agree with recent findings related with anomalous Warburg impedance experiments. The autocorrelation function for sites near the boundary is carefully discussed ; in presence of reflecting boundary conditions it can be different from the (spatial) average of the autocorrelation at variance with the normal diffusion case. Interesting issues from a methodological point of view are discussed in the renormalization groups analysis. Scaling arguments are given relating various exponents.
0540 - Fluctuation phenomena, random processes, noise, and Brownian motion.
0560 - Transport processes.
Key words
diffusion -- fractals