[1] We have imaged sea ice single crystals with X-ray computed tomography, and characterized the thermal evolution of the pore space with percolation theory. Between !18!C and !3!C the porosity ranged from 2 to 12% and we found arrays of near-parallel intracrystalline brine layers whose connectivity and complex morphology varied with temperature. We have computed key porosity-dependent function...

An exact enumeration approach is developed for the backbone fractal of the incipient infinite cluster at the percolation threshold. We use this approach to calculate exactly the first low-density expansion of LBB@) for arbitrary system dimensionality d, where L B B @ ) is the mean number of backbone bonds and p is the bond occupation probability. Standard series extrapolation methods provide es...

Many modern nanostructured materials and doped polymers are morphologically too complex to be interpreted by classical percolation theory. Here, we develop the concept of a hierarchical percolating (percolation-within-percolation) system to describe such complex materials and illustrate how to generalize the conventional percolation to double-level percolation. Based on Monte Carlo simulations,...

We study the percolation model on Boltzmann triangulations using a generating function approach. More precisely, we consider a Boltzmann model on the set of finite planar triangulations, together with a percolation configuration (either site-percolation or bondpercolation) on this triangulation. By enumerating triangulations with boundaries according to both the boundary length and the number o...

We prove that there exist natural generalizations of the classical bootstrap percolation model on Z that have non-trivial critical probabilities, and moreover we characterize all homogeneous, local, monotone models with this property. Van Enter [28] (in the case d = r = 2) and Schonmann [25] (for all d > r > 2) proved that r-neighbour bootstrap percolation models have trivial critical probabili...