287,249 research outputs found
Scalar, vectorial and tensorial damage parameters from the mesoscopic background
In the mesoscopic theory a distribution of different crack sizes and crack
orientations is introduced. A scalar damage parameter, a second order damage
tensor and a vectorial damage parameter are defined in terms of this
distribution function. As an example of a constitutive quantity the free energy
density is given as a function of the damage tensor. This equation is reduced
in the uniaxial case to a function of the damage vector and in case of a
special geometry to a function of the scalar damage parameter.Comment: 14 pages, 2 figure
The spectral density function for the Laplacian on high tensor powers of a line bundle
For a symplectic manifold with quantizing line bundle, a choice of almost
complex structure determines a Laplacian acting on tensor powers of the bundle.
For high tensor powers Guillemin-Uribe showed that there is a well-defined
cluster of low-lying eigenvalues, whose distribution is described by a spectral
density function. We give an explicit computation of the spectral density
function, by constructing certain quasimodes on the associated principle
bundle.Comment: AMS-Latex, 17 page
The average number of critical rank-one approximations to a tensor
Motivated by the many potential applications of low-rank multi-way tensor
approximations, we set out to count the rank-one tensors that are critical
points of the distance function to a general tensor v. As this count depends on
v, we average over v drawn from a Gaussian distribution, and find formulas that
relates this average to problems in random matrix theory.Comment: Several minor edit
Frequency-dependent effective permeability tensor of unsaturated polycrystalline ferrites
Frequency-dependent permeability tensor for unsaturated polycrystalline
ferrites is derived through an effective medium approximation that combines
both domain-wall motion and rotation of domains in a single consistent
scattering framework. Thus derived permeability tensor is averaged on a
distribution function of the free energy that encodes paramagnetic states for
anhysteretic loops. The initial permeability is computed and frequency spectra
are given by varying macroscopic remanent field.Comment: 24 pages, 3 figure
The radiative transfer for polarized radiation at second order in cosmological perturbations
This article investigates the full Boltzmann equation up to second order in
the cosmological perturbations. Describing the distribution of polarized
radiation by using a tensor valued distribution function, the second order
Boltzmann equation, including polarization, is derived without relying on the
Stokes parameters.Comment: 4 pages, no figure; replaced to match published versio
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