A comparison of transformation methods for evaluating two‐dimensional weakly singular integrals

Accurate numerical evaluation of integrals arising in the boundary element method is fundamental to achieving useful results via this solution technique. In this paper, a number of techniques are considered to evaluate the weakly singular integrals which arise in the solution of Laplace's equation in three dimensions and Poisson's equation in two dimensions. Both are two‐dimensional weakly singular integrals and are evaluated using (in a product fashion) methods which have recently been used for evaluating one‐dimensional weakly singular integrals arising in the boundary element method. The methods used are based on various polynomial transformations of conventional Gaussian quadrature points where the transformation polynomial has zero Jacobian at the singular point. Methods which split the region of integration into sub‐regions are considered as well as non‐splitting methods. In particular, the newly introduced and highly accurate generalized composite subtraction of singularity and non‐linear transformation approach (GSSNT) is applied to various two‐dimensional weakly singular integrals. A study of the different methods reveals complex relationships between transformation orders, position of the singular point, integration kernel and basis function. It is concluded that the GSSNT method gives the best overall results for the two‐dimensional weakly singular integrals studied. Copyright © 2002 John Wiley & Sons, Ltd.     

Revised Estimates of Dimension and Exercise Variance Components in Assessment Center Postexercise Dimension Ratings.

The authors reanalyzed assessment center (AC) multitrait-multimethod (MTMM) matrices containing correlations among postexercise dimension ratings (PEDRs) reported by F. Lievens and J. M. Conway (2001). Unlike F. Lievens and J. M. Conway, who used a correlated dimension-correlated uniqueness model, we used a different set of confirmatory-factor-analysis-based models (1-dimension-correlated Exercise and 1-dimension-correlated uniqueness models) to estimate dimension and exercise variance components in AC PEDRs. Results of reanalyses suggest that, consistent with previous narrative reviews, exercise variance components dominate over dimension variance components after all. Implications for AC construct validity and possible redirections of research on the validity of ACs are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Hopping and optical absorption of electrons in nano-porous crystal 12CaO·7Al2O3

Recently it has been discovered that a nano-porous main group oxide 12CaO·7Al₂O₃ (C12A7) can be converted from a wide-gap insulator to a good transparent conductor. Using ab initio modelling we explain good conductivity of this material by very small barriers for hopping of localised electrons between neighbouring positive cages. We show that optical absorption of C12A7 in infrared region and at energies higher than 2.7 eV is due to inter-cage and intra-cage electron transitions, respectively. The proposed mechanisms can be useful in further search for conducting transparent media.     

STRESS INTENSITY FACTORS AND WEIGHT FUNCTIONS FOR SEMI-ELLIPTICAL SURFACE CRACKS IN FINITE-THICKNESS PLATES UNDER TWO-DIMENSIONAL STRESS DISTRIBUTION

Abstract— A Fourier series approach is proposed to calculate stress intensity factors using weight functions for semi-elliptical surface cracks in flat plates subjected to two-dimensional stress distributions. The weight functions were derived from reference stress intensity factors obtained by three-dimensional finite element analyses. The close form weight functions derived are suitable for the calculation of stress intensity factors for semi-elliptical surface cracks in flat plates under two-dimensional stress distributions with the crack aspect ratio in the range of 0.1 ≤ a/c ≤ 1 and relative depth in the range of 0 ≤ a/t ≤ 0.8. Solutions were verified using several two-dimensional non-linear stress distributions; the maximum difference being 6%.     

Management of multidimensional discrete data

Spatial database management involves two main categories of data: vector and raster data. The former has received a lot of in-depth investigation; the latter still lacks a sound framework. Current DBMSs either regard raster data as pure byte sequences where the DBMS has no knowledge about the underlying semantics, or they do not complement array structures with storage mechanisms suitable for huge arrays, or they are designed as specialized systems with sophisticated imaging functionality, but no general database capabilities (e.g., a query language). Many types of array data will require database support in the future, notably 2-D images, audio data and general signal-time series (1-D), animations (3-D), static or time-variant voxel fields (3-D and 4-D), and the ISO/IEC PIKS (Programmer's Imaging Kernel System) BasicImage type (5-D). In this article, we propose a comprehensive support ofmultidimensional discrete data (MDD) in databases, including operations on arrays of arbitrary size over arbitrary data types. A set of requirements is developed, a small set of language constructs is proposed (based on a formal algebraic semantics), and a novel MDD architecture is outlined to provide the basis for efficient MDD query evaluation.     

The aditi deductive database system

Deductive databases generalize relational databases by providing support for recursive views and non-atomic data. Aditi is a deductive system based on the client-server model; it is inherently multi-user and capable of exploiting parallelism on shared-memory multiprocessors. The back-end uses relational technology for efficiency in the management of disk-based data and uses optimization algorithms especially developed for the bottom-up evaluation of logical queries involving recursion. The front-end interacts with the user in a logical language that has more expressive power than relational query languages. We present the structure of Aditi, discuss its components in some detail, and present performance figures.     

Konzept zur Maßstabsübertragung beim Suspendieren im Rührbehälter

Concept for Scale-up on Suspension in a Stirred Tank. The relationships derived for the suspension of solids in a propeller loop can be applied to corresponding processes in a stirred tank by means of analogy considerations. Accordingly, the ratio of stirrer power to slip power of laminar flow state is inversely proportional to the vessel diameter. In contrast, the power ratio remains constant in turbulent flow. There is a pronounced transition range between these two limiting states. The author's own experimental studies performed over a wide range of Re numbers for the recycling flow confirm this relationship. The observations presented explain why numerous authors have determined scale-up rules lying between these two extremes. The experiments shows that the power input for suspension is always significantly greater than the slip power. Under otherwise identical conditions, the necessary stirrer power is smaller by a factor of three for a propeller stirrer than for a disk impeller. The suspension of small solids concentrations can also be approximated by the flow model presented. The somewhat different physical relations valid in this case are substantiated by the author's experiments. The model also provided information relevant to scale-up when the particle properties are unknown. This is demontrated for an example in a 21 m³ vessel.     

Type inference in stack based languages

We consider a language of operations which pass parameters by means of a stack. An algebra over the set of type signatures is introduced, which allows the type signature of a program to be obtained from the type signatures of its constituent operations.Although the theories apply in principle to any stack based language, they have been evolved with particular regard to the proposed ANSI Standard Forth language, which is currently implemented in a type free manner. We hope this work will stimulate an interest in Forth amongst those applying algebraic techniques in software engineering, and we hope to lay the theoretical foundations for implementing practical type checkers to support Forth.