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searching for Volume element 101 found (166 total)

alternate case: volume element

Representative elementary volume (1,646 words) [view diff] exact match in snippet view article find links to article

representative elementary volume (REV) (also called the representative volume element (RVE) or the unit cell) is the smallest volume over which a measurement
Thomas–Fermi model (2,457 words) [view diff] exact match in snippet view article find links to article
small volume element ΔV (i.e. locally) but the electron density n ( r ) {\displaystyle n(\mathbf {r} )} can still vary from one small volume element to the
Volume rendering (2,829 words) [view diff] exact match in snippet view article find links to article
pattern. This is an example of a regular volumetric grid, with each volume element, or voxel represented by a single value that is obtained by sampling
Thomson scattering (1,537 words) [view diff] exact match in snippet view article find links to article
depending on where an observer is located, the light scattered from a small volume element may appear to be more or less polarized. In the diagram, everything
Classical electromagnetism (1,840 words) [view diff] exact match in snippet view article find links to article
{\displaystyle \mathbf {r} -\mathbf {r'} } is the vector that points from the volume element d 3 r ′ {\displaystyle \mathrm {d^{3}} \mathbf {r'} } to the point in
Random field (1,128 words) [view diff] exact match in snippet view article find links to article
fields[clarification needed] in which the key role is played by a statistical volume element (SVE), which is a spatial box over which properties can be averaged;
Surfel (136 words) [view diff] exact match in snippet view article find links to article
an abbreviated term for a "surface element," analogous to a "voxel" (volume element) or a "pixel" (picture element). In 3D computer graphics, the use of
Hydrostatic equilibrium (4,416 words) [view diff] exact match in snippet view article find links to article
{\displaystyle F_{\text{top}}=-P_{\text{top}}A} Similarly, the force on the volume element from the pressure of the fluid below pushing upwards is F bottom = P
Gravity darkening (330 words) [view diff] exact match in snippet view article find links to article
^{2}\rho ,} where m {\displaystyle m} is mass (in this case of a small volume element of the star), Ω {\displaystyle \Omega } is the angular velocity, and
Micromechanics (2,216 words) [view diff] exact match in snippet view article find links to article
micromechanics are typically based on the concept of the representative volume element (RVE). An RVE is understood to be a sub-volume of an inhomogeneous medium
Asymptotic homogenization (1,203 words) [view diff] case mismatch in snippet view article find links to article
be representative of that material), is known as the "Representative Volume Element" in homogenization and micromechanics. This element contains enough
Ellipsoidal coordinates (1,152 words) [view diff] exact match in snippet view article find links to article
\right)\left(\nu -\mu \right)}{S(\nu )}}}} Hence, the infinitesimal volume element equals d V = ( λ − μ ) ( λ − ν ) ( μ − ν ) 8 − S ( λ ) S ( μ ) S ( ν
Finite strain theory (10,029 words) [view diff] exact match in snippet view article find links to article
{F} \,\!} . The corresponding formula for the transformation of the volume element is d v = J   d V {\displaystyle dv=J~dV} Derivation of Nanson's relation
Additive manufacturing file format (2,834 words) [view diff] no match in snippet view article find links to article
<y> and <z> elements. After the vertex information, at least one <volume> element must be included. Each volume encapsulates a closed volume of the object
Elliptic cylindrical coordinates (1,404 words) [view diff] exact match in snippet view article find links to article
factor h z = 1 {\displaystyle h_{z}=1} . Consequently, an infinitesimal volume element equals d V = a 2 ( sinh 2 ⁡ μ + sin 2 ⁡ ν ) d μ d ν d z {\displaystyle
Prior probability (6,753 words) [view diff] exact match in snippet view article find links to article
is here (in the case of a continuum) proportional to the phase space volume element Δ q Δ p {\displaystyle \Delta q\Delta p} divided by h {\displaystyle
Rayleigh–Gans approximation (1,215 words) [view diff] exact match in snippet view article find links to article
incident field is not greatly altered within one particle so that each volume element is considered to be illuminated by an intensity and phase determined
Number density (809 words) [view diff] exact match in snippet view article find links to article
N=\iiint _{V}n(x,\,y,\,z)\,\mathrm {d} V,} where dV = dx dy dz is a volume element. If each object possesses the same mass m0, the total mass m of all
Optic axis of a crystal (324 words) [view diff] exact match in snippet view article find links to article
average of the orientation of the long molecular axis within a small volume element of material demonstrating a mesophase. Electrical manipulation of the
Electrostatics (2,615 words) [view diff] exact match in snippet view article find links to article
\mathrm {d} ^{3}r=\mathrm {d} x\ \mathrm {d} y\ \mathrm {d} z} is a volume element. If the charge is distributed over a surface or along a line, replace
Prolate spheroidal coordinates (1,931 words) [view diff] exact match in snippet view article find links to article
)d\varphi ^{2}\right].\end{aligned}}} Consequently, an infinitesimal volume element equals d V = a 3 sinh ⁡ μ sin ⁡ ν ( sinh 2 ⁡ μ + sin 2 ⁡ ν ) d μ d ν
Tensor density (3,670 words) [view diff] exact match in snippet view article find links to article
{\mathfrak {J}}^{2}} is the amount of electric charge crossing the 3-volume element d x 3 d x 4 d x 1 {\displaystyle dx^{3}\,dx^{4}\,dx^{1}} divided by
Oblate spheroidal coordinates (3,478 words) [view diff] exact match in snippet view article find links to article
{\displaystyle h_{\phi }=a\cosh \mu \ \cos \nu } Consequently, an infinitesimal volume element equals d V = a 3 cosh ⁡ μ   cos ⁡ ν   ( sinh 2 ⁡ μ + sin 2 ⁡ ν ) d μ
Van Hove singularity (1,416 words) [view diff] exact match in snippet view article find links to article
{L^{3}}{(2\pi )^{3}}}\,d^{3}k} where d 3 k {\displaystyle d^{3}k} is a volume element in k-space, and which, for electrons, will need to be multiplied by
Fluid mechanics (2,660 words) [view diff] exact match in snippet view article find links to article
molecular length scale. Fluid properties can vary continuously from one volume element to another and are average values of the molecular properties. The continuum
Microstructure (1,698 words) [view diff] exact match in snippet view article find links to article
12. Sanei, Seyed Hamid Reza; Fertig, Ray S. (2015). "Uncorrelated volume element for stochastic modeling of microstructures based on local fiber volume
Continuum mechanics (7,422 words) [view diff] exact match in snippet view article find links to article
finer resolution than the size of the representative volume element (RVE), a statistical volume element (SVE) is employed, which results in random continuum
Emission spectrum (2,640 words) [view diff] exact match in snippet view article find links to article
practical applications. If X dV dΩ dλ is the energy scattered by a volume element dV into solid angle dΩ between wavelengths λ and λ + dλ per unit time
Bispherical coordinates (901 words) [view diff] exact match in snippet view article find links to article
{a\sin \sigma }{\cosh \tau -\cos \sigma }}} Thus, the infinitesimal volume element equals d V = a 3 sin ⁡ σ ( cosh ⁡ τ − cos ⁡ σ ) 3 d σ d τ d ϕ {\displaystyle
Doppler broadening (1,141 words) [view diff] exact match in snippet view article find links to article
distribution of speeds both toward and away from the observer in any volume element of the radiating body, the net effect will be to broaden the observed
Tomography (1,694 words) [view diff] exact match in snippet view article find links to article
pattern. This is an example of a regular volumetric grid, with each volume element, or voxel represented by a single value that is obtained by sampling
Arruda–Boyce model (3,036 words) [view diff] exact match in snippet view article find links to article
the statistical mechanics of a material with a cubic representative volume element containing eight chains along the diagonal directions. The material
Parabolic coordinates (1,115 words) [view diff] exact match in snippet view article find links to article
h_{\tau }} are the same as in the two-dimensional case. The infinitesimal volume element is then d V = h σ h τ h φ d σ d τ d φ = σ τ ( σ 2 + τ 2 ) d σ d τ d
Gauss's law for magnetism (1,439 words) [view diff] exact match in snippet view article find links to article
a particular computation. The law in this form states that for each volume element in space, there are exactly the same number of "magnetic field lines"
Volume of an n-ball (5,506 words) [view diff] exact match in snippet view article find links to article
n ( R ) {\displaystyle V_{n}(R)} can be computed by integrating the volume element in spherical coordinates. The spherical coordinate system has a radial
Computational fluid dynamics (8,648 words) [view diff] exact match in snippet view article find links to article
the volume of the control volume element, and A {\displaystyle \mathbf {A} } is the surface area of the control volume element. The finite element method
Bipolar cylindrical coordinates (758 words) [view diff] exact match in snippet view article find links to article
scale factor h z = 1 {\displaystyle h_{z}=1} . Thus, the infinitesimal volume element equals d V = a 2 ( cosh ⁡ τ − cos ⁡ σ ) 2 d σ d τ d z {\displaystyle
Thermodynamic equilibrium (7,950 words) [view diff] exact match in snippet view article find links to article
material in any small volume element of the system can be interchanged with the material of any other geometrically congruent volume element of the system, and
Scientific visualization (3,071 words) [view diff] exact match in snippet view article find links to article
pattern. This is an example of a regular volumetric grid, with each volume element, or voxel represented by a single value that is obtained by sampling
Born equation (457 words) [view diff] exact match in snippet view article find links to article
{E}}|={\frac {ze}{4\pi \varepsilon _{0}\varepsilon _{r}r^{2}}}} and the volume element d V {\displaystyle dV} can be expressed as d V = 4 π r 2 d r {\displaystyle
Rollin film (518 words) [view diff] exact match in snippet view article find links to article
film can be calculated by the energy balance. Consider a small fluid volume element Δ V {\displaystyle \Delta V} which is located at a height h {\displaystyle
Wave equation (10,783 words) [view diff] exact match in snippet view article find links to article
can be obtained by applying a force equilibrium to an infinitesimal volume element. If the medium has a modulus of elasticity E {\displaystyle E} that
Dirac equation (13,120 words) [view diff] exact match in snippet view article find links to article
elements, and so on. With this in mind, one can find the form of the unit volume element on spacetime in terms of the gammas as follows. By definition, it is
Soil moisture sensor (934 words) [view diff] exact match in snippet view article find links to article
Reflectometry (TDR soil moisture sensor): The dielectric constant of a certain volume element around the sensor is obtained by measuring the speed of propagation
Paraboloidal coordinates (1,534 words) [view diff] exact match in snippet view article find links to article
\right)\left(\lambda -c\right)}}\right]^{1/2}} Hence, the infinitesimal volume element is d V = ( μ − ν ) ( μ − λ ) ( λ − ν ) [ ( μ − b ) ( μ − c ) ( b − ν
Uncorrelatedness (probability theory) (1,739 words) [view diff] case mismatch in snippet view article
distribution: Covariance between two binomials[broken anchor] Uncorrelated Volume Element Papoulis, Athanasios (1991). Probability, Random Variables and Stochastic
Polarization density (3,348 words) [view diff] exact match in snippet view article find links to article
neutral in charge, yet an electric dipole moment forms. For a certain volume element Δ V {\displaystyle \Delta V} in the material, which carries a dipole
Lyapunov exponent (3,176 words) [view diff] exact match in snippet view article find links to article
justification. If the system is conservative (i.e., there is no dissipation), a volume element of the phase space will stay the same along a trajectory. Thus the sum
Triple product (3,621 words) [view diff] exact match in snippet view article find links to article
bivector is an oriented plane element and a trivector is an oriented volume element, in the same way that a vector is an oriented line element. Given vectors
X-ray microtomography (2,946 words) [view diff] exact match in snippet view article find links to article
pattern. This is an example of a regular volumetric grid, with each volume element, or voxel represented by a single value that is obtained by sampling
Computer graphics (8,842 words) [view diff] exact match in snippet view article find links to article
pattern. This is an example of a regular volumetric grid, with each volume element, or voxel represented by a single value that is obtained by sampling
Siméon Denis Poisson (4,498 words) [view diff] exact match in snippet view article find links to article
y,z)}{r}}\,dV,\;} where r {\displaystyle r} is a distance between a volume element d V {\displaystyle dV} and a point P {\displaystyle P} . The integration
Liouville's theorem (Hamiltonian) (4,046 words) [view diff] exact match in snippet view article
Retrieved January 6, 2014. A rigorous proof based on how the Jacobian volume element transforms under Hamiltonian mechanics. "Physics 127a: Class Notes"
Confocal microscopy (5,308 words) [view diff] exact match in snippet view article find links to article
In CLSM a specimen is illuminated by a point laser source, and each volume element is associated with a discrete scattering or fluorescence intensity.
Divergence theorem (7,538 words) [view diff] exact match in snippet view article find links to article
{g(x',0)}}\,dx'={\sqrt {g_{\partial \Omega }(x')}}\,dx'=dS} is the volume element on ∂ Ω {\displaystyle \partial \Omega } and the above formula reads
Melnikov distance (3,735 words) [view diff] exact match in snippet view article find links to article
intersection, along the unstable manifold of a fixed point. Clearly, when this volume element approaches the hyperbolic fixed point it will be distorted considerably
ShapeJS (294 words) [view diff] exact match in snippet view article find links to article
representations. A voxel is similar to a 2D pixel but it represents a volume element in 3 dimensional space. This avoids some typical accuracy issues with
Poisson point process (15,356 words) [view diff] exact match in snippet view article find links to article
{\mathrm {d} x}} is a ( d {\displaystyle \textstyle d} -dimensional) volume element, then for every collection of disjoint bounded Borel measurable sets
Gauge fixing (4,271 words) [view diff] exact match in snippet view article find links to article
distribution), the ∇ {\displaystyle \nabla } operates on r and d3 r is the volume element at r. The instantaneous nature of these potentials appears, at first
Multivariate t-distribution (5,719 words) [view diff] exact match in snippet view article find links to article
density function, ie. the probability Δ P {\displaystyle \Delta _{P}} in volume element d x 1 … d x p {\displaystyle dx_{1}\dots dx_{p}} is Δ P ( f X ( X |
Causal sets (5,420 words) [view diff] exact match in snippet view article find links to article
the spacetime. This volume factor can be recovered by specifying a volume element for each space time point. The volume of a space time region could then
Einstein coefficients (4,653 words) [view diff] exact match in snippet view article find links to article
× volume × solid angle). ε dt dV dΩ is then the energy emitted by a volume element d V {\displaystyle dV} in time d t {\displaystyle dt} into solid angle
Reciprocal lattice (5,496 words) [view diff] exact match in snippet view article find links to article
of V* to V is not intrinsic; it depends on a choice of Haar measure (volume element) on V. But given an identification of the two, which is in any case
Liquid crystal (11,527 words) [view diff] exact match in snippet view article find links to article
axis and the local director (which is the 'preferred direction' in a volume element of a liquid crystal sample, also representing its local optical axis)
Moment of inertia (17,179 words) [view diff] exact match in snippet view article find links to article
the z {\displaystyle z} -axis with the axis of the disc and define a volume element as d V = s r d r d θ {\displaystyle dV=sr\,dr\,d\theta } , then I C
Heat equation (9,878 words) [view diff] exact match in snippet view article find links to article
change at x is proportional to the heat flowing into an infinitesimal volume element, where the constant of proportionality is dependent on a constant κ
Rubber elasticity (7,352 words) [view diff] exact match in snippet view article find links to article
model is required to simulate the effects of strain on a representative volume element of a network. The Molecular Kink Paradigm envisions a representative
Functionally graded material (2,101 words) [view diff] case mismatch in snippet view article find links to article
weight fraction, and the graphene/ matrix ratio in the Representative Volume Element. The dynamic behavior of this functionally graded polymer-based composite
Four-gradient (8,619 words) [view diff] exact match in snippet view article find links to article
{\displaystyle \partial \Omega =S} is its 3D boundary with its own 3D volume element d S {\displaystyle dS} N = N μ {\displaystyle \mathbf {N} =N^{\mu }}
Carbon nanotube (21,562 words) [view diff] exact match in snippet view article find links to article
of the studied mechanical properties. The concept of representative volume element (RVE) is used to determine the appropriate size and configuration of
CandyFab (457 words) [view diff] exact match in snippet view article find links to article
weight. The resolution of features produced correspond to a smallest volume element of 2.5 x 2.5 x 2.7 mm or less. Pieces produced from ordinary granular
Radiation trapping (1,744 words) [view diff] exact match in snippet view article find links to article
photon emitted at r {\displaystyle \mathbf {r} } is absorbed within the volume element d r {\displaystyle d\mathbf {r} } about the point r {\displaystyle \mathbf
Numerical modeling (geology) (9,089 words) [view diff] exact match in snippet view article
dV=-\int \limits _{S}\rho u_{j}dS_{j}} where V {\displaystyle V} is the volume element and u j {\displaystyle u_{j}} is the velocity at x j {\displaystyle
Bures metric (2,505 words) [view diff] exact match in snippet view article find links to article
measurements to distinguish two different states and the use of the volume element as a candidate for the Jeffreys prior probability density for mixed
Geometric algebra (13,801 words) [view diff] exact match in snippet view article find links to article
_{1}\gamma _{2}\gamma _{3}} is the unit pseudoscalar (or four-dimensional volume element), γ 0 {\displaystyle \gamma _{0}} is the unit vector in time direction
Planck's law (18,064 words) [view diff] exact match in snippet view article find links to article
coefficient" jν is equal to the radiance per unit volume of a small volume element divided by its mass (since, as for the mass absorption coefficient,
Schur orthogonality relations (2,618 words) [view diff] exact match in snippet view article find links to article
0\leq \beta \leq \pi } . Not only the recipe for the computation of the volume element ω ( x ) d x 1 d x 2 ⋯ d x r {\displaystyle \omega (\mathbf {x} )\,dx_{1}dx_{2}\cdots
Computational materials science (2,306 words) [view diff] exact match in snippet view article find links to article
Crystal orientation μm - mm μs - ms Hardening function and yield surface Finite element Volume element mm - m ms - s beam equation, heat equation, etc.
Magnetic current (1,090 words) [view diff] exact match in snippet view article find links to article
variable, d 3 r ′ {\displaystyle \mathrm {d} ^{3}\mathbf {r} '} , is a volume element around position r ′ {\displaystyle \mathbf {r} '} . The earlier time
Indentation plastometry (1,756 words) [view diff] case mismatch in snippet view article find links to article
(2006). "Material Spatial Randomness: From Statistical to Representative Volume Element". Probabilistic Engineering Mechanics. 21 (2): 112–132. doi:10.1016/j
Elasticity of cell membranes (2,053 words) [view diff] exact match in snippet view article find links to article
one) as: where dA and dV are the area element of the membrane and the volume element enclosed by the closed bilayer, respectively, and λ is the Lagrange
Entrance length (fluid dynamics) (2,803 words) [view diff] exact match in snippet view article
Perimeter of the wet part of the pipe By doing a force balance on a small volume element in the fully developed flow region in the pipe (Laminar Flow), we get
Superfluid helium-4 (5,010 words) [view diff] exact match in snippet view article find links to article
250403. PMID 12857119. S2CID 25309672. K. G. Zloshchastiev (2012). "Volume element structure and roton-maxon-phonon excitations in superfluid helium beyond
Micro-mechanics of failure (1,941 words) [view diff] exact match in snippet view article find links to article
a repetition of a single element, named unit cell or representative volume element (RVE), which consists of all three constituents. With periodical boundary
Rotation formalisms in three dimensions (9,999 words) [view diff] exact match in snippet view article find links to article
}}=\mathbf {i} {\hat {\mathbf {v} }}\,,} where i = x̂ŷẑ is the unit volume element, the only trivector (pseudoscalar) in three-dimensional space. The result
Turbulent diffusion (2,340 words) [view diff] exact match in snippet view article find links to article
particle is described by its probability of existing in a specific volume element at time t, that is described by Ψ(x1, x2, x3, t) dx1 dx2 dx3 = Ψ(x,t)dx
Turbulent diffusion (2,340 words) [view diff] exact match in snippet view article find links to article
particle is described by its probability of existing in a specific volume element at time t, that is described by Ψ(x1, x2, x3, t) dx1 dx2 dx3 = Ψ(x,t)dx
Articulated body pose estimation (3,192 words) [view diff] exact match in snippet view article find links to article
The representations include the following: Image appearance, Voxel (volume element) reconstruction, 3D point clouds, and sum of Gaussian kernels 3D surface
Lagrangian coherent structure (10,382 words) [view diff] exact match in snippet view article find links to article
{\displaystyle [t_{0},t_{1}]} of interest. A challenge in that in each material volume element, all individual material fibers (tangent vectors to trajectories) perform
Photoconductive polymer (2,776 words) [view diff] exact match in snippet view article find links to article
p(r,\Theta ,E)g(r,\Theta )d^{3}r} d 3 r {\displaystyle d^{3}r} is a volume element, ϕ {\displaystyle \phi } is the primary quantum yield, p ( r , Θ , E
Interchange instability (4,027 words) [view diff] exact match in snippet view article find links to article
boundary (one fluid tube and one magnetic flux tube) are interchanged the volume element doesn't change and the field lines are straight. Therefore, the magnetic
List of formulas in Riemannian geometry (5,403 words) [view diff] exact match in snippet view article find links to article
well as the covariant derivatives of the metric's determinant (and volume element) ∇ k | g | = 0 {\displaystyle \nabla _{k}{\sqrt {|g|}}=0} The geodesic
Quantization of the electromagnetic field (5,083 words) [view diff] exact match in snippet view article find links to article
λ/(2π) = 48 cm and the volume is 0.109 m3. The energy content of this volume element at 5 km from the station is 2.1 × 10−10 × 0.109 = 2.3 × 10−11 J, which
Size effect on structural strength (5,168 words) [view diff] exact match in snippet view article find links to article
initiation from one material element, or more precisely one representative volume element (RVE), causes the whole structure to fail, like the failure of one link
Poromechanics (5,657 words) [view diff] exact match in snippet view article find links to article
{\displaystyle \sigma '=\sigma -p} , is the total stress acting on the volume element, σ {\displaystyle \sigma } , subtracted by the pressure of the fluid
Transfer length method (5,102 words) [view diff] exact match in snippet view article find links to article
horizontal and vertical resistor elements describe the situation within a volume element of length Δ x {\displaystyle \Delta x} in a metallic pad area. This
Plancherel theorem for spherical functions (11,769 words) [view diff] exact match in snippet view article find links to article
{\displaystyle ds^{2}=r^{-2}\left(dx^{2}+dy^{2}+dr^{2}\right)} with associated volume element d V = r − 3 d x d y d r {\displaystyle dV=r^{-3}\,dx\,dy\,dr} and Laplacian
Solution-friction model (1,530 words) [view diff] exact match in snippet view article find links to article
tot {\displaystyle P^{\text{tot}}} is the total pressure acting on a volume element of water, which is equal to the hydrostatic pressure minus the osmotic
Neural radiance field (2,619 words) [view diff] exact match in snippet view article find links to article
parallelized architectures which run fast on modern GPUs. Plenoxel (plenoptic volume element) uses a sparse voxel representation instead of a volumetric approach
Action principles (4,194 words) [view diff] exact match in snippet view article find links to article
R{\sqrt {-g}}\,\mathrm {d} ^{4}x,} contained a relativistically invariant volume element − g d 4 x {\displaystyle {\sqrt {-g}}\,\mathrm {d} ^{4}x} and the Ricci
Plane-based geometric algebra (4,361 words) [view diff] exact match in snippet view article find links to article
grade-3 – but their geometric interpretation is very different from the usual geometric interpretation of a "trivector" as an "oriented volume element".