# ⓘ Percolation

## ⓘ Percolation

In physics, chemistry and materials science, percolation refers to the movement and filtering of fluids through porous materials. It is described by Darcys law. Broader applications have since been developed that cover connectivity of many systems modeled as lattices or graphs, analogous to connectivity of lattice components in the filtration problem that modulates capacity for percolation.

## 1. Background

During the last decades, percolation theory, the mathematical study of percolation, has brought new understanding 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 determine whether the intended structure is likely to succeed or fail.

Percolation typically exhibits universality. Statistical physics concepts such as scaling theory, renormalization, phase transition, critical phenomena and fractals are used to characterize percolation properties. Percolation is the downward movement of water through pores and other spaces in the soil due to gravity. Combinatorics is commonly employed to study percolation thresholds.

Due to the complexity involved in obtaining exact results from analytical models of percolation, computer simulations are typically used. The current fastest algorithm for percolation was published in 2000 by Mark Newman and Robert Ziff.

## 2. Examples

• Dental percolation, increase rate of decay under crowns because of a conducive environment for strep mutants and lactobacillus
• Surface roughening.
• Collapse and robustness of biological virus shells to random subunit removal experimentally verified fragmentation and disassembly of viruses.
• Transport in porous media.
• Potential sites for septic systems are tested by the "perk test". Example/theory: A hole usually 6–10 inches in diameter is dug in the ground surface usually 12–24" deep. Water is filled in to the hole, and the time is measured for a drop of one inch in the water surface. If the water surface quickly drops, as usually seen in poorly-graded sands, then it is a potentially good place for a septic "leach field". If the hydraulic conductivity of the site is low usually in clayey and loamy soils, then the site is undesirable.
• Robustness of networks to random and targeted attacks.
• Cracking of trees with the presence of two conditions, sunlight and under the influence of pressure.
• Movement of weathered material down on a slope under the earths surface.
• Coffee percolation, where the solvent is water, the permeable substance is the coffee grounds, and the soluble constituents are the chemical compounds that give coffee its color, taste, and aroma.

• Geneva in 2003. Smirnov has worked on percolation theory, where he proved Cardy s formula for critical site percolation on the triangular lattice, and deduced
• liquid. Although this method of extraction differs from infusion and percolation the resultant liquids can sometimes be similar in their effects, or
• Erdos Renyi process is in fact unweighted link percolation on the complete graph. One refers to percolation in which nodes and or links are removed with
• elements in a network and its relation to percolation theory was introduced by Majdandzic. In percolation it is usually assumed that nodes or links
• dimension is 2d for the Ising model, or for directed percolation but 1d for undirected percolation and above the upper critical dimension the critical
• Morris he studied bootstrap percolation with Oliver Riordan he proved that the critical probability in random Voronoi percolation in the plane is 1 2 and
• material is oxidized. The percolation rate after resting may approach, but is unlikely to match, the original clean water percolation rate of the site. Septic
• iron droplets. The percolation hypothesis assumes that crystals in the mantle have no preferred orientation. Likewise, percolation requires the dihedral
• decoction - a method of extraction involving boiling the plant material - and percolation in which water is passed through the material as in a coffeemaker
• to the percolation paths depend on the percolation levels assigned to the source nodes, based on the premise that the higher the percolation level of
• surface to site percolation and each cell is mapped to a site on the underlying graph or lattice that represents the system. Using percolation theory, one

#### Users also searched:

smirnov mathematician,

...
 ...
...