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.     

Colloidal processing of polymer ceramic nanocomposite integral capacitors

Polymer ceramic composites form a suitable material system for low temperature fabrication of embedded capacitors appropriate for the MCM-L technology. Improved electrical properties such as permittivity can be achieved by efficient filling of polymers with high dielectric constant ceramic powders such as lead magnesium niobate-lead titanate (PMN-PT) and barium titanate (BT). Photodefinable epoxies as the matrix polymer allow fine feature definition of the capacitor elements by conventional lithography techniques. The optimum weight percent of dispersant is tuned by monitoring the viscosity of the suspension. The dispersion mechanism (steric and electrostatic contribution) in a slightly polar solvent such as propylene glycol methyl ether acetate (PGMEA) is investigated from electrophoretic measurements. A high positive zeta potential is observed in the suspension, which suggests a strong contribution of electrostatic stabilization. By optimizing the particle packing using a bimodal distribution and modified processing methodology, a dielectric constant greater than 135 was achieved in PMN-PT/epoxy system. Suspensions are made with the lowest PGMEA content to ensure the efficiency of the dispersion and efficient particle packing in the dried film. Improved colloidal processing of nanoparticle-filled epoxy is a promising method to obtain ultra-thin capacitor films (<2/spl mu/m) with high capacitance density and improved yield. Capacitance of 35 nF/cm/sup 2/ was achieved with the thinnest films (2.5-3.0 /spl mu/m).     

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.     

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.     

Wear in check valves due to flow induced motion

Experiments showing the frequency and amplitude of the flow induced motion of the gate for a 2- and a 4-in. swing check valve have been performed. The gate motion is due to turbulence in approach flow. We have found the dominant turbulent frequency of the approach flow is about half the natural frequency of the valves. The valves appear to be almost critically damped. Because of this, the valves respond almost as they would to a static force of the magnitude characteristic of the turbulent fluctuation in the flow. Both the dimensionless exciting force and the damping ratio have been found to be independent of valve size so the above statements are true for larger valves also. The recommended valve oscillation amplitudes and frequencies are used to calculate the wear at the shaft and at the stop. For an unpegged check valve, such as one of the 10-in. valves which was used at the San Onofre Nuclear Generation Station, it was found that shaft bearing wear would amount to 0.27 in.³/year and stop wear to 0.03 in.³/year.