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We investigate bq numerical simulation the higher moments for S , , the number of distinct sites visited in an N-step random walk on fractal structures: the Sierpinski gasket, the Sierpinski web, and the percolation clusters of the square planar and the simple cubic lattices. We find that these moments scale similarly, e.g., the ratio of the standard deviation to (S,), the average S, , is constant in time.

The bimolecular reaction A + B .... products, where [A] < [B], was studied by fluorescence probing of small unilamellar vesicles of dipalmitoylphosphatidylglycerol with pyrene, and by computer simulation on a square lattice containing non percolating clusters. The decay curves of the minority species were fitted with an equation obtained from the theory of random walks in fractal domains. The analysis of the data has allowed redefinition of the reaction rate in restricted geometries, which is now time dependent, and sets the basis for simple treatment of bimolecular reactions in organized assemblies. The values of the spectral dimension calculated from this work are in the range 0.35-0.66, where the upper limit reflects the Alexander-Orbach conjecture, and the lower values are used to monitor the solubilizate aggegation in vesicles.

We consider here the A + B -0 reaction between particles that diffuse, interact through short-range forces, and react on contact. In a plausible approximation the reaction can be described through a nonlinear diffusion equation, from which the scaling behavior of the respective A and B concentrations follows. We focus here on steady particle generation and obtain the exponents that govern the concentration's growth. Through explicit Monte Carlo simulations of the underlying stochastic process we obtain directly these exponents; furthermore we show that the assumption of particle segregation in clusters is correct, by computing the correlation length.