Optimization of an acoustic horn with respect to efficiency and directivity

We consider the problem of designing an acoustic horn in order to efficiently transmit the incoming wave energy and favorably distribute the energy in the far field. A finite element solution of the Helmholtz equation, in planar or cylindrical symmetry, models the wave propagation. The transmission efficiency is monitored by measuring the back reflections into the feeding waveguide, and the far‐field directivity pattern is computed using an integral expression known from scattering theory. The design problem is formulated as a non‐linear least‐squares problem, which is solved using a gradient‐based algorithm, where the gradients are provided by solutions of the associated adjoint equations. The results demonstrate that this approach can generate horns with almost perfect transmission in a wide frequency band. Due to the improved transmission properties at the lower‐frequency region, the optimization with respect to efficiency also generates improved far‐field directivity patterns, that is, patterns that vary less with frequency. It is possible to obtain even more uniform directivity patterns by explicitly including directivity requirements in the optimization. However, those improvements in directivity seem to be associated with a substantial loss of efficiency. Copyright © 2007 John Wiley & Sons, Ltd.     

An iterative solution of the two-dimensional electromagnetic inverse scattering problem

A new method, based on an iterative procedure, for solving the two-dimensional inverse scattering problem is presented. This method employs an equivalent Neumann series solution in each iteration step. The purpose of the algorithm is to provide a general method to solve the two-dimensional imaging problem when the Born and the Rytov approximations break down. Numerical simulations were calculated for several cases where the conditions for the first order Born approximation were not satisfied. The results show that in both high and low frequency cases, good reconstructed profiles and smoothed versions of the original profiles can be obtained for smoothly varying permittivity profiles (lossless) and discontinuous profiles (lossless), respectively. A limited number of measurements around the object at a single frequency with four to eight plane incident waves from different directions are used. The method proposed in this article could easily be applied to the three-dimensional inverse scattering problem, if computational resources are available.     

The diagonalized contrast source inversion approach for elastic wave inversion

This study focuses on the inverse scattering of objects embedded in a homogeneous elastic background. The medium is probed by ultrasonic sources, and the scattered fields are observed along a receiver array. The goal is to retrieve the shape, location, and constitutive parameters of the objects through an inversion procedure. The problem is formulated using a vector integral equation. As is well-known, this inverse scattering problem is nonlinear and ill-posed. In a realistic configuration, this nonlinear inverse scattering problem involves a large number of unknowns, hence the application of full nonlinear inversion approaches such as Gauss-Newton or nonlinear gradient methods might not be feasible, even with present-day computer power. Hence, in this study we use the so-called diagonalized contrast source inversion (DCSI) method in which the nonlinear problem is approximately transformed into a number of linear problems. We will show that, by using a three-step procedure, the nonlinear inverse problem can be handled at the cost of solving three constrained linear inverse problems. The robustness and efficiency of this approach is illustrated using a number of synthetic examples.     

Level‐set topology optimization with many linear buckling constraints using an efficient and robust eigensolver

Linear buckling constraints are important in structural topology optimization for obtaining designs that can support the required loads without failure. During the optimization process, the critical buckling eigenmode can change; this poses a challenge to gradient‐based optimization and can require the computation of a large number of linear buckling eigenmodes. This is potentially both computationally difficult to achieve and prohibitively expensive. In this paper, we motivate the need for a large number of linear buckling modes and show how several features of the block Jacobi conjugate gradient (BJCG) eigenvalue method, including optimal shift estimates, the reuse of eigenvectors, adaptive eigenvector tolerances and multiple shifts, can be used to efficiently and robustly compute a large number of buckling eigenmodes. This paper also introduces linear buckling constraints for level‐set topology optimization. In our approach, the velocity function is defined as a weighted sum of the shape sensitivities for the objective and constraint functions. The weights are found by solving an optimization sub‐problem to reduce the mass while maintaining feasibility of the buckling constraints. The effectiveness of this approach in combination with the BJCG method is demonstrated using a 3D optimization problem. Copyright © 2016 John Wiley & Sons, Ltd.     

Prediction of analyte retention for ion chromatography separations performed using elution profiles comprising multiple isocratic and gradient steps

This study addresses the simulation of ion chromatographic (IC) separations performed under conditions where the elution profile consists of a sequence of isocratic and gradient elution steps (referred to as "complex elution profiles"). First, models for prediction of retention under gradient elution conditions in IC were evaluated using an extensive database of gradient elution retention data. It is shown that one such model is preferred on the basis that it can be used to predict gradient retention times on the basis of isocratic input data. A method is then proposed for using this model for complex elution profiles whereby each step of the elution profile is treated separately and analyte movement through the column is mapped. An empirically based algorithm for predicting peak width under complex elution conditions is also proposed. Evaluation of the suggested approaches was undertaken on a set of 24 analyte anions and 13 analyte cations on 5 different Dionex columns using a range of 5-step complex elution profiles that gave R2 values for correlations between predicted and observed retention times of 0.987 for anions and 0.997 for cations. The simulation of separations of anions and cations using a 3-step complex elution profile is demonstrated, with good correlation between observed and predicted chromatograms. The proposed approach is useful for the rapid development of separations when complex elution profiles are used in IC.     

弹性波三维散射快速多极子间接边界元法求解

边界元方法对于无限域中弹性波散射求解具有独特优势,但求解矩阵的非对称稠密特征极大限制了该方法在大规模实际工程中的应用。为此,基于单层位势理论,结合快速多极子展开技术,通过对球面压缩波和剪切波势函数的泰勒级数展开,建立一种新的快速多极间接边界元方法,以实现大规模弹性波三维散射的精确高效模拟。算例分析表明所提方法能够大幅度降低计算时间和存储量,可在目前普通计算机上快速实现上百万自由度弹性波三维散射问题的快速精确求解。最后以全空间椭球形孔洞群对平面P波、SV波的散射为例,揭示了三维孔洞群周围稳态位移场和应力场的若干分布规律。该文方法对低无量纲频率（ka<5.0）的大规模多体散射问题尤为适合。     

Monte Carlo gradient estimation in high dimensions

A Monte Carlo procedure to estimate efficiently the gradient of a generic function in high dimensions is presented. It is shown that, adopting an orthogonal linear transformation, it is possible to identify a new coordinate system where a relatively small subset of the variables causes most of the variation of the gradient. This property is exploited further in gradient‐based algorithms to reduce the computational effort for the gradient evaluation in higher dimensions. Working in this transformed space, only few function evaluations, i.e. considerably less than the dimensionality of the problem, are required. The procedure is simple and can be applied by any gradient‐based method. A number of different examples are presented to show the accuracy and the efficiency of the proposed approach and the applicability of this procedure for the optimization problem using well‐known gradient‐based optimization algorithms such as the descent gradient, quasi‐Newton methods and Sequential Quadratic Programming. Copyright © 2009 John Wiley & Sons, Ltd.     

Zero-order bows in radially inhomogeneous spheres: direct and inverse problems

Zero-order ray paths are examined in radially inhomogeneous spheres with differentiable refractive index profiles. It is demonstrated that zero-order and sometimes twin zero-order bows can exist when the gradient of refractive index is sufficiently negative. Abel inversion is used to "recover" the refractive index profiles; it is therefore possible in principle to specify the nature and type of bows and determine the refractive index profile that induces them. This may be of interest in the field of rainbow refractometry and optical fiber studies. This ray-theoretic analysis has direct similarities with the phenomenon of "orbiting" and other phenomena in scattering theory and also in seismological, surface gravity wave, and gravitational "lensing" studies. For completeness these topics are briefly discussed in the appendixes; they may also be of pedagogic interest.     

On the asymptotic analysis of surface-stress-driven thin-layer flow

It has been demonstrated experimentally that thin liquid layers may be applied to a solid surface or substrate if a temperature gradient is applied which results in a surface tension gradient and surface traction. Two related problems are considered here by means of the long-wave or lubrication theory. In the first problem, an improved estimate of the applied liquid coating thickness for a liquid being drawn from a bath is found through asymptotic and numerical matching. Secondly, the theory is extended to consider substrates that are not perfectly wetted but exhibit a finite equilibrium contact angle for the coating liquid. This extension incorporates the substrate energetics using a disjoining pressure functional. Unsteady flows are calculated on a substrate of nonuniform wettability. The finite contact angle value required to stop stress-driven flow is predicted and the resulting steady profiles are compared with experimental results for several values of the applied stress.     

全息窄带带阻滤光片用于拉曼光谱测试仪

在测量物质的拉曼光谱时,存在着比拉曼散射光强103~06倍的瑞利散射光,会严重影响拉曼光谱信号的获取。为此,研制了半宽度分别为18nm(峰值波长532nm)和25nm(峰值波长633nm)、光学密度均大于4的重铬酸盐明胶全息窄带带阻滤光片,并将它们用于由平场光谱仪、CCD探测器和计算机控制系统等组成的小型拉曼光谱测试仪中,以滤除瑞利散射光,获得信噪比较高的拉曼光谱信号。对四氯化碳、乙醇以及丙酮等液体样品进行测量的结果表明,在拉曼光谱测试仪中采用该全息窄带带阻滤光片后,可快速测得待测样品的波数低至217cm-1的拉曼光谱。     

Derivatives of scattering profiles: tools for nanoparticle characterization

This paper presents a new approach to characterize nanoparticles using derivatives of scattering profiles of evanescent waves/surface plasmons. We start the procedure using the scattering profiles for an unknown configuration of nanoparticles, either from physical experiments or numerical simulations conducted for different nanoparticles on surfaces. We apply the statistical technique of compound estimation to recover the derivatives of scattering profiles. The L(1) discrepancies with the corresponding curves from known configurations are used to identify the most plausible configuration of particles that could yield the "experimental" profiles. We conduct a simulation study to see how often the new procedure correctly recovers the agglomeration level for gold spherical nanoparticles on a thin gold film. The results suggest that first derivatives are much more effective for characterization than undifferentiated profiles and that M(33) is the most useful element for distinguishing among configurations. The proposed compound estimation technique is more effective than typical inverse analyses based on look-up tables and can be used effectively in nanoparticle characterization platforms.     

Numerical resolution of the boundary integral equations for elastic scattering by a plane crack

The problem of wave scattering by a plane crack is solved, either in the case of acoustic waves or in the case of elastic waves incidence using the boundary integral equation method. A collocation method is often used to solve that equation, but here we will use a variational method, first writing the problem of Fourier variables, and then writing the associated integrals in the sesquilinear form with weak singularity kernels. This representation is used in the numerical approach, made with a finite element method in the surface of the crack. Numerical tests were made with circular and elliptical cracks, but this method can be extended to other shapes, with the same convergence profiles. Extensive results are given concerning the crack opening displacement, the scattering cross-section, the back-scattered amplitude and far-field patterns.     

Fictive temperature in silica-based glasses and its application to optical fiber manufacturing

This paper will thus give an overview of methods to reduce efficiently the Rayleigh scattering loss via the fictive temperature in silica-based optical fibers. We will first recall what the concept of fictive temperature T_f is and its limitations in section 2. We will see that both Raman and IR spectroscopy can be used to determine T_f (Section 3). Section 4 will thus give some examples of T_f profiles measured in optical fibers manufactured in different conditions. Finally, section 5 will present the main approaches to reduce Rayleigh scattering loss in silica-based fibers via a reduction of T_f.     

Reconstruction of Two-Dimensional Randomly Rough Surfaces Based on Bidirectional Reflectance Distribution Function

This article presents an inverse method for reconstructing two-dimensional randomly rough surfaces based on the available (experimental or given) data of the bidirectional reflectance distribution function (BRDF). The Maxwell’s equations of electromagnetic waves are applied to describe the light scattering process of rough surfaces by accounting for the near-field effect. Such a forward problem is numerically solved with the finite-difference time-domain algorithm. The inverse scattering problem of reconstructing the surface profile is handled by means of an optimization technique—the particle swarm optimizer algorithm. As an example, reconstruction of a Gaussian rough surface is conducted based on the experimental data of BRDFs. The retrieved results of the surface profile are compared with those measured by atomic force microscopy from the samples, which shows that the reconstruction algorithm can provide the credible prediction of surface profiles. The reconstruction approach studied in this study can make reliable predictions of the actual or required surface profiles.     

Analysis of the ideal model for a single component in preparative gradient elution chromatography

The analytical solutions of the ideal model of chromatography for a single component were studied by using the method of characteristics for solving partial differential equations. By assuming that the mobile-phase gradient entering the column is not affected by any sorption of mobile-phase solvents on the column, we demonstrated that the stationary-phase concentration of the component is kept constant along the characteristic curve irrespective of the isotherm and gradient profile used. By using this property and assuming a Langmiur isotherm, we also calculated the band profiles for single linear, stepwise, and ladderlike gradients, respectively. These band profiles were compared with those computed by using the finite-difference method. The results were found to be in good agreement.     

Metal ion complexes of EDTA: a solute system for density gradient ultracentrifugation analysis of lipoproteins

In the study reported here, we apply some of the features of coordination chemistry to solve a long-standing problem in the separation and characterization of lipoprotein particles. Lipoproteins are circulating micelle-like particles responsible for lipid transport. They exist in three major classes: very-low-density lipoprotein, low-density lipoprotein, and high-density lipoprotein in well-defined density ranges using the density gradient ultracentrifugation (DGU) method. The analytical instrumentation of DGU has improved over the years in response to clinical evidence that certain lipoprotein species are linked to a high risk for developing cardiovascular disease. A long-standing problem has been a lack of appropriate gradient-forming solutes that can generate a useful gradient from a homogeneous solution. We have found that a new class of solutes based on metal ion complexes has the potential of providing a wide selection of compounds where the features can be modulated by choice of ligand, complexing metal ion, and counterion. In this study, we have chosen the cesium salt of BiEDTA (CsBiEDTA) and have investigated the dynamics of density gradient formation in the ultracentrifuge. We show that a useful density gradient can be formed within a few hours beginning with a homogeneous solution. We also present data on the migration behavior of lipoproteins under gradient-forming conditions and show that high-resolution density profiles can be obtained with good precision. The resolution of the CsBiEDTA profile is compared with those obtained using high molecular weight organic solutes.     

A technique for dielectric measurement of cylindrical objects in arectangular waveguide

In this paper, the inverse scattering problem of a homogeneous dielectric post in a rectangular waveguide is considered. A novel inversion algorithm, based on the method of moments and eigen analysis, for computation of the dielectric constant of the post (ϵ) from the measured voltage reflection coefficient is introduced. In this method the integral equation for the polarization current induced in the dielectric post is cast into a matrix equation, and then the contribution of ϵ to the resulting reflection coefficient is expressed explicitly using the eigen analysis. It is shown that the dielectric constant can be obtained from the solution of a complex polynomial function which in turn can be obtained numerically using the conjugate gradient method. Practical aspects of dielectric measurement using this technique are discussed. The HP-8510 network analyzer is used to measure the reflection coefficient of dielectric posts in an X-band waveguide sample holder. Metallic and known dielectric posts are used to determine the accuracy of the dielectric measurement technique     

Image reconstruction for a partially immersed imperfectly conducting cylinder by genetic algorithm

This article presents a computational approach to the imaging of a partially immersed imperfectly conducting cylinder. An imperfectly conducting cylinder of unknown shape and conductivity scatters the incident transverse magnetic (TM) wave in free space while the scattered field is recorded outside. Based on the boundary condition and the measured scattered field, a set of nonlinear integral equations, and the inverse scattering problem are reformulated into an optimization problem. We use genetic algorithm (GA) to reconstruct the shape and the conductivity of a partially immersed imperfectly conducting cylinder. The genetic algorithm is then used to find out the global extreme solution of the cost function. Numerical results demonstrated that, even when the initial guess is far away from the exact one, good reconstruction can be obtained. In such a case, the gradient‐based methods often get trapped in a local extreme. In addition, the effect of random noise on the reconstruction is investigated. © 2009 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 19, 299–305, 2009     

Interferometric measurement of light scattering behavior in continuous SiO2 fiber in PMMA matrix composite

Possibility of an interferometric method was examined for evaluating local light scattering behaviors in light transmitting materials. Phase profiles of wavefronts through a continuous SiO₂ glass fiber–PMMA composite was measured by detecting transmitted light though the composite using the interferometric system with a pair of interferometers. Wavefront though the composite shows an anisotropic phase profile, and the phase delay originates from local light scattering due to refractive index difference at an interface between SiO₂ fiber and PMMA matrix. Measured wavefronts demonstrated that the interferometric method is effective tool for an evaluation of local light scattering.     

Simulation of the inhomogeneous medium with a self-adapting grid

It is difficult to solve the problem of tracing rays through an inhomogeneous medium such as the atmosphere or a flowing liquid with the existing methods whose refractive distribution cannot be characterized by any combination of formulas. A new method is developed to efficiently describe such a medium. The method essentially consists of characterizing the inhomogeneous medium with a self-adapting grid, the cell size of which can be automatically varied according to the gradient of the refractive index at each position within the medium. The advantage of this method is its capability to trace rays through a medium with random refractive distribution in an accurate way. To test its correctness, the ray trace through a regular gradient medium has also been made with this method, and the results are compared with those from other commercial lens design codes. It is shown that for appropriate parameter settings this method can obtain great accuracy.