How to Measure Subdiffusion Parameters

Details How to Measure Subdiffusion Parameters How to Measure Subdiffusion Parameters

2005-04-11

arxiv.org/abs/cond-mat/0504261v1

Physics

Condensed Matter

Statistical Mechanics

short version of cond-mat/0309072, to appear in Phys. Rev. Lett

Scientific paper

10.1103/PhysRevLett.94.170602

We propose a method to measure the subdiffusion parameter $\alpha$ and subdiffusion coefficient $D_{\alpha}$ which are defined by means of the relation $ =\frac{2D_\alpha} {\Gamma(1+\alpha)} t^\alpha$ where $$ 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 $\alpha$ and $D_{\alpha}$, using a fully analytic solution of the fractional subdiffusion equation.

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