# Anomalous Diffusion - Explore the Science & Experts | ideXlab

## Anomalous Diffusion

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### Libin Lin – One of the best experts on this subject based on the ideXlab platform.

• ##### AnomalousDiffusion on the Percolating Networks
Fractals, 1998
Co-Authors: De Liu, Fuxuan Chang, Libin Lin

Abstract:

According to the standard Diffusion equation, by introducing reasonably into an Anomalous Diffusion coefficient, the generalized Diffusion equation, which describes Anomalous Diffusion on the percolating networks with a power-law distribution of waiting times, is derived in this paper. This solution of the generalized Diffusion equation is obtained by using the method, which is used by Barta. The problems of Anomalous Diffusion on percolating networks with a power-law distribution of waiting times, which are not solved by Barta, are resolved.

• ##### AnomalousDiffusion on the percolating networks
Communications in Nonlinear Science and Numerical Simulation, 1997
Co-Authors: De Liu, Fuxuan Chang, Libin Lin

Abstract:

Abstract According to the standard Diffusion equation, by introducing reasonably into a Anomalous Diffusion coefficient, the generalized Diffusion equation, which describes Anomalous Diffusion on the percolating networks with a power-law distribution of waiting times, is derived in this paper. The solution of the generalized Diffusion equation is obtained by using the method, which is used by Barta. The problems of Anomalous Diffusion on percolating networks with a power-law distribution of waiting times, which aren’t solved by Barta, are resolved.

### Sithi V. Muniandy – One of the best experts on this subject based on the ideXlab platform.

• ##### Self-similar Gaussian processes for modeling AnomalousDiffusion.
Physical Review E, 2002
Co-Authors: S C Lim, Sithi V. Muniandy

Abstract:

We study some Gaussian models for Anomalous Diffusion, which include the time-rescaled Brownian motion, two types of fractional Brownian motion, and models associated with fractional Brownian motion based on the generalized Langevin equation. Gaussian processes associated with these models satisfy the Anomalous Diffusion relation which requires the mean-square displacement to vary with ${t}^{\ensuremath{\alpha}},$ $0l\ensuremath{\alpha}l2.$ However, these processes have different properties, thus indicating that the Anomalous Diffusion relation with a single parameter is insufficient to characterize the underlying mechanism. Although the two versions of fractional Brownian motion and time-rescaled Brownian motion all have the same probability distribution function, the Slepian theorem can be used to compare their first passage time distributions, which are different. Finally, in order to model Anomalous Diffusion with a variable exponent $\ensuremath{\alpha}(t)$ it is necessary to consider the multifractional extensions of these Gaussian processes.

• ##### Self-similar Gaussian processes for modeling AnomalousDiffusion.
Physical review. E Statistical nonlinear and soft matter physics, 2002
Co-Authors: S C Lim, Sithi V. Muniandy

Abstract:

We study some Gaussian models for Anomalous Diffusion, which include the time-rescaled Brownian motion, two types of fractional Brownian motion, and models associated with fractional Brownian motion based on the generalized Langevin equation. Gaussian processes associated with these models satisfy the Anomalous Diffusion relation which requires the mean-square displacement to vary with t(alpha), 0

### De Liu – One of the best experts on this subject based on the ideXlab platform.

• ##### AnomalousDiffusion on the Percolating Networks
Fractals, 1998
Co-Authors: De Liu, Fuxuan Chang, Libin Lin

Abstract:

According to the standard Diffusion equation, by introducing reasonably into an Anomalous Diffusion coefficient, the generalized Diffusion equation, which describes Anomalous Diffusion on the percolating networks with a power-law distribution of waiting times, is derived in this paper. This solution of the generalized Diffusion equation is obtained by using the method, which is used by Barta. The problems of Anomalous Diffusion on percolating networks with a power-law distribution of waiting times, which are not solved by Barta, are resolved.

• ##### AnomalousDiffusion on the percolating networks
Communications in Nonlinear Science and Numerical Simulation, 1997
Co-Authors: De Liu, Fuxuan Chang, Libin Lin

Abstract:

Abstract According to the standard Diffusion equation, by introducing reasonably into a Anomalous Diffusion coefficient, the generalized Diffusion equation, which describes Anomalous Diffusion on the percolating networks with a power-law distribution of waiting times, is derived in this paper. The solution of the generalized Diffusion equation is obtained by using the method, which is used by Barta. The problems of Anomalous Diffusion on percolating networks with a power-law distribution of waiting times, which aren’t solved by Barta, are resolved.