「Tensor」の共起表現(1語右で並び替え)

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「Tensor」の共起表現一覧(1語右で並び替え)

Tensor

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Thermal ellipsoids can be defined by a tensor, a mathematical object which allows the defini
meaning of "rank" is similar to its meaning in tensor algebra but not to the linear algebra concept
mmatic notation is very useful in manipulating tensor algebra.
This possibility is a tensor analogue of the well known that a null vector
Later Schouten wrote Tensor Analysis for Physicists attempting to present
am, J. E. Marsden, and T. S. Ratiu, Manifolds, Tensor Analysis, and Applications, Springer-Verlag (1
where W is the Weyl tensor, and P the Schouten tensor given in terms of t
See also: theory of elasticity, strain tensor and holographic interferometry.
ey matching conditions stating that the metric tensor and extrinsic curvature tensor must agree.
some ambiguity in regulating the stress-energy tensor, and this depends upon the curvature.
for a more detailed discussion of the Lanczos tensor and spinor.
me in the presence of matter-contain the Ricci tensor, and so calculating the Christoffel symbols is
iative processes tend to stand out, with heavy tensor and scalar mesons decaying dominantly into vec
blished on the theories of Symmetry groups and Tensor and Matrix algebra, then applied mathematics a
Ramond field appears, together with the metric tensor and dilaton, as a set of massless excitations
In that case the components of the tensor are different, say
ace, 1 time) gives , the trace of the Einstein tensor, as the negative of , the Ricci tensor's trace
ry in this category has the square of the Weyl tensor as the Lagrangian
uantization is based on decomposing the metric tensor as follows,
asymptotically approach a well-defined metric tensor at infinity - for example a spacetime that asy
theory of lifts in tensor bundles
sformations on the manifold, it behaves like a tensor, but under general coordinate transformations,
In coordinates, and denoting the Ricci tensor by Rij and the scalar curvature by R, the comp
ten independent degrees of freedom of the Weyl tensor Cabcd in the Newman-Penrose Formalism for gene
He is most famous as the inventor of the tensor calculus but published important work in many
tions, and he used the newly developed tool of tensor calculus to extend the special theory's global
Dirk J. Struik, "J A Schouten and the tensor calculus," Nieuw Arch.
In addition the Bianchi formula for the Weyl tensor can be rewritten to
The left Cauchy-Green deformation tensor can then be expressed as
The topogravitic tensor can be interpreted as representing the section
vita connection , the variation of the Riemann tensor can be calculated as,
Riemannian or Lorentzian manifold whose metric tensor can be written in form
tion, which can be viewed as projection onto a tensor component.
As indicated above, the tensor components correspond to gravitational waves.
where Tab are the energy-momentum tensor components.
hat in general relativity, the electrogravitic tensor controls tidal stresses on small objects, as m
But it is also possible to look for tensor currents.
It is a functional of the metric tensor defined at a (D-1)-dimensional compact surface
A metric tensor describes the geometry of spacetime.
where Tab is the stress-energy tensor describing the amount and motion of all matter
context, they are sometimes called birdtracks, tensor diagrams, or Penrose graphical notation.
The geometrical shape has the Ricci tensor equal to zero; this fact makes it relevant as
his formulation is that the scalar, vector and tensor evolution equations are decoupled.
The Tensor Fascia Lata attaches about 5cm away at the ili
Has rich feature set for scalar, vector, and tensor field visualization.
transforms as a two-form i.e. an antisymmetric tensor field with two indices.
in addition to the metric, which is a rank two tensor field, there is a scalar field, φ, which has t
is widely used in mathematical physics, these tensor fields should also give rise to specific contr
These tensor fields should obey any relevant physical laws
up Elastic Liquids with his second text, Body Tensor Fields in Continuum Mechanics (Academic Press,
is a Lorentzian manifold equipped with certain tensor fields which are taken to model states of ordi
extbooks in rheology (Elastic Liquids and Body Tensor Fields in Continuum Mechanics) he was one of t
systems, and is usually expressed in terms of tensor fields.
As with scalar fluctuations, tensor fluctuations are expected to follow a power la
The presence of primordial tensor fluctuations (manifested as gravity waves) is
d as a function of the deviation of the metric tensor from its prescribed asymptotic form.
description of how one can determine the tidal tensor from observations of a single timelike congrue
r field φ comes from a component of the metric tensor g55 where the figure 5 labels an additional, f
oted as ds and is given in terms of the metric tensor gab as
Tensor Geometry: The Geometric Viewpoint and its Uses
f triangle covariance in definition of inertia tensor gives eventually
ential Aμ comes from a component of the metric tensor gμ5 where the figure 5 labels an additional, f
where the Lanczos tensor has the symmetries
Diffusion tensor imaging (DTI) is a related use of MR to measur
Diffusion tensor imaging is a non-invasive method to study the
ography, magnetic resonance imaging, diffusion tensor imaging tractography techniques, and the new f
A 2009 meta-analysis of diffusion tensor imaging studies identified two consistent loca
Newer technologies such as fMRI and diffusion tensor imaging can help identify biologically relevan
cts in the spinal cord and brain via Diffusion Tensor Imaging.
Four-tensor is a frequent abbreviation for a tensor in a four-dimensional spacetime.
A tensor in the theory of quadratic Lagrangians, which
cle, we will only attempt to define the metric tensor in the domain of a single chart.
The idea of a tensor in physical science evolved from attempts to d
ion rule differs from the rule for an ordinary tensor in the intermediate treatment only by the pres
Therefore we can decompose the expansion tensor into its traceless part plus a the trace part.
y and then placing the resulting stress-energy tensor into the Einstein field equations.
The Einstein tensor is symmetric
Thus another name for the Einstein tensor is the trace-reversed Ricci tensor.
In abstract indices the Bach tensor is given by
In general relativity, the topogravitic tensor is one of the three pieces of the Bel decompos
The metric tensor is represented by a U-shaped loop or an upside
The Levi-Civita antisymmetric tensor is represented by a thick horizontal bar with
ds are Riemannian manifolds in which the Ricci tensor is proportional (by some constant, not otherwi
Thus, the Lanczos potential tensor is a gravitational field analog of the vector
In these coordinates, the metric tensor is well-approximated by the Euclidean metric,
is a Lorentzian manifold in which the Einstein tensor is null.
The tensor is positive definite as the component of the f
e-third of the trace of the orthogonalized Uij tensor) is listed in these columns.
r-Newman metric, the determinant of the metric tensor is everywhere equal to negative one, even near
aterial in a strong magnetic field, the stress tensor is non-symmetric.
hen the expectation value of the stress-energy tensor is M/2 at A and M/2 at B, but we would never o
The stress-energy tensor is the source of the gravitational field in th
ces taking integral values from 0 to 3. Such a tensor is said to have contravariant rank n and covar
on in which the only term in the stress-energy tensor is a cosmological constant term.
and therefore, the stress-energy tensor isn't symmetric.
usually involves a few simple "identities" of tensor manipulations.
Diffusion tensor MRI (DTI) allows for the investigation of whit
The first context is essentially a tensor multiplied by an extra sign factor, such that
The cricothyroid muscle is the only tensor muscle of the larynx, aiding with phonation.
evolution of the metric and the stress-energy tensor must be solved for together.
In general relativity, the Einstein tensor occurs in the Einstein field equations for gra
The source for the conserved stress tensor of the boundary theory is the boundary value o
y and general relativity, the trace-free Ricci tensor of a pseudo-Riemannian manifold (M,g) is the t
eld equations are the components of the metric tensor of spacetime.
The strain tensor of the motion of turning the rod produces a no
The curvature tensor of this anti-Mach-metric is of the null-type i
The traceless quadrupole moment tensor of a system of charges (or masses, for example
the effective vanishing of the Weyl curvature tensor of the cosmological gravitational field near t
be used in conjunction with Darcy's law and a tensor of hydraulic conductivity to determine the flu
ongruence, is a way of breaking up the Riemann tensor of a pseudo-Riemannian manifold into four piec
of a flat background represented by the metric tensor of Minkowski spacetime.
s denoted a scalar-it may also be considered a tensor of rank 0. The next level of complexity concer
is the metric tensor on the manifold.
In differential geometry, the Cotton tensor on a (pseudo)-Riemannian manifold of dimension
geometrical applications of tensor operators
In general relativity, the tidal tensor or gravitoelectric tensor is one of the pieces
al field is considered to be the stress-energy tensor or matter tensor.
an be approximated by the infinitesimal strain tensor or Cauchy's strain tensor, .
he Segre classification of the energy-momentum tensor or the Petrov classification of the Weyl tenso
Since χ is a tensor, P is not necessarily colinear with E.
The tensor perturbation is truly gauge independent, since
n these evolve independently of the vector and tensor perturbations and are the predominant ones aff
rturbations vanish in cosmic inflation and the tensor perturbations are gravitational waves, which h
The Einstein tensor plays the role of distinguishing these frames.
Cadabra has extensive functionality for tensor polynomial simplification including multi-term
provided the coordinate system and the metric tensor possess some common symmetries.
partite quantum syste whose state space is the tensor product
Day's tensor product construction can be used to generate c
o superselection sectors, each of which is the tensor product of in irreducible representation of G
the connection between graph coloring and the tensor product of graphs.
that determine the exact decomposition of the tensor product of two representations of a group into
milies associated with a primary field and the tensor product is realized by operator product expans
In the illustration, each vertex in the tensor product is shown using a color from the first
When the energy-momentum tensor represents an electromagnetic field, a Killing
When the energy-momentum tensor represents a perfect fluid, every Killing vect
The Weyl tensor represents the part of the gravitational field
the vorticity tensor represents any tendency of the initial sphere
ction of such motion relative to the alignment tensor; scaling factors therefore will differ with th
are known as the Harvard CMTs (centroid moment tensor solutions) and are continued today at Lamont-D
The tensor STij is gauge invariant: it does not change un
includes the quantum corrections to the metric tensor, such as the worldsheet instantons.
apted frame can be found in which the Einstein tensor takes the form
It is the only known conformally invariant tensor that is algebraically independent of the Weyl
A dielectric tensor that is not Hermitian gives rise to complex ei
tter and energy in the form of a stress-energy tensor, the EFE are understood to be equations for th
ck proposed his generalization of the Einstein tensor, the physicists began to discuss the quadratic
ute only a traceless term to the stress-energy tensor, this implies that in a region of spacetime co
pending on the fluid, which relates the stress tensor to the shear rate tensor.
The local reduction of the general metric tensor to the Minkowski metric corresponds to free-fa
Addition of the matter stress-energy-momentum tensor to the Landau-Lifshitz pseudotensor results in
skate companies: Almost, Enjoi, Speed Demons, Tensor Trucks, Blind, Cliche, and Darkstar Skateboard
wall are the orifice of the semicanal for the Tensor tympani muscle and the tympanic orifice of the
e pressure and density from the energy density tensor Tμν, and g* as the effective number of degrees
r is usually a quantity that transforms like a tensor under an orientation preserving coordinate tra
Regions of spacetime in which the Weyl tensor vanishes contain no gravitational radiation an
ons, are associated with places where the Weyl tensor vanishes identically.
ymptotically empty in the sense that its Ricci tensor vanishes in a neighbourhood of the boundary of
h theories are obtained when the stress-energy tensor vanishes.
us part of the tube, and blends below with the Tensor veli palatini muscle.
The tensor veli palatini is lateral to the levator and do
is plugged into the symmetric part of the Weyl tensor W.
an important identity regarding the curl of a tensor we know that for a continuous, single-valued d
r Pulay) is an error that occurs in the stress tensor when using density functional theory.
t cause a variation of a medium's permittivity tensor when an external electric field is applied, pr
They depend on the stress-energy tensor, which in turn depends on the (unknown) metric
on of numbers at every point in space (i.e., a tensor) which would describe how much it was bent or
is an equation involving the Riemann curvature tensor, which measures the change in separation of ne
e a nonzero cosmological constant or a Riemann tensor which is not self-dual.
itten as a functional integral over the metric tensor, which is now the quantum field under consider
omplex refractive index or dielectric function tensor, which gives access to fundamental physical pa
in's idea of introducing a nonsymmetric metric tensor with the symmetric part corresponding to the u