During drainage, as a voxel of porous material is being actively invaded prior to percolation, the invading nonwetting fluid cannot be transmitted neighboring downstream until critical saturation (Snc) reached. This occurs when forms percolating path across voxel. We present novel laboratory observations gravitationally stable, air/water drainage in thin bead packs, with 2D fields monitored at ...

We propose a "nonconsensus" opinion model that allows for stable coexistence of two opinions by forming clusters of agents holding the same opinion. We study this nonconsensus model on lattices, several model complex networks, and a real-life social network. We find that the model displays a phase transition behavior characterized by a large spanning cluster of nodes holding the same opinion ap...

Employing highly efficient algorithms for simulating invasion percolation (IP), whose execution time scales as O[M log(M)] or better for a cluster of M sites, and for determining the backbone of the cluster, we obtain precise estimates for the fractal dimensions of the samplespanning cluster, the backbone, and the minimal path in order to identify the universality classes of four different IP p...

Recent developments in hydraulic fracturing (fracking) have enabled the recovery of large quantities of natural gas and oil from old, low-permeability shales. These developments include a change from low-volume, high-viscosity fluid injection to high-volume, low-viscosity injection. The injected fluid introduces distributed damage that provides fracture permeability for the extraction of the ga...

This paper investigates the parallel complexity of several non-equilibrium growth models. Invasion percolation, Eden growth, ballistic deposition and solid-on-solid growth are all seemingly highly sequential processes that yield self-similar or self-affine random clusters. Nonetheless, we present fast parallel randomized algorithms for generating these clusters. The running times of the algorit...

The concept of immiscible displacement as an invasion percolation (IP) process driven by heat and mass transfer is used in a pore network model for convective drying of capillary porous media. The coupling between heat and mass transfer occurs at the liquid-gas interface through temperature dependent equilibrium vapour pressure, surface tension and phase change enthalpy (in evaporation and cond...

We study invasion percolation on Aldous’ Poisson-weighted infinite tree, and derive two distinct Markovian representations of the resulting process. One of these is the σ →∞ limit of a representation discovered by Angel et al. [Ann. Appl. Probab. 36 (2008) 420–466]. We also introduce an exploration process of a randomly weighted Poisson incipient infinite cluster. The dynamics of the new proces...

The competition between local and global driving forces is significant in a wide variety of naturally occurring branched networks. We have investigated the impact of a global minimization criterion versus a local one on the structure of spanning trees. To do so, we consider two spanning tree structures-the generalized minimal spanning tree (GMST) defined by Dror et al. [1] and an analogous stru...