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Percolation
Percolation (from Latin ''percolare'', "to filter" or "trickle through"), in physics, chemistry and materials science, refers to the movement and filtering of fluids through porous materials. It is described by Darcy's 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. 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Percolation Threshold
The percolation threshold is a mathematical concept in percolation theory that describes the formation of long-range connectivity in Randomness, random systems. Below the threshold a giant connected component (graph theory), connected component does not exist; while above it, there exists a giant component of the order of system size. In engineering and coffee making, percolation represents the flow of fluids through porous media, but in the mathematics and physics worlds it generally refers to simplified Lattice model (physics), lattice models of random systems or networks (Graph (discrete mathematics), graphs), and the nature of the connectivity in them. The percolation threshold is the critical value of the occupation probability ''p'', or more generally a critical surface for a group of parameters ''p''1, ''p''2, ..., such that infinite connectivity (''percolation'') first occurs. Percolation models The most common percolation model is to take a regular lattice, like a squar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Percolation Theory
In statistical physics and mathematics, percolation theory describes the behavior of a network when nodes or links are added. This is a geometric type of phase transition, since at a critical fraction of addition the network of small, disconnected clusters merge into significantly larger connected, so-called spanning clusters. The applications of percolation theory to materials science and in many other disciplines are discussed here and in the articles network theory and percolation. Introduction A representative question (and the source of the name) is as follows. Assume that some liquid is poured on top of some porous material. Will the liquid be able to make its way from hole to hole and reach the bottom? This physical question is modelled mathematically as a three-dimensional network of vertices, usually called "sites", in which the edge or "bonds" between each two neighbors may be open (allowing the liquid through) with probability , or closed with probability , and th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Percolation
Percolation (from Latin ''percolare'', "to filter" or "trickle through"), in physics, chemistry and materials science, refers to the movement and filtering of fluids through porous materials. It is described by Darcy's 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. 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fractal
In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illustrated in successive magnifications of the Mandelbrot set. This exhibition of similar patterns at increasingly smaller scales is called self-similarity, also known as expanding symmetry or unfolding symmetry; if this replication is exactly the same at every scale, as in the Menger sponge, the shape is called affine self-similar. Fractal geometry lies within the mathematical branch of measure theory. One way that fractals are different from finite geometric figures is how they scale. Doubling the edge lengths of a filled polygon multiplies its area by four, which is two (the ratio of the new to the old side length) raised to the power of two (the conventional dimension of the filled polygon). Likewise, if the radius of a filled sphere i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infiltration Basin
An infiltration basin (or recharge basin) is a form of engineered sump or percolation pond that is used to manage stormwater runoff, prevent flooding and downstream erosion, and improve water quality in an adjacent river, stream, lake or bay. It is essentially a shallow artificial pond that is designed to infiltrate stormwater through permeable soils into the groundwater aquifer. Infiltration basins do not release water except by infiltration, evaporation or emergency overflow during flood conditions. It is distinguished from a detention basin, sometimes called a dry pond, which is designed to discharge to a downstream water body (although it may incidentally infiltrate some of its volume to groundwater); and from a retention basin, which is designed to include a permanent pool of water. Design considerations Infiltration basins must be carefully designed to infiltrate the soil on a given site at a rate that will not cause flooding. They may be less effective in areas with: * H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Universality (dynamical Systems)
In statistical mechanics, universality is the observation that there are properties for a large class of systems that are independent of the dynamical details of the system. Systems display universality in a scaling limit, when a large number of interacting parts come together. The modern meaning of the term was introduced by Leo Kadanoff in the 1960s, but a simpler version of the concept was already implicit in the van der Waals equation and in the earlier Landau theory of phase transitions, which did not incorporate scaling correctly. The term is slowly gaining a broader usage in several fields of mathematics, including combinatorics and probability theory, whenever the quantitative features of a structure (such as asymptotic behaviour) can be deduced from a few global parameters appearing in the definition, without requiring knowledge of the details of the system. The renormalization group provides an intuitively appealing, albeit mathematically non-rigorous, explanation of un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phase Transition
In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of matter: solid, liquid, and gas, and in rare cases, plasma. A phase of a thermodynamic system and the states of matter have uniform physical properties. During a phase transition of a given medium, certain properties of the medium change as a result of the change of external conditions, such as temperature or pressure. This can be a discontinuous change; for example, a liquid may become gas upon heating to its boiling point, resulting in an abrupt change in volume. The identification of the external conditions at which a transformation occurs defines the phase transition point. Types of phase transition At the phase transition point for a substance, for instance the boiling point, the two phases involved - liquid and vapor, have identic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Percolation Test
A percolation test (colloquially called a perc test) is a test to determine the water absorption rate of soil (that is, its capacity for percolation) in preparation for the building of a septic drain field (leach field) or infiltration basin. The results of a percolation test are required to properly design a septic system. In its broadest terms, percolation testing is simply observing how quickly a known volume of water dissipates into the subsoil of a drilled hole of known surface area. While every jurisdiction will have its own laws regarding the exact calculations for the length of line, depth of pit, etc., the testing procedures are the same. In general, sandy soil will absorb more water than soil with a high concentration of clay or where the water table is close to the surface. Testing method A percolation test consists of digging one or more holes in the soil of the proposed leach field to a specified depth, presoaking the holes by maintaining a high water level in the h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Network
In the context of network theory, a complex network is a graph (network) with non-trivial topological features—features that do not occur in simple networks such as lattices or random graphs but often occur in networks representing real systems. The study of complex networks is a young and active area of scientific research (since 2000) inspired largely by empirical findings of real-world networks such as computer networks, biological networks, technological networks, brain networks, climate networks and social networks. Definition Most social, biological, and technological networks display substantial non-trivial topological features, with patterns of connection between their elements that are neither purely regular nor purely random. Such features include a heavy tail in the degree distribution, a high clustering coefficient, assortativity or disassortativity among vertices, community structure, and hierarchical structure. In the case of directed networks these feat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Percolation Test
A percolation test (colloquially called a perc test) is a test to determine the water absorption rate of soil (that is, its capacity for percolation) in preparation for the building of a septic drain field (leach field) or infiltration basin. The results of a percolation test are required to properly design a septic system. In its broadest terms, percolation testing is simply observing how quickly a known volume of water dissipates into the subsoil of a drilled hole of known surface area. While every jurisdiction will have its own laws regarding the exact calculations for the length of line, depth of pit, etc., the testing procedures are the same. In general, sandy soil will absorb more water than soil with a high concentration of clay or where the water table is close to the surface. Testing method A percolation test consists of digging one or more holes in the soil of the proposed leach field to a specified depth, presoaking the holes by maintaining a high water level in the h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mark Newman
Mark Newman is an English-American physicist and Anatol Rapoport Distinguished University Professor of Physics at the University of Michigan, as well as an external faculty member of the Santa Fe Institute. He is known for his fundamental contributions to the fields of complex networks and complex systems, for which he was awarded the 2014 Lagrange Prize. Career Mark Newman grew up in Bristol, England, where he was a pupil at Bristol Cathedral School, and earned both an undergraduate degree and a PhD in physics from the University of Oxford, before moving to the United States to conduct research first at Cornell University and later at the Santa Fe Institute, a private research institute in northern New Mexico devoted to the study of complex systems. In 2002 Newman moved to the University of Michigan, where he is currently the Anatol Rapoport Distinguished University Professor of Physics and a professor in the university's Center for the Study of Complex Systems. Research ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Septic Drain Field
Septic drain fields, also called leach fields or leach drains, are subsurface wastewater disposal facilities used to remove contaminants and impurities from the liquid that emerges after anaerobic digestion in a septic tank. Organic materials in the liquid are catabolized by a microbial ecosystem. A septic drain field, a septic tank, and associated piping compose a septic system. The drain field typically consists of an arrangement of trenches containing perforated pipes and porous material (often gravel) covered by a layer of soil to prevent animals (and surface runoff) from reaching the wastewater distributed within those trenches. Primary design considerations are both ''hydraulic'' for the volume of wastewater requiring disposal and ''catabolic'' for the long-term biochemical oxygen demand of that wastewater. The land area that is set aside for the septic drain field may be called a septic reserve area (SRA). Sewage farms similarly dispose of wastewater through a series of d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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