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.     

Decreasing miscibility with greater heterogeneity in ternary polymer blend: poly(cyclohexyl methacrylate), poly(α‐methyl styrene) and poly(4‐methyl styrene)

A ternary blend system comprising poly(cyclohexyl methacrylate) (PCHMA), poly(α‐methyl styrene) (PαMS) and poly(4‐methyl styrene) (P4MS) was investigated by thermal analysis, optical and scanning electron microscopy. Ternary phase behaviour was compared with the behaviour for the three constituent binary pairs. This study showed that the ternary blends of PCHMA/PαMS/P4MS in most compositions were miscible, with an apparent glass transition temperature (T_g) and distinct cloud‐point transitions, which were located at lower temperatures than their binary counterparts. However, in a closed‐loop range of compositions roughly near the centre of the triangular phase diagram, some ternary blends displayed phase separation with heterogeneity domains of about 1 µm. Therefore, it is properly concluded that ternary PCHMA/PαMS/P4M is partially miscible with a small closed‐loop immisciblity range, even though all the constituent binary pairs are fully miscible. Thermodynamic backgrounds leading to decreased miscibility and greater heterogeneity in a ternary polymer system in comparison with the binary counterparts are discussed. © 2003 Society of Chemical Industry     

Nanoweb Formation: 2D Self‐Assembly of Semiconductor Gallium Oxide Nanowires/Nanotubes

This paper reports a method to produce networks of crystalline gallium oxide comprised of one‐dimensional (1D) nanostructures. Because of the unique arrangement of wires, these crystalline networks are termed as ‘nanowebs’. Nanowebs are of great technological interest since they contain wire densities of the order of 10⁹ cm^–2. A possible mechanism for the fast self‐assembly of crystalline metal oxide nanowires involves multiple nucleation and coalescence via oxidation–reduction reactions at the molecular level. The preferential growth of nanowires parallel to the substrate enabled them to coalesce into regular polygonal networks. The individual segments of the polygonal network consist of both nanowires and nanotubules of β‐gallium oxide. Individual wire properties contribute to a nanoweb’s overall capacity and the implications for devices based on nanowebs are expected to be enormous.     

Positively Thermo‐Sensitive Monodisperse Core–Shell Microspheres

In this paper, we report on a novel family of monodisperse thermo‐sensitive core–shell hydrogel microspheres that is featured with high monodispersity and positively thermo‐responsive volume phase transition characteristics with tunable swelling kinetics, i.e., the particle swelling is induced by an increase rather than a decrease in temperature. The microspheres were fabricated in a three‐step process. In the first step, monodisperse poly(acrylamide‐co‐styrene) seeds were prepared by emulsifier‐free emulsion polymerization. In the second step, poly(acrylamide) or poly[acrylamide‐co‐(butyl methacrylate)] shells were fabricated on the microsphere seeds by free radical polymerization. In the third step, the core–shell microspheres with poly‐ (acrylamide)/poly(acrylic acid) based interpenetrating polymer network (IPN) shells were finished by a method of sequential IPN synthesis. The proposed monodisperse core–shell microspheres provide a new mode of the phase transition behavior for thermo‐sensitive “smart” or “intelligent” monodisperse micro‐actuators that is highly attractive for targeting drug delivery systems, chemical separations, sensors, and so on.     

Copolymerization of bromophenylmaleimide with ethyl or butyl methacrylate

N‐p‐Bromophenylmaleimide (BrPMI) does not polymerize in solution by conventional free radical mechanism. However, it readily polymerized in bulk when mixed with a free radical initiator and heated in a microwave oven for 7–8 min. Copolymerization of ethyl methacrylate or butyl methacrylate with BrPMI was conducted in dioxane. The copolymers were characterized by IR and ¹H NMR spectroscopy and gel permeation chromatography. The monomer reactivity ratios were calculated by a non‐linear least‐square analysis. Thermal analysis indicated a great improvement in thermal stability of the copolymers compared with the methacrylate homopolymers. BrPMI was also polymerized in bulk in the DSC pan, which allowed the calculation of the activation energy of its polymerization. Copyright © 2003 Society of Chemical Industry     

Possibilities and extension of XRD material response analysis in failure research for the advanced evaluation of the damage level of Hertzian loaded components

Due to clearly distinguishable damage symptoms, it is differentiated between the surface and sub‐surface failure mode of rolling bearings. Material states red out by X‐ray diffraction (XRD) residual stress measurements point to a variety of loading conditions especially at raceway surfaces that are associated with several competing failure mechanisms. The corresponding lifetime reduction can range from the lower fatigue strength region to material ratcheting in extreme cases. Relevant position of the microstructural changes and nature of the failure mechanisms are characterized. The time alteration of the XRD material parameters measured at or near the surface and at the depth of the maximum equivalent stress correlates, in a different manner, with the statistical parameter of the 10 % bearing life. Both failure modes are illustrated by concrete examples. Contaminated lubricant and boundary lubrication, which represent practically important surface‐induced failures, are discussed in more detail. Gray staining, i.e. shallow pitting, often occurs without distinct indication of global material aging by means of XRD characteristics. Here, scanning electron microscopy observations and electron microprobe analyses point to corrosion fatigue as acting surface failure mechanism. The interaction between material and lubricant under complex loading regimes particularly of mixed friction and corrosion opens further failure research areas in the field of tribology.