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Topic: Voigt notation

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Woldemar Voigt

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	[No title] (Site not responding. Last check: 2007-10-29)
		Woldemar Voigt (September 2, 1850 - December 13, 1919) was a German physicist.
		Voigt profile and Voigt notation are named after him.
		Voigt's work was far ahead of its time and went apparently un-noticed by all those who contributed to the development of special relativity (George FitzGerald and Oliver Heaviside, Joseph Larmor, Hendrik Lorentz, Henri PoincarÃ© and Albert Einstein)
	en.encyclopediahome.com /wiki/Woldemar_Voigt (814 words)

	Woldemar Voigt - WoldemarVoigt
		Voigt was also a musician and became known as a Bach expert.
		In 1887 Voigt formulated a form of the Lorentz transformation between a rest frame of reference and a frame moving with speed v in the x direction.
		Voigt's work was far ahead of its time and went apparently un-noticed by all those who contributed to the development of special relativity (George FitzGerald and Oliver Heaviside, Joseph Larmor, Hendrik Lorentz, Henri Poincaré and Albert Einstein).
	www.kopete.org /Woldemar-Voigt.html (993 words)

	Tensor Information - tensor lamps
		The tensor table lamps notation was developed around 1890 by Gregorio Ricci-Curbastro under the title absolute differential geometry, and was made accessible to many mathematicians by the publication of Tullio Levi-Civita's cumulant tensor decomposition classic text The Absolute Differential Calculus in 1900 (in Italian; translations followed).
		Physicists and engineers are among the first to recognise that vectors and tensors have tensor lamps a physical significance as entities, which goes beyond the (often arbitrary) co-ordinate system in which their components are enumerated.
		Thus, einstein's tensor notation instead of simply having 70 values as indicated in the above example, for a rank 3 tensor field with dimensions <2, 5, 7> every point in the space would have 70 values associated with tensor fascia muscle it.
	www.inanot.com /Ina-Electronics_Topics_T-/Tensor.html (1961 words)

	Woldemar Voigt - Wikipedia, the free encyclopedia
		He was born in Leipzig, and died in Göttingen.
		Since Voigt's transformation preserves the speed of light in all frames, the Michelson-Morley experiment and the Kennedy-Thorndike experiment can not distinguish between the two transformations.
		According to Voigt's first judgement, the Michelson experiment must yield a null result, independently of whether the Earth transports the luminiferous aether with it (Fizeau's 1st aether hypothesis), or whether the Earth moves through an entirely independent, self-consistent universal luminiferous aether (Fizeau's 2nd aether hypothesis).
	en.wikipedia.org /wiki/Woldemar_Voigt (1022 words)

	Stress (physics) Encyclopedia Article @ Quivering.net (Site not responding. Last check: 2007-10-29)
		The correspondence with the former notation is thus:
		Einstein notation in which repeated indices are summed.
		The equilibrium conditions may be derived from the condition that the net force on an infinitesimal volume element must be zero.
	www.quivering.net /encyclopedia/Stress_(physics) (3400 words)

	Numerical Notes: December 2005 Archives (Site not responding. Last check: 2007-10-29)
		To matrix analysts, this might be the distinction between a row and a column vector; to physicists more comfortable with Dirac notation, it is the distinction between a bra and a ket.
		I was exposed roughly concurrently to two different perspectives on tensor algebra: in an abstract algebra class we talked about tensor products of groups and modules and vector spaces in a very general setting, and in a Riemannian geometry class we spoke of tensors in terms of multilinear forms.
		Notation is also under-appreciated, and not only as the way that programmers tell comptuers what to do.
	www.cs.berkeley.edu /~dbindel/blog/archives/2005/12 (5507 words)

	5. File Formats
		C [GPa] and 6 values of the other properties (represented by symmetric 3x3 matrices) are stored in Voigt notation (on one line of the material file).
		C [GPa] arranged in Voigt notation in a lower-left triangular matrix (it is optional to write the full symmetric matrix but the values above the diagonal are simply ignored).
		Density of the composite, assuming that the inclusions have perfect shapes; the density value in brackets shows the effective density obtained with the current resolution of the surface meshes.
	www.matsim.ch /Guide24/PaGuide-5.html (4331 words)

	23. Continuum mechanics
		In consequence, subscript notation, which explicitly shows how to carry out an operation and needs no special symbols, is more common in tensor analysis than in vector analysis.
		Mathematicians and physicists tend to regard, with some justification, kinematic quantities such as displacement, deformation and strain as more fundamental than force and stress and so their textbooks usually deal with these first.
		hydrostatic (hence the notation), since it’s the state that would be generated in a static, pressurised fluid environment.
	www.mech.gla.ac.uk /~rthomson/teaching/lecnotes/ch23.htm (2537 words)

	stress_(physics) (Site not responding. Last check: 2007-10-29)
		These six components are sometimes written in Voigt notation as a 6x1 column matrix which is often, misleadingly, called the stress vector.
		The correspondence with the former notation is thus:{-
		These equations can be compactly written using Einstein notation in which repeated indices are summed.
	www.customwheels.com /wiki/?title=Stress_(physics) (3257 words)

	Voigt's lines - definition of Voigt's lines in the Medical dictionary - by the Free Online Medical Dictionary, ... (Site not responding. Last check: 2007-10-29)
		Voigt's lines - definition of Voigt's lines in the Medical dictionary - by the Free Online Medical Dictionary, Thesaurus and Encyclopedia.
		Boundaries on a skin area innervated by a main cutaneous nerve.
		This information should not be considered complete, up to date, and is not intended to be used in place of a visit, consultation, or advice of a legal, medical, or any other professional.
	medical-dictionary.thefreedictionary.com.cob-web.org:8888 /Voigt%27s+lines (84 words)

	Envisioning n-th Order Tensors ©
		Here the second order stress tensor is transformed into an eigenvalue-eigenvector problem using tensor notation instead of matrices because of its notational brevity.
		This equation is a tensor equation and can not be written in matrix notation unless using contracted Voigt notation.
		For the reader only interested in the previous example of the principal stress state, it is not difficult to show that equation (36) reduces to equation (15).
	www.sv.vt.edu /classes/ESM4714/methods/EEG.html (8960 words)

	THERMAL3D.F
		c The array prob(i) contains the volume fractions of the i'th phase, c strxx, etc. are the six independent (Voigt notation) volume c averaged stresses, sxx, etc. are the six independent (Voigt notation) c volume averaged strains (not counting the thermal strains).
		c The variable cmod(i,6,6) gives the elastic moduli tensor c of the i'th phase, eigen(i,6) gives the six independent elements c of the eigenstrain tensor for the i'th phase (Voigt notation) c and dk(i,8,3,8,3) is the stiffness matrix of the i'th c phase.
		The parameter nphase gives the number of phases being considered c in the problem, and is set by the user.
	ciks.cbt.nist.gov /garboczi/manual/node55.html (636 words)

	Elastic moduli
		The total energy is obtained by summing over all pixels.
		Since the strain tensor is symmetric, a simpler notation is usually used, the Voigt notation, where the strain is taken to be a 6-vector containing the six independent strains (ε
		When the solution displacements to the problem are obtained, these can be used to compute the average stress and strain in the system, which define the effective quantities and can also give insight into local stress and strain fields around microstructural features.
	ciks.cbt.nist.gov /garboczi/manual/node8.html (652 words)

	5 YEAR MECHANICS SYLLABUS
		notation which is consistent throughout the whole of the course means that most
		There is one major departure from the notation used in most of the literature
		This differs from modern mathematical notation which would just write
	www.mech.gla.ac.uk /~rthomson/teaching/ch0notation.htm (840 words)

	Behaviour of the A15 compounds under non-hydrostatic stress
		He has shown that both the C-T transition and the SC should be affected by the Gamma
		are the stress components in the Voigt notation.
		Apart from explaining several experimental results, he has pointed out that the origin of some seemingly different anomalies in the A15 compounds is due to the presence of stress in the samples.
	stacks.iop.org /0022-3719/21/1441 (291 words)

	Voigtsche Notation - Wikipedia
		Unter der Voigtschen Notation versteht man eine praktische Schreibweise für symmetrische Tensoren in der Kristallographie, benannt nach dem Göttinger Physiker Woldemar Voigt.
		Diese Notation erlaubt es, das Hookesche Gesetz als Matrixgleichung zu schreiben: die Verknüpfung von Verzerrung und Verspannung erfolgt dann durch eine einfach zu handhabende quadratische 6×6-Matrix.
		Die erhebliche Vereinfachung dieser Notation wird allerdings damit erkauft, dass in dieser Darstellung die Tensoreigenschaften des Hookeschen Gesetzes verlorengehen!
	de.wikipedia.org /wiki/Voigtsche_Notation (208 words)

	denny voigt - ResearchIndex document query (Site not responding. Last check: 2007-10-29)
		We are grateful to R. Hempel and J. Voigt for some useful remarks.
		In [52] the baseline is modeled by a sum of Voigt lines and in [4] by a set of Gaussian peaks.
		To avoid this, one applies the Voigt notation (see e.g.
	citeseer.ist.psu.edu /cis?q=Denny+Voigt (553 words)

	API description: msA_TRJ_ValueDouble
		- Cell vectors as a lower diagonal portion of a matrix in voigt notation (Angstroms)
		- Stress as a lower diagonal portion of a matrix in voigt notation (GPa)
		- Average stress as a lower diagonal portion of a matrix in voigt notation (GPa)
	www.scs.uiuc.edu /documentation/c2sdk/api/msA/msA_TRJ_ValueDouble.html (219 words)

	NURBS-FEM for Simulation of Skeletal Muscle
		For the convenience of notation and the convention of FEM, in the following text the subscripts
		to a second order matrix using Voigt notation.
		In this report, we use constant direction vector N in the undeformed configuration to model parallel-fibred muscles and unipennate-fibred muscles which have only one distinct fiber direction.
	digital-humans.org /Report2004/Documents/13-MuscleStressAndStrain.htm (5012 words)

	Treat strain
		This subroutine provides the strain tensor for a point on the material grid as specified in the input file.
		that provides the strain tensor in Voigt notation (needed for k.p / electronic structure) in the crystal system.
		Last modified: 17-Sep-2006 - optimised for Microsoft Internet Explorer 6.0
	www.wsi.tu-muenchen.de /nextnano3/structure/block_1/treat_strain.html (226 words)

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