Efficient calculation of eddy current responses due to defects

The eddy current responses due to three dimensional defects embedded in a conducting half space are evaluated with an iterative numerical technique using a volume integral formulation in conjunction with a variational expression for the response. This approach is applied to defects of spherical and cylindrical geometry with dimensions up to several skin depths. Computations of the eddy current responses converge in one to four iterations and the comparison to moment-method results and experimental values is discussed. The iterative numerical approach has been found to be robust, to require modest computer time/storage, and to provide a model which can accomodate a wide range of defect parameters.     

Steady-state response of a Cosserat medium with a spherical inclusion

Summary Two concepts of asymmetric eigenstrain and eigentorsion are employed to derive a general steady-state theory of inhomogeneous anisotropic micropolar media containing defects with the help of Green's function technique. In particular, a dynamic inclusion problem for homogeneous isotropic centrosymmetric micropolar elasticity is investigated. By means of Green's functions an exact closed-form solution is presented for the case of a spherical inclusion embedded in an infinitely extended Cosserat medium. With this result, the micropolar dynamic Eshelby tensors for the inside and outside elastic fields of the spherical inclusion are defined and determined. It is confirmed that the classical dynamic and static Eshelby tensors are obtained as two special cases of the micropolar dynamic Eshelby tensors, respectively.     

Quantitative Detection of the Defects in Thin-Walled Pressure Vessels with Holography and Shearing Speckle Interferometry

Quantitative assessment of the coordinates, size, embedding depth, and type of defects of a thin-walled pressure vessel is becoming increasingly important for both economic and safety reasons. Nondestructive testing methods, holographic interferometry, shearing speckle interferometry, and simple mechanical models are combined to quantitatively estimate these defect characteristic parameters (DCPs). Experimental tests were conducted to demonstrate the efficiency and the accuracy of this combined technique for thin-walled spherical vessels that contain the cavities or cracks. Relationships between the DCPs and partial fringe patterns caused by the local defects are presented, and factors that affect the estimative accuracy of DCPs are discussed.     

Preparation of hydroxyapatite spheres with an internal cavity as a scaffold for hard tissue regeneration

Microparticulates are currently regarded as a useful matrix for the delivery of bioactive molecules and tissue cells. Herein, hydroxyapatite (HA) spherical microparticulates with an internal cavity were produced using an oil-in-water emulsion technique. The HA slurry in the organic solvent was formulated into spherical particles in a water bath containing a surfactant. Rapid evaporation of the solvent helped create a cavity within the microparticulates. The microparticulates were heat-treated at 1,200 degrees C to produce bioactive HA particles with a mean size of approximately 363 microm. Osteoblastic cells were observed to spread and grow favorably over the surface as well as within the cavity of the microparticulates. The currently developed HA microparticulates with an internal cavity are considered to be useful as a scaffolding matrix for bone tissue engineering and direct filling skeletal defects.     

Eshelby tensors for a spherical inclusion in microelongated elastic fields

Eshelby tensors are found for a spherical inclusion in a microelongated elastic field. Here, a special micromorphic model is introduced to describe the damaged material which defines the damage as the formation and the growth of microcracks and microvoids occurred in the material at the microstructural level. To determine the new material coefficients of the model, an analogy is established between the damaged body and the composite materials and then Mori–Tanaka homogenization technique is considered to obtain overall material moduli. Following this idea, the determination of the Eshelby tensors which establish the relation between the strains of the matrix material and of the inclusion becomes the first task. Introducing the concept of eigenstrain and microeigenstrain, the general constitutive theory is given for a homogeneous isotropic centrosymmetric microelongated media with defects. Then by the use of Green’s functions, micro and macro elastic fields are presented for the case of spherical inclusions embedded in an infinite microelongated material. Thus, the Eshelby tensors are obtained for a microelongated elastic field with a spherical inclusion and it is also shown that the classical Eshelby tensors can be obtained as a limit case of the microelongation.     

Off-Axis Electron Holography of Nearly-Spherical Faceted Voids in Self-Annealed Implanted Silicon

Nearly spherical voids, with a size on the order of some tens of nanometers, are defects that have recently attracted a renewed interest, due to their capability to getter impurities and point defects in silicon. High-resolution electron holography is employed here to study the three-dimensional configuration of nearly spherical cavities obtained by 100keV P+ ion bombardment of a silicon wafer using an ion beam with a power density of about 40 W/cm² for 4 sec. Reconstructed phase maps have been used to obtain the qualitative topography of the cavity shape as well as quantitative measurements of the depth variations. Faceting of the nearly spherical voids is discussed in detail.     

Order-N study of the structure and energetics of stacking faults in silicon

Formation energies and structural features of two-dimensional extended defects (twin boundaries and stacking faults) in silicon are investigated using an order-N density-matrix tight-binding technique. A slow numerical convergence of the formation energies with respect to calculational parameters is observed and analyzed. Structural features are found to converge faster than formation energies. These observations are shown to be associated with the small energies involved in the formation of these defects, which make the reference to a bulk crystal calculation (needed for the evaluation of the formation energies) to be adequate only at relatively high values of the real-space truncation cutoff associated with the density-matrix approximation. Our results are obtained assuming separation-based spherical cutoffs, and suggest that calculations of stacking-fault energies may be used to compare the different truncation schemes for the density matrix that have been proposed in the literature. Converged tight-binding values for the formation energies agree well with those from available experimental studies.     

Multi-step ART1 algorithm for recognition of defect patterns on semiconductor wafers

The integrated circuits (ICs) on wafers are highly vulnerable to defects generated during the semiconductor manufacturing process. The spatial patterns of locally clustered defects are likely to contain information related to the defect generating mechanism. For the purpose of yield management, we propose a multi-step adaptive resonance theory (ART1) algorithm in order to accurately recognise the defect patterns scattered over a wafer. The proposed algorithm consists of a new similarity measure, based on the p-norm ratio and run-length encoding technique and pre-processing procedure: the variable resolution array and zooming strategy. The performance of the algorithm is evaluated based on the statistical models for four types of simulated defect patterns, each of which typically occurs during fabrication of ICs: random patterns by a spatial homogeneous Poisson process, ellipsoid patterns by a multivariate normal, curvilinear patterns by a principal curve, and ring patterns by a spherical shell. Computational testing results show that the proposed algorithm provides high accuracy and robustness in detecting IC defects, regardless of the types of defect patterns residing on the wafer.     

Three-dimensional shape measurement of non-full-field reflective surfaces

We describe a technique for the measurement of non-full-field reflective surfaces by using phase-stepping profilometry. We explain the principles of phase demodulation and discuss three-dimensional (3-D) height reconstruction in the case of measuring surfaces with reflective properties such as plain glass and mirrored glass. A number of required calibration algorithms are described to obtain surface slopes and reconstructed 3-D heights of the whole surface. Masking for non-full-field objects and the surface reconstruction procedure are demonstrated mathematically and algorithmically. Several experimental results are given for glass with different shapes and defects. Measurement of a spherical mirror with a known radius has also allowed us to show the performance of the proposed technique. This allows for the possibility to compare 3-D data from the known object with data taken from the measurement system.     

Ground state of3He-A in a sphere

We compare the free energies and currents of four trial states of³He-A in spherical geometries. The spherical boojum texture is found to be energetically stable for all container radii down to R ～46ξ, where ξ is the superfluid coherence length. Textures with line defects in the bulk will become energetically favorable below this radius.     

Laws of approach to magnetic saturation for interacting and isolated spherical and cylindrical defects in isotropic magnetostrictive media

Laws of approach to magnetic saturation are derived for interacting spherical and cylindrical defects in isotropic magnetostrictive media like amorphous materials. The normalized longitudinal magnetic deviation ΔM/M goes as 1/H²for both cases, provided all defects have the same sign. For randomly signed defects, 1/H^5/4and 1/H^3/2laws for spheres and cylinders, respectively. Isolated cylindrical defects obey a 1/H or 1/H²law depending on whether the defect is small or large compared to an exchange length.     

Application of invariant integrals to the problems of defect identification

A problem of parameters identification for embedded defects in a linear elastic body using results of static tests is considered. A method, based on the use of invariant integrals is developed for solving this problem. A problem on identification the spherical inclusion parameters is considered as an example of the proposed approach application. It is shown that the radius, elastic moduli and coordinates of a spherical inclusion center are determined from one uniaxial tension (compression) test. The explicit formulae expressing the spherical inclusion parameters by means of the values of corresponding invariant integrals are obtained for the case when a spherical defect is located in an infinite elastic solid. If the defect is located in a bounded elastic body, the formulae can be considered as approximate ones. The values of the invariant integrals can be calculated from the experimental data if both applied loads and displacements are measured on the surface of the body in the static test. A numerical analysis of the obtained explicit formulae is fulfilled. It is shown that the formulae give a good approximation of the spherical inclusion parameters even in the case when the inclusion is located close enough to the surface of the body.     

An efficient solid angle sampling technique using bounding volume approach

Abstract

Solid angle sampling is an important variance‐reduced technique when solving global illumination problems by Monte Carlo methods. In this paper, we present an efficient solid angle sampling technique where a paraboloidal luminaire is taken as a case study. The efficiency of our technique is due to the fact that we employ a tight bounding volume to approximate the solid angle. Our technique includes three processes. The construction process builds a bounding volume. It is a convex, frustum‐like polyhedron with a compromise between the tightness and the vertex numbers. The projection process approximates the solid angle as a convex spherical polygon on a unit hemisphere. Finally, the triangulation process triangulates the convex spherical polygon into spherical triangles for stratified sampling. We analyzed our technique in Monte Carlo direct lighting and Monte Carlo path tracing rendering algorithms. The results show that our technique provides up to 90% sampling efficiency. The significance of the proposed technique is that solid angle sampling, from being not possible for the paraboloidal luminaire, is now feasible. In addition, this technique is efficient for sampling, and it is also applicable to other types of luminaires, such as cylindrical and conic luminaires.     

Twist disclination loop in an elastic spheroid

A solution of the boundary-value problem in the isotropic theory of elasticity for a twist disclination loop (TDL) in a spherical body (spheroid) has been obtained for the first time using the method of virtual defects. The virtual defects are represented by TDLs with elastic fields, which are expanded into series with respect to Legendre polynomials. The elastic fields and energy of a TDL are determined depending on its position in the spheroid.     

球面端坯料热滚切成形仿真及机理分析

坯料端部预加工成球面状是改善楔横轧件凹心缺陷的有效方法.为了避免传统机加工制坯带来的材料损失,本文提出了一种基于金属塑性成形的球面端部热滚切成形方法.建立了球面端坯料热滚切成形的有限元模型,通过仿真分析了成形过程中滚切区金属的位移场变化规律和应变场分布特征,阐述了球面端坯料的成形机理以及在挡块作用下堆料的抑制机理,并对...     

The Shrinkage Characteristic of a Spherical Cavity in Three-Dimensional Piezoelectric Grain

In this article, an analytical method is presented to solve the shrinkage rate and the healing history of a spherical cavity in three-dimensional piezoelectric grains under electric field, interface pressure, and internal gas pressure. From example calculations, it is seen that because of the influence of piezoelectric characteristics and electric fields, a spherical cavity in three-dimensional piezoelectric grain subjected to hydrostatic interface pressures does not completely eliminate, which is obviously consistent with some experimental observations from the micro-hole healing process. The result is useful to reveal the healing mechanism of defects in piezoelectric materials under electric and mechanical loads.     

Acoustic diffraction by two concentric coaxial soft spherical caps

Summary The subject of this paper is the problem of diffraction of a time-harmonic axially symmetric acoustic wave by two concentric coaxial soft spherical caps. An integral equation technique is employed to solve such a boundary value problem involving two concentric coaxial spherical caps. Approximate expressions are derived for the far field amplitude as well as the scattering cross section for this problem when the incident wave is a low frequency axially symmetric plane wave travelling along the common axis of the two caps. By taking appropriate limits, the formulae for scattering cross section for the corresponding problems for a soft spherical cap, a soft sphere and a soft sphere bounded by a concentric soft spherical cap are also derived. Furthermore, the total electrostatic charge required to raise the two concentric coaxial spherical caps to unit potentials in a free space is readily evaluated from the analysis of this paper.     

Study of crystal defects using ion channelling and channelling radiation

The channelling technique to study crystal defects is described and its applications to various kind of defects to study their atomistic nature have been reviewed. Special emphasis has been placed on the applications to extended defects like dislocations. Finally a related new technique being developed for the last few years, namely the channelling radiation technique has been discussed along with its applications to study the dislocations.     

Virus Matryoshka: A Bacteriophage Particle—Guided Molecular Assembly Approach to a Monodisperse Model of the Immature Human Immunodeficiency Virus

Immature human immunodeficiency virus type 1 (HIV‐1) is approximately spherical, but is constructed from a hexagonal lattice of the Gag protein. As a hexagonal lattice is necessarily flat, the local symmetry cannot be maintained throughout the structure. This geometrical frustration presumably results in bending stress. In natural particles, the stress is relieved by incorporation of packing defects, but the magnitude of this stress and its significance for the particles is not known. In order to control this stress, we have now assembled the Gag protein on a quasi‐spherical template derived from bacteriophage P22. This template is monodisperse in size and electron‐transparent, enabling the use of cryo‐electron microscopy in structural studies. These templated assemblies are far less polydisperse than any previously described virus‐like particles (and, while constructed according to the same lattice as natural particles, contain almost no packing defects). This system gives us the ability to study the relationship between packing defects, curvature and elastic energy, and thermodynamic stability. As Gag is bound to the P22 template by single‐stranded DNA, treatment of the particles with DNase enabled us to determine the intrinsic radius of curvature of a Gag lattice, unconstrained by DNA or a template. We found that this intrinsic radius is far larger than that of a virion or P22‐templated particle. We conclude that Gag is under elastic strain in a particle; this has important implications for the kinetics of shell growth, the stability of the shell, and the type of defects it will assume as it grows.     

Analysis of scattering by a linear chain of spherical inclusions in an optical fiber

The scattering by a linear chain of spherical dielectric inclusions, embedded along the axis of an optical fiber, is analyzed using a rigorous integral equation formulation, based on the dyadic Green's function theory. The coupled electric field integral equations are solved by applying the Galerkin technique with Mie-type expansion of the field inside the spheres in terms of spherical waves. The analysis extends the previously studied case of a single spherical inhomogeneity inside a fiber to the multisphere-scattering case, by utilizing the classic translational addition theorems for spherical waves in order to analytically extract the direct-intersphere-coupling coefficients. Results for the transmitted and reflected power, on incidence of the fundamental HE(11) mode, are presented for several cases.