We present a phase diagram for fluid invasion of porous media as a function of pressure P and the contact angle \ensuremath{\theta} of the invading fluid. Increasing P leads to perculation above a critical ${\mathrm{\ensuremath{\theta}}}_{\mathit{c}}$, and depinning below ${\mathrm{\ensuremath{\theta}}}_{\mathit{c}}$. Depinning is characterized by a diverging coherence length and the power-law distribution of events typical of self-organized critical phenomena. At the transition from percolation to depinning another correlation length diverges and an order parameter, an effective macroscopic surface tension, becomes nonzero. The fluid interface changes from self-similar to self-affine. Results are compared to experiments.
A critical wetting (or interface delocalization) transition occurs when the interface between two fluid phases becomes infinitesimally bound to an attracting wall. It is shown t...
We examine the effect of long-range spatially correlated disorder on the Anderson localization transition in $d=2+\ensuremath{\epsilon}$ dimensions. This is described as a phase...
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