How to Measure Subdiffusion Parameters
Abstract
We propose a method to measure the subdiffusion parameter α and subdiffusion coefficient D_{α} which are defined by means of the relation <x^{2}>=2D_{α}/Γ(1+α)t^{α}, where <x^{2}> denotes a mean square displacement of a random walker starting from x=0 at the initial time t=0. The method exploits a membrane system where a substance of interest is transported in a solvent from one vessel to another across a thin membrane which plays here only an auxiliary role. We experimentally study a diffusion of glucose and sucrose in a gel solvent, and we precisely determine the parameters α and D_{α}, using a fully analytic solution of the fractional subdiffusion equation.
 Publication:

Physical Review Letters
 Pub Date:
 May 2005
 DOI:
 10.1103/PhysRevLett.94.170602
 arXiv:
 arXiv:condmat/0504261
 Bibcode:
 2005PhRvL..94q0602K
 Keywords:

 05.40.a;
 66.10.x;
 Fluctuation phenomena random processes noise and Brownian motion;
 Diffusion and ionic conduction in liquids;
 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Soft Condensed Matter
 EPrint:
 short version of condmat/0309072, to appear in Phys. Rev. Lett