Geodesic
Continuous Time Random Walks with Reactions Forcing and Trapping
C. N. Angstmann1 ; I. C. Donnelly1 ; B. I. Henry1
1 School of Mathematics and Statistics, University of New South Wales, Sydney, Australia
Mathematical modelling of natural phenomena, Tome 8 (2013) no. 2, pp. 17-27.

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One of the central results in Einstein’s theory of Brownian motion is that the mean square displacement of a randomly moving Brownian particle scales linearly with time. Over the past few decades sophisticated experiments and data collection in numerous biological, physical and financial systems have revealed anomalous sub-diffusion in which the mean square displacement grows slower than linearly with time. A major theoretical challenge has been to derive the appropriate evolution equation for the probability density function of sub-diffusion taking into account further complications from force fields and reactions. Here we present a derivation of the generalised master equation for an ensemble of particles undergoing reactions whilst being subject to an external force field. From this general equation we show reductions to a range of well known special cases, including the fractional reaction diffusion equation and the fractional Fokker-Planck equation.
DOI : 10.1051/mmnp/20138202

C. N. Angstmann 1 ; I. C. Donnelly 1 ; B. I. Henry 1

1 School of Mathematics and Statistics, University of New South Wales, Sydney, Australia 
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C. N. Angstmann; I. C. Donnelly; B. I. Henry. Continuous Time Random Walks with Reactions Forcing and Trapping. Mathematical modelling of natural phenomena, Tome 8 (2013) no. 2, pp. 17-27. doi : 10.1051/mmnp/20138202. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20138202/

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