Lamé polynomials, hyperelliptic reductions and Lamé band structure

The band structure of the Lamé equation, viewed as a one-dimensional Schr?dinger equation with a periodic potential, is studied. At integer values of the degree parameter l, the dispersion relation is reduced to the l=1 dispersion relation, and a previously published l=2 dispersion relation is shown to be partly incorrect. The Hermite-Krichever Ansatz, which expresses Lamé equation solutions in terms of l=1 solutions, is the chief tool. It is based on a projection from a genus-l hyperelliptic curve, which parametrizes solutions, to an elliptic curve. A general formula for this covering is derived, and is used to reduce certain hyperelliptic integrals to elliptic ones. Degeneracies between band edges, which can occur if the Lamé equation parameters take complex values, are investigated. If the Lamé equation is viewed as a differential equation on an elliptic curve, a formula is conjectured for the number of points in elliptic moduli space (elliptic curve parameter space) at which degeneracies occur. Tables of spectral polynomials and Lamé polynomials, i.e. band-edge solutions, are given. A table in the earlier literature is corrected.     

Prediction of ground multipath parameters from range-gain measurements using Prony?s technique

Prony's technique is used to estimate multipath parameters from range-gain patterns produced by ground multipath interference in line-of-sight radio links. The field distribution at the transmitting antenna side is obtained by digital reconstruction from the range-gain pattern that is recorded, at constant height, along ground surface. The technique is presented as a competitive alternative to the Fourier transform, where much shorter data windows are sufficient for the proposed technique. The technique is validated by calculated and measured range-gain patterns, and the predicted values are in good agreement with the actual ones. Prony's technique produced predictions with comparable errors to the Fourier technique from much smaller data windows.     

Moiré technique for spatial coherence measurements of soft-x-ray lasers

We present a novel moiré diagnostic that allows the time-averaged spatial coherence properties of soft-x-ray lasers to be measured. The technique is an extension of the theoretical work in a recent paper [J. Opt. Soc. Am. A 16, 323 (1999)] and is based on the concept of decompositions of the far-field divergence for partially coherent beams. An appealing feature of the approach is that the spatial coherence width at other planes can be evaluated from the measured one at a given plane on the assumption of shape-invariant beams.     

Computation of green’s tensor and wave propagation in the random granular elastic medium

Abstract

A linear differential operator equation involving randomly variable field parameters, characterising the heterogeneous granular elastic medium is considered. The appropriate Green’s tensor is evaluated for the non-deterministic operator equations in the form of Fourier integrals in the frequency space; the exact evaluation is carried out to obtain the 36 components of Green’s tensor. The problem of wave propagation in the random granular elastic medium is then carried out with the help of the associated Green’s tensor. The effect of random variation of parameters on wave propagation in the granular elastic medium is examined. Dispersion equations have been analysed in details.     

Piecewise oblique boundary treatment for the elastic–plastic wave equation on a cartesian grid

Numerical schemes for hyperbolic conservation laws in 2-D on a Cartesian grid usually have the advantage of being easy to implement and showing good computational performances, without allowing the simulation of “real-world” problems on arbitrarily shaped domains. In this paper a numerical treatment of boundary conditions for the elastic–plastic wave equation is developed, which allows the simulation of problems on an arbitrarily shaped physical domain surrounded by a piece-wise smooth boundary curve, but using a PDE solver on a rectangular Cartesian grid with the afore-mentioned advantages.     

Error estimates for the Fourier-finite-element approximation of the Lamé system in nonsmooth axisymmetric domains

This paper is concerned with the effective implementation of the Fourier-finite-element method, which combines the approximating Fourier and the finite-element methods, for treating the Dirichlet problem for the Lamé equations in axisymmetric domains with conical vertices and reentrant edges. The partial Fourier decomposition reduces the three-dimensional boundary value problem to an infinite sequence of decoupled two-dimensional boundary value problems on the plane meridian domain The asymptotic behavior of the solutions of the reduced problems near angular points of _a is described by suitable singular functions and treated numerically by linear finite elements on locally graded meshes. For it is proved that the rate of convergence of the combined approximations in is of the order where h and N are the parameters of the finite-element- and Fourier-approximation, respectively, with h0 and N.Acknowledgements This work was done while the author was visiting the Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste, Italy, under the Junior Associateship Scheme. The visit was sponsored by the Swedish International Development Cooperation Agency (SIDA). The author gratefully acknowledges this support.Junior Associate of the Abdus Salam ICTP.     

Adjustable refractive power from diffractive moiré elements

We show how suitable combinations of cascaded diffractive optical elements (DOEs) can form a combined "moiré DOE" of adjustable refractive power and high diffraction efficiency. The optical power can be adjusted continuously by a mutual rotation of one DOE with respect to the other. Fresnel lenses and axicons of variable refractive power or spiral phase plates of adjustable helical charge can be realized this way.     

Deviation of deformation of piston and cylinder of high-pressure piston pair from deformation as calculated with the use of a solution of the Lamé problem

The deviations of the deformation of a piston and cylinder from the deformation as calculated from formulas in the solution of the Lamé problem as well as the influence of the pressure distribution in the working channel of a piston pair on these deviations are considered. Conclusions regarding certain aspects of the design of high-pressure piston pairs are presented.     

What can wave energy learn from offshore oil and gas?

This title may appear rather presumptuous in the light of the progress made by the leading wave energy devices. However, there may still be some useful lessons to be learnt from current 'offshore' practice, and there are certainly some awful warnings from the past. Wave energy devices and the marine structures used in oil and gas exploration as well as production share a common environment and both are subject to wave, wind and current loads, which may be evaluated with well-validated, albeit imperfect, tools. Both types of structure can be designed, analysed and fabricated using similar tools and technologies. They fulfil very different missions and are subject to different economic and performance requirements; hence 'offshore' design tools must be used appropriately in wave energy project and system design, and 'offshore' cost data should be adapted for 'wave' applications. This article reviews the similarities and differences between the fields and highlights the differing economic environments; offshore structures are typically a small to moderate component of field development cost, while wave power devices will dominate overall system cost. The typical 'offshore' design process is summarized and issues such as reliability-based design and design of not normally manned structures are addressed. Lessons learned from poor design in the past are discussed to highlight areas where care is needed, and wave energy-specific design areas are reviewed. Opportunities for innovation and optimization in wave energy project and device design are discussed; wave energy projects must ultimately compete on a level playing field with other routes to low CO? energy and/or energy efficiency. This article is a personal viewpoint and not an expression of a ConocoPhillips position.     

Dynamic holographic moiré patterns in photorefractive Bi12TiO20 and small-angle measurements

A procedure for obtaining real-time holographic moirélike patterns and measuring small angles is proposed. Two rotated sinusoidal phase gratings are superposed, and the result represents a promising technique for making small-angle measurements in metrological applications. The experiments are performed with a diffusion-only recording mechanism in the photorefractive crystal Bi(12)TiO(20) illuminated by lambda = 0.633 mum light from a He-Ne laser.     

Identifying author–inventors from Spain: methods and a first insight into results

The purpose of this paper is twofold: methodological and empirical. Methodologically, we describe a matching and disambiguation procedure for the identification of author–inventors (researchers who publish and patent) located in the same country. Our methodology aims to maximize precision and recall rates by taking into account national name writing customs and country-specific dictionaries for person and institution names (academic and non-academic) in the name matching stage and by including a recursive validation step in the person disambiguation stage. An application of this methodology to the identification of Spanish author–inventors is described in detail. Empirically, we present the first results of applying the described methodology to the matching of all SCOPUS 2003–2008 publications of Spanish authors to all 1978–2009 EPO applications with Spanish inventors. Using this data, we identify 4,194 Spanish author–inventors. A first look at their patenting and publication patterns reveals that they make quite a significant contribution to the country’s overall scientific and technological production in the time period considered: 27 % of all EPO patent applications invented in Spain and 15 % of all SCOPUS publications authored in Spain, excluding non-technological disciplines. To our knowledge, this is the first time that a large scale identification of author–inventors from Spain has been done, with no limitation in terms of fields, regions or types of institutions. We also make available online for scientific use an anonymized subset of the database (patent applications invented by authors affiliated to Spanish public universities).     

Identifying through-thickness material properties of carbon-fiber-reinforced plastics using the virtual fields method combined with moiré interferometry

An investigation into the use of a novel curved-beam composite specimen is conducted to measure the interlaminar (through-thickness) tensile properties of carbon-fiber-reinforced plastic. A combination of a numerical model and full-field displacement/strain measurement with moiré interferometry is utilized in this study. Through-thickness material properties are identified from the measured displacement distribution using the virtual fields method. Because of the shape and the loading condition of the proposed curved composite beam, both tensile and shear stresses exist in the through-the-thickness direction. Therefore, the interlaminar tensile modulus, as well as the interlaminar shear modulus, can be evaluated. The measurement results by moiré interferometry provide the material properties through inverse analysis.     

How well can radiance reflected from the ocean-atmosphere system be predicted from measurements at the sea surface?

There is interest in the prediction of the top-of-the-atmosphere (TOA) reflectance of the ocean-atmosphere system for in-orbit calibration of ocean color sensors. With the use of simulations, we examine the accuracy one could expect in estimating the reflectance ρ(T) of the ocean-atmosphere system based on a measurement suite carried out at the sea surface, i.e., a measurement of the normalized sky radiance ρ(B) and the aerosol optical thickness (τ(a)), under ideal conditions-a cloud-free, horizontally homogeneous atmosphere. Briefly, ρ(B) and τ(a) are inserted into a multiple-scattering inversion algorithm to retrieve the aerosol optical properties-the single-scattering albedo and the scattering phase function. These retrieved quantities are then inserted into the radiative transfer equation to predict ρ(T). Most of the simulations were carried out in the near infrared (865 nm), where a larger fraction of ρ(T) is contributed by aerosol scattering compared with molecular scattering, than in the visible, and where the water-leaving radiance can be neglected. The simulations suggest that ρ(T) can be predicted with an uncertainty typically Θ1% when the ρ(B) and τ(a) measurements are error free. We investigated the influence of the simplifying assumptions that were made in the inversion-prediction process, such as modeling the atmosphere as a plane-parallel medium, using a smooth sea surface in the inversion algorithm, using the scalar radiative transfer theory, and assuming that the aerosol was confined to a thin layer just above the sea surface. In most cases, these assumptions did not increase the error beyond ±1%. An exception was the use of the scalar radiative transfer theory, for which the error grew to as much as ~2.5%, suggesting that the use of ρ(B) inversion and ρ(T) prediction codes that include polarization would be more appropriate. However, their use would necessitate measurement of the polarization associated with ρ(B). We also investigated the uncertainty introduced by an unknown aerosol vertical structure and found it to be negligible if the aerosols were nonabsorbing or weakly absorbing. An extension of the analysis to the blue, which requires measurement of the water-leaving radiance, showed significantly better predictions of ρ(T) because the major portion of ρ(T) is the result of molecular scattering, which is known precisely. We also simulated the influence of calibration errors in both the Sun photometer and the ρ(B) radiometer. The results suggest that the relative error in the predicted ρ(T) is similar in magnitude to that in ρ(B) (actually it was somewhat less). However, the relative error in ρ(T) induced by error in τ(a) is usually much less than the relative error in τ(a). Currently, it appears that radiometers can be calibrated with an uncertainty of ~±2.5%, therefore it is reasonable to conclude that, at present, the most important error source in the prediction of ρ(T) from ρ(B) is likely to be error in the ρ(B) measurement.     

Derivation of optical constants from transmission measurements alone—applied to MoSe2

Because of the anisotropy of MoSe₂ crystals and the difficulties in accurately determining their reflectivity, the optical constants have been calculated solely from measurements of the transmission normal to the major crystal faces.Experimental results were fitted with computer assistance to a theoretical expression for the optical transmission of a thin film on a transparent substrate. The dispersion relation between the absorption coefficient and the refractive index was used to check and improve the detail of the results. Use of Fabry-Perot fringes to determine crystal thicknesses involved careful consideration of fringe order number.     

Influence of several grating sensor parameters on the modulation depth of moiré signals under incoherent illumination

Theoretical expressions for the modulation depth of moiré signals under incoherent illumination are derived. Consequently, the modulation depth of a moiré signal is related to the following factors: the geometric shape and the size of the light source; the diffraction effect of the grating, which relates to the number of lines in the grating; the line and the space ratio; the grating pair gap; the geometric shape and the size of the receiving window; etc. In addition, the influence of the grating pair on the period and the inclination of moiré fringes under noncollimated illumination are discussed, and the changes in the moiré signal modulation depth under noncollimated illumination with that under collimated illumination are made. Finally, some experimental results are given to verify the theoretical expressions. This research is useful for the actual design of grating sensors.     

Identification of thermomechanical parameters based on the virtual fields method combined with the sampling moiré method

Thermomechanical parameters are important indicators for evaluating the mechanical properties of superalloys and generally include the coefficients of stiffness and thermal expansion at high temperatures. At present, there are few methods for simultaneously characterising the thermomechanical parameters of superalloys, especially single-crystal superalloys. To satisfy the demand for simultaneously identifying the thermomechanical parameters of orthotropic superalloys, an optimised virtual fields method for decoupling the thermomechanical parameters was developed in this study by combining the self-developed heat-resistant grids and the sampling moiré method. First, several factors, including the oblique angle of the grids, image noise and thermomechanical coupling phenomena, were studied through numerical experiments to analyse their influences on the identification accuracy. Then, an optimised identification strategy was established. Finally, the thermomechanical parameters of Ni-based polycrystalline and single-crystal superalloys were successfully identified and comparatively studied. The identification results demonstrate that the proposed method is highly accurate and robust. This research will provide an effective way to accurately characterise the multiple parameters of superalloys at high temperatures.     

Specific heat capacity of solids under pressure from measurements of (∂T/∂P)s

A procedure is described for calculating specific heat capacity under pressure, c _p (T, P), from data for c _p (T, 0) and adiabatic (T/P) _s. The main advantage is that (T/P)_s can be readily measured under high-pressure conditions.