61 research outputs found
Time evolution of the reaction front in a subdiffusive system
Using the quasistatic approximation, we show that in a subdiffusion--reaction
system the reaction front evolves in time according to the formula
, with being the subdiffusion parameter. The
result is derived for the system where the subdiffusion coefficients of
reactants differ from each other. It includes the case of one static reactant.
As an application of our results, we compare the time evolution of reaction
front extracted from experimental data with the theoretical formula and we find
that the transport process of organic acid particles in the tooth enamel is
subdiffusive.Comment: 18 pages, 3 figure
How to Measure Subdiffusion Parameters
We propose a method to measure the subdiffusion parameter and
subdiffusion coefficient which are defined by means of the
relation where
denotes a mean square displacement of a random walker starting from at
the initial time . 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 and , using a fully analytic solution of
the fractional subdiffusion equation.Comment: short version of cond-mat/0309072, to appear in Phys. Rev. Let
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