Europhys. Lett.
Volume 61, Number 5, March 2003
Page(s) 586 - 592
Section General
Published online 01 February 2003
DOI: 10.1209/epl/i2003-00135-4
Europhys. Lett., 61 (5) , pp. 586-592 (2003)

Reactive dynamics on fractal sets: Anomalous fluctuations and memory effects

E. Abad1, A. Provata2 and G. Nicolis1

1  Centre for Nonlinear Phenomena and Complex Systems Université Libre de Bruxelles - CP 231, 1050 Bruxelles, Belgium
2  Institute of Physical Chemistry, National Research Center "Demokritos" 15310 Athens, Greece

(Received 5 August 2002; accepted in final form 17 December 2002)

We study the effect of fractal initial conditions in closed reactive systems in the cases of both mobile and immobile reactants. For the reaction $A+A\rightarrow A$, 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 $\langle N(t)\rangle$ decays asymptotically as $t^{-d_{\ab{f}}/2}$, the memory of the initial conditions being now carried by the dynamical power law exponent. The latter is fully determined by the fractal dimension $d_{\ab{f}}$ of the initial conditions.

05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.
05.45.Df - Fractals.
82.20.-w - Chemical kinetics and dynamics.

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