Exact calculation of the spatiotemporal correlations in the Takayasu modeland in the q model of force fluctuations in bead packs

We calculate exactly the two point mass-mass correlations in arbitrary spat ial dimensions in the aggregation model of Takayasu. In this model, masses diffuse on a lattice, coalesce upon contact, and adsorb unit mass from outs ide at a constant rate. Our exact calculation of the variance of mass at a given site proves explicitly, without making any assumption of scaling, tha t the upper critical dimension of the model is 2. We also extend our method to calculate the spatiotemporal correlations in a generalized class of mod els with aggregation, fragmentation, and injection, which include, in parti cular, the q model of force fluctuations in bead packs. We present explicit expressions for the spatiotemporal force-force correlation function in the q model. These can be used to test the applicability of the a model in exp eriments.