Reactive dynamics on fractal sets: Anomalous fluctuations and memory effects
Abstract
We study the effect of fractal initial conditions in closed reactive systems in the cases of both mobile and immobile reactants. For the reaction A + A → A, in the absence of diffusion, the mean number of particles A is shown to decay exponentially to a steady state which depends on the details of the initial conditions. The nature of this dependence is demonstrated both analytically and numerically. In contrast, when diffusion is incorporated, it is shown that the mean number of particles langleN(t)rangle decays asymptotically as t^{df/2}, the memory of the initial conditions being now carried by the dynamical power law exponent. The latter is fully determined by the fractal dimension d_{f} of the initial conditions.
 Publication:

EPL (Europhysics Letters)
 Pub Date:
 March 2003
 DOI:
 10.1209/epl/i2003001354
 arXiv:
 arXiv:condmat/0305167
 Bibcode:
 2003EL.....61..586A
 Keywords:

 05.40.a;
 05.45.Df;
 82.20.w;
 Fluctuation phenomena random processes noise and Brownian motion;
 Fractals;
 Chemical kinetics and dynamics;
 Condensed Matter  Statistical Mechanics
 EPrint:
 7 pages, 2 figures, uses epl.cls