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moment | A Wisdom Archive on moment |  | moment A selection of articles related to moment |  |
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| ARTICLES RELATED TO moment | | |  |  |  | moment: Encyclopedia II - White noise - Mathematical definition
White noise - White random vector.
A random vector is a white random vector if and only if its mean vector and autocorrelation matrix are the following:
I.e., it is a zero mean random vector, and its autocorrelation matrix is a multiple of the identity matrix. When the autocorrelation matrix is a multiple of the identity, we say that it has spherical correlation.
See also:White noise, White noise - Statistical properties, White noise - Colors of noise, White noise - Applications, White noise - Mathematical definition, White noise - White random vector, White noise - White random process white noise, White noise - Random vector transformations, White noise - Simulating a random vector, White noise - Whitening a random vector, White noise - Random signal transformations, White noise - Simulating a continuous-time random signal, White noise - Whitening a continuous-time random signal, White noise - External link Read more here: » White noise: Encyclopedia II - White noise - Mathematical definition |
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|  |  |  | moment: Encyclopedia II - Dam - Other considerationsThe best place for building a dam is a narrow part of a deep river valley; the valley sides can then act as natural walls. The primary function of the dam's structure is to fill the gap in the natural reservoir line left by the stream channel. The sites are usually those where the gap becomes a minimum for the required storage capacity. The most economical arrangement is often a composite structure such as a masonry dam flanked by earth embankments. The current use of t ...
See also:Dam, Dam - Types of dams, Dam - Diversionary dams, Dam - Timber dams, Dam - Embankment dams, Dam - Masonry dams, Dam - Cofferdams, Dam - Spillways, Dam - Other considerations, Dam - Environmental impacts, Dam - Stream flow, Dam - Barrier to migration, Dam - Water quality impacts, Dam - Examples of dams, Dam - Failed dams Read more here: » Dam: Encyclopedia II - Dam - Other considerations |
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| | | |  |  |  | moment: Encyclopedia II - Fluid statics - BuoyancyA solid body immersed in a fluid will have an upward buoyant force acting on it equal to the weight of displaced fluid. This is due to the hydrostatic pressure in the fluid.
In the case of a container ship, for instance, its weight force is balanced by a buoyant force from the displaced water, allowing it to float. If more cargo is loaded onto the ship, it would sit lower in the water - displacing more water and thus receive a higher buoyant force to balance the increased weight force.
Discovery of the principle of buoyancy is attributed to Archimedes.
< ...
See also:Fluid statics, Fluid statics - Static pressure in fluids, Fluid statics - Hydrostatic pressure, Fluid statics - Atmospheric pressure, Fluid statics - Buoyancy, Fluid statics - Stability, Fluid statics - Liquids-fluids with free surfaces, Fluid statics - Surface tension effects Read more here: » Fluid statics: Encyclopedia II - Fluid statics - Buoyancy |
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|  |  |  | moment: Encyclopedia II - Dam - SpillwaysA spillway is a section of a dam designed to pass water from the upstream side of a dam to the downstream side. Many spillways have floodgates designed to control the flow through the spillway.
A service spillway or primary spillway passes normal flow. An auxiliary spillway releases flow in excess of the capacity of the service spillway. An emergency spillway is designed for extreme conditions, such as a serious malfunction of the service spillway. A fuse-plug spillway is a low embankment designed to be overtopped and washed aw ...
See also:Dam, Dam - Types of dams, Dam - Diversionary dams, Dam - Timber dams, Dam - Embankment dams, Dam - Masonry dams, Dam - Cofferdams, Dam - Spillways, Dam - Other considerations, Dam - Environmental impacts, Dam - Stream flow, Dam - Barrier to migration, Dam - Water quality impacts, Dam - Examples of dams, Dam - Failed dams Read more here: » Dam: Encyclopedia II - Dam - Spillways |
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|  |  |  | moment: Encyclopedia II - Leonhard Euler - DiscoveriesEuler, with Daniel Bernoulli, established the law that the torque on a thin elastic beam is proportional to a measure of the elasticity of the material and the second moment of area of a cross section, about an axis through the center of mass and perpendicular to the plane of the moment, see Euler-Bernoulli beam equation.
He also deduced the Euler equations, a set of laws of motion in fluid dynamics, directly from Newton's laws of motion. These equations are formally identical to the Navier-Stokes equations with zero viscosity. They are interesting ch ...
See also:Leonhard Euler, Leonhard Euler - Biography, Leonhard Euler - Discoveries, Leonhard Euler - Honours, Leonhard Euler - Quotes Read more here: » Leonhard Euler: Encyclopedia II - Leonhard Euler - Discoveries |
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|  |  |  | moment: Encyclopedia II - Dam - Environmental impacts(Source: Canadian Geographic)
More than half of the world’s large rivers have been dammed, regulating and flooding approximately 400,000 square kilometres of land worldwide. These diversions have an effect on diverse ecosystems and habitats around the globe, replacing them with uniform structures and reservoirs and ultimately changing the way otherwise balanced, stable ecosystems function. See also:Dam, Dam - Types of dams, Dam - Diversionary dams, Dam - Timber dams, Dam - Embankment dams, Dam - Masonry dams, Dam - Cofferdams, Dam - Spillways, Dam - Other considerations, Dam - Environmental impacts, Dam - Stream flow, Dam - Barrier to migration, Dam - Water quality impacts, Dam - Examples of dams, Dam - Failed dams Read more here: » Dam: Encyclopedia II - Dam - Environmental impacts |
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|  |  |  | moment: Encyclopedia II - Dipole - Field from a magnetic dipole
Dipole - Magnitude.
The strength, B, of a dipole magnetic field is given by:
where:
B is the strength of the field, measured in teslas
r is the distance from the center, measured in metres
λ is the magnetic latitude (90°-θ) where θ = magnetic colatitude, measured in radians or degrees from the dipole axis (magnetic colatitude is 0 along the dipole's axis and 90° in the plane perpendicular to its axis) ...
See also:Dipole, Dipole - Alignment of a dipole to an applied field, Dipole - Physical dipoles point dipoles and approximate dipoles, Dipole - Molecular dipoles, Dipole - Field from a magnetic dipole, Dipole - Magnitude, Dipole - Vector form, Dipole - Magnetic vector potential, Dipole - Field from an electric dipole, Dipole - Electrostatic potential, Dipole - Dipole radiation Read more here: » Dipole: Encyclopedia II - Dipole - Field from a magnetic dipole |
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|  |  |  | moment: Encyclopedia II - Dipole - Molecular dipolesMany molecules have such dipole moments due to non-uniform distributions of positive and negative charges on the various atoms. For example:
(positive) H-Cl (negative)
A molecule with a permanent dipole moment is called a polar molecule and is polarized. The physical chemist Peter J. W. Debye was the first scientist to study molecular dipoles extensively, and dipole moments are consequently measur ...
See also:Dipole, Dipole - Alignment of a dipole to an applied field, Dipole - Physical dipoles point dipoles and approximate dipoles, Dipole - Molecular dipoles, Dipole - Field from a magnetic dipole, Dipole - Magnitude, Dipole - Vector form, Dipole - Magnetic vector potential, Dipole - Field from an electric dipole, Dipole - Electrostatic potential, Dipole - Dipole radiation Read more here: » Dipole: Encyclopedia II - Dipole - Molecular dipoles |
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|  |  |  | moment: Encyclopedia II - Dipole - Field from an electric dipoleThe electric field of an electric point dipole is
where
E is the field
r, r, are as above
p is the (vector) dipole moment
ε0 is the permittivity of free space.
Notice that this is formally identical to the magnetic field of a point magnetic dipole; only a few names have changed.
Dipole - Electrostatic potential.
The electrostatic ...
See also:Dipole, Dipole - Alignment of a dipole to an applied field, Dipole - Physical dipoles point dipoles and approximate dipoles, Dipole - Molecular dipoles, Dipole - Field from a magnetic dipole, Dipole - Magnitude, Dipole - Vector form, Dipole - Magnetic vector potential, Dipole - Field from an electric dipole, Dipole - Electrostatic potential, Dipole - Dipole radiation Read more here: » Dipole: Encyclopedia II - Dipole - Field from an electric dipole |
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|  |  |  | moment: Encyclopedia II - Dipole - Dipole radiationIn addition to dipoles in electrostatics, it is also common to consider an electric or magnetic dipole that is oscillating in time.
In particular, a harmonically oscillating electric dipole is described by a dipole moment of the form where ω is the angular frequency. In vacuum, this produces fields:
Far away (for ), the fields approach the limiting form of a radiating spherical wave:
which produces a total time-average radiated po ...
See also:Dipole, Dipole - Alignment of a dipole to an applied field, Dipole - Physical dipoles point dipoles and approximate dipoles, Dipole - Molecular dipoles, Dipole - Field from a magnetic dipole, Dipole - Magnitude, Dipole - Vector form, Dipole - Magnetic vector potential, Dipole - Field from an electric dipole, Dipole - Electrostatic potential, Dipole - Dipole radiation Read more here: » Dipole: Encyclopedia II - Dipole - Dipole radiation |
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|  |  |  | moment: Encyclopedia II - Dam - Examples of dams
Dam - Failed dams.
South Fork Dam - 1889
St. Francis Dam - 1928
Malpasset - 1959
Vajont Dam - 1961
Baldwin Hills Dam - 1963
Buffalo Creek Flood - 1972
Banqiao and Shimantan Dams - 1975
Teton Dam - 1976
Kelly Barnes Dam - 1977
Lawn Lake Dam - 1982
Opuha Dam - 1997
Camará Dam - 2004
Shakidor Dam - 2005
Taum Sauk reservoir - 2005
Big Bay Dam, Mississippi, USA - 2004
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See also:Dam, Dam - Types of dams, Dam - Diversionary dams, Dam - Timber dams, Dam - Embankment dams, Dam - Masonry dams, Dam - Cofferdams, Dam - Spillways, Dam - Other considerations, Dam - Environmental impacts, Dam - Stream flow, Dam - Barrier to migration, Dam - Water quality impacts, Dam - Examples of dams, Dam - Failed dams Read more here: » Dam: Encyclopedia II - Dam - Examples of dams |
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|  |  |  | moment: Encyclopedia II - Fluid statics - Liquids-fluids with free surfacesLiquids can have free surfaces at which they interface with gases, or with a vacuum. In general, the lack of the ability to sustain a shear stress entails that free surfaces rapidly adjust towards an equilibrium. However, on small length scales, there is an important balancing force from surface tension.
Fluid statics - Surface tension effects.
When liquids are constrained in vessels whose dimensions are small, compared to the relevant length scales, surface tension effects become important leadi ...
See also:Fluid statics, Fluid statics - Static pressure in fluids, Fluid statics - Hydrostatic pressure, Fluid statics - Atmospheric pressure, Fluid statics - Buoyancy, Fluid statics - Stability, Fluid statics - Liquids-fluids with free surfaces, Fluid statics - Surface tension effects Read more here: » Fluid statics: Encyclopedia II - Fluid statics - Liquids-fluids with free surfaces |
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|  |  |  | moment: Encyclopedia II - Earthquake - CausesMost earthquakes are powered by the release of the elastic strain that accumulate over time, typically, at the boundaries of the plates that make up the Earth's lithosphere via a process called Elastic-rebound theory. The Earth is made up of tectonic plates driven by the heat in the Earth's mantle and core. Where these plates meet stress accumulates. Eventually when enough stress accumulates, the plates move, causing an earthquake. Deep focus earthquakes, at depths of 100's km, are possibly generated as subducted lithospheric material catast ...
See also:Earthquake, Earthquake - Characteristics, Earthquake - Earthquake Size, Earthquake - Causes, Earthquake - Preparation for earthquakes, Earthquake - Specific fault articles, Earthquake - Specific earthquake articles Read more here: » Earthquake: Encyclopedia II - Earthquake - Causes |
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|  |  |  | moment: Encyclopedia II - Bell number - Partitions of a setIn general, Bn is the number of partitions of a set of size n. A partition of a set S is defined as a set of nonempty, pairwise disjoint subsets of S whose union is S. For example, B3 = 5 because the 3-element set {a, b, c} can be partitioned in 5 distinct ways:
{{a}, {b}, {c}}
{{a}, {b, c}}
{{b}, {a, c}}
{{c}, {a, b ...
See also:Bell number, Bell number - Partitions of a set, Bell number - Another view of Bell numbers, Bell number - Properties of Bell numbers, Bell number - Triangle scheme for calculating Bell numbers Read more here: » Bell number: Encyclopedia II - Bell number - Partitions of a set |
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| |  |  |  | moment: Encyclopedia II - White noise - Random vector transformationsTwo theoretical applications using a white random vector are the simulation and whitening of another arbitrary random vector. To simulate an arbitrary random vector, we transform a white random vector with a carefully chosen matrix. We choose the transformation matrix so that the mean and covariance matrix of the transformed white random vector matches the mean and covariance matrix of the arbitrary random vector that we are simulating. To whiten an arbitrary random vector, we transform it by a different carefully chosen matr ...
See also:White noise, White noise - Statistical properties, White noise - Colors of noise, White noise - Applications, White noise - Mathematical definition, White noise - White random vector, White noise - White random process white noise, White noise - Random vector transformations, White noise - Simulating a random vector, White noise - Whitening a random vector, White noise - Random signal transformations, White noise - Simulating a continuous-time random signal, White noise - Whitening a continuous-time random signal, White noise - External link Read more here: » White noise: Encyclopedia II - White noise - Random vector transformations |
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|  |  |  | moment: Encyclopedia II - Dipole - Alignment of a dipole to an applied fieldWhen placed in an electric (E) or magnetic (B) field, equal but opposite forces arise on each side of the dipole creating a torque τ:
for an Electric dipole moment p (in coulomb-meters), or
for a Magnetic dipole moment m (in ampere-square meters).
The resulting torque will tend to align the dipole with the applied field.
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See also:Dipole, Dipole - Alignment of a dipole to an applied field, Dipole - Physical dipoles point dipoles and approximate dipoles, Dipole - Molecular dipoles, Dipole - Field from a magnetic dipole, Dipole - Magnitude, Dipole - Vector form, Dipole - Magnetic vector potential, Dipole - Field from an electric dipole, Dipole - Electrostatic potential, Dipole - Dipole radiation Read more here: » Dipole: Encyclopedia II - Dipole - Alignment of a dipole to an applied field |
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