Dynamic scaling of dissipative networks

The dynamics of complex systems of soft condensed matter has been often measured to contain non-trivial power law scaling over some range. Here we investigate the dependence of dynamic scaling on system structure. We focus our attention on overdamped fractal networks as colloidal and polymer gels close by and away from gelling threshold and even linear polymers and membranes in cases where hydrodynamic interactions can be neglected. We show that self diffusion of such dissipative networks decay in time as power law with a scaling exponent of half the network spectral dimension. This scaling analysis leads to a classification of anomalous diffusion into free, critical and bounded regimes upon increasing network constraining. We also note that the Edwards–Wilkinson deposition problem can be mapped in the network diffusion model described here.