1,590 research outputs found
Optical Activities as Computing Resources for Space-time Symmetries
It is known that optical activities can perform rotations. It is shown that
the rotation, if modulated by attenuations, can perform symmetry operations of
Wigner's little group which dictates the internal space-time symmetries of
elementary particles.Comment: 13 pages, to be published in J. Mod. Optic
Review and Perspectives: Shape Memory Alloy Composite Systems
Following their discovery in the early 60's, there has been a continuous quest for ways to take advantage of the extraordinary properties of shape memory alloys (SMAs). These intermetallic alloys can be extremely compliant while retaining the strength of metals and can convert thermal energy to mechanical work. The unique properties of SMAs result from a reversible difussionless solid-to-solid phase transformation from austenite to martensite. The integration of SMAs into composite structures has resulted in many benefits, which include actuation, vibration control, damping, sensing, and self-healing. However, despite substantial research in this area, a comparable adoption of SMA composites by industry has not yet been realized. This discrepancy between academic research and commercial interest is largely associated with the material complexity that includes strong thermomechanical coupling, large inelastic deformations, and variable thermoelastic properties. Nonetheless, as SMAs are becoming increasingly accepted in engineering applications, a similar trend for SMA composites is expected in aerospace, automotive, and energy conversion and storage related applications. In an effort to aid in this endeavor, a comprehensive overview of advances with regard to SMA composites and devices utilizing them is pursued in this paper. Emphasis is placed on identifying the characteristic responses and properties of these material systems as well as on comparing the various modeling methodologies for describing their response. Furthermore, the paper concludes with a discussion of future research efforts that may have the greatest impact on promoting the development of SMA composites and their implementation in multifunctional structures
Exact computation of image disruption under reflection on a smooth surface and Ronchigrams
We use geometrical optics and the caustic-touching theorem to study, in an
exact way, the change in the topology of the image of an object obtained by
reflections on an arbitrary smooth surface. Since the procedure that we use to
compute the image is exactly the same as that used to simulate the ideal
patterns, referred to as Ronchigrams, in the Ronchi test used to test mirrors,
we remark that the closed loop fringes commonly observed in the Ronchigrams
when the grating, referred to as a Ronchi ruling, is located at the caustic
place are due to a disruption of fringes, or, more correctly, as disruption of
shadows corresponding to the ruling bands. To illustrate our results, we assume
that the reflecting surface is a spherical mirror and we consider two kinds of
objects: circles and line segments.Comment: 31 pages, 23 figure
Application of Sharafutdinov's Ray Transform in Integrated Photoelasticity
We explain the main concepts centered around Sharafutdinov's ray transform,
its kernel, and the extent to which it can be inverted. It is shown how the ray
transform emerges naturally in any attempt to reconstruct optical and stress
tensors within a photoelastic medium from measurements on the state of
polarization of light beams passing through the strained medium. The problem of
reconstruction of stress tensors is crucially related to the fact that the ray
transform has a nontrivial kernel; the latter is described by a theorem for
which we provide a new proof which is simpler and shorter as in Sharafutdinov's
original work, as we limit our scope to tensors which are relevant to
Photoelasticity. We explain how the kernel of the ray transform is related to
the decomposition of tensor fields into longitudinal and transverse components.
The merits of the ray transform as a tool for tensor reconstruction are studied
by walking through an explicit example of reconstructing the
-component of the stress tensor in a cylindrical photoelastic
specimen. In order to make the paper self-contained we provide a derivation of
the basic equations of Integrated Photoelasticity which describe how the
presence of stress within a photoelastic medium influences the passage of
polarized light through the material
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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