In [1], Shao et al. claim, based on low statistics simulations , that a model with majority rule coarsening exhibits in d ¼ 2 a percolation transition in the universality class of invasion percolation with trapping (IPT). They report also that the system reaches its final state rapidly with no diverging time scale. Since the original configurations are random and thus in the ordinary percolatio...

A model of the capillary condensation process, i.e., of adsorption-desorption isotherms, having only porepore interactions is constructed. The model yields ~1! hysteretic isotherms, ~2! invasion percolation on desorption, and ~3! hysteresis with discrete memory for interior chemical potential loops. All of these features are seen in experiment. The model is compared to a model with no pore-pore...

The competition between local and global driving forces is signi,cant 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) de,ned by Dror et al. (Eur. J. Oper. Res. 120 (20...

We study the cluster, the backbone and the elastic backbone structures of the multiple invasion percolation for both the perimeter and the optimized versions. We investigate the behavior of the mass, the number of red sites (i. e., sites through which all the current passes) and loops of those structures. Their corresponding scaling exponents are also estimated. By construction, the mass of the...

We analyze the combined effect of a Laplacian field and quenched disorder for the generation of fractal structures with a study, both numerical and theoretical, of the quenched dielectric breakdown model (QDBM). The growth dynamics is shown to evolve from the avalanches of invasion percolation (IP) to the smooth growth of Laplacian fractals, i. e. diffusion limited aggregation (DLA) and the die...

In this lecture we present an overview of the physics of irreversible fractal growth process, with particular emphasis on a class of models characterized by quenched disorder. These models exhibit self-organization, with critical properties developing spontaneously, without the fine tuning of external parameters. This situation is different from the usual critical phenomena, and requires the in...

This work presents a methodology for determining the interface between wetting and nonwetting phases inside a three-dimensional porous space, at a given equilibrium state. The work is limited to the study of mechanical equilibrium. The method is based on a three dimensional extension of the opening method from image analysis presented in [1] and applied on threedimensional stochastically recons...

We present a discrete element model for the simulation, at the grain scale, of gas migration in brine-saturated deformable media. We account rigorously for the presence of two fluids in the pore space by incorporating grain forces due to pore fluid pressures, and surface tension between fluids. The coupled model permits investigating an essential process that takes place at the base of the hydr...

We suggest that the dynamics of stable viscous invasion fronts in porous media depends on the volume capacitance of the media. At high volume capacitance, our network simulations provide numerical evidence of a scaling relation between the front width and its velocity. In the low volume capacitance regime, we derive a new effective scaling supported by network simulations and that is in agreeme...

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