LONG-TERM-MEMORY EFFECTS IN CLOSED RANDOM AGGREGATING SYSTEMS

We study the problem of fractal initial conditions in closed aggregati ng systems (no external input). When the initial distribution of aggre gating particles has a fractal dimension D-f, the number of surviving particles decreases as N(t) similar to t(-Df/2), for D-f < 2. Logarith mic corrections are necessary for D-f = 2. This fractal decay indicate s that in closed aggregating systems the memory of the initial distrib ution is always present in the dynamical exponent which characterizes the decay of the particle number.