The properties of bulk water come from a delicate balance of interactions on length scales encompassing several orders of magnitudes: i) the Hydrogen Bond (HBond) at the molecular scale and ii) the extension of this HBond network up to the macroscopic level. Here, we address the physics of water when the three dimensional extension of the HBond network is frustrated, so that the water molecules...

Consider the standard continuous percolation in R 4 , and choose the parameters so that the induced percolation on a xed two dimensional linear subspace is critical. Although two dimensional critical percolation dies, we show that there are exceptional two dimensional linear subspaces, in which percolation occurs.

In 1980, Kesten showed the exponential decay of percolation probability in the subcritical phase for the two-dimensional percolation model. This result implies his celebrated computation that pc = 0.5 for bond percolation in the square lattice, and site percolation in the triangular lattice, respectively. In this paper, we present a simpler proof for Kesten’s theorem.

A percolation model is an infinite random graph model for phase transitions and critical phenomena. The percolation threshold corresponds to a phase transition point, such as a melting or freezing temperature. The exact value of the percolation threshold is not known for any three-dimensional percolation models, which are important for physical applications. Furthermore, rigorous bounds for the...

We have studied experimentally and numerically the displacement of a highly viscous wetting fluid by a non-wetting fluid with low viscosity in a random two-dimensional porous medium under stabilizing gravity. In situations where the magnitudes of the viscous-, capillaryand gravity forces are comparable, we observe a transition from a capillary fingering behavior to a viscous fingering behavior,...

We present the results of extensive Monte Carlo simulations of the invasion percolation model with trapping (TIP) with long-range correlations, a problem which is relevant to multiphase flow in field-scale porous media, such as oil reservoirs and groundwater aquifers, as well as flow in rock fractures. The correlations are generated by a fractional Brownian motion characterized by a Hurst expon...

In recent years, many variants of percolation have been used to study network structure and the behavior of processes spreading on networks. These include bond percolation, site percolation, k-core percolation, bootstrap percolation, the generalized epidemic process, and the Watts threshold model (WTM). We show that-except for bond percolation-each of these processes arises as a special case of...

Consider the following process, known as r-bootstrap percolation, on a graph G. Designate some initial infected set A and infect any vertex with at least r infected neighbors, continuing until no new vertices can be infected. We say A percolates if it eventually infects the entire graph. We say A is a minimal percolating set if A percolates, but no proper subset percolates. We compute the size ...

Five methods to assess percolation rate from alternative earthen final covers (AEFCs) are described in the context of the precision with which the percolation rate can be estimated: trend analysis, tracer methods, water balance method, Darcy’s Law calculations, and lysimetry. Trend evaluation of water content data is the least precise method because it cannot be used alone to assess the percola...

We consider a random field (Xn)n∈Zd and investigate when the set Ah = {k ∈ Zd; ‖Xk‖ ≥ h} has infinite clusters. The main problem is to decide whether the critical level hc = sup{h ∈ R; P (Ah has an infinite cluster) > 0} is neither 0 nor +∞. Thus, we say that a percolation transition occurs. In a first time, we show that weakly dependent Gaussian fields satisfy to a wellknown criterion implying...