Percolation from Latin percolare, "to filter" or "trickle through", in physics, chemistry in addition to materials science, planned to a movement & filtering of fluids through porous materials. It is referenced by Darcy's law. Broader applications defecate since been developed that advance connectivity of many systems modeled as lattices or graphs, analogous to connectivity of lattice components in a filtration problem that modulates capacity for percolation.
During the last decades, percolation theory, the mathematical study of percolation, has brought new apprehension and techniques to a broad range of topics in physics, materials science, complex networks, epidemiology, and other fields. For example, in geology, percolation refers to filtration of water through soil and permeable rocks. The water flows to recharge the groundwater in the water table and aquifers. In places where infiltration basins or septic drain fields are planned to dispose of substantial amounts of water, a percolation test is needed beforehand to build whether the intended cut is likely to succeed or fail. In two dimensional square lattice percolation is defined as follows. A site is "occupied" with probability p or "empty" in which effect its edges are removed with probability 1 – p; the corresponding problem is called site percolation, see Fig. 2.
Percolation typically exhibits universality. Statistical physics picture such as scaling theory, renormalization, phase transition, critical phenomena and fractals are used to characterize percolation properties.
Due to the complexity involved in obtaining exact results from analytical models of percolation, data processor simulations are typically used. The current fastest algorithm for percolation was published in 2000 by Mark Newman and Robert Ziff.