Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1
1
1

Citation Types

2
81
0
5

Year Published

2003
2003
2015
2015

Publication Types

Select...
5
3

Relationship

0
8

Authors

Journals

citations
Cited by 400 publications
(88 citation statements)
references
References 361 publications
(3 reference statements)
2
81
0
5
Order By: Relevance
“…Theoretical investigations instigated by Scher and Montroll [58] in their description of dispersive transport in amorphous semi-conductors, found that traditional methods based on Brownian models failed. In the physical sciences, over the last half century, anomalous diffusion models have been developed with important contributions from Weiss and Rubin [76] and Shlesinger [62]. Currently, the list of complex systems displaying anomalous diffusion behaviour is quite extensive [4,35,59,75,77], and the problem of trapping (more commonly known as system flux) is well known in physics.…”
Section: The Mean Field and Individual Based Descriptionmentioning
confidence: 99%
“…Theoretical investigations instigated by Scher and Montroll [58] in their description of dispersive transport in amorphous semi-conductors, found that traditional methods based on Brownian models failed. In the physical sciences, over the last half century, anomalous diffusion models have been developed with important contributions from Weiss and Rubin [76] and Shlesinger [62]. Currently, the list of complex systems displaying anomalous diffusion behaviour is quite extensive [4,35,59,75,77], and the problem of trapping (more commonly known as system flux) is well known in physics.…”
Section: The Mean Field and Individual Based Descriptionmentioning
confidence: 99%
“…scaling properties of these random walks were extensively investigated in several papers inger, 1974;Metzler and Klafter, 2000;Grigolini et al, 2001Grigolini et al, , 2002 by applying the analytithods of CTRW model, i.e., the Montroll-Weiss equation for the Fourier-Laplace transform of bability distribution p(x,t)dx = P r[x < X(t) ≤ x + dx] (Montroll, 1964;Weiss and Rubin, or by applying simple scaling relationships in the case of AJ rule (Lowen and Teich, 1993;Alet al, 2009a). In particular, two scaling indices were found in the asymptotic long-time limit:…”
Section: Symmetric Jump (Sj) Rulementioning
confidence: 99%
“…In the following we give some definitions used in the theory of renewal processes (Cox, 1962). Then, we briefly discuss the fractal dimension of renewal point processes and, finally, we review the concept of event-driven diffusion, based on the model known as Continuous Time Random Walk (CTRW) (Montroll, 1964;Kenkre et al, 1973;Weiss and Rubin, 1983). The diffusion scaling of the event-driven random walk can be investigated to characterize not only the transport properties of turbulence in the ABL, but also the complexity of the system.…”
Section: Detecting Critical Events In Turbulencementioning
confidence: 99%
See 1 more Smart Citation
“…Examples range from hopping transport in semiconductors to single-molecule enzyme kinetics and intracellular transport by molecular motors. [1][2][3][4][5][6][7][8][9][10] When (1) the random walk occurs on a periodic lattice and (2) the observation time is sufficiently long so that a typical displacement exceeds the lattice period, one can use a coarse-grained description of the motion. In this description, all information about the underlying random walk is packed into the effective drift velocity, V eff , and diffusion coefficient, D eff .…”
mentioning
confidence: 99%