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searching for Volume element 102 found (168 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

{\displaystyle n(\mathbf {r} )} can still vary from one volume element to the next. For a small volume element ΔV, and for the atom in its ground state, we can

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

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

{\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

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;

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

{\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

^{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 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

\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

be representative of that material), is known as the "Representative Volume Element" in homogenization and micromechanics. This element contains enough

{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

<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

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

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

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

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

average of the orientation of the long molecular axis within a small volume element of material demonstrating a mesophase. Electrical manipulation of the

)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

\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

{\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

{\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

molecular length scale. Fluid properties can vary continuously from one volume element to another and are average values of the molecular properties. The continuum

12. Sanei, Seyed Hamid Reza; Fertig, Ray S. (2015). "Uncorrelated volume element for stochastic modeling of microstructures based on local fiber volume

finer resolution than the size of the representative volume element (RVE), a statistical volume element (SVE) is employed, which results in random continuum

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

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

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

{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

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

the statistical mechanics of a material with a cubic representative volume element containing eight chains along the diagonal directions. The material

n ( R ) {\displaystyle V_{n}(R)} can be computed by integrating the volume element in spherical coordinates. The spherical coordinate system has a radial

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

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

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"

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

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

{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

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

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

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

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

Reflectometry (TDR soil moisture sensor): The dielectric constant of a certain volume element around the sensor is obtained by measuring the speed of propagation

\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

Retrieved January 6, 2014. A rigorous proof based on how the Jacobian volume element transforms under Hamiltonian mechanics. "Physics 127a: Class Notes"

distribution: Covariance between two binomials[broken anchor] Uncorrelated Volume Element Papoulis, Athanasios (1991). Probability, Random Variables and Stochastic

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

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

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

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

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

In CLSM a specimen is illuminated by a point laser source, and each volume element is associated with a discrete scattering or fluorescence intensity.

– solvent and polymer – a molecule exists for any arbitrarily small volume element.[3] The expression for the entropy of mixing of small molecules in terms

{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

intersection, along the unstable manifold of a fixed point. Clearly, when this volume element approaches the hyperbolic fixed point it will be distorted considerably

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

{\mathrm {d} x}} is a ( d {\displaystyle \textstyle d} -dimensional) volume element, then for every collection of disjoint bounded Borel measurable sets

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

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

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 |

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

× 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

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)

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

of the studied mechanical properties. The concept of representative volume element (RVE) is used to determine the appropriate size and configuration of

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

weight fraction, and the graphene/ matrix ratio in the Representative Volume Element. The dynamic behavior of this functionally graded polymer-based composite

{\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 }}

model is required to simulate the effects of strain on a representative volume element of a network. The Molecular Kink Paradigm envisions a representative

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

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

measurements to distinguish two different states and the use of the volume element as a candidate for the Jeffreys prior probability density for mixed

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

_{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

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,

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

Crystal orientation μm - mm μs - ms Hardening function and yield surface Finite element Volume element mm - m ms - s beam equation, heat equation, etc.

variable, d 3 r ′ {\displaystyle \mathrm {d} ^{3}\mathbf {r} '} , is a volume element around position r ′ {\displaystyle \mathbf {r} '} . The earlier time

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

(2006). "Material Spatial Randomness: From Statistical to Representative Volume Element". Probabilistic Engineering Mechanics. 21 (2): 112–132. doi:10.1016/j

250403. PMID 12857119. S2CID 25309672. K. G. Zloshchastiev (2012). "Volume element structure and roton-maxon-phonon excitations in superfluid helium beyond

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

a repetition of a single element, named unit cell or representative volume element (RVE), which consists of all three constituents. With periodical boundary

generalized Laguerre functions to unity. This normalization is with the usual volume element r2 dr. First we scale the radial coordinate y = γ r with γ ≡ m 0 ω ℏ

generalized Laguerre functions to unity. This normalization is with the usual volume element r2 dr. First we scale the radial coordinate y = γ r with γ ≡ m 0 ω ℏ

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

The representations include the following: Image appearance, Voxel (volume element) reconstruction, 3D point clouds, and sum of Gaussian kernels 3D surface

{\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

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

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

well as the covariant derivatives of the metric's determinant (and volume element) ∇ k | g | = 0 {\displaystyle \nabla _{k}{\sqrt {|g|}}=0} The geodesic

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

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

{\displaystyle \sigma '=\sigma -p} , is the total stress acting on the volume element, σ {\displaystyle \sigma } , subtracted by the pressure of the fluid

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

{\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

{1}}'\end{bmatrix}}} . To define U {\displaystyle U} , the differential volume element at the transformation input ( p ∈ Δ n − 1 {\displaystyle \mathbf {p}

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

parallelized architectures which run fast on modern GPUs. Plenoxel (plenoptic volume element) uses a sparse voxel representation instead of a volumetric approach

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

grade-3 – but their geometric interpretation is very different from the usual geometric interpretation of a "trivector" as an "oriented volume element".