Thoughts about Anomalous Diffusion: Time-Dependent Coefficients versus Memory Functions

2007 ◽  
pp. 147-160 ◽  
Author(s):  
V. M. Kenkre ◽  
F. J. Sevilla
Keyword(s):  
Anomalous Diffusion ◽  
Diffusion Time ◽  
Time Dependent ◽  
Memory Functions

scholarly journals Anomalous diffusion with absorption: Exact time-dependent solutions

2000 ◽  
Vol 61 (2) ◽  
pp. 1417-1422 ◽  
Author(s):  
German Drazer ◽  
Horacio S. Wio ◽  
Constantino Tsallis
Keyword(s):  
Anomalous Diffusion ◽  
Time Dependent ◽  
Exact Time

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 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.

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