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Название: Rate Processes on Fractals: Theory, Simulations, and Experiments
Автор: Kopelman R.
Heterogeneous kinetics are shown to differ drastically from homogeneous kinetics. For the elementary reaction A + A-> products we show that the diffusion-limited reaction rate is proportional to t-h[A] 2 or to [A] x, where
h = 1 - d,/2, X= 1 + 2/d, - (h - 2)(h- 1 ), and d s is the effective spectral dimension. We note that for d d~.= 1, h= 1/2 and X=3, for percolating clusters d s = 4/3, h = 1/3 and X = 5/2, while for "dust" d e, < 1, 1 > h > 1/2 and oo > X > 3. Scaling arguments, supercomputer simulations and experiments give a consistent picture. The interplay of energetic and geometric heterogeneity results in fractal-like kinetics and is relevant to excitation fusion experiments in porous membranes, films, and polymeric glasses. However, in isotopic mixed crystals, the geometric fractal nature (percolation clusters) dominates.