Elastodynamic response of a coplanar periodic layer of elastic spherical inclusions

Reflection and transmission spectra of a plane longitudinal wave normally incident on a coplanar periodic array of identical spherical elastic inclusions in a solid (polyester) matrix are measured at wavelengths that are comparable to the inter-particle distance. These spectra exhibit pronounced Wood's anomalies i.e., a sharp variations in amplitude at the onset of a shear wave diffraction order as well as a drop in the transmission and a corresponding maximum in the reflection coefficients due to an enhancement of the resonance of the particles (for the case reported herein, this is the rigid body translational “dipole” resonance). An approximate low frequency (ka<1) self-consistent model is developed in which multiple scattering is explicitly taken into account by adding appropriate terms to the well-known solution for the scattering of a plane longitudinal wave by a single spherical particle in an unbounded matrix. The results of the numerical calculations show excellent agreement with the experimental data.     

Physical properties of wave scattering by a chiral grating

Wave scattering by a chiral grating is studied in this paper. Numerical results are given, and physical properties are discussed, including the influence of frequency, angle of incidence, and aspect ratio. At high frequencies we find anomalous coupling regions known as Wood's anomalies, which are explained by the excitation and reradiation of leaky waveguide modes in the periodic layer. The chiral grating can possess both frequency-selection and mode-conversion properties.     

APPLICATION OF WAVELETS ON THE INTERVAL TO NUMERICAL ANALYSIS OF INTEGRAL EQUATIONS IN ELECTROMAGNETIC SCATTERING PROBLEMS

The wavelet expansions on the interval are employed for solving the problems of the electromagnetic (EM) scattering from two-dimensional (2-D) conducting objects. The arbitrary configurations of scatterers are modeled using the boundary element method (BEM). By using the wavelets on the interval as basis and test functions, a sparse matrix equation is generated from the integral equation under study. The resulted sparse matrix equation allows the use of sparse matrix solvers or multi-level iterations for rapid solution. The utilization of wavelets on the interval circumvents the difficulties in the application of the wavelets on the real line to finite interval problems, and has no periodicity constraint to the unknown function that is usually imposed by periodic wavelets. Numerical examples are provided and compared with the previously published data or other methods. © 1997 by John Wiley & Sons, Ltd.     

Automatic defect inspection of patterned thin film transistor-liquid crystal display (TFT-LCD) panels using one-dimensional Fourier reconstruction and wavelet decomposition

Large-sized flat-panel displays have become increasingly important for use in computer monitors and televisions. This paper has considered the problem of automatic visual inspection of micro-defects including pinholes, scratches and particles in patterned thin film transistor-liquid crystal display (TFT-LCD) panel surfaces. For large-sized TFT-LCD panel inspection, high-resolution line scan is demanded. We propose a global one-dimensional (1-D) Fourier-based image reconstruction scheme that directly works on the 1-D line images instead of the traditional two-dimensional area images. The proposed method fully uses the inherent geometric structure of a TFT-LCD panel. It first eliminates the frequency components that represent the periodic pattern of a TFT-LCD line image in the 1-D Fourier spectrum and then back-transforms the 1-D Fourier-domain image to the 1-D spatial domain image using the inverse Fourier transform. The Fourier reconstruction process can effectively remove the patterned background and distinctly preserve local anomalies in the resulting 1-D image. Wavelet decomposition is further applied to remove uneven illumination in the filtered image so that defects can be easily segmented with simple statistical control limits. Experimental results on a number of micro-defects embedded in TFT-LCD panels show that the proposed method can reliably detect various ill-defined defects without designing and measuring the quantitative features of individual defect types.     

Plane Problem for Layered Composites with Periodic Array of Interfacial Cracks Under Compressive Static Loading

The current paper addresses the problem of 2-D modelling of the onset of failure process in a layered composite with periodic array of interfacial cracks under static compression along layers. The statement of the problem is based on the most accurate approach, the model of piecewise-homogenous medium. The condition of plane strain state is considered. The shear and the extensional buckling modes are examined. The laminae are modelled by transversally isotropic material (a matrix reinforced by continuous parallel fibres). The complex non-classical failure mechanics problem is solved utilizing finite element analysis. It is found that the 0°-plies volume fraction, the crack length and the mutual position of cracks influence the critical strain in the composite.     

二维金属光栅的矢量模式研究

用矢量模式场来描述二维金属光栅各层中的电磁场。由边界条件,推导出模式场方程组;借助反射透射系数阵递推算法,得出了方程组的解。这种矢量模式方法物理概念清晰且稳定收敛,可以处理任意偏振态平面波入射到二维亚波长金属光栅中的衍射问题。     

Preconditioned Krylov solvers for BEA

The performance of a number of preconditioned Krylov methods is analysed for a large variety of boundary element formulations. Low- and high-order element, two-dimensional (2-D) and three-dimensional 3-D, regular, singular and hypersingular, collocation and symmetric Galerkin, single- and multi-zone, thermal and elastic, continuous and discontinuous boundary formulations with and without condensation are considered. Preconditioned Conjugate Gradient (CG) solvers in standard form and a form effectively operating on the normal equations (CGN), Generalized Minimal Residual (GMRES), Conjugate Gradient Squared (CGS) and Stabilized Bi-conjugate Gradient (Bi-CGSTAB) Krylov solvers are employed in this study. Both the primitive and preconditioned matrix operators are depicted graphically to illustrate the relative amenability of the alternative formulations to solution via Kryiov methods, and to contrast and explain their computational performances. A notable difference between 2-D and 3-D BEA operators is readily visualized in this manner. Numerical examples are presented and the relative conditioning of the various discrete BEA operators is reflected in the performance of the Krylov equation solvers. A preconditioning scheme which was found to be uncompetitive in the collocation BEA context is shown to make iterative solution of symmetric Galerkin BEA problems more economical than employing direct solution techniques. We conclude that the preconditioned Krylov techniques are competitive with or superior to direct methods in a wide range of boundary formulated problems, and that their performance can be partially correlated with certain problem characteristics.     

拉压不同模量材料的参变量变分原理和有限元方法

对具有拉伸和压缩不同模量的材料,建立了平面静力问题的参变量变分原理.基于参变量变分原理,并结合有限元方法,将拉压不同模量平面问题转化为互补问题求解.经典的Lemke算法被用于求解此互补问题.该方法避免了应力状态的假设和刚度矩阵的更新,算法稳定,且收敛速度快.     

A generalized two point ellipsoidal anisotropic ray tracing for converted waves

Rocks can be anisotropic due to a variety of reasons. When estimating rock velocities from seismic data, failure to introduce anisotropy into earth models could generate distortions in the final images that can have enormous economic impact. To estimate anisotropic earth velocities by tomographic methods, it is necessary to trace rays or to solve the wave equation in models where anisotropy has been properly considered. Thus, in this work we present a 3-D generalized ellipsoidal travel time formulation that allow us to trace rays in an anisotropic medium. We propose to trace rays in anisotropic media by solving a set of nonlinear optimization problems, where the group velocities for P and S wave propagation modes are 3-D ellipsoidal approximations that have been recently obtained. Moreover, we prove that this 3-D ellipsoidal anisotropic ray tracing formulation is a convex nonlinear optimization problem, and therefore any solution of the problem is a global minimum. Each optimization problem is solved by the global spectral gradient method, which requires first order information and has low computation and low storage requirements. Our approach for tracing rays in anisotropic media is a generalization in the sense that handles titled axis of symmetry and, close to the axis of symmetry, it is an accurate formulation for 2-D transversely isotropic media and 3-D orthorhombic media, depending on the input parameters. Moreover, this formulation gives the exact ray trajectories in 2-D and 3-D homogeneous isotropic media. The simplicity of the formulation and the low computational cost of the optimization method allow us to present a variety of numerical results that illustrate the behavior and computational advantages of the approach, and the difficulties when working in anisotropic media. Partially supported by Fonacit project UCV-97-003769     

Depth extraction by using the correlation of the periodic function with an elemental image in integral imaging

We propose a depth extraction method by using the correlation between an elemental image and a periodic function in computational integral imaging. Because each elemental image corresponds to a different perspective of the three-dimensional (3-D) object, an elemental image is regarded as the sum of the periodic spatial frequencies depending on the depth of a 3-D object. In this regard, we analyze the property of correlation between the same periodic functions and vice versa. To show the feasibility of the proposed method, we carried out our experiment and presented the results.     

A Linear Algorithm for Tracing Magnet Position and Orientation by Using Three-Axis Magnetic Sensors

For medical diagnoses and treatments, it is often desirable to wirelessly trace an object that moves inside the human body. A magnetic tracing technique suggested for such applications uses a small magnet as the excitation source, which does not require the power supply and connection wire. It provides good tracing accuracy and can be easily implemented. As the magnet moves, it establishes around the human body a static magnetic field, whose intensity is related to the magnet's 3-D position and 2-D orientation parameters. With magnetic sensors, these magnetic intensities can be detected in some predetermined spatial points, and the position and orientation parameters can be computed. Typically, a nonlinear optimization algorithm is applied to such a problem, but a linear algorithm is preferable for faster, more reliable computation, and lower complexity. In this paper, we propose a linear algorithm to determine the 5-D magnet's position and orientation parameters. With the data from five (or more) three-axis magnetic sensors, this algorithm results in a solution by the matrix and algebra computations. We applied this linear algorithm on the real localization system, and the results of simulations and real experiments show that satisfactory tracing accuracy can be achieved by using a sensor array with enough three-axis magnetic sensors.     

Application of MFS for determination of effective thermal conductivity of unidirectional composites with linearly temperature dependent conductivity of constituents

In this paper the problem of the effective conductivity in composite material is considered. It is assumed that the thermal conductivity coefficients of both the matrix and fibres materials are temperature-dependent. It yields the temperature-dependency of the effective thermal conductivity. To determine the effective thermal conductivity a unit-cell approach is used, i.e. heat flow in repeated element, which consists of one fibre in the matrix, is considered. It leads to 2-D nonlinear boundary value problems in matrix and fibre regions. In the paper, it is proposed to solve the given nonlinear boundary value problem by Picard iteration. For every iteration step, the linear boundary value problem with two uncoupled linear partially differential equations and coupled boundary conditions is solved. The method of fundamental solution, supported by radial basis functions approximation, is implemented to obtain the required solutions. The numerical experiment has been performed. The results of the experiment and some conclusions are included as well.     

Two-dimensional phase unwrapping with use of statistical models for cost functions in nonlinear optimization

Interferometric radar techniques often necessitate two-dimensional (2-D) phase unwrapping, defined here as the estimation of unambiguous phase data from a 2-D array known only modulo 2pi rad. We develop a maximum a posteriori probability (MAP) estimation approach for this problem, and we derive an algorithm that approximately maximizes the conditional probability of its phase-unwrapped solution given observable quantities such as wrapped phase, image intensity, and interferogram coherence. Examining topographic and differential interferometry separately, we derive simple, working models for the joint statistics of the estimated and the observed signals. We use generalized, nonlinear cost functions to reflect these probability relationships, and we employ nonlinear network-flow techniques to approximate MAP solutions. We apply our algorithm both to a topographic interferogram exhibiting rough terrain and layover and to a differential interferogram measuring the deformation from a large earthquake. The MAP solutions are complete and are more accurate than those of other tested algorithms.     

The Governing Parameter Method for implicit integration of viscoplastic constitutive relations for isotropic and orthotropic metals

A general algorithm of implicit stress integration in viscoplasticity, based on the governing parameter method (GPM) is briefly presented. It is assumed that the associative viscoplastic constitutive relations are governed by the Perzyna formulation with a generalization suggested by Simo and Hughes. The algorithm is first applied to isotropic metals obeying the von Mises yield condition with mixed hardening and then, to orthotropic metals with a generalized Hill's yield condition including a mixed hardening assumption. Derivation of consistent tangent moduli is presented for both viscoplastic material models. The proposed computational procedures are efficient, since they reduce the problem of stress integration to the solution of one nonlinear equation, can use large time steps and are applicable to 2-D, 3-D, shell and beam structures. The tangent elastic viscoplastic matrix provides high convergence rate in the overall equilibrium iterations. Numerical examples illustrate the main characteristics of the developed computational procedures.     

On the effective medium theory of subwavelength periodic structures

Abstract

The effective medium theory of one-dimensional and two-dimensional periodic structures are investigated. A method based on a Fourier decomposition of the wave propagating along the direction perpendicular to the periodic structures allows one to determine the zeroth-, first- and second-order effective indices. For one-dimensional problems, we derive closed-form expressions of the effective indices for both TE and TM polarization. Our result can be applied to arbitrary periodic structure with symmetric or non-symmetric lamellar or continuously varying index profiles. The theoretical predictions are carefully validated using rigorous coupled-wave analysis. For the two-dimensional case, only symmetric structures are discussed and the computation of the zeroth-, first-, and second-order effective indices requires the inversion of an infinite matrix which can be truncated and simply solved numerically. The EMT prediction is qualitatively validated using rigorous computation for small period-to-wavelength ratios. It is shown that for large period-to-wavelength ratios near the cutoff value, no analogy between 2-D periodic structures and homogeneous media holds for highly modulated lamellar gratings.     

Sparse 2-D arrays for 3-D phased array imaging--design methods

One of the most promising techniques for limiting complexity for real-time 3-D ultrasound systems is to use sparse 2-D layouts. For a given number of channels, optimization of performance is desirable to ensure high quality volume images. To find optimal layouts, several approaches have been followed with varying success. The most promising designs proposed are Vernier arrays, but also these suffer from high peaks in the sidelobe region compared with a dense array. In this work, we propose new methods based on the principles of suppression of grating lobes to form symmetric and non-symmetric regular sparse periodic and radially periodic designs. The proposed methods extend the concept of sparse periodic layouts by exploiting either an increased number of symmetry axes or radial symmetry. We also introduce two new strategies to form designs with nonoverlapping elements. The performance of the new layouts range from the performance of Vernier arrays to almost that of dense arrays. Our designs have simplicity in construction, flexibility in the number of active elements, and the possibility of trade off sidelobe peaks against sidelobe energy.     

Semi-three-dimensional algorithm for time-resolved diffuse optical tomography by use of the generalized pulse spectrum technique

Although a foil three-dimensional (3-D) reconstruction with both 3-D forward and inverse models provide, the optimal solution for diffuse optical tomography (DOT), because of the 3-D nature of photon diffusion in tissue, it is computationally costly for both memory requirement and execution time in a conventional computing environment. Thus in practice there is motivation to develop an image reconstruction algorithm with dimensional reduction based on some modeling approximations. Here we have implemented a semi-3-D modified generalized pulse spectrum technique for time-resolved DOT, where a two-dimensional (2-D) distribution of optical properties is approximately assumed, while we retain 3-D distribution of photon migration in tissue. We have validated the proposed algorithm by reconstructing 3-D structural test objects from both numerically simulated and experimental date. We demonstrate our algorithm by comparing it with the calibrated 2-D reconstruction that is in widespread use as a shortcut to 3-D imaging and proving that the semi-3-D algorithm outperforms the calibrated 2-D algorithm.     

Channel Modeling and Target Design for Two-Dimensional Optical Storage Systems

In this paper, we first show that the symbol response of the two-dimensional (2-D) optical storage (TwoDOS) channel can be computed by a one-dimensional (1-D) Hankel transform, instead of the 2-D Fourier transform. This results in a computationally efficient approach for generating readback signals in the presence of pit-size variations. We also show how to design a 2-D minimum mean-square error (MMSE) equalizer for channels with these distortions. Second, we present a novel way to jointly design equalizer and target under linear constraints on the target, by transforming the 2-D target design problem into a 1-D form. Using a 2-D Viterbi detector, we investigated different target constraints. The results show that the newly proposed “2-D monic constraint” is a reasonable target constraint for a TwoDOS system.     

Periodic review and joint replenishment in stochastic demand environments

In this paper we consider periodic review systems under stochastic demands. First, we study the single product periodic review problem and propose a simple solution procedure which is near optimal. Then, given the existence of this simple procedure, we study the joint replenishment problem for multiple items under stochastic demands and suggest simple heuristics which provide very good results. We find the simple procedures combined with the robustness of the cost function to be very attractive in other applications which require coordination of cycle times under stochastic demands.     

Face verification through tracking facial features.

We propose an algorithm for face verification through tracking facial features by using sequential importance sampling. Specifically, we first formulate tracking as a Bayesian inference problem and propose to use Markov chain Monte Carlo techniques for obtaining an empirical solution. A reparameterization is introduced under parametric motion assumption, which facilitates the empirical estimation and also allows verification to be addressed along with tracking. The facial features to be tracked are defined on a grid with Gabor attributes (jets). The motion of facial feature points is modeled as a global two-dimensional (2-D) affine transformation (accounting for head motion) plus a local deformation (accounting for residual motion that is due to inaccuracies in 2-D affine modeling and other factors such as facial expression). Motion of both types is processed simultaneously by the tracker: The global motion is estimated by importance sampling, and the residual motion is handled by incorporating local deformation into the measurement likelihood in computing the weight of a sample. Experiments with a real database of face image sequences are presented.