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 $\sigma_{33}$-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