Journal Article10.1016/0370-1573(90)90099-N
Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications
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TL;DR: In this article, the authors consider the specific effects of a bias on anomalous diffusion, and discuss the generalizations of Einstein's relation in the presence of disorder, and illustrate the theoretical models by describing many physical situations where anomalous (non-Brownian) diffusion laws have been observed or could be observed.
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About: This article is published in Physics Reports. The article was published on 01 Nov 1990. The article focuses on the topics: Anomalous diffusion.
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Citations
The random walk's guide to anomalous diffusion: a fractional dynamics approach
Ralf Metzler,Joseph Klafter +1 more
TL;DR: Fractional kinetic equations of the diffusion, diffusion-advection, and Fokker-Planck type are presented as a useful approach for the description of transport dynamics in complex systems which are governed by anomalous diffusion and non-exponential relaxation patterns.
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Brownian motors: noisy transport far from equilibrium
TL;DR: In this paper, the main emphasis is put on directed transport in so-called Brownian motors (ratchets), i.e. a dissipative dynamics in the presence of thermal noise and some prototypical perturbation that drives the system out of equilibrium without introducing a priori an obvious bias into one or the other direction of motion.
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The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
Ralf Metzler,Joseph Klafter +1 more
TL;DR: Fractional dynamics has experienced a firm upswing during the past few years, having been forged into a mature framework in the theory of stochastic processes as mentioned in this paper, and a large number of research papers developing fractional dynamics further, or applying it to various systems have appeared since our first review article on the fractional Fokker-Planck equation.
Anderson Transitions
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TL;DR: Measurements of trajectories of individual proteins or lipids in the plasma membrane of cells show a variety of types of motion, including directed motion, confined motion, and anomalous diffusion, which requires a revision of existing views of membrane structure and dynamics.
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References
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The Fractal Geometry of Nature
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TL;DR: This book is a blend of erudition, popularization, and exposition, and the illustrations include many superb examples of computer graphics that are works of art in their own right.
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Introduction to percolation theory
Dietrich Stauffer,Amnon Aharony +1 more
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TL;DR: In this paper, a scaling solution for the Bethe lattice is proposed for cluster numbers and a scaling assumption for cluster number scaling assumptions for cluster radius and fractal dimension is proposed.
11.6K