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Topic: Percolation

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	Soil Percolation
		The ability of soil to absorb water is known as soil percolation.
		In specifying the size and type of absorption field (drain field, leach field, seepage pits) a soil percolation test or "perc test" should be performed.
		If the water drains very slowly or remains in the hole with no drop in level by the next morning, the soil percolation is considered bad and will require soil exchange or other special design measures.
	www.drainfieldrepair.com /percolation.htm (247 words)

	Percolation theory - Wikipedia, the free encyclopedia
		In mathematics, percolation theory describes the behavior of connected clusters in a random graph.
		The applications of percolation theory to materials science and other domains is discussed in the article percolation.
		In dimension 2, the first fact ("no percolation in the critical phase") is proved for all latices, but the rest have only been proved for site percolation on the honeycomb or hexagonal lattice, and of course, universality is not proved.
	en.wikipedia.org /wiki/Percolation_theory (799 words)

	Preface of `Percolation'
		Quite apart from the fact that percolation theory has its origin in an honest applied problem, it is a source of fascinating problems of the best kind for which a mathematician can wish: problems which are easy to state with a minimum of preparation, but whose solutions are apparently difficult and require new methods.
		Percolation technology has emerged as a cornerstone of the theory of disordered physical systems, and the methods of this book are now being applied and extended in a variety of important settings.
		Chapter 11 is devoted to percolation in two dimensions, where the technique of planar duality leads to the famous exact calculation that $\pc =\half$ for bond percolation on $\zz^2$.
	www.statslab.cam.ac.uk /~grg/papers/perc/preface.html (1575 words)

	How to Run a Percolation Test
		The lawn area required for the soil treatment unit depends on the percolation rate of the soil (soil texture) and the amount of sewage discharged by the proposed or existing residence.
		Percolation rates determined for each test hole should be averaged in order to determine the design percolation rate.
		The trench bottom area required for a percolation rate in the range of 16 to 30 is 1.67 square feet per gallon of waste per day.
	www.extension.umn.edu /distribution/naturalresources/DD0583.html (2132 words)

	Percolation Models
		The name ``percolation'' derives from fluid flow through a coffee percolator, and it has been used extensively to model various aspects of flow through porous media [241, 155, 42, 154, 157, 114, 242, 243, 244, 245, 228].
		Percolation theory itself is a well developed branch in the theory of disordered systems and critical phenomena, and the reader is referred to [250, 199, 251, 215] for thorough information on the subject.
		Percolation as a geometrical model for porous media is closely related both to grain models and to network models.
	www.ica1.uni-stuttgart.de /local/WWW/papers/acp/node35.html (661 words)

	Percolation Theory
		Often in percolation studies, one is interested in the fraction of a phase (or phases) which is connected across the microstructure as a function of the total volume fraction of the phase.
		The setting of cement pastes, mortars, and concretes, illustrates the percolation of the total solids, as the individual cement particles become bonded one to another by hydration products, leading to the formation of a percolated backbone and the strength development of the material.
		Thus, if the capillary porosity in the individual ITZs remains percolated and the ITZs themselves are percolated, a convenient escape route for the ``steam'' generated during fire exposure might exist.
	www.bfrl.nist.gov /861/vcctl/software/hcss/firefiber/node3.html (664 words)

	Conservation Ecology: Detecting Critical Scales in Fragmented Landscapes
		Percolation theory is the study of connectivity in stochastically generated structures (Stauffer and Aharony 1985).
		Most applications of percolation theory in ecology (Gardner et al.1987) are based on lattice percolation, in which cells on a lattice are occupied with probability p and are left unoccupied with probability 1 - p.
		Percolation problems where connection probabilities vary across the landscape are referred to as"gradient" or "non-uniform" percolation (Milne et al.
	www.ecologyandsociety.org /vol1/iss1/art4 (5699 words)

	Technologies for water harvesting and soil moisture conservation in small watersheds for small-scale irrigation, R.K. ...
		Additionally, percolation ponds, silt detention tanks and irrigation tanks are constructed to harvest water and recharge it to the groundwater for use in agriculture (irrigation).
		Percolation Pond: The percolation pond is a multipurpose conservation structure depending on its location and size.
		In the case of percolation tanks and irrigation tanks, the capacity of the tank has to be calculated on the basis of the rainfall and catchment area of the tank.
	www.fao.org /docrep/W7314E/w7314e0q.htm (3336 words)

	8. Voronoi Tessellation & Percolation (Site not responding. Last check: 2007-10-09)
		The application of a non parametric percolation to the tessellation cells exceeding this noise level leads directly to a source list which is free of any assumptions about the source geometry.
		Figure 8.7 shows the result of the final percolation Three sources are found: the upper one contains 34.5 photons more than would be expected from the background field in the same area and is thus clearly a real detection.
		If fields of very high source densities are studied problems may arise by the tendency of the percolation algorithm to leave filamentary bridges between nearby adjacent sources leading to errors in the computation of both the position and the flux of the source.
	ledas-cxc.star.le.ac.uk /udocs/docs/swdocs/detect/html/node16.html (3205 words)

	Percolation
		The x-axis is the probability you ran at (0.3 in this case) and the y-axis is the probability of percolation (0.15 in this case).
		We continue our analysis of the character of percolating clusters by examining the fraction of squares which are in the percolating cluster.
		What it means in this case is that the structure of the percolating cluster doesn't depend on the details of the model that you use to study percolation.
	fafnir.phyast.pitt.edu /myjava/perc/percTest.html (2993 words)

	Percolation Tests (Site not responding. Last check: 2007-10-09)
		The suitability of soil for the subsurface disposal of sewage is determined by its physical characteristics and percolation rates.
		A percolation test is a measure the rate clear water seeps into the soil from a standard test hole.
		Percolation tests are then conducted and results are mailed to the applicant and filed at the Health Department until a well and/or application is received.
	www.carr.org /cchd/env/newcon/perctest.htm (268 words)

	Percolation Theory (Site not responding. Last check: 2007-10-09)
		Percolation theory considers the "connectedness" of a phase or multiple phases across a microstructure [24].
		26,27]: the commonly measured "set point" is a measure of the percolation of the solids in a hydrating cement paste system, the percolation/depercolation of the capillary porosity dominates the transport properties of these materials, and the percolation of calcium hydroxide can have a large influence on their durability [5,
		A common measure of percolation is the fraction of a phase that is part of a connected pathway across a microstructure.
	ciks.cbt.nist.gov /bentz/hermite/node5.html (218 words)

	PERCOLATION TESTING (Site not responding. Last check: 2007-10-09)
		Percolation tests are also required for repairs to existing septic systems that are malfunctioning.
		Percolation tests are required under the authority of Chapter 216 of the Harford County Code entitled "Sewage Disposal Systems, Private", Paragraph 21 which states "Percolation tests are required to determine the absorptive capacity of the soil.
		Other conditions that lead to a previous percolation test no longer being valid are: locations of the tests are questionable, previous percolation tests indicate evidence of rock or groundwater, previous tests are located to close or in an environmental feature not acceptable for septic systems, e.g.
	www.co.ha.md.us /health/ER/percsept.htm (1397 words)

	Percolation
		Given the probability p to have switched on each of the 25 x 25 sites, what are the odds that a connection is established?
		For an introduction to percolation see 'G. Grimmet, Percolation, Springer-Verlag, 1989'.
		Push the refresh button to realize a new random configuration using a new randomly choosen p.
	www.mathematik.com /Percolation/Percolation.html (65 words)

	The Fermi Paradox: An Approach Based on Percolation Theory
		I propose a model for the problem based on the assumption that long-term colonization of the galaxy proceeds via a "percolation" process similar to the percolation problem which is well studied in condensed-matter physics.
		The percolation rule is as follows: A culture may have a colonization drive, or may not.
		The irregular shape of the boundary and large voids in the percolation structure are clearly visible.
	www.sff.net /people/Geoffrey.Landis/percolation.htp (2469 words)

	Thesis: peat soils and acid sulphate soils
		Percolation requires: 1) a certain Effective Drainage Depth during the growing season(=average water levels in the adjoining tertiary canal are about 30-40 cm below field level surface) and 2) sufficient water supply by rainfall or irrigation (tidal flooding or pump irrigation).
		Research in China showed that by improving the percolation rate and lowering the groundwater table in the off-season causes padi yield increases from 2-3 ton/ha to 6-8 ton/ha.
		Percolation rates were measured by daily recording of rainfall, irrigation, water levels and evapotranspiration at selected locations.
	www.eelaart.com /thesis.htm (3034 words)

	025 Pa. Code § 73.15. Percolation tests.
		Percolation holes located within the proposed absorption area shall be used in the calculation of the arithmetic average percolation rate.
		Immediately before the percolation test, water shall be placed in the hole to a minimum depth of 6 inches over the gravel and readjusted every 30 minutes for 1 hour.
		If no anomaly is discovered, the local agency may accept the percolation test results from the remaining holes if the results are supplemented with the results of additional percolation testing conducted outside of the area in which the dry percolation holes were found.
	www.pacode.com /secure/data/025/chapter73/s73.15.html (762 words)

	Residential On-site Wastewater Treatment: Conducting a Soil Percolation Test, G02-1472-A
		The soil percolation rate indicates how quickly water moves through soil and helps evaluate the ability of the soil to absorb and treat effluent, wastewater that has received preliminary treatment in a septic tank.
		Using loamy sand soil with a percolation rate of 15 to 20 minutes per inch, install a one-foot thick soil liner in the bottom of the trench to improve soil characteristics.
		The percolation rate is used to select the most appropriate system, and to determine the proper size for the system.
	ianrpubs.unl.edu /wastemgt/g1472.htm (1778 words)

	King's American Dispensatory, 1898: Extracts And Fluid Extracts (Site not responding. Last check: 2007-10-09)
		The percolator is best constructed of glass or stoneware, but, unless otherwise directed, may be made of any suitable material not affected by the drug or menstruum.
		The 16 troy ounces of powder intended for percolation should, as soon as it is ready, be placed in the percolator, about one-fourth its bulk at a time; the surface should be smoothed after each addition, and then pressed as directed, for each drug.
		By means of Mohr's continuous displacing apparatus, as the percolated tincture falls into the receiver, the ether is driven off to pass again through the articles, and thus continues until all their strength is exhausted; the whole process of tincturing and forming an extract being thus performed at the same time.
	www.ibiblio.org /herbmed/eclectic/kings/extracta.html (4940 words)

	Rigidity Percolation (Site not responding. Last check: 2007-10-09)
		Near this percolation threshold, large fluctuations in the floppy, isostatic and overconstrained regions are found.
		This is a generalization of using the number of clusters in connectivity percolation as a free energy.
		The analogy is clear once it is seen that the connectivity percolation problem is a 1D-rigidity problem where the total number of clusters is the total number of floppy modes.
	www.pa.msu.edu /people/jacobs/rigidityperc.html (529 words)

	Amazon.com: Books: Percolation (Grundlehren der mathematischen Wissenschaften) (Site not responding. Last check: 2007-10-09)
		Percolation theory is the study of an idealized random medium in two or more dimensions.
		Percolation theory began in the 50's; its mathematics is now quite mature, but the theory has recently acquired new techniques because many of the questions initially raised by percolation theory are still unanswered.
		Percolation technology is now a cornerstone of the theory of disordered systems, and the methods of this book are now being extended into dynamical systems theory and the life sciences.
	www.amazon.com /exec/obidos/tg/detail/-/3540649026?v=glance (891 words)

	Percolation
		A procedure to study percolation is to generate a random number and then occupy a site if the random number is less than p.
		Site percolation is a simple model that is applicable to a number of physical processes including 1) electrical conductivity of a mixture of metallic and insulating materials, 2) the behavior of magnets diluted by non-magnetic materials, 3) the characterization of gels (e.g.
		Many properties of the geometric phase transition associated with percolation are similar to those of thermodynamic phase transitions.
	www.physics.udel.edu /~jim/percolation/percolation.htm (728 words)

	Directed Percolation (Site not responding. Last check: 2007-10-09)
		For example, in the percolation of coffee making, the top surface of the grounded coffee that's receiving the water is the source and the activity is to have water flow.
		Directed percolation is percolation with a special direction along which the activity can only propagate one way but not the other.
		Some examples of percolation has a straight forward extension to the directed percolation when we include the consideration of the time as the special direction.
	ccdw.org /~cjj/dp (495 words)

	Critical Percolation on Any Nonamenable Group Has No Infinite Clusters - Benjamini, Lyons, Peres, Schramm ... (Site not responding. Last check: 2007-10-09)
		We show that independent percolation on any Cayley graph of a nonamenable group has no infinite components at the critical parameter.
		This result was obtained in Benjamini, Lyons, Peres, and Schramm (1997) as a corollary of a general study of group-invariant percolation.
		39 The critical probability of bond percolation on the square l..
	citeseer.ist.psu.edu /benjamini99critical.html (629 words)

	In Depth Invasion Percolation (Site not responding. Last check: 2007-10-09)
		If one were to start the percolation on a point in a cluster, when the percolation finished all of the cluster would have reacted, but the rest of the array would be unaffected.
		How long the percolation took in that cluster depends on two parameters: the cluster's size and how connected it is. The first has the obvious effect that if there are more trees, the fire will burn for a longer time.
		The wonder in percolation comes when the probability, and thus the density, approaches.6: at this value, the likelyhood of a reactive point being adjacent to at least two others passes a threshold value, where afterwards, a phenomenon occurs called a supercluster.
	www.ucls.uchicago.edu /people/02/Beckett_Sterner/perc_exp.html (1076 words)

	GROUND WATER - Basics - Hydrologic Cycle - Percolation (Site not responding. Last check: 2007-10-09)
		Percolation is the downward movement of water through soil and rock.
		Ground water percolates through the soil much as water fills a sponge, and moves from space to space along fractures in rock, through sand and gravel, or through channels in formations such as cavernous limestone.
		The terms infiltration and percolation are often used interchangeably.
	danpatch.ecn.purdue.edu /~epados/ground/src/prcolat.htm (64 words)

	Michael Cohen: The Percolation Problem
		Many very good approximations have been done for percolation problems. They utilized more computer power than was available for this project. Below is a table of some of the best approximations of percolation thresholds for a few percolation problems, researched prior to the experiment.
		Below is a picture of a cluster that may well be percolated. This is only a 201 by 201 lattice, so the picture may not be very accurate. However, you can see that the cluster extends to the border of the image.
		Percolate - A cluster has percolated if it's size is infinite. In my simulation a cluster will be said to percolate if it touches the edge of my lattice.
	cpcug.org /user/scifair/2004/MCohen.htm (725 words)

	Finite Percolation Network (Site not responding. Last check: 2007-10-09)
		There are many possible percolation models of networks on spanning trees and other graph structures.
		The percolation network is finite since we have a number of target absorbing states, roadways, buildings, streams and other barriers which the fire spread network is directed towards.
		The Delaunay network and the initiation of its percolation tree is illustrated in Figure 2 for the 20-node network.
	www.coe.neu.edu /~emelas/finite_percolation_network.htm (231 words)

	Directed Percolation (Site not responding. Last check: 2007-10-09)
		Percolation is a simple model for connectivity in random media.
		However, in the directed case the percolation threshold is somewhat higher.
		Directed percolation is one of very few critical phenomena in 1+1 dimensions which have not been solved analytically.
	www.comphys.uni-duisburg.de /~hinrichs/dp.html (774 words)

	Graphics in the Percolation Model (Site not responding. Last check: 2007-10-09)
		One of the most important applications of percolation is mapping how liquids move into and through rocks, whether to determine the probability of a large oilfield being underground or the patterns that water creates fractures in dams.
		When mixing two substances, one non-conducting and one conducting, the percolation threshold (see More on Percolation) is the concentration at which there is sufficient conducting material for a current to pass through the solid.
		Percolation is therefore extremely useful for economizing the use of expensive materials for industry and manufacturing, and thus forms the third set of graphics in the program.
	www.ucls.uchicago.edu /people/02/Beckett_Sterner/perc_pics.html (295 words)

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