scholarly journals Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes

2016 ◽  
Vol 18 (34) ◽  
pp. 23840-23852 ◽  
Author(s):  
Andrey G. Cherstvy ◽  
Ralf Metzler
Keyword(s):  
Power Law ◽  
Anomalous Diffusion ◽  
Diffusion Time ◽  
Ergodic Properties ◽  
Disordered Medium

We investigate the diffusive and ergodic properties of massive and confined particles in a model disordered medium, in which the local diffusivity fluctuates in time while its mean has a power law dependence on the diffusion time.

scholarly journals Observing Power-Law Dynamics of Position-Velocity Correlation in Anomalous Diffusion

2017 ◽  
Vol 119 (6) ◽  
Author(s):  
Gadi Afek ◽  
Jonathan Coslovsky ◽  
Arnaud Courvoisier ◽  
Oz Livneh ◽  
Nir Davidson
Keyword(s):  
Power Law ◽  
Anomalous Diffusion ◽  
Velocity Correlation

Anomalous Diffusion on the Percolating Networks

Fractals ◽  
1998 ◽  
Vol 06 (02) ◽  
pp. 139-144 ◽  
Author(s):  
De Liu ◽  
Houqiang Li ◽  
Fuxuan Chang ◽  
Libin Lin
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Equation ◽  
Power Law ◽  
Anomalous Diffusion ◽  
Waiting Times ◽  
Power Law Distribution

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.

scholarly journals Anomalous Diffusion of Brain Metabolites Evidenced by Diffusion-Weighted Magnetic Resonance Spectroscopy in Vivo

2012 ◽  
Vol 32 (12) ◽  
pp. 2153-2160 ◽  
Author(s):  
Charlotte Marchadour ◽  
Emmanuel Brouillet ◽  
Philippe Hantraye ◽  
Vincent Lebon ◽  
Julien Valette
Keyword(s):  
Magnetic Resonance ◽  
Magnetic Resonance Spectroscopy ◽  
Active Transport ◽  
Anomalous Diffusion ◽  
Molecular Motion ◽  
Diffusion Time ◽  
Resonance Spectroscopy ◽  
Diffusion Weighted ◽  
Geometrically Constrained

Translational displacement of molecules within cells is a key process in cellular biology. Molecular motion potentially depends on many factors, including active transport, cytosol viscosity and molecular crowding, tortuosity resulting from cytoskeleton and organelles, and restriction barriers. However, the relative contribution of these factors to molecular motion in the cytoplasm remains poorly understood. In this work, we designed an original diffusion-weighted magnetic resonance spectroscopy strategy to probe molecular motion at subcellular scales in vivo. This led to the first observation of anomalous diffusion, that is, dependence of the apparent diffusion coefficient (ADC) on the diffusion time, for endogenous intracellular metabolites in the brain. The observed increase of the ADC at short diffusion time yields evidence that metabolite motion is characteristic of hindered random diffusion rather than active transport, for time scales up to the dozen milliseconds. Armed with this knowledge, data modeling based on geometrically constrained diffusion was performed. Results suggest that metabolite diffusion occurs in a low-viscosity cytosol hindered by ~2- μm structures, which is consistent with known intracellular organization.

scholarly journals General fractional-order anomalous diffusion with non-singular power-law kernel

2017 ◽  
Vol 21 (suppl. 1) ◽  
pp. 1-9 ◽  
Author(s):  
Xiao-Jun Yang ◽  
Hari Srivastava ◽  
Delfim Torres ◽  
Amar Debbouche
Keyword(s):  
Fractional Order ◽  
Power Law ◽  
Anomalous Diffusion ◽  
Fractional Derivatives ◽  
Diffusion Models

In this paper, we investigate general fractional derivatives with a non-singular power-law kernel. The anomalous diffusion models with non-singular power-law kernel are discussed in detail. The results are efficient for modelling the anomalous behaviors within the frameworks of the Riemann-Liouville and Liouville-Caputo general fractional derivatives.

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