Anomalous diffusion and response in branched systems: a simple analysis

@article{Forte2013AnomalousDA,
  title={Anomalous diffusion and response in branched systems: a simple analysis},
  author={Giuseppe Forte and Raffaella Burioni and Fabio Cecconi and Angelo Vulpiani},
  journal={Journal of Physics: Condensed Matter},
  year={2013},
  volume={25}
}
We revisit the diffusion properties and the mean drift induced by an external field of a random walk process in a class of branched structures, as the comb lattice and the linear chains of plaquettes. A simple treatment based on scaling arguments is able to predict the correct anomalous regime for different topologies. In addition, we show that even in the presence of anomalous diffusion, Einstein’s relation still holds, implying a proportionality between the mean square displacement of the… 

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References

SHOWING 1-10 OF 53 REFERENCES

Generalized Einstein relation: A stochastic modeling approach

generalized Einstein relation between anomalous diffusion and the linear response of the walkers to an external fieldF is studied, using a stochastic modeling approach. A departure from the Einstein

Use of comb-like models to mimic anomalous diffusion on fractal structures

Abstract We discuss some properties of random walks on comb-like structures. These have been used as analogues for the study of anomalous diffusion along a percolation cluster intersected by loopless

On anomalous diffusion and the out of equilibrium response function in one-dimensional models

We study how the Einstein relation between spontaneous fluctuations and the response to an external perturbation holds in the absence of currents, for the comb model and the elastic single-file,

Anomalous diffusion and Hall effect on comb lattices.

An analytical technique is developed to study the Lorentz force effects on the asymptotic diffusion laws and allows the description of the combined action of an electric and a magnetic field (Hall effect).

RANDOM WALKS ON KEBAB LATTICES: LOGARITHMIC DIFFUSION ON ORDERED STRUCTURES

Kebab lattices are ordered lattices obtained matching an infinite two-dimensional lattice to each point of a linear chain. Discrete time random walks on these structures are studied by analytical

Anomalous diffusion in intermittent chaotic systems

It is shown that anomalous diffusion (i.e., nonlinear growth of mean square displacements) can be caused by a specifically chaotic mechanism. It depends on deterministic diffusion and intermittency

Analytic method for calculating properties of random walks on networks.

A method for calculating the properties of discrete random walks on networks by dividing complex networks into simpler units whose contribution to the mean first-passage time is calculated.

Diffusion and Reactions in Fractals and Disordered Systems

Preface Part I. Basic Concepts: 1. Fractals 2. Percolation 3. Random walks and diffusion 4. Beyond random walks Part II. Anomalous Diffusion: 5. Diffusion in the Sierpinski gasket 6. Diffusion in
...