Determination of electromagnetic medium from the Fresnel surface

We study Maxwell's equations on a 4-manifold where the electromagnetic medium is described by an antisymmetric $2\choose 2$-tensor $\kappa$. In this setting, the Tamm-Rubilar tensor density determines a polynomial surface of fourth order in each cotangent space. This surface is called the Fresnel surface and acts as a generalisation of the light-cone determined by a Lorentz metric; the Fresnel surface parameterises electromagnetic wave-speed as a function of direction. Favaro and Bergamin have recently proven that if $\kappa$ has only a principal part and if the Fresnel surface of $\kappa$ coincides with the light cone for a Lorentz metric $g$, then $\kappa$ is proportional to the Hodge star operator of $g$. That is, under additional assumptions, the Fresnel surface of $\kappa$ determines the conformal class of $\kappa$. The purpose of this paper is twofold. First, we provide a new proof of this result using Gr\"obner bases. Second, we describe a number of cases where the Fresnel surface does not determine the conformal class of the original $2\choose 2$-tensor $\kappa$. For example, if $\kappa$ is invertible we show that $\kappa$ and $\kappa^{-1}$ have the same Fresnel surfaces.Comment: 23 pages, 1 figur

Wave propagation in linear electrodynamics

The Fresnel equation governing the propagation of electromagnetic waves for the most general linear constitutive law is derived. The wave normals are found to lie, in general, on a fourth order surface. When the constitutive coefficients satisfy the so-called reciprocity or closure relation, one can define a duality operator on the space of the two-forms. We prove that the closure relation is a sufficient condition for the reduction of the fourth order surface to the familiar second order light cone structure. We finally study whether this condition is also necessary.Comment: 13 pages. Phys. Rev. D, to appea

On the strain-energy density in linear elasticity

Standard results from matrix theory are used to derive optimal upper and lower bounds for the strain-energy density in terms of the norm of the stress tensor in two and three dimensions. The approach also yields directly necessary and sufficient conditions for positive-definiteness.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42704/1/10665_2005_Article_BF01535284.pd

Multiscale analysis of materials with anisotropic microstructure as micropolar continua

Multiscale procedures are often adopted for the continuum modeling of materials composed of a specific micro-structure. Generally, in mechanics of materials only two-scales are linked. In this work the original (fine) micro-scale description, thought as a composite material made of matrix and fibers/particles/crystals which can interact among them, and a scale-dependent continuum (coarse) macro-scale are linked via an energy equivalence criterion. In particular the multiscale strategy is proposed for deriving the constitutive relations of anisotropic composites with periodic microstructure and allows us to reduce the typically high computational cost of fully microscopic numerical analyses. At the microscopic level the material is described as a lattice system while at the macroscopic level the continuum is a micropolar continuum, whose material particles are endowed with orientation besides position. The derived constitutive relations account for shape, texture and orientation of inclusions as well as internal scale parameters, which account for size effects even in the elastic regime in the presence of geometrical and/or load singularities. Applications of this procedure concern polycrystals, wherein an important descriptor of the underlying microstructure gives the orientation of the crystal lattice of each grain, fiber reinforced composites, as well as masonry-like materials. In order to investigate the effects of micropolar constants in the presence of material non central symmetries, some numerical finite element simulations, with elements specifically formulated for micropolar media, are presented. The performed simulations, which extend several parametric analyses earlier performed [1], involve two-dimensional media, in the linear framework, subjected to compression loads distributed in a small portion of the medium

Measurement Properties of Questionnaires Assessing Complementary and Alternative Medicine Use in Pediatrics: A Systematic Review

Complementary and alternative medicine (CAM) is commonly used by children, but estimates of that use vary widely partly due to the range of questionnaires used to assess CAM use. However, no studies have attempted to appraise measurement properties of these questionnaires. The aim of this systematic review was to critically appraise and summarize measurement properties of questionnaires of CAM use in pediatrics.A search strategy was implemented in major electronic databases in March 2011 and conference websites, scientific journals and experts were consulted. Studies were included if they mentioned a questionnaire assessing the prevalence of CAM use in pediatrics. Members of the team independently rated the methodological quality of the studies (using the COSMIN checklist) and measurement properties of the questionnaires (using the Terwee and Cohen criteria).A total of 96 CAM questionnaires were found in 104 publications. The COSMIN checklist showed that no studies reported adequate methodological quality. The Terwee criteria showed that all included CAM questionnaires had indeterminate measurement properties. According to the Cohen score, none were considered to be a well-established assessment, two approached the level of a well-established assessment, seven were promising assessments and the remainder (n = 87) did not reach the score's minimum standards.None of the identified CAM questionnaires have been thoroughly validated. This systematic review highlights the need for proper validation of CAM questionnaires in pediatrics, which may in turn lead to improved research and knowledge translation about CAM in clinical practice

Evidence for Updating the Core Domain Set of Outcome Measures for Juvenile Idiopathic Arthritis: Report from a Special Interest Group at OMERACT 2016

Objective. The current Juvenile Idiopathic Arthritis (JIA) Core Set was developed in 1997 to identify the outcome measures to be used in JIA clinical trials using statistical and consensus-based techniques, but without patient involvement. The importance of patient/parent input into the research process has increasingly been recognized over the years. An Outcome Measures in Rheumatology (OMERACT) JIA Core Set Working Group was formed to determine whether the outcome domains of the current core set are relevant to those involved or whether the core set domains should be revised.Methods. Twenty-four people from the United States, Canada, Australia, and Europe, including patient partners, formed the working group. Guided by the OMERACT Filter 2.0 process, we performed (1) a systematic literature review of outcome domains, (2) a Web-based survey (142 patients, 343 parents), (3) an idea-generation study (120 parents), (4) 4 online discussion boards (24 patients, 20 parents), and (5) a Special Interest Group (SIG) activity at the OMERACT 13 (2016) meeting.Results. A MEDLINE search of outcome domains used in studies of JIA yielded 5956 citations, of which 729 citations underwent full-text review, and identified additional domains to those included in the current JIA Core Set. Qualitative studies on the effect of JIA identified multiple additional domains, including pain and participation. Twenty-one participants in the SIG achieved consensus on the need to revise the entire JIA Core Set.Conclusion. The results of qualitative studies and literature review support the need to expand the JIA Core Set, considering, among other things, additional patient/parent-centered outcomes, clinical data, and imaging data

Generation of an ultrabroadband supercontinuum in the mid-infrared region using dispersion-engineered GeAsSe photonic crystal fiber

An ultrabroadband mid-infrared (MIR) region supercontinuum (SC) is demonstrated numerically through dispersion-engineered traditional chalcogenide (ChG) photonic crystal fiber (PCF). By varying structural parameters pitch (hole to hole spacing) and air-hole diameter to pitch ratio, a number of 10-mm-long hexagonal PCFs made employing GeAsSe ChG glass as a core and air-holes of hexagonal lattice running through their lengths as a cladding are optimized to predict an efficient mid-infrared region SC spectral emission by pumping them using a tunable pump source between 2.9 and 3.3 µm. Simulations are carried out using an ultrashort pump pulse of 100-fs duration with a low pulse peak powers of between 3 and 4 kW into the optimized designs. It is found through numerical analysis that efficient SC spectral broadening with flattened output can be obtained by increasing the PCF pitch rather than increasing the PCF cladding containing air-hole diameter although a larger nonlinear coefficient could be obtained through increasing air-hole diameter of an optimized design. Simulation results show that the SC spectra can be broadened up to 12.2 µm for a certain design with a peak power of 3 kW. Using a peak power of 4 kW, it is possible to obtain SC spectral broadening beyond 14 µm with an optimized design spanning the wavelength range from 1.8 to 14 µm which covers the electromagnetic spectrum required for MIR molecular fingerprint region applications such as sensing and biological imaging

Phase field approach with anisotropic interface energy and interface stresses: Large strain formulation

A thermodynamically consistent, large-strain, multi-phase field approach (with consequent interface stresses) is generalized for the case with anisotropic interface (gradient) energy (e.g. an energy density that depends both on the magnitude and direction of the gradients in the phase fields). Such a generalization, if done in the “usual” manner, yields a theory that can be shown to be manifestly unphysical. These theories consider the gradient energy as anisotropic in the deformed configuration, and, due to this supposition, several fundamental contradictions arise. First, the Cauchy stress tensor is non-symmetric and, consequently, violates the moment of momentum principle, in essence the Herring (thermodynamic) torque is imparting an unphysical angular momentum to the system. In addition, this non-symmetric stress implies a violation of the principle of material objectivity. These problems in the formulation can be resolved by insisting that the gradient energy is an isotropic function of the gradient of the order parameters in the deformed configuration, but depends on the direction of the gradient of the order parameters (is anisotropic) in the undeformed configuration. We find that for a propagating nonequilibrium interface, the structural part of the interfacial Cauchy stress is symmetric and reduces to a biaxial tension with the magnitude equal to the temperature- and orientation-dependent interface energy. Ginzburg–Landau equations for the evolution of the order parameters and temperature evolution equation, as well as the boundary conditions for the order parameters are derived. Small strain simplifications are presented. Remarkably, this anisotropy yields a first order correction in the Ginzburg–Landau equation for small strains, which has been neglected in prior works. The next strain-related term is third order. For concreteness, specific orientation dependencies of the gradient energy coefficients are examined, using published molecular dynamics studies of cubic crystals. In order to consider a fully specified system, a typical sixth order polynomial phase field model is considered. Analytical solutions for the propagating interface and critical nucleus are found, accounting for the influence of the anisotropic gradient energy and elucidating the distribution of components of interface stresses. The orientation-dependence of the nonequilibrium interface energy is first suitably defined and explicitly determined analytically, and the associated width is also found. The developed formalism is applicable to melting/solidification and crystal-amorphous transformation and can be generalized for martensitic and diffusive phase transformations, twinning, fracture, and grain growth, for which interface energy depends on interface orientation of crystals from either side

The problem of sharp notch in microstructured solids governed by dipolar gradient elasticity

In this paper, we deal with the asymptotic problem of a body of infinite extent with a notch (re-entrant corner) under remotely applied plane-strain or anti-plane shear loadings. The problem is formulated within the framework of the Toupin-Mindlin theory of dipolar gradient elasticity. This generalized continuum theory is appropriate to model the response of materials with microstructure. A linear version of the theory results by considering a linear isotropic expression for the strain-energy density that depends on strain-gradient terms, in addition to the standard strain terms appearing in classical elasticity. Through this formulation, a microstructural material constant is introduced, in addition to the standard Lamé constants . The faces of the notch are considered to be traction-free and a boundary-layer approach is followed. The boundary value problem is attacked with the asymptotic Knein-Williams technique. Our analysis leads to an eigenvalue problem, which, along with the restriction of a bounded strain energy, provides the asymptotic fields. The cases of a crack and a half-space are analyzed in detail as limit cases of the general notch (infinite wedge) problem. The results show significant departure from the predictions of the standard fracture mechanics

Eigenvalue problems associated with Korn's inequalities

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46189/1/205_2004_Article_BF00251798.pd