Single-file diffusion of subdiffusive particlesT. Bandyopadhyay
Theoretical Chemistry Section, Chemistry Group, Bhabha Atomic Research Centre - Trombay, Mumbai 400 085, India
received 16 July 2007; accepted in final form 2 November 2007; published January 2008
published online 4 December 2007
We introduce a fractional single-file diffusion (FSFD) model describing the stochastic evolution of an assembly of nonpassing particles (single-file (SF) system), where in addition to the excluded-volume interaction between the particles, they individually follow sticky trajectories (fractional diffusion (FD)) on a fractal support. While the long-range correlations between the particles mediated through the former interaction is treated through the reflection principle, the sticky trajectories involve fractional time derivatives whose order is distributed over the interval from zero to one. A detailed study of the propagators of FSFD is made and compared with the normal SF diffusion through their time evolution in state space. Both the diffusion mechanisms, SF and FD, are known for anomalous subdiffusive behaviour; their combined entity, FSFD has been found to exhibit further anomality leading to ultraslow diffusion. Through an integral transformation of the Gaussian propagator, a generalised expression for the mean square displacement of a tagged particle undergoing FSFD is obtained.
66.30.Pa - Diffusion in nanoscale solids.
47.53.+n - Fractals in fluid dynamics.
02.50.Ey - Stochastic processes.
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