Network models and their dynamics: Probes of topological structure

In this work we focus on the mechanical relaxation of macromolecules. Based on linear response theory, this relaxation is in general related to the set of eigenmodes and eigenfunctions of the system. Of particular importance are situations which lead to scaling in the time and frequency domains. Thus the relaxation of star polymers, of dendrimers and of hyperbranched structures does not display scaling. On the other hand, one expects that the relaxation of fractals, as in fact that of linear chains, does scale. Here we numerically analyse the behavior of networks modelled through finite Sierpinski-type lattices, for which we have previously established that in the Rouse picture the mechanical relaxation scales in frequency and in time. As we show here, in the Zimm. model based on the preaveraged Oseen-tensor, the picture changes drastically; taking the hydrodynamic interactions into account leads to relaxation forms which do not scale.