We construct a measure valued Markov process which we call infinite canonical superBrownian motion, and which corresponds to the canonical measure of super-Brownian motion conditioned on non-extinction. Infinite canonical super-Brownian motion is a natural candidate for the scaling limit of various random branching objects on Zd when these objects are (a) critical; (b) mean-field and (c) infini...

This note is motivated by results in [1, 8] about global relations between the invasion percolation cluster (IPC) and the incipient infinite cluster (IIC) on regular trees and on two dimensional lattices, respectively. Namely, that the laws of the two objects are mutually singular, and, in the case of regular trees, that the IIC stochastically dominates the IPC. We prove that on two dimensional...

We consider the dynamics and kinetic roughening of single-valued interfaces in two-dimensional fractal media. Assuming that the local height difference distribution function of the fronts obeys Levý statistics with a well-defined power-law decay exponent, we derive analytic expressions for the local scaling exponents. We also show that the kinetic roughening of the interfaces displays anomalous...

A recently introduced cluster acceleration algorithm for spin models @J. Machta et al., Phys. Rev. Lett. 75, 2792 ~1995!# based on invasion percolation is generalized to temperatures away from the critical point using concepts of random bond percolation. The generalized algorithm is equivalent to an ‘‘optimized’’ version of the Swendsen-Wang cluster algorithm @R. H. Swendsen and J. S. Wang, Phy...

We investigate the displacement of one fluid by another in a deformable medium with pore-scale disorder. We develop a model that captures the dynamic pressure redistribution at the invasion front and the feedback between fluid invasion and microstructure rearrangement. Our results suggest how to collapse the transition between invasion percolation and viscous fingering in the presence of quench...

We study minimal spanning forests in infinite graphs, which are weak limits of minimal spanning trees from finite subgraphs corresponding to i.i.d. random labels on the edges. These limits can be taken with free or wired boundary conditions, and are denoted FMSF (free minimal spanning forest) and WMSF (wired minimal spanning forest), respectively. The WMSF is also the union of the trees that ar...

The structure and transport properties of drying water clusters in porous media have been studied with a site-bond invasion percolation (IP) model. In this model an invader (air) enters a lattice (porous network) filled with defender (water) via a sequence of invasion steps. The decision to invade a site (pore) is made on the basis of the resistance of the bonds (throats). It is found that the ...

The relationship between biological scaffold interconnectivity and cell migration is an important but poorly understood factor in tissue regeneration. Here a scale-independent technique for characterization of collagen scaffold interconnectivity is presented, using a combination of X-ray microcomputed tomography and percolation theory. Confocal microscopy of connective tissue cells reveals this...