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.     

A new approach to modelling of single droplet drying

A model was developed to predict the change in droplet mass and temperature when it is exposed to hot air, as in spray drying of droplets containing solids. The droplet was assumed first to undergo sensible rapid heating with no mass change. Then the droplet experiences some shrinkage, with no temperature change but rapid mass losses, followed by a period of crust formation with a significant change in droplet mass and temperature and finally a short period of sensible heating of the dried particle. The model, unlike previous models, accounts for shrinkage and for the temperature distribution in the droplet. It provided a good prediction for the change in droplet temperature and mass for some of the experimental measurements available in the literatures.     

Effects of solidification structure on fatigue crack initiation and fatigue strength in Al−Si−Mg cast alloys

Rotating-bending uniaxial fatigue tests and micro-fatigue crack initiation tests were carried out using a permanent mold cast (PMC) and semi-solid die cast (SDC) with Al−7%Si−0.35%Mg composition in order to examine the relationship between solidification structures and fatigue behaviors. The crack length was measured using a replication method. Fatigue strength was improved in SDC, which was almost consistent with the predicted fatigue strength using the size of Si particle cluster. Resistance to fatigue crack initiation and fatigue strength were improved in SDC owing to the finer Si cluster and to higher ultimate tensile strength. Fatigue crack in PMC was preferentially initiated at pores. For SDC, the fatigue crack was initiated at the Si particle/matrix interface, and then sucessively grew along eutectic cell boundaries.     

Effects of hot-carrier stress on high performance polycrystalline silicon thin film transistor with a single perpendicular grain boundary

This paper is a report on the effect of a single perpendicular grain boundary on the hot-carrier and high current stability in high performance polycrystalline silicon (poly-Si) thin film transistors (TFTs). Under a hot carrier stress condition (Vg = Vth + 1 V, Vd = 12 V), the poly-Si TFT with a single grain boundary is superior to the poly-Si without any grain boundary because of the smaller free carriers available for electric conduction. The shift of transconductance in poly-Si TFT with a single grain boundary is less than 5% after hot carrier stress during a period of 1000 s. The shift of transconductance is about 25% in the case of the poly-Si TFTs without a grain boundary in the channel. On high current stress, the poly-Si TFT without the grain boundary is less degraded than the poly-Si TFT with the grain boundary because the concentrated electric field near the drain junction is lower.     

Grain growth kinetics in Dy-doped Bi0.5Na0.5TiO3 ceramics

Dysprosium-doped bismuth sodium titanate ceramics were prepared using the conventional mixed-oxide method. The amount of dysprosium used was varied from 0 to 2 at.%. The mixed powders were calcined at 800 °C and checked for phase purity using X-ray diffraction technique. The calcined powders were then cold-pressed into pellets and sintered at 1050 °C for the time ranging from 2 to 48 h. The ceramics were checked for phases and microstructures using an X-ray diffractometer and a scanning electron microscope, respectively. The analysis showed that undoped BNT ceramics sintered at longer time exhibited a significant grain growth with non-uniform grain size distribution and shape. The Dy-doped BNT however showed a much more limited grain growth behavior, resulting in smaller grain size and more equiaxed grain shape. It was also found that all Dy-doped BNT ceramics sintered at 48 h possessed lower porosity than those sintered for shorter time.     

Drag coefficient of flow around a sphere: Matching asymptotically the wide trend

An empirical relationship of drag coefficient of flow around a sphere is developed for the entire range of Particle Reynolds numbers reported in the literature from Stokes regime to the condition when turbulent boundary layer prevails. The relationship is obtained using an approach to match asymptotically the wide trend of drag coefficient. The matching approach, which relies on dividing the wide trend into smaller segments that can be combined into an overall relationship, employs regression techniques and thus warrants the best-fit accuracy results. The relationship is calibrated with experimental data available in the literature covering the entire range for Reynolds numbers up to ~ 10⁶. For Reynolds values greater than 10⁶, the relationship renders a drag coefficient of 0.2. The performance of the relationship is tested and compared with other suitable models found in the literature. This relationship is also transformed into an explicit expression for settling velocity calculations.     

高温和低张应力引起的非平衡晶界偏聚动力学(Ⅱ)--实验结果的动力学模拟

以文献[1]建立的张应力引起的非平衡晶界偏聚动力学方程模拟了Shinoda T等的磷在钢中的应力时效实验结果和Misra R D K的硫在钢中的应力时效实验结果，模拟结果与实验结果互相吻合。通过模拟发现，张应力使磷-空位复合体以及硫-空位复合体在钢中的扩散系数均增加3个数量级，且磷原子和硫原子的扩散系数分别降低3个和5个数量级。     

Sintering studies of nano-crystalline zinc oxide

Sintering and grain growth of nano-crystalline undoped ZnO has been studied in detail over a wide range of temperature and holding time. Below 800 °C, sintering of over 70% theoretical density is not observed, irrespective of particle size. At 900 °C for 6 h, the nano-crystalline sample sinters to 99% of theoretical density whereas the density for as received sample is 93% of theoretical density. However, at 1300 °C or higher, the densification is found to be much faster and after a few hours becomes independent of holding time. Grain growth studies reveal a similar feature of attaining saturation over holding time. The average saturated grain size is found to be ∼1.5 and ∼2.2 μm at 800 and 900 °C, respectively, while at 1300 °C or higher, it is in between 12 and 13 μm.     

Low temperature synthesis of aluminium titanate by an aqueous sol-gel route

Formation of aluminium titanate (AT) has been achieved at low temperature through sol-gel process using boehmite and titanium hydroxide as precursors by controlling the particle size at nanoscale followed by in-situ peptisation. The formations of AT phase, particle size distributions, sintering and thermal expansion characteristics, and microstructural features have been reported. DTA and XRD analysis have been performed to confirm the formation of AT. A 94% relative density was obtained for aluminium titanate sintered at 1550 °C with controlled grain size in the range of 2-3 μm.