AGGREGATION WITH POWER-LAW AND FRACTAL INPUT

We study an aggregation model of charged particles in the cases of weighted input (power-law input) and spatially fractal input. For 1-dimensional and mean-field models we obtain the behaviour of the steady state as well as the time dependence of perturbations during the relaxation to the steady state. For input of particles that follows a power law in the charge distribution (p(I) approximately absolute value of I-1-beta, 0 < beta less-than-or-equal-to 2), we show that the steady-state charge distribution and the relaxation follow power laws with exponents depending on the input exponent beta and on the dimensionality (d(f)) of the input subspace.