Force distribution, multiscaling, and fluctuations in disordered elastic media

Abstract

We investigate the scaling properties of the distribution of the forces that are exerted on the bonds of an elastic percolation network near the percolation threshold ${p}_{c}$. It is shown that the moments of this force distribution (FD) provide useful insight about topological, transport, and fracture properties of percolation systems near ${p}_{c}$, and that elastic percolation clusters possess multifractal properties. From the properties of the FD, we argue that the distribution of fracture strength near ${p}_{c}$ cannot be in the form of an exponential, which is presumably valid far from ${p}_{c}$. We also propose that the universality class of elastic percolation networks should be defined in terms of the universality of all exponents that are associated with the various moments of the FD. Thus, elastic percolation networks with and without bond-bending forces may belong to two different universality classes, since the critical exponents of only the zeroth and the second moments of their FD appear to be the same. We introduce and investigate the concept of elastic noise ${S}_{e}$ in percolation systems, i.e., the macroscopic fluctuations in the elastic properties of the system that arise as a result of microscopic fluctuations in the elastic constants of the bonds of the system. Near ${p}_{c}$, ${S}_{e}$ vanishes according to a power law with a new exponent, which is related to the exponents that characterize the moments of the FD.