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Libin Lin - One of the best experts on this subject based on the ideXlab platform.
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Anomalous Diffusion on the Percolating Networks
Fractals, 1998Co-Authors: De Liu, Fuxuan Chang, Libin LinAbstract: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.
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Anomalous Diffusion on the percolating networks
Communications in Nonlinear Science and Numerical Simulation, 1997Co-Authors: De Liu, Fuxuan Chang, Libin LinAbstract: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.
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Self-similar Gaussian processes for modeling Anomalous Diffusion.
Physical Review E, 2002Co-Authors: S C Lim, Sithi V. MuniandyAbstract: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.
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Self-similar Gaussian processes for modeling Anomalous Diffusion.
Physical review. E Statistical nonlinear and soft matter physics, 2002Co-Authors: S C Lim, Sithi V. MuniandyAbstract: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.
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Anomalous Diffusion on the Percolating Networks
Fractals, 1998Co-Authors: De Liu, Fuxuan Chang, Libin LinAbstract: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.
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Anomalous Diffusion on the percolating networks
Communications in Nonlinear Science and Numerical Simulation, 1997Co-Authors: De Liu, Fuxuan Chang, Libin LinAbstract: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.
Aleksander Weron - One of the best experts on this subject based on the ideXlab platform.
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Accelerating and retarding Anomalous Diffusion: A Bernstein function approach.
Physical review. E, 2020Co-Authors: Aleksander Stanislavsky, Aleksander WeronAbstract:We have discovered here a duality relation between infinitely divisible subordinators which can produce both retarding and accelerating Anomalous Diffusion in the framework of the special Bernstein function approach. As a consequence, we show that conjugate pairs of Bernstein functions taken as Laplace exponents can produce in a natural way both retarding and accelerating Anomalous Diffusion (either subDiffusion or superDiffusion). This provides a unified way to control the dynamics of complex biological processes leading to transient Anomalous Diffusion in single-particle tracking experiments. Moreover, this permits one to explain better the relaxation diagram positioning two different power laws of relaxation, including the celebrated Havriliak-Negami law.
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transient Anomalous Diffusion with prabhakar type memory
Journal of Chemical Physics, 2018Co-Authors: A A Stanislavsky, Aleksander WeronAbstract:In this paper, we derive the general properties of Anomalous Diffusion and non-exponential relaxation from the Fokker-Planck equation with the memory function related to the Prabhakar integral operator. The operator is a generalization of the Riemann-Liouville fractional integral and permits one to study transient Anomalous Diffusion processes with two-scale features. The aim of this work is to find a probabilistic description of the Anomalous Diffusion from the Fokker-Planck equation, more precisely from the memory function. The temporal behavior of such phenomena exhibits changes in time scaling exponents of the mean-squared displacement through time domain—a more general picture of the Anomalous Diffusion observed in nature.In this paper, we derive the general properties of Anomalous Diffusion and non-exponential relaxation from the Fokker-Planck equation with the memory function related to the Prabhakar integral operator. The operator is a generalization of the Riemann-Liouville fractional integral and permits one to study transient Anomalous Diffusion processes with two-scale features. The aim of this work is to find a probabilistic description of the Anomalous Diffusion from the Fokker-Planck equation, more precisely from the memory function. The temporal behavior of such phenomena exhibits changes in time scaling exponents of the mean-squared displacement through time domain—a more general picture of the Anomalous Diffusion observed in nature.
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Anomalous Diffusion with transient subordinators: a link to compound relaxation laws.
The Journal of chemical physics, 2014Co-Authors: Aleksander Stanislavsky, Karina Weron, Aleksander WeronAbstract:This paper deals with a problem of transient Anomalous Diffusion which is currently found to emerge from a wide range of complex processes. The nonscaling behavior of such phenomena reflects changes in time-scaling exponents of the mean-squared displacement through time domain – a more general picture of the Anomalous Diffusion observed in nature. Our study is based on the identification of some transient subordinators responsible for transient Anomalous Diffusion. We derive the corresponding fractional Diffusion equation and provide links to the corresponding compound relaxation laws supported by this case generalizing many empirical dependencies well-known in relaxation investigations.
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Anomalous Diffusion and semimartingales
EPL (Europhysics Letters), 2009Co-Authors: Aleksander Weron, Marcin MagdziarzAbstract:We argue that the essential part of the currently explored models of Anomalous (non-Brownian) Diffusion are actually Brownian motion subordinated by the appropriate random time. Thus, in many cases, Anomalous Diffusion can be embedded in Brownian Diffusion. Such an embedding takes place if and only if the Anomalous Diffusion is a semimartingale process. We also discuss the structure of Anomalous Diffusion models. Categorization of semimartingales can be applied to differentiate among various Anomalous processes. In particular, identification of the type of subdiffusive dynamics from experimental data is feasible.
S C Lim - One of the best experts on this subject based on the ideXlab platform.
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Accelerating and Retarding Anomalous Diffusion
Journal of Physics A: Mathematical and Theoretical, 2012Co-Authors: Chai Hok Eab, S C LimAbstract:In this paper Gaussian models of retarded and accelerated Anomalous Diffusion are considered. Stochastic differential equations of fractional order driven by single or multiple fractional Gaussian noise terms are introduced to describe retarding and accelerating subDiffusion and superDiffusion. Short and long time asymptotic limits of the mean squared displacement of the stochastic processes associated with the solutions of these equations are studied. Specific cases of these equations are shown to provide possible descriptions of retarding or accelerating Anomalous Diffusion.
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Self-similar Gaussian processes for modeling Anomalous Diffusion.
Physical Review E, 2002Co-Authors: S C Lim, Sithi V. MuniandyAbstract: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.
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Self-similar Gaussian processes for modeling Anomalous Diffusion.
Physical review. E Statistical nonlinear and soft matter physics, 2002Co-Authors: S C Lim, Sithi V. MuniandyAbstract: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