Boundary knot method for 2D and 3D Helmholtz and convection–diffusion problems under complicated geometry

The boundary knot method (BKM) of very recent origin is an inherently meshless, integration‐free, boundary‐type, radial basis function collocation technique for the numerical discretization of general partial differential equation systems. Unlike the method of fundamental solutions, the use of non‐singular general solution in the BKM avoids the unnecessary requirement of constructing a controversial artificial boundary outside the physical domain. The purpose of this paper is to extend the BKM to solve 2D Helmholtz and convection–diffusion problems under rather complicated irregular geometry. The method is also first applied to 3D problems. Numerical experiments validate that the BKM can produce highly accurate solutions using a relatively small number of knots. For inhomogeneous cases, some inner knots are found necessary to guarantee accuracy and stability. The stability and convergence of the BKM are numerically illustrated and the completeness issue is also discussed. Copyright © 2003 John Wiley & Sons, Ltd.     

A study on bioglass ceramics in the Na2O-CaO-SiO2-P2O5 system

A new bioglass ceramic with composition of Na₂O 12%, CaO 28%, P₂O₅ 10% and SiO₂ 50% with a high bending strength (120–140 MPa) and compressive strength (600–750 MPa) was studied. The crystallized phases of-Ca₂P₂P₇ and Na₂Ca₃Si₆O₁₆ were determined by X-ray diffraction. Optical microscopy of the material revealed that a very uniform crystal size of about 30 m was obtained with high nucleation frequency. The nucleation and crystallization processes were also investigated. The rat shoulder test showed that the material formed a tight chemical bond with biological texture and had good biocompatibility.     

Growth characteristics of β-SiC by chemical vapour deposition

A twin-plane re-entrant corner effect (TPRE) in growth of chemical vapour deposited (CVD) -SiC is described by the film and particles of gas-phase homogeneous nucleation. The structural morphology has been characterized by scanning electron microscopy and transmission electron microscopy. Morphological characteristics of the deposited crystals, such as triangularity, hexagons or facets have been explained in terms of the re-entrant corner effect at twin junctions, which were proposed as preferential growth sites for perfect crystals. For real deposits, screw dislocations and/or the re-entrant corner effect are not expected to be compatible. The majority of chemical vapour deposited SiC crystals have a high defect density comprised of {111} twins and dislocations associated with the process variables. Infrared transmission spectra and electron spectroscopy of chemical analysis indicated that the major chemical bonds of CVD -SiC were Si-C and C-H bonds. The positions of the 1s or 2p corelevel peaks for deposits are described.     

An NMR study of acid sites on chlorided alumina catalysts using trimethylphosphine as a probe

The MAS-NMR spectra of adsorbed trimethylphosphine (TMP) were used to determine the concentration of Brønsted and Lewis acid sites on pure and chlorinated-Al₂O₃ samples. Chlorination with CHCl₃,CCl₄ or AlCl₃ promoted the formation of Brønsted acid centers, which are characterized by the protonated adduct of TMP. This adduct has a³¹P chemical shift of ca. –3.8 ppm and a J_P–H scalar coupling of 517 Hz. Additional resonances in the –44 to –54 ppm range are attributed to Lewis acid-base pairs. In some cases a partially resolved J_P–Al coupling is observed, which confirms the assignment. Upon thermal treatment of a chlorinated sample at temperatures > 200°C, the concentration of Brønsted acid centers decreased; the concentration of one type of Lewis acid increased and another remained almost constant. In a parallel set of experiments the initial conversion ofn-hexane at 150°C and the yields of cracking and isomerization products were determined. Comparable functional relationships were observed between the loss of Brønsted acid sites and the decrease in yields of both cracking and isomerization products. These results suggest that Bransted acidity is responsible for the cracking and isomerization ofn-hexane over chlorided aluminas at 150°C.     

Formation and behavior of mechanoradicals in pulp cellulose

The mechanical degradation of pulp cellulose fiber was studied at ambient temperature and at 77°K. ESR findings reveal that mechanical degradation occurs via free-radical routes. Three types of mechanoradicals contributing singlet, doublet, and triplet ESR signals are identified. The singlet signals are derived from the alkoxy radicals at C₄ positions as a consequence of the cleavage of glucosidic bonds, the radical pairs generated at C₁ positions contributing the doublet signals. Triplet signals are derived from the C₂ and C₃ positions due to the cleavage of C₂ and C₃ bonds. Of these radicals, alkoxy radicals are the most stable at ambient temperature. Carbon radicals are capable of interacting rapidly with oxygen molecules to produce peroxy radical intermediates, where alkoxy radicals are inert toward oxygen molecules. ESR study also reveals that cellulose mechanoradicals are capable of initiating vinyl polymerization. MMA propagating radicals are identified when the monomers are in contact with cellulose mechanoradicals. The ability of mechanoradicals to initiate graft copolymerization from cellulose fiber is discussed.     

The optical properties of hot-pressed magnesium fluoride and single-crystal magnesium fluoride in the 0.1 to 9.0 μm range

A polycrystalline high-density magnesium fluoride, fabricated into plates or shapes by hot-pressing, exhibits high in-line transmittance from 2.5 to 6.0 m, and single-crystal magnesium fluoride extends from 0.1 to 6.0 m. The ultimate and practical transmittance of hot-pressed magnesium fluoride using intrinsic and extrinsic reflectance, absorptance and scattering mechanisms, are investigated. The intrinsic scattering mechanism due to the polycrystalline structure is basically responsible for the tremendous difference in transmittance in the short wavelength region of the spectrum. The in-line transmittance of polycrystalline and singlecrystal MgF₂ is discussed in terms of sample thickness.     

Scheduling for electricity cost in a smart grid

We study an offline scheduling problem arising in demand response management in a smart grid. Consumers send in power requests with a flexible set of timeslots during which their requests can be served. For example, a consumer may request the dishwasher to operate for 1 h during the periods 8am to 11am or 2pm to 4pm. The grid controller, upon receiving power requests, schedules each request within the specified duration. The electricity cost is measured by a convex function of the load in each timeslot. The objective of the problem is to schedule all requests with the minimum total electricity cost. As a first attempt, we consider a special case in which the power requirement and the duration a for which a request needs service are both unit-size. For this problem, we present a polynomial time offline algorithm that gives an optimal solution and shows that the time complexity can be further improved if the given set of timeslots forms a contiguous interval.     

The Electrochemical Response of Single Crystalline Copper Nanowires to Atmospheric Air and Aqueous Solution

In this paper, single crystalline copper nanowires (CuNWs) have been electrochemically grown through anodic aluminum oxide template. The environmental stability of the as‐obtained CuNWs in both 40% relative humidity (RH) atmosphere and 0.1 m NaOH aqueous solution has been subsequently studied. In 40% RH atmosphere, a uniform compact Cu₂O layer is formed as a function of exposure time following the logarithmic law and epitaxially covers the CuNW surfaces. It is also found that the oxide layers on CuNWs are sequentially grown when subjected to the cyclic voltammetry measurement in 0.1 m NaOH solution. An epitaxially homogeneous Cu₂O layer is initially formed over the surface of the CuNW substrates by solid‐state reaction (SSR). Subsequently, the conversion of Cu₂O into epitaxial CuO based on the SSR takes place with the increase of applied potential. This CuO layer is partially dissolved in the solution forming Cu(OH)₂, which then redeposited on the CuNW surfaces (i.e., dissolution‐redeposition (DR) process) giving rise to a mixed polycrystalline CuO/Cu(OH)₂ layer. The further increase of applied potential allows the complete oxidation of Cu₂O into CuO to form a dual‐layer structure (i.e., CuO inner layer and Cu(OH)₂ outer layer) with random orientations through an enhanced DR process.