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.     

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.     

影色迷人的小天地--夏新LC-17HWT1液晶电视

液晶电视具有图像逼真、画质细腻、层次丰富、立体感强，以及高亮度、宽视角、高清晰等优点；而且轻薄、省电、无闪烁、无辐射，可有效减轻人们的视觉疲劳；液晶电视的接口也极为丰富，可接驳电脑、DVD等音视频设备，现在一些厂家还将读取Flash卡的功能整合进了液晶电视，这让液晶电视具备了更多的数码味道。在一些发达国家，液晶电视已向许多家庭的厨房、起居室和浴室渗透，这让液晶电视的超薄、壁挂、平面、节能环保的优点充分显示出来。而夏新LC-17HWT1液晶电视则是这一方面的佼佼者。     

Low-truncation-error finite difference equations for photonicssimulation. II. Vertical-cavity surface-emitting lasers

For part I see, ibid., p. 134, 1998. The basic approach outlined in the previous article is applied to the difficult problem of computing the optical modes of a vertical-cavity surface-emitting laser. The formulation utilizes a finite difference equation based upon the lowest order term of an infinite series solution of the scalar Helmholtz equation in a local region. This difference equation becomes exact in the one-dimensional (1-D) limit, and is thus ideally suited for nearly 1-D devices such as vertical-cavity lasers. The performance of the resulting code is tested on both a simple cylindrical cavity with known solutions and an oxide-confined vertical-cavity laser structure, and the results compared against second-order-accurate code based upon Crank-Nicolson differencing     

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.