We review a simple model of random walks on a rugged landscape, representing energy or (negative) fitness, and with many peaks and valleys. This paradigm for trapping on long timescales by metastable states in complex systems may be visualized as a terrain with lakes in the valleys whose water level depends on the observational timescale. The “broken ergodicity” structure in space and time of t...

Using large scale computer simulations and pore network models of porous rock, we investigate the e€ect of correlated heterogeneity on two-phase ̄ow through porous media. First, we review and discuss the experimental evidence for correlated heterogeneity. We then employ the invasion percolation model of two-phase ̄ow in porous media to study the e€ect of correlated heterogeneity on rate-control...

We introduce a general theoretical scheme for a class of phenomena characterized by an extremal dynamics and quenched disorder. The approach is based on a transformation of the quenched dynamics into a stochastic one with cognitive memory and on other concepts which permit a mathematical characterization of the self-organized nature of the avalanche type dynamics. In addition it is possible to ...

We consider invasion percolation on the square lattice. In [3] it has been proved that the probability that the radius of a so-called pond is larger than n, differs at most a factor of order log n from the probability that in critical Bernoulli percolation the radius of an open cluster is larger than n. We show that these two probabilities are, in fact, of the same order. Moreover, we prove an ...

2014 We report experimental measurements on the structure of invasion fronts obtained by slow vertical injection of liquid, non wetting, Wood metal into non consolidated crushed glass. The geometry of plane cuts of the invasion front both parallel and perpendicular to the flow direction is analysed. The structure of perpendicular cuts is self similar in a length scale range of 1 to 20 with a fr...

We propose a modified Invasion Percolation (IP) model to simulate the infiltration of glue into a porous medium under gravity in 2D. Initially, the medium is saturated 15 with air and then invaded by a fluid that has a hardening effect taking place from the interface towards the interior by contact with the air. To take into account that interfacial 17 hardening, we use an IP model where capill...

We investigate the multiscaling behaviour of usual and directed invasion percolation, with and without a power-law decay with the distance from an initial seed in the distribution of random numbers. We find universal multiscaling behaviour only in the presence of a power-law gradient in space. Invasion percolation [ 11 is a geometrical growth model that has been used to describe the penetration...

A new cluster algorithm based on invasion percolation is described. The algorithm samples the critical point of a spin system without a priori knowledge of the critical temperature and provides an efficient way to determine the critical temperature and other observables in the critical region. The method is illustrated for the twoand three-dimensional Ising models. The algorithm equilibrates sp...

A multi-scale scheme for the invasion percolation of rock fracture networks with heterogeneous fracture aperture fields is proposed. Inside fractures, fluid transport is calculated on the finest scale and found to be localized in channels as a consequence of the aperture field. The channel network is characterized and reduced to a vectorized artificial channel network (ACN). Different realizati...

We study a plant population model introduced recently by J. Wallinga [OIKOS 74, 377 (1995)]. It is similar to the contact process (‘simple epidemic’, ‘directed percolation’), but instead of using an infection or recovery rate as control parameter, the population size is controlled directly and globally by removing excess plants. We show that the model is very closely related to directed percola...