More footnotes date April 2012 See also Quantum statistical mechanics A densitymatrix is a matrix math matrix that describes a quantum system in a mixed state , a statistical ensemble of several quantum state s. In contrast, a pure state is described by a single quantum state state vector . The densitymatrix is the quantum mechanical analogue to a phase space phase space probability measure probability ... system is in a pure state. The densitymatrix is also a crucial tool in quantum decoherence theory. The densitymatrix is a representation of a linear operator called the density operator . The close ..., the terms densitymatrix and density operator are often used interchangeably. Both matrix and operator are self adjoint or Hermitian matrix Hermitian , positive semidefinite matrix positive semi definite ... by DensityMatrix and Operator Techniques journal Reviews of Modern Physics volume 29 pages 74&ndash ... is math psi 2 rangle math . This system would be in a mixed state . The densitymatrix is especially ... matrix is that there is just one densitymatrix for each mixed state, whereas there are many statistical ensembles of pure states for each mixed state. Nevertheless, the densitymatrix contains ... as the eigenvalues of the densitymatrix. In operator language, a density operator is a positive ... of a quantum system with densitymatrix math rho math is math S sum i lambda i ln , lambda ... irreversible change on the densitymatrix this is analogous to the collapse of the state ... A H t math is some Heisenberg picture operator but in this picture the densitymatrix is not time dependent ... , Moyal s equation The densitymatrix operator may also be realized in phase space . Under the Wigner ... practice, solution seeking follows different methods. Composite Systems The joint densitymatrix ... are described by their Reduced densitymatrix Reduced density matrices reduced density operator ... Reflist DEFAULTSORT DensityMatrix Category Quantum mechanics Category Functional analysis ... more details
The densitymatrix renormalization group DMRG is a numerical variational technique devised to obtain the low energy physics of quantum many body systems with high accuracy. It was invented in 1992 by Steven R. White and it is nowadays the most efficient method for 1 dimensional systems. The idea behind DMRG The main problem of quantum many body physics is the fact that the Hilbert space grows exponentially with size. For example, a spin 1 2 chain of length L has 2 sup L sup degrees of freedom. The DMRG is an iterative , variational method that reduces effective degrees of freedom to those most important for a target state. The target state is often the ground state. After a warmup cycle, the method splits the system into two blocks, which need not have equal sizes, and two sites in between. A set of representative states has been chosen for the block during the warmup. This set of left block two sites right block is known as the superblock . Now a candidate for the ground state of the superblock, which is a reduced version of the full system, may be found. It may have a rather poor accuracy, but the method is iterative and improves with the steps below ... block using a densitymatrix , whence the name. Thus, the relevant states for each block are updated ... site to a block at each step as well as by using the densitymatrix to identify the most important ... tricks are these The ground state for the superblock is obtained using the Lanczos algorithm of matrix ... strongly correlated systems. The matrix product ansatz The success of the DMRG for 1D systems is related to the fact that it is a variational method within the space of matrix product state s. These are states ... to implement real time evolution of Matrix Product States. The idea is based on the classical ..., extending the definition of the Matrix Product States. See this paper by F. Verstraete and I ... of matrix product states http arxiv.org abs 1008.3477 The Ph.D. thesis of Javier Rodr guez Laguna http ... more details
about mass density semiprotected small yes pp move indef The mass density or density of a material is defined as its mass per unit volume . The symbol most often used for density is the lower case Greek letter Rho letter rho . In some cases for instance, in the United States oil and gas industry , density ... title Density definition in Oil Gas Glossary publisher Oilgasglossary.com date accessdate 2010 ... have different densities, so density is an important concept regarding buoyancy , purity and packaging ... dense fluids. If the average density including any air below the waterline of an object is less than .... In some cases density is expressed as the dimensionless quantities specific gravity SG or relative density RD , in which case it is expressed in multiples of the density of some other standard ... floats in water. The mass density of a material varies with temperature and pressure. The variance ... on an object decreases the volume of the object and therefore increase its density. Increasing the temperature of a substance with some exceptions decreases its density by increasing the volume of that substance ... bottom to top of the fluid due to the decrease of the density of the heated fluid. This causes it to rise relative to more dense unheated material. The reciprocal of the density of a substance is called its specific volume , a representation commonly used in thermodynamics . Density is an intensive property in that increasing the amount of a substance does not increase its density rather it increases ... the Term Eureka in the Bath , Scientific American , December 2006. ref Mathematically, density is defined as mass divided by volume math rho frac m V , math where math is the density, math m is the mass, and math V is the volume. From this equation, mass density must have units of a unit of mass per ... number of units for mass density in use. The SI unit of kilogram per cubic metre math ... for density. The cubic centimeter can be alternately called a millilitre or a cc . math 1000kg m equals ... more details
wiktionary Matrix may refer to TOCright Math and science Matrix mathematics , a rectangular array of numbers, symbols or expressions Matrix biology , the material or tissue between cells in which more specialized structures are embedded Matrix chemical analysis , the non analyte components of a sample Matrix geology , the fine grained material in which larger objects are embedded Harris matrix , an archeological tool Metal matrix , material used in a metal matrix composite Matrix isolation , an experimental technique in chemistry and physics Film and television The Matrix franchise The Matrix franchise , a science fiction franchise The Matrix , the first film in the franchise The Matrix Music from the Motion Picture , a soundtrack album Matrix TV series Matrix TV series Matrix Doctor Who Matrix Doctor Who , a computer system Matrix, a ReBoot character John Matrix, a Commando film Commando character Music and audio Matrix music , an unchanging element of variations Matrix artist , a British DJ Matrix jazz group The Matrix production team M rix , an album by P.A.L. Clave matrix Keyboard matrix circuit Matrix decoder , a technology for converting audio channels Matrix or matrix master , a master disc used in the production of gramophone records Matrix , a song by Chick Corea on the album Now He Sings, Now He Sobs Comics and literature Matrix comics , a DC Comics character Matrix Doctor Who novel Matrix Doctor Who novel , by Robert Perry and Mike Tucker Matrix of Leadership , a Transformers plot element Matrix, a Neuromancer plot element Business and law MATRIX Northern Ireland Science Industry Panel Matrix Business Technologies , a telecommunications firm Matrix Chambers , a barristers set Matrix Games , an American video game publisher founded 1999 Matrix management , an organizational management style Matrix Partners , a private equity investment firm Matrix Software , a Japanese video game developer founded 1994 Growth share matrix , a business analysis technique Transportation ... more details
About the 1999 film the franchise it initiated The Matrix franchise other uses Infobox film name The Matrix image The Matrix Poster.jpg caption Theatrical release poster director ubl The Wachowskis Andy ... name boxoffice The Matrix is a 1999 American science fiction film science fiction action film written ... sequels, and the The Matrix franchise Matrix franchise was further expanded through the production ... source. Upon learning this, computer programmer Neo The Matrix Neo is drawn into a rebellion against ... detail to this summary. Computer programmer Neo The Matrix Thomas Anderson Keanu Reeves is secretly ... references to the Matrix appearing on his computer. A female hacker named Trinity The Matrix Trinity Carrie Anne Moss confirms that a man named Morpheus The Matrix Morpheus Laurence Fishburne can help him however, three sinister Agent The Matrix Agents , led by Agent Smith Hugo Weaving , arrest ... energy of humans, who are kept docile within the Matrix, a simulated reality of the world as it was in 1999. Morpheus and his crew belong to a group of free humans who unplug others from the Matrix ... within the Matrix by using their understanding of its true nature to manipulate its physical law s. Neo is warned that fatal injuries within the Matrix will also kill one s physical body, and that the Agents ... the Matrix to visit the Oracle The Matrix Oracle Gloria Foster , who predicted the emergence of the One ... escape. Their ally Cypher The Matrix Cypher Joe Pantoliano had betrayed them, making a deal for a permanent return to the comfortable life of the Matrix in exchange for giving Morpheus to the Agents. Cypher murders three crew members before he is killed by Tank The Matrix Tank Marcus Chong . The Agents ... in Zion The Matrix Zion , the humans subterranean refuge in the real world. Neo and Trinity return to the Matrix and rescue their leader in the process, Neo becomes more confident in his ability to manipulate the Matrix, ultimately dodging bullets fired at him. Morpheus and Trinity use a telephone ... more details
Well logging Density logging is a well logging tool that can provide a continuous record of a Formation geology formation s bulk density along the length of a borehole . In geology, bulk density is a function of the density of the minerals forming a rock i.e. rock matrixmatrix and the fluid enclosed in the pore spaces. This is one of three well logging tools that are commonly used to calculate porosity ... the long spaced detector. ref http www.glossary.oilfield.slb.com Display.cfm?Term compensated density 20log Schlumberger Oilfield Glossary. Compensated density Log. ref Inferring porosity from bulk density Assuming that the measured bulk density math rho text bulk math only depends on rock matrixmatrixdensity math rho text matrix math and fluid density math rho text fluid math , and that these values ... frac rho text matrix rho text bulk rho text matrix rho text fluid math Common values of matrixdensity math rho text matrix math in gram g cm are Quartz sand 2.65 Limestone 2.71 Dolomite 2.87 This method is the most reliable porosity indicator for sandstones and limestones because their density is well known. ref name Gluyas On the other hand, the density of clay mineral clay minerals such as mudstone ... distance from the emitter, is related to the formation s electron density, ref name Gluyas Gluyas ... to the formation s bulk density. The number of Compton scattering collisions is related directly to the number of the electron density of the formation. Consequently, the electron density determines the response of the density tool. Electron density is related through equation math rho dot epsilon ... way to how the sonic logging tool was improved to compensate for borehole effects, density logging ... is not as useful for determining their porosity. A fluid bulk density math rho text fluid math of 1 gram g cm is appropriate where the water is fresh but highly saline water has a slightly higher density ... density and residual saturation. In some applications hydrocarbons are indicated by the presence ... more details
tensor density when an odd number of the factors are odd tensor densities. Matrix inversion and matrix ... two tensor density of weight W with covariant indices then its matrix inverse will be a rank ... is a rank two tensor density of weight W with covariant indices then the matrix determinant math det ...General relativity In differential geometry , a tensor density or relative tensor is a generalization of the tensor concept. A tensor density transforms as a tensor when passing from one coordinate system ... and odd tensor densities. A tensor density can also be regarded as a section of the tensor product of a tensor bundle with a density bundle . Definition Unreferenced section date June 2011 Some ... tensor densities and odd tensor densities. When a tensor density weight is an integer there is an equivalence ... two authentic tensor density of weight W transforms as math mathfrak T alpha beta left det left frac ... authentic tensor density of integer weight W where math bar mathfrak T math is the rank two tensor density in the math bar x math coordinate system, math mathfrak T math is the transformed tensor density ... that a tensor density is a pseudotensor density when there is an additional sign flip under an orientation reversing coordinate transformation. A mixed rank two pseudotensor density of weight W transforms ... pseudotensor density of integer weight W where sgn is a function that returns ... when W is not an integer. Thus one can speak of, say, an odd tensor density of weight 2 or an even tensor density of weight 1 2. When W is an even integer the above formula for an authentic tensor density can be rewritten as math mathfrak T alpha beta left vert det left frac partial bar x iota partial ... partial x beta , bar mathfrak T delta epsilon ,. math even tensor density ... number. Similarly, when W is an odd integer the formula for an authentic tensor density can be rewritten ... ,. math odd tensor density of weight W This formula has the advantage of being ... more details
, File ElectronDensityFormula.PNG center Electron Density Formula Image ElectronDensityAniline.PNG 300px thumb right Electron density calculated for aniline , high density values indicate atom positions, intermediate density values emphaisize Chemical bond bonding , low values provide information on a molecule s shape and size. P is the densitymatrix . Electron densities are often be rendered ...About the quantum mechanical probability density of an electron the number density of electrons in a plasma, also called electron density Plasma physics Merge electronic density date September 2010 Electron density is the measure of the probability of an electron being present at a specific location. In molecule s, regions of electron density are usually found around the atom , and its bonds. In de ... , the electron density covers an entire region, i.e., in benzene they are found above and below ... the electron density is higher next to the single bonds. ref e.g., the white line in the diagram ... as chromophores. In Quantum chemistry quantum chemical calculations , the electron density, ... by the value of the density chosen, or in terms of a percentage of total electrons enclosed. List ... images of electron density. For example, in aniline see image at right . Graphical models, including electron density are a commonly employed tool in chemistry education. ref cite journal title Teaching Chemistry with Electron Density Models authors Alan J. Shusterman and Gwendolyn P. Shusterman ... to choose a value for the electron density, often called the IsoValue. Some software ref http ... allows for specification of the electron density in terms of percentage of total electrons enclosed ... of total electrons enclosed, the electron density surface can be used to locate atoms, emphasize ... pages 61 86 isbn 1 890661 18 X ref Graphically, the electron density surface also serves as a canvas ... of electrostatic potential mapped upon the electron density provides an indicator for charge ... more details
In mathemtics, density theorem may refer to Density conjecture for Kleinian groups Chebotarev s density theorem in algebraic number theory Jacobson density theorem in algebra Kaplansky density theorem in algebra Lebesgue s density theorem mathdab ... more details
dablink This page is about the electric current density in electromagnetism . For the probability current density in quantum mechanics, see Probability current . In physics , current density in general is a measure of the density of flow of a conserved charge physics charge , in other words flux of the charge sometimes used synonymously . As such the term current density can also be applied to other ... etc., the charge is electric charge , in which case the associated current density is the electric current ... current per cross sectional area. In SI unit s, the electric current density is measured ... Electric current density J is simply the electric current per unit area . Its magnitude can be written ... density vector J also affect the Norm mathematics magnitude math mathbf J mathbf hat t frac mathrm ... through a surface area S perpendicular to the flow, in other words the net flux of the current density vector field flowing through the surface S . Importance Current density is important to the design ... current level, and the current density then is determined by the dimensions of the conducting ... frequencies, current density can increase because the conducting region in a wire becomes confined ... Power physics power in the form of heat. The current density must be kept sufficiently low to prevent ... excessive current density may generate a strong enough magnetic field to cause spontaneous loss of the superconductive property. The analysis and observation of current density also is used ... Press year 2006 isbn 9780521845083 ref The current density is an important parameter in Amp re s circuital law one of Maxwell s equations , which relates current density to magnetic field . In special ... density, which are given by expressions such as those in this section. Electric current is a coarse ... of electric charge charge flowing is described by the current density ref The Cambridge Handbook ... density vector, v sub d sub r ,&thinsp t is the particles average drift velocity SI unit ... more details
wiktionary density wiktionary dense Density and dense usually refer to a measure of how much of some entity is within a fixed amount of space. Types of density include In physics , density of mass Density , mass per volume Area density or surface density, mass over a two dimensional area Linear density , mass over a one dimensional line Bulk density , mass of many particles of a particulate solid or a powder divided by the total volume they occupy Particle density or true density, density of the particles that make up a particulate solid or a powder Relative density or specific gravity , a measure of density in comparison to the density of something else Vapour density , a relative density used for gases Planck density , Planck mass per Planck length In physics, densities of entities other than mass Number density , number of particles per unit volume, area, or length Current density , the ratio of electric current to area Charge density , the electric charge per volume Energy density , potential energy per unit volume or mass, depending on context Force density , force per unit volume Optical density, the absorbance of an element In mathematics Dense set and nowhere dense set in topology Schnirelmann density in number theory Natural density also called asymptotic density in number theory Lebesgue s density theorem in measure theory Probability density function , a function which maps probabilities across the real line and whose integral is 1 Density estimation is the construction of an estimate of a probability density function Kernel density estimation , used in statistics to estimate a probability density function of a random variable Tensor density in differential geometry Dense graph Density in graph theory, the fraction of possible edges that exist in a graph Dense ... mathematics forcing . Density polytope in geometry Density on a manifold Dense submodule in abstract algebra In other scientific fields Population density , population per unit area Memory storage ... more details
The physiological density or real population density is the Population number of people per unit area of arable land . ref http www.valpo.edu geomet geo courses geo101 glossary.html p GEO 101 World Human Geography Glossary ref A higher physiological density suggests that the available agricultural land is being used by more and may reach its output limit sooner than a country that has a lower physiological density. See also Population density List of countries by real population density based on food growing capacity List of countries by physiological density References Reflist Population Category Demographics Category Demography ... more details
In fluid mechanics , the force density is the negative gradient of pressure. It has the physical dimensions of force physics force per unit volume . Force density is a vector field representing the flux density of the hydrostatic force within the bulk of a fluid . Force density is represented by the symbol f , and given by the following equation, where P is the pressure math mathbf f nabla P math . The net force on a differental volume element dV of the fluid is math d mathbf F mathbf f dV math Thus, the force density at a point in a fluid, divided by the density , is the acceleration of the fluid at that point. DEFAULTSORT Force Density Category Density ref http scienceworld.wolfram.com physics ForceDensity.html Force Density . Eric Weisstein s World of Physics. Accessed March 8th, 2012. ref References references Fluiddynamics stub es Densidad de fuerza ar ... more details
The maximum density of a Chemical substance substance is the highest attainable density of the substance under given conditions. Attaining maximum density Almost all known substances undergo thermal expansion in response to heating, meaning that a given mass of substance contracts to a low volume at low temperature s, when little thermal energy is present. Substances, especially fluid s in which intermolecular force s are weak, also undergo compression physical compression upon the application of pressure . Nearly all substances therefore reach a density maximum at very low temperatures and very high pressures, characteristic properties of the solid State of matter state of matter . Water see Water molecule Density of water and ice An especially notable irregular maximum density is that of water , which reaches a density peak at convert 3.98 C F . This has important ramifications in Earth s ecosystem . Fact date March 2007 Citation help is here http www.google.com search?&q Wetzel 3.98 Density of water References Unreferenced date December 2006 references Reflist See also List of elements by densityDensity Specific Gravity Specific weight Charge density Buoyancy Hydrometer Category Density Category Condensed matter physics Category Physical chemistry Category Physical quantities physical chemistry stub ... more details
The particle density or true density of a particulate solid or powder, is the density of the particles that make up the powder, in contrast to the bulk density , which measures the average density of a large volume of the powder in a specific medium usually air . The particle density is a relatively well defined quantity, as it is not dependent on the degree of compaction of the solid, whereas the bulk density has different values depending on whether it is measured in the freely settled or compacted state tap density . However, a variety of definitions of particle density are available, which differ in terms of whether pores are included in the particle volume, and whether voids are included. Measurement The measurement of particle density can be done in a number of ways Archimedes principle The powder is placed inside of known volume, and weighed. The Relative density Pycnometer Pycnometer is then filled with a fluid of known density, in which the powder is not soluble. The volume of the powder is determined by the difference between the volume as shown by the pycnometer, and the volume ... volume, is to suspend a known mass of particles in molten wax of known density, allow any bubbles .... A slurry of the powder in a liquid of known density can also be used with a hydrometer to measure particle density by buoyancy . Another method based on buoyancy is to measure the weight of the sample in air, and also in a liquid of known density. A column of liquid with a density gradient can ... density at the bottom is higher than that of the solid, and the minimum density is lower. If a small ... the liquid density is equal to the particle density. Volumetric measurement A gas pycnometer can ... characterization of the sample s porosity. See also Bulk density Porosity Number density External links http www.particletesting.com docs density determinations.pdf An excellent overview of particle density and porosity measurements, with references Category Density Category Particulates de Reindichte ... more details
Probability density may refer to Probability density function in probability theory The product of the probability amplitude with its complex conjugate in quantum mechanics According to quantum mechanics, these two are the same thing. disambig cs Hustota pravd podobnosti ... more details
for power per unit area surface power density Power density or volume power density or volume specific power is the amount of Power physics power time rate of energy transfer per unit volume. In energy transformation energy transformers like batteries, fuel cell s, motors, etc. but also power supply units or similar, power density refers to a volume. It is then also called volume power density which is expressed as W m sup 3 sup . Volume power density is sometimes an important consideration where space is constrained. In reciprocated internal combustion engines, power density power per swept volume is an important metric. See also Energy density energy per unit volume Power to weight ratio Specific energy energy per unit mass Specific absorption rate SAR References Reflist Category Thermodynamics Category Power physics de Leistungsdichte it Potenza specifica ja ru engineering stub ... more details
Bulk density is a property of powder substance powder s, granular material granules and other divided solid s, especially used in reference to mineral components soil , gravel , chemical substance s, pharmaceutical ingredient s, foodstuff or any other masses of corpuscular or particulate matter . It is defined as the mass of many particle s of the material divided by the total volume they occupy. The total ... year 1960 edition 6th ref Bulk density is not an intrinsic property of a material it can change depending ... bulk density if the cylinder is disturbed, the powder particles will move and usually settle closer together, resulting in a higher bulk density. For this reason, the bulk density of powders is usually reported both as freely settled or poured density and tapped density where the tapped density refers to the bulk density of the powder after a specified compaction process, usually involving vibration of the container. Soil The bulk density of soil depends greatly on the mineral make up of soil and the degree of Soil compaction compaction . The density of quartz is around 2.65g cm but the bulk density of a mineral soil is normally about half that density, between 1.0 and 1.6g cm . Soils high in organics and some friable clay may have a bulk density well below 1g cm Bulk density of soil ... depth and horizon. The samples are then oven dried and weighed. Bulk density mass of soil volume as a whole math rho frac M s V t math The bulk density of soil is Inverse relationship inversely ... density. Bulk density of a region in the interior of the earth is also related to the seismic ... . The higher the density, the faster the velocity. See also Brazil nut effect Characterisation of pore space in soil Effective porosity Particle density Porosity Notes reflist External links http ... How to measure dry bulk density http www.powtec.de download smg engl.pdf Determination of bulk density Category Density Category Particulates Category Soil physics ca Densitat aparent de Rohdichte ... more details
The term nutrient density has several meanings. Most commonly, nutrient density is defined as a ratio of nutrient content in grams to the total energy content in kilocalorie s or joule s . Nutrient dense food is opposite to energy dense food also called empty calorie food . According to the Dietary Guidelines for Americans 2005, nutrient dense foods are those foods that provide substantial amounts of vitamins and minerals and relatively few calories. Fruits and vegetables are the nutrient dense foods, while products containing added sugar s, processed cereals , and alcohol are not. ref http www.sciencedirect.com science article B758G 4HP5YFV D 2 c86659719922a2736490366333062119 A Nutrient Density Standard for Vegetables and Fruits Nutrients per Calorie and Nutrients per Unit Cost ref ref http www.drfuhrman.com library article17.aspx Nutrient Density by Joel Fuhrman M.D. ref ref http www.clemson.edu extension hgic food nutrition nutrition dietary guide hgic4062.html Clemson University Cooperative Extension Service Nutrient Density ref Second, nutrient density is defined as a ratio of food energy from carbohydrate , protein or fat to the total food energy. To calculate nutrient density in percent , divide the food energy in calories or joules from one particular nutrient by the total food energy in the given food. Third, nutrient density is understood as the ratio of the nutrient composition of a given food to the nutrient requirements of the human body. Therefore, a nutrient dense food is the food that delivers a complete nutritional package. See also Aggregate Nutrient Density Index ANDI References reflist Category Nutrition ... more details
cleanup date August 2008 In computational linguistics , lexical density constitutes the estimated measure of content per functional grammatical and lexical units lexeme s in total. It is used in discourse analysis as a descriptive parameter which varies with register and genre. Spoken texts tend to have a lower lexical density than written ones, for example. Lexical density may be determined thus math Ld Nlex N x 100 math Where Ld the analysed text s lexical density NLex the number of lexical word tokens nouns, adjectives, verbs, adverbs in the analysed text N the number of all tokens total number of words in the analysed text small Please note that the variable symbols applied herein are by no means conventional, they are simply random chosen designations that serve to illustrate the example in question. small See also Content analysis Further reading Ure, J 1971 . Lexical density and register differentiation. In G. Perren and J.L.M. Trim eds , Applications of Linguistics , London Cambridge University Press. 443 452. External links http www.usingenglish.com showdef.php?p lexical density test.html Lexical Density Test definition NOTE This page gives an incorrect formula and confuses lexical density with type token ratio. http textalyser.net Lexical density Textalyser Category Computational linguistics Category Applied linguistics Category Formal sciences ling stub de Lexikalische Dichte ... more details
For computer memory comparisons, see computer storage density . For other meanings, see Density disambiguation The area density also known as areal density , surface density , or superficial density of a two dimensional object is calculated as the mass per unit area . The SI derived unit is kilogram per square metre kg m sup 2 sup . It can be calculated as math rho A frac m A math or math rho A rho cdot l math where math sub A sub average area density math m total mass of the object math A total area of the object math average density math l average thickness of the object A special type of area density is called columnar density it is obtained integrating density volumetric density math rho math over a vertical column ref Cite book last1 Visconti first1 Guido title Fundamentals of physics and chemistry of the atmosphere date 2001 publisher Springer location Berlin isbn 978 3 540 67420 7 pages 470 ref math rho A int rho dz, math where math z math denotes the vertical coordinate e.g., height or depth . An example is the Dobson unit for atmospheric ozone. Columnar density math rho A math is closely related to the vertically averaged volumetric density math bar rho math as math bar rho rho A Delta z, math where math Delta z int 1 dz math notice that math bar rho math , math rho A math , and math Delta z math have units of, e.g., grams per cubic metre, grams per square metre, and metres, respectively. Usage The area density is often used to describe the thickness of paper, e.g. 80 g m sup 2 sup is very common. It is also an important quantity for the Absorption electromagnetic radiation absorption of radiation . When studying bodies falling through air, area density is important because resistance depends on area, and gravitational force is dependent on mass. Bone density ... of area density. Citation needed date April 2011 See talk page References references DEFAULTSORT Area Density Category Density Category Classical mechanics Classicalmechanics stub ar de ... more details
Orphan date February 2009 The orthobaric density of a compound is the density of the coexisting phase matter phases liquid , gas , or solid at a given temperature. Liquid Gas Equilibrium For any temperature below the critical point thermodynamics critical point , the density of the gas will be less than that of the liquid, at the critical point the density of the liquid and gas phases are identical and the compound becomes a supercritical fluid . ref McQuarrie, Donald A. and Siman, John D., Physical Chemistry A Molecular Approach . Sausalito University Science Books, 1997. ref References reflist Category Density physics stub ... more details
Urban density is a term used in urban planning and urban design to refer to the number of people inhabiting ... density . Urban density is considered an important factor in understanding how cities function. Research related to urban density occurs across diverse areas, including economics, health, innovation, psychology and geography as well as sustainability . Urban density and sustainability File Revised petrol use urban density.JPG thumb A graph showing the relationship between urban density and petrol use. It is commonly asserted that higher density cities are more sustainable than low density cities ... growth . However, the link between urban density and aspects of sustainability remains a contested ... experts on sustainable urbanism , including prominent urban designer Jan Gehl , argue that low density ... the total energy consumption of a city and its overall urban density, i.e. the lower the density ... 1559636602 ref Measuring urban density Urban density is a very specific measurement of the population ..., agriculture and water bodies. There are a variety of other ways of measuring the density of urban areas ... on Residential density the number of dwelling units in any given area Population density the number of people in any given area employment density the number of jobs in any given area Gross density any density figure for a given area of land that includes uses not necessarily directly relevant to the figure usually roads and other transport infrastructure Net density a density figure for a given area of land that excludes land not directly related to the figure. Weighted density a density metric which measures the density at which the average citizen lives. It is determined by calculating the standard density of each census tract, assigning each a weight equal to its share of the total population, and then adding the segments. See also List of cities proper by population density Transportation ... conc8en urbanenergy.html Urban Density and Energy Consumption http www.planetizen.com node 23176 Deriving ... more details
Unreferenced date December 2009 For other meanings of densityDensity disambiguation Linear density , linear mass density or linear mass is a measure of mass per unit of length , and it is a characteristic of strings or other one dimensional objects. The SI unit of linear density is the kilogram per metre kg m . The linear density, math sometimes denoted by math , of an object is defined as math mu frac partial m partial x math where math m is the mass, and math x is a coordinate along the one dimensional object. For the common case of a homogeneous substance of length math L and total mass math m , this simplifies to math mu frac m L math In drawing or printing, the term linear density also refers to how densely or heavily a line is drawn. Units See also Units of textile measurement Common units include kilogram per meter ounce mass per foot ounce mass per inch pound mass per yard used in the North American railway industry for the linear density of Rail tracks rail s pound mass per foot pound mass per inch Units of textile measurement Denier denier , a unit of measure for the linear density of fiber s, defined as the mass in grams per 9,000 meters. Units of textile measurement Tex decitex dtex , the International System of Units SI unit for the linear density of fiber s, defined as the mass in grams per 10,000 meters DEFAULTSORT Linear Density Category Density physics stub ar eo Lineara denseco fr Masse lin ique ko it Densit lineare nl Lineaire dichtheid fi Lineaarinen tiheys zh ... more details
zeta function which has a pole of order 1 at 0, so the set of all primes has Dirichlet density 1. More generally, one can define the Dirichlet density of a sequence of primes or prime powers , possibly with repetitions, in the same way. Properties If a subset of primes A has a natural density, given ... a Dirichlet density, and the two densities are the same. However it is usually easier to show that a set of primes has a Dirichlet density, and this is good enough for many purposes. For example, in proving Dirichlet s theorem on arithmetic progressions , it is easy to show that the Dirichlet density of primes in an arithmetic progression a nb for a , b coprime has Dirichlet density ... that this is the natural density. Roughly speaking, proving that some set of primes has a non zero Dirichlet density usually involves showing that certain L function L functions do not vanish at the point s 1, while showing that they have a natural density involves showing that the L functions have ... density, then it also has a natural density, but it is possible to find artificial counterexamples for example, the set of primes whose first decimal digit is 1 has no natural density, but has Dirichlet density log 2 log 10 . ref This is attributed by J. P. Serre to a private communication from ... more details
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