We study the optimal distance ℓopt in random networks in the presence of disorder implemented by assigning random weights to the links. The optimal distance between two nodes is the length of the path for which the sum of weights along the path (“cost”) is a minimum. We study the case of...

We present a scaling Ansatz for the distribution function of the shortest paths connecting any two points on a percolating cluster which accounts for (i) the effect of the finite size of the system, and (ii) the dependence of this distribution on the site occupancy probability p. We present...

We determine the backbone mass distributions for bond percolation between two lines of arbitrary orientations in three dimensions. All simulations were performed at the percolation threshold pc. The slope of the power law regime of the backbone mass distribution is dependent upon the angle...

Generic three-dimensional (3D) exact relations were found recently (Phys. Rev. B (2002) 184416) between macroscopic or bulk effective moduli of composite systems with related microstructures which are, in general, different. As an example of possible application of these relations, a new...

This talk briefly reviews the subject of fluid flow through disordered media. In particular, we focus on the sorts of considerations that may be necessary to move statistical physics from the description of idealized flows in the limit of zero Reynolds number to more realistic flows of real...