407 research outputs found
Spreading of slip from a region of low friction
Recent models of earthquake faults involve heterogeneous slip regions along the faults. Some of this work suggests the following problem: two solids of different material properties are pressed together and sheared. Then, slip propagates asymmetrically from a region of low friction.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41713/1/707_2005_Article_BF01176501.pd
Determination of the characteristic directions of lossless linear optical elements
We show that the problem of finding the primary and secondary characteristic
directions of a linear lossless optical element can be reformulated in terms of
an eigenvalue problem related to the unimodular factor of the transfer matrix
of the optical device. This formulation makes any actual computation of the
characteristic directions amenable to pre-implemented numerical routines,
thereby facilitating the decomposition of the transfer matrix into equivalent
linear retarders and rotators according to the related Poincare equivalence
theorem. The method is expected to be useful whenever the inverse problem of
reconstruction of the internal state of a transparent medium from optical data
obtained by tomographical methods is an issue.Comment: Replaced with extended version as published in JM
The closest elastic tensor of arbitrary symmetry to an elasticity tensor of lower symmetry
The closest tensors of higher symmetry classes are derived in explicit form
for a given elasticity tensor of arbitrary symmetry. The mathematical problem
is to minimize the elastic length or distance between the given tensor and the
closest elasticity tensor of the specified symmetry. Solutions are presented
for three distance functions, with particular attention to the Riemannian and
log-Euclidean distances. These yield solutions that are invariant under
inversion, i.e., the same whether elastic stiffness or compliance are
considered. The Frobenius distance function, which corresponds to common
notions of Euclidean length, is not invariant although it is simple to apply
using projection operators. A complete description of the Euclidean projection
method is presented. The three metrics are considered at a level of detail far
greater than heretofore, as we develop the general framework to best fit a
given set of moduli onto higher elastic symmetries. The procedures for finding
the closest elasticity tensor are illustrated by application to a set of 21
moduli with no underlying symmetry.Comment: 48 pages, 1 figur
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