Simple stochastic models showing strong anomalous diffusion |
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Authors: | KH Andersen P Castiglione A Mazzino A Vulpiani |
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Institution: | (1) Dipartimento di Fisica, and INFM, Università“La Sapienza”, P.le A. Moro 2, 00185 Roma, Italy, IT;(2) Laboratoire de Physique Statistique, école Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex 05, France, FR;(3) INFM-Dipartimento di Fisica, Università di Genova, 16146 Genova, Italy, IT |
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Abstract: | We show that strong anomalous diffusion, i.e.
where is a nonlinear function of q, is a generic phenomenon within a class of generalized continuous-time random walks. For such class of systems it is possible
to compute analytically where n is an integer number. The presence of strong anomalous diffusion implies that the data collapse of the probability density
function cannot hold, a part (sometimes) in the limit of very small , now . Moreover the comparison with previous numerical results shows that the shape of is not universal, i.e., one can have systems with the same but different F.
Received 14 April 2000 |
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Keywords: | PACS 05 45 -a Nonlinear dynamics and nonlinear dynamical systems - 05 60 -k Transport processes |
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