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Topic: Volume element

	Aural style sheets
		Volume refers to the median volume of the waveform.
		When present, this keyword means that the sound inherited from the parent element's 'play-during' property continues to play and the sound designated by the is mixed with it.
		The sound of the parent element continues to play (it is not restarted, which would have been the case if this property had been inherited).
	www.w3.org /TR/REC-CSS2/aural.html (2332 words)

	11.4 Computing the Volume Element: the Jacobian (Site not responding. Last check: 2007-10-21)
		In any coordinate system, in computing an integral over a volume, you break the volume up into little pieces, and sum the value of the integrand at a point in each piece, times the volume of the piece.
		The volume we want is the volume in the small parallelopiped determined by these vectors.
		But we know the volume in a parallelopiped determined by three vectors: it is the magnitude of the determinant having them as rows.
	www-math.mit.edu /~djk/18_022/chapter11/section04.html (498 words)

	USC File # 2254 - Volume Holographic Element
		In this patent, novel multiplexed volume holographic optical elements are disclosed that exhibit high optical throughput and low crosstalk even under conditions of high diffraction efficiency and dense holographic multiplexing.
		This type of holographic element is unusual in that the stored holographic patterns produce a double angularly multiplexed array of output beams, in the sense that each stored pattern is read out at a different angle of incidence, and also produces a different angle of emergence.
		This feature eliminates a common cause of pattern-to-pattern crosstalk known as beam degeneracy crosstalk, which is capable of causing very large errors in the process of reading out a given pattern (in the high diffraction efficiency regime), based on the presence of other stored patterns within the hologram.
	www.usc.edu /academe/otl/volume.htm (286 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		FE Edit is not only a general editor for volume elements, boundary elements, and sources, it is a tool for generating finite element meshes from boundaries, a tool to process and analyze meshes, and a tool to quickly and easily display finite element solutions.
		Volume elements or boundary elements that use a node that has been removed are also removed.
		Finite elements are used to break down a large problem that is not easy to mathematically model (such as a blob shape) into a small problem that is well defined (triangle or bilinear geometry).
	www.dartmouth.edu /~rc/tools/engineering/feedit.html (8499 words)

	GAMBIT MODELING GUIDE: 3. MESHING THE MODEL, 3.4
		The volume represents the union of a cube, a cylinder, and a triangular prism.
		If any quadrilateral face elements exist on the volume faces (or the tops of their attached boundary layers), generate pyramidal volume elements to create a transition from the associated hexahedral/quadrilateral elements to the tetrahedral elements that will occupy the remainder of the volume.
		Mesh the remainder of the volume with tetrahedral elements.
	www.ent.ohiou.edu /~juwt/HTMLS/fluent/gambit2/html/modeling_guide/mg0304.htm (5369 words)

	Amazon.ca: Books: The Finite Element Method Volume 2 Solid and Structural Mechanics (Site not responding. Last check: 2007-10-21)
		Volume Two: Solid and Structural Mechanics is intended for readers studying structural mechanics at a higher level.
		Although it is an ideal companion volume to Volume One: The Basis, this advanced text also functions as a "stand-alone" volume, accessible to those who have been introduced to the Finite Element Method through a different route.
		Volume 2 of the Finite Element Method provides a complete introduction to the method and is essential reading for undergraduates, postgraduates and professional engineers.
	www.amazon.ca /exec/obidos/ASIN/0470395052 (424 words)

	Wiley::The Boundary Element Method, Volume 2, Applications in Solids and Structures
		The boundary element method (BEM) is a modern numerical technique, which has enjoyed increasing popularity over the last two decades, and is now an established alternative to traditional computational methods of engineering analysis.
		Each volume is a self-contained book including a substantial amount of material not previously covered by other text books on the subject.
		Volume 1 covers applications to heat transfer, acoustics, electrochemistry and fluid mechanics problems, while volume 2 concentrates on solids and structures, describing applications to elasticity, plasticity, elastodynamics, fracture mechanics and contact analysis.
	www.wiley.com /WileyCDA/WileyTitle/productCd-0470842989.html (466 words)

	CCSD thèses-EN-ligne: Notion of representative volume element for heterogeneous materials: statistical and numerical ... (Site not responding. Last check: 2007-10-21)
		The Representative Volume Element (RVE) plays a central role in the mechanics and physics of random heterogeneous materials with a view to predicting their effective properties.
		Large scale finite element simulations of volumes of different sizes are performed in the case of linear elasticity (thermal conductivity respectively), using parallel computing.
		The volumes are subjected to homogeneous strain (gradient of temperature respectively), stress (heat flux respectively) at the boundary or periodic boundary conditions.
	tel.ccsd.cnrs.fr /documents/archives0/00/00/57/51 (566 words)

	Visualizations for Volumes of Solids in Calculus (Site not responding. Last check: 2007-10-21)
		Rather than introduce volumes of solids of revolution by a purely formula-driven approach, these demos provide the opportunity for visualization of the basic approximating elements that lead to the standard calculus expressions that, when computed, give the desired volumes.
		A natural extension of the area of a planar region is the volume of a solid.
		The symbolic form of the volume element depends on whether the axis of revolution is the x-axis or y-axis.
	mathdemos.gcsu.edu /solids (972 words)

	Basic volume element test cases
		The hexahedon, or cubic, elements, are loaded on one face with a pressure load and the displacements are compared to the analytical solution.
		While the 4 node tetrahedron element is integrated using the default 1-point scheme the 10 node tetrahedron element is integrated with the default 4-point integration scheme and the 5 point integration scheme.
		The elements should be distorted, as rectangular elements may satisfy the patch test, while arbitrarily shaped quadrilaterals do not.
	www.smr.ch /local/doc/B2000/html/bk05ch02s02.html (543 words)

	MODELING GUIDE: 3. MESHING THE MODEL, 3.4 (Site not responding. Last check: 2007-10-21)
		As noted above, the volumes shown in Figure 3-64(b), (c), and (d) are not mappable in their primitive forms, but each can be transformed into a mappable volume by means of either vertex-type specifications or virtual geometry operations.
		The volumes shown in Figure 3-70(a), (b), and (c) are submappable, because the faces of each volume are, themselves, submappable.
		The volume shown in Figure 3-70(d) is not submappable, because the end face of the cylindrical protrusion on the top of the volume is neither mappable nor submappable.
	zsc.zcu.cz /sw/manuals/gambit/modeling_guide/mg0304.htm (4046 words)

	SolidMesh: Volume Grid Generation Application
		AFLR3 generates a tetrahedral isotropic volume grid or a mixed element (tetrahedra, pentahedra and prisms) anisotropic boundary layer volume grid from a surface triangulation.
		The volume element size in the field is determined by using interpolation to smoothly propagate the point spacing within the field from the boundary surfaces.
		With optional growth, the element size is determined from interpolation and geometric growth normal to the boundary surfaces.
	www.erc.msstate.edu /simcenter/docs/solidmesh/volgridgen.html (1248 words)

	18.013A Calculus with Applications, Fall 2001, Online Textbook
		The integrand is the integrand itself, which is a scalar field, and the volume element is dxdydz.
		In this case as in the volume case, the problem of reducing the surface integral to integrals dxdy does not exist.
		In the case of area, the comparable expression is the same thing: the ratio of the area element in one set of variables dxdy to the other, dudv, is the magnitude of the determinant formed by the derivatives of x and y with respect to u and v.
	ocw.mit.edu /ans7870/18/18.013a/textbook/chapter31/section04.html (464 words)

	UGTK: ugioUgridType class Reference (Site not responding. Last check: 2007-10-21)
		Given a node index, return a pointer to the indices of volume elements that the node is part of.
		Given a volume element index, return the number of nodes in the volume element.
		purpose: Given a volume element and interpolation weights for the nodes, outputs a point which is the weighted sum of the nodes.
	www.erc.msstate.edu /~mjk/reader/html/classugioUgridType.html (3970 words)

	Diffusion (Site not responding. Last check: 2007-10-21)
		As we add more compound to a volume element in time, the system must respond in a manner consistent with Fick's first law; the concentration gradient that builds with time must be relieved by an increase in diffusion.
		The physical interpretation of this expression is that the more a compound is added to a volume element, the greater the amount of diffusion of the compound from the volume element.
		An alternative way to view the partial specific volume is that it is equal to the volume of the macromolecule divided by the mass of the molecule.
	faculty1.coloradocollege.edu /~hdrossman/CH345/Diff.htm (1693 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		You just want to know the volume element, that is, the determinant of the appropriate Jacobian to use in the Change-of-Variables theorem (your "g").
		Well, on the one hand, this is just a scaling by c, whose effect on M(n,p) is to multiply volume by c^(n*p).
		So I believe the correct volume element is dX = (detR)^((2n-p-1)/2) dR dT = (det R'R)^((2n-p-1)/4) dR dT = (det X'X)^((2n-p-1)/4) dR dT according to taste.
	www.mat.niu.edu /~rusin/known-math/98/integ.gln (584 words)

	31.4 Determining the Area or Volume Element
		In the case of a volume integral, the issues discussed up to now do not exist.
		The integrand is the integrand itself, which is a scalar field, and the volume element is
		However the issue of how to express this volume element when you change variables does arise, and we consider that question here.
	www-math.mit.edu /18.013A/MathML/chapter31/section04.xhtml (293 words)

	Error Estimates for a Combined Finite Volume--Finite Element Method for Nonlinear Convection--Diffusion Problems
		The subject of this paper is the analysis of error estimates of the combined finite volume--finite element (FV--FE) method for the numerical solution of a scalar nonlinear conservation law equation with a diffusion term.
		Nonlinear convective terms are approximated with the aid of a monotone finite volume scheme considered over the finite volume mesh dual to a triangular grid, whereas the diffusion term is discretized by piecewise linear conforming triangular finite elements.
		Under the assumption that the exact solution possesses some regularity properties and the triangulations are of a weakly acute type, with the aid of the discrete maximum principle and a priori estimates, error estimates of the method are proved.
	epubs.siam.org /sam-bin/dbq/article/31469 (221 words)

	Bookworkz.com: The Boundary Element Method, Volume 2, Applications in Solids and Structures,
		This two volume book set is designed to provide the readers with a comprehensive and up-to-date account of the boundary element method and its application to solving engineering problems.
		This volume, Applications in Solids and Structures, provides a comprehensive presentation of the BEM from fundamentals to advanced engineering applications and encompasses: *Elasticity for 2D, 3D and plates and shells
		An important feature of this book is the in-depth presentation of BEM formulations in all of the above fields, including detailed discussions of the basic theory, numerical algorithms and where possible simple examples are included, as well as test results for practical engineering applications of the method.
	www.bookworkz.com /construction/mechanical/0470842989.html (399 words)

	7th Element: Volume One - Music Recommendations - Al Menconi Ministries
		7th Element is an a cappella group, but their smooth sound was so appealing that I had to review their debut project.
		While hearing them harmonize, it's not hard to imagine that the four Greene brothers in the group have done more than just a little singing together over the years.
		Volume One offers up a good mix of original material and classic spirituals and hymns.
	www.almenconi.com /topics/chr_music/music_reviews/seventhelement.html (239 words)

	Volume per Element Chart
		The Volume per Element chart displays the maximum, minimum, and average volume observed for any of the elements in the group or group list during the report period.
		Use the Network Volume by Group chart to observe the maximum, minimum, and average volume for all the elements in a group or group list.
		Use the Network Volume chart to observe the total network volume for all the elements in the group list.
	www.concord.com /help/files/reports/service/charts/DlyVolElem.html (598 words)

	Element Volume vs Baseline Chart
		The Element Volume vs Baseline chart shows the volume for each of the elements in the group.
		The Element Volume vs Baseline chart compares an element's volume during the report period to its volume during the baseline period.
		Investigate this immediately by examining the Volume Change Leaders chart to identify other elements that might not be operational; then shift work to this element.
	www.concord.com /help/files/reports/health/charts/dvb.html (379 words)

	FAST RAY TRACKING THROUGH UNIFORM VOLUME ELEMENTS AS APPLIED TO BORON NEUTRON CAPTURE THERAPY
		Here, each uniform volume element has the same length, width, and height but the shape is not necessarily a cube.
		The algorithm investigating representative elements will increase whichever component it arbitrarily decided was changing most rapidly and at the same time see that it must also correspondingly increase each of the other two components.
		A typical 1 mm resolution is already quite fine and so skipping such a tiny volume element is not substantial, especially considering that the original segmentation of the images cannot be expected to be accurate to the original pixel level.
	www.cs.montana.edu /bnct/publications/mike/thesis3.html (9301 words)

	Replacing a Disk for a Plexed Volume
		The example used is for a disk that is used for a plexed volume element.
		This example also assumes that there are two plexes, and that each plex has only a single volume element.
		In this case, you will need to use the volume configuration information you saved as part of regular system backup and maintenance.
	docs.cray.com /books/S-2377-22/html-S-2377-22/x3515.html (299 words)

	On the Accuracy of the Finite Volume Element Method Based on Piecewise Linear Polynomials
		On the Accuracy of the Finite Volume Element Method Based on Piecewise Linear Polynomials: SIAM Journal on Numerical Analysis Vol.
		We present a general error estimation framework for a finite volume element (FVE) method based on linear polynomials for solving second-order elliptic boundary value problems.
		This framework treats the FVE method as a perturbation of the Galerkin finite element method and reveals that regularities in both the exact solution and the source term can affect the accuracy of FVE methods.
	epubs.siam.org /sam-bin/dbq/article/36887 (185 words)

	Size of a Representative Volume Element in a Second-Order Computational Homogenization Framework - Begell House Inc. (Site not responding. Last check: 2007-10-21)
		In this paper the intrinsic role of the size of the microstructural representative volume element (RVE) in a second-order computational homogenization is investigated.
		The presented second-order computational homogenization is an extension of the classical first-order computational homogenization scheme and is based on a proper incorporation of the macroscopic gradient of the deformation tensor and the associated higher-order stress measure into the multiscale framework.
		Based on the obtained results, some conclusions are drawn with respect to the choice of the microstructural RVE in the second-order computational homogenization analysis.
	dx.doi.org /10.1615/IntJMultCompEng.v2.i4.50 (332 words)

	CGR: Allen & Allen Music Group Announces Volume One - From New Artist, 7th Element
		Although songs from Volume One are already being played on popular stations such as Star 94.5 in Orlando and WCBS 101.5 in New York, AAMG will debut the a cappella arrangement of “Ride The Chariot” to Gospel radio formats, with the simultaneous release of “Everything That’s Beautiful” to Adult Contemporary stations.
		With all of the members of 7th Element taking part in the songwriting process, Volume One is already attracting critical acclaim in the industry, drawing comparisons to multi-GRAMMY winning and platinum-selling artist, Take 6, while exploring a creative and innovative style.
		In addition to the release of Volume One, the members of 7th Element have also set up the E7 Youth Development Group (E7YDG) in order to help young people obtain an education and pursue their dreams in music.
	www.christianguitar.org /forums/showthread.php?t=26523 (884 words)

	SINUM Volume 27 Issue 3
		This paper develops the finite volume element (FVE) method, which is similar to the so-called control volume finite element method but tailored to composite grid applications.
		FVE is described for the general two-dimensional diffusion equation in divergence form; $O(h^{{3 / 2}})$ discretization error estimates are then developed for the case of triangular elements.
		These results are improved to $O(h^2)$ using a special modification involving rectilinear elements at the grid interface.
	locus.siam.org /SINUM/volume-27/art_0727039.html (128 words)

	BCIT ~ Mathematics - Examples
		To find the moment of inertia about the y-axis, we need to choose another volume element dv such that the distance from the y-axis to any point in dv will be the same.
		From physics we know that the work needed to lift a particle by a vertical distance h is mgh, which is the increase in potential energy.
		Then, the element of volume should be chosen such that all the points in the element are at the same height.
	www.math.bcit.ca /examples/mech/integral_calc/index.shtml (399 words)

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