TY - JOUR
T1 - Transport aspects in anomalous diffusion
T2 - Lévy walks
AU - Blumen, A.
AU - Zumofen, G.
AU - Klafter, J.
PY - 1989
Y1 - 1989
N2 - In this paper we present a combined analytical and numerical study of transport properties of Lévy walks. Here, within the framework of continuous-time random walks (CTRW) with coupled memories, we focus on the probability P0(t) of being at the initial site at time t and on S(t), the mean number of distinct sites visited in time t. We use the connection between P0(t) and S(t), which are related via their Laplace transform, and we reanalyze our previous findings for r2(t), the mean-squared displacement. Furthermore, S(t) shows, as a function of the memory parameters, a very interesting, nonuniversal, nonmonotonic behavior, which we corroborate by numerical simulations in one dimension. We compare the findings with those for decoupled CTRWs on regular lattices and on fractals.
AB - In this paper we present a combined analytical and numerical study of transport properties of Lévy walks. Here, within the framework of continuous-time random walks (CTRW) with coupled memories, we focus on the probability P0(t) of being at the initial site at time t and on S(t), the mean number of distinct sites visited in time t. We use the connection between P0(t) and S(t), which are related via their Laplace transform, and we reanalyze our previous findings for r2(t), the mean-squared displacement. Furthermore, S(t) shows, as a function of the memory parameters, a very interesting, nonuniversal, nonmonotonic behavior, which we corroborate by numerical simulations in one dimension. We compare the findings with those for decoupled CTRWs on regular lattices and on fractals.
UR - http://www.scopus.com/inward/record.url?scp=0000914304&partnerID=8YFLogxK
U2 - 10.1103/PhysRevA.40.3964
DO - 10.1103/PhysRevA.40.3964
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AN - SCOPUS:0000914304
SN - 1050-2947
VL - 40
SP - 3964
EP - 3973
JO - Physical Review A
JF - Physical Review A
IS - 7
ER -