Analytical Results for Nontrivial Polydispersity Exponents in Aggregation Models

We study a Smoluchowski equation describing a simple mean-field model of particles moving in $d$ dimensions and aggregating with conservation of `mass' $s=R^D$ ($R$ is the particle radius). In the scaling regime the scaled mass distribution $P(s)\sim s^{-\tau}$, and $\tau$ can be computed by perturbative and non perturbative expansions. A possible application to two-dimensional decaying turbulence is briefly discussed.