Radiative Heat Transfer in a Resistance Heated Floating Zone Furnace: A Numerical Study with FIDAPTM

This paper presents a numerical study of radiative heat transfer in a floating zone (FZ) furnace which was performed by using the commercial finite element program FIDAP^TM. This resistance furnace should provide a temperature higher than the melting temperature of silicon (i.e. T_max ≈ 1500 °C) and a variable temperature gradient at the liquid/solid interface (≥ 25 K/cm). Due to the high working temperatures, heat radiation plays the dominant role for the heat transfer in the furnace. For this reason, the quality of view factors used in the wall‐to‐wall model was carefully inspected with energy‐balance checks. A numerical model with two control parameters is applied to study the influence of material and geometrical parameters on the temperature field. In addition, this model allows us to estimate the internal thermal conditions which were used as thermal boundary conditions for partial 3D simulations. The influences of an optical lens system on the radial symmetry of the temperature field were examined with these partial 3D simulations. Furthermore, we used the inverse modeling method to achieve maximum possible temperature gradients at the liquid/solid interface according to the limitation of maximum available power and the maximum stable height of a melt zone.     

Analysis of flow in the plate‐spiral of a reaction turbine using a streamline upwind Petrov–Galerkin method

The prediction of the flow field in a novel spiral casing has been accomplished. Hydraulic turbine manufacturers are considering the potential of using a special type of spiral casing because of the easier manufacturing process involved in its fabrication. These special spiral casings are known as plate‐spirals. Numerical simulation of complex three‐dimensional flow through such spiral casings has been accomplished using a finite element method (FEM). An explicit Eulerian velocity correction scheme has been deployed to solve the Reynolds‐average Navier–Stokes equations. The simulation has been performed to describe the flow in high Reynolds number (10⁶) regimes. For spatial discretization, a streamline upwind Petrov–Galerkin (SUPG) technique has been used. The velocity field and the pressure distribution inside the spiral casing reveal meaningful results. Copyright © 2000 John Wiley & Sons, Ltd.     

Real valued iterative methods for solving complex symmetric linear systems

Complex valued systems of equations with a matrix R + 1S where R and S are real valued arise in many applications. A preconditioned iterative solution method is presented when R and S are symmetric positive semi‐definite and at least one of R, S is positive definite. The condition number of the preconditioned matrix is bounded above by 2, so only very few iterations are required. Applications when solving matrix polynomial equation systems, linear systems of ordinary differential equations, and using time‐stepping integration schemes based on Padé approximation for parabolic and hyperbolic problems are also discussed. Numerical comparisons show that the proposed real valued method is much faster than the iterative complex symmetric QMR method. Copyright © 2000 John Wiley & Sons, Ltd.     

Twin Structure of (La,Nd)GaO3 Solid Solutions

For La_1‐xNd_xGaO₃ crystals the La‐Nd substitution leads to decrease of spontaneous strains and for composition with x≈0.32 the six possible twin states of orthorhombic phase (m3mFmmm) may be degenerated in three twin states inhered in m3mF4/mmm species when a distorted perovskite pseudocell becomes tetragonal. The {110} and {112} reflection twins and axial twins with compositional planes close to (211) and (21‐1) (S‐walls) were identified in La_1‐xNd_xGaO₃ (x=0.07, 0.12, 0.20) solid solutions crystals. All observed twins are typical for crystals with GdFeO₃ type perovskite‐like structure. It has been shown that for x≤0.2 and x≥0.5 orientations of S‐walls weakly depend on La/Nd ratio, whereas in the range of 0.2<x<0.5 they depend strongly on the solid solution composition. The tilt angle between two twin states across twin boundary in La_1‐xNd_xGaO₃ (x<0.6) solid solutions is smaller than that between two twins in pure LaGaO₃ or NdGaO₃.     

X‐ray Rotation‐Tilt‐Method — First Results of a new X‐ray Diffraction Technique

That from us as X‐ray Rotation‐Tilt Technique (XRT Method) designated procedure principle represents a world innovation and overcomes essential disadvantages of comparable diffraction techniques known up to now. Starting from the origin and the informational content of the XRT interferences a realization of a special equipment and selected examples of some first applications are presented.     

Semiconvergence analysis of the randomized row iterative method and its extended variants

The row iterative method is popular in solving the large‐scale ill‐posed problems due to its simplicity and efficiency. In this work we consider the randomized row iterative (RRI) method to tackle this issue. First, we present the semiconvergence analysis of RRI method for the overdetermined and inconsistent system, and derive upper bounds for the noise error propagation in the iteration vectors. To achieve a least squares solution, we then propose an extended version of the RRI (ERRI) method, which in fact can converge in expectation to the solution of the overdetermined or underdetermined, consistent or inconsistent systems. Finally, some numerical examples are given to demonstrate the convergence behaviors of the RRI and ERRI methods for these types of linear system.     

目标红外光谱辐射强度测量技术研究

本文从理论上分析了测量野外目标红外光谱辐射强度方法，提出了实现测量装置的结构形式，并对测量中的关键技术，例如测量速度、系统噪声、分光、信号处理等进行了重点探讨。     

Ring currents in condensed ring systems

We have studied magnetism and aromaticity of polycyclic ring systems by analyzing ring currents for different circulations in these molecules. The technique employed for calculating ring currents uses correction vectors which implicitly includes all the eigenstates of the Hamiltonian in the space of the chosen configurations. We have employed the Pariser–Parr–Pople Hamiltonian and have carried out full configuration interaction (CI) calculations for small systems and approximate CI calculations for large systems. The systems studied include polyacenes, nonaromatic ring systems including the C₆₀ fragments pyracylene, fluoranthene, and corannulene, and heteroatomic systems with upto two six-membered rings. We find that in polyacenes, the aromaticity of the extreme phenyl rings reduces with increasing number of phenyl rings in the system, and it saturates at ≈⅔ the benzene value. In systems containing nonaromatic rings, we find paramagnetic or diamagnetic behavior for different circulations depending upon the number of atoms in the chosen ring cycle, in agreement with the 4n+2 rule. In corannulene, the largest fragment of C₆₀ we have studied, the five-membered ring is weakly diamagnetic while the six-membered ring is more diamagnetic, although much less than in isolated benzene. The ring structures with heteroatoms studied are pyridine, pyrimidine, and its isomers, s-triazine, quinoline and its isomer, and quinazoline and its isomers. All these have similar ring currents as in their purely carbon counterparts, although ions of these molecules show interesting behavior. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 70: 503–513, 1998     

A nearly optimal preconditioning based on recursive red–black orderings

Considering matrices obtained by the application of a five-point stencil on a 2D rectangular grid, we analyse a preconditioning method introduced by Axelsson and Eijkhout, and by Brand and Heinemann. In this method, one performs a (modified) incomplete factorization with respect to a so-called ‘repeated’ or ‘recursive’ red–black ordering of the unknowns while fill-in is accepted provided that the red unknowns in a same level remain uncoupled. Considering discrete second order elliptic PDEs with isotropic coefficients, we show that the condition number is bounded by 𝒪(n ${}^{\text{½ log}{}_{\text{2}}\text{(√(5) −1)}}$ ) where n is the total number of unknowns (½ log₂(√(5) − 1) = 0.153), and thus, that the total arithmetic work for the solution is bounded by 𝒪(n^1.077). Our condition number estimate, which turns out to be better than standard 𝒪(log² n) estimates for any realistic problem size, is purely algebraic and holds in the presence of Neumann boundary conditions and/or discontinuities in the PDE coefficients. Numerical tests are reported, displaying the efficiency of the method and the relevance of our analysis. © 1997 John Wiley & Sons, Ltd.     

Multilevel Deep Feature Generation Framework for Automated Detection of Retinal Abnormalities Using OCT Images

Optical coherence tomography (OCT) images coupled with many learning techniques have been developed to diagnose retinal disorders. This work aims to develop a novel framework for extracting deep features from 18 pre-trained convolutional neural networks (CNN) and to attain high performance using OCT images. In this work, we have developed a new framework for automated detection of retinal disorders using transfer learning. This model consists of three phases: deep fused and multilevel feature extraction, using 18 pre-trained networks and tent maximal pooling, feature selection with ReliefF, and classification using the optimized classifier. The novelty of this proposed framework is the feature generation using widely used CNNs and to select the most suitable features for classification. The extracted features using our proposed intelligent feature extractor are fed to iterative ReliefF (IRF) to automatically select the best feature vector. The quadratic support vector machine (QSVM) is utilized as a classifier in this work. We have developed our model using two public OCT image datasets, and they are named database 1 (DB1) and database 2 (DB2). The proposed framework can attain 97.40% and 100% classification accuracies using the two OCT datasets, DB1 and DB2, respectively. These results illustrate the success of our model.