Gap Functions and Existence of Solutions to Generalized Vector Quasi-Equilibrium Problems

This paper deals with generalized vector quasi-equilibrium problems. By virtue of a nonlinear scalarization function, the gap functions for two classes of generalized vector quasi-equilibrium problems are obtained. Then, from an existence theorem for a generalized quasi-equilibrium problem and a minimax inequality, existence theorems for two classes of generalized vector quasi-equilibrium problems are established. This research is partially supported by the Postdoctoral Fellowship Scheme of The Hong Kong Polytechnic University and the National Natural Science Foundation of China.     

Mimicking optical activity for generating radially polarized light

We propose a new scheme for generating radially polarized light by mimicking optical activity using linear birefringence. It involves a birefringent spirally varying retarder sandwiched between two orthogonally oriented quarter-wave plates. Using Poincaré sphere representation, we show that the polarization transformation of such a scheme is equivalent to that of a spirally varying optical activity and is capable of generating radially polarized light. We demonstrate the proof-of-concept using y-cut crystalline quartz.     

Numerical study of steady/unsteady flow and heat transfer in porous media using a characteristics-based matrix-free implicit FV method on unstructured grids

In this study, a high-resolution characteristic-based finite-volume (FV) method on unstructured grids [Int. J. Numer. Method Eng. 50 (2001) 11; Int. J. Heat Fluid Flow 21 (2000) 432] is extended by a matrix-free implicit dual-time stepping scheme for the numerical simulation of steady and unsteady flow and heat transfer with porous media. The method has been used to study the characteristics of a complex problem: flow and heat transfer in a channel with multiple discrete porous blocks, which was originally proposed by Huang and Vafai [J. Thermophys. Heat Transfer 8 (3) (1994) 563]. In addition, flow and heat transfer in a channel partially or fully filled with porous layers and containing solid protruding blocks with constant heat flux on its lower surface are also investigated in details. Hydrodynamic and heat transfer results are reported for both steady and transient flow cases. In particular, the effects of Darcy and Reynolds numbers on heat transfer augmentation and pressure loss are studied. An in-depth discussion of the formation and variation of recirculation is presented and the existence of optimum porous insert is demonstrated. At high Reynolds numbers the flow in the porous channel exhibits a cyclic characteristics although unlike the non-porous channel flow, the cyclic vortex development is only restricted to a small area behind the last solid block, while temperature changes more slowly and does not exhibit cyclic variations over a long period of time. It is shown that for all the cases studied altering some parametric values can have significant and interesting effects on both flow pattern as well as heat transfer characteristics.     

Determination of Bone Trabeculae Modulus—An Ultrasonic Scanning and MicroCT (μCT) Imaging Combination Approach

To date, there is no method to measure non-destructively the modulus of trabeculae within cancellous bone, whilst retaining its structural integrity. In this study ultrasonic scanning, coupled with microCT imaging, is employed to determine trabeculae modulus along the three major anatomical axes non-destructively. The proposed method allows cancellous bone specimens to remain intact, for possible use in subsequent studies. Volume rendering of the microCT images allows three-dimensional visualization of cancellous bone specimens to be tested. This facilitates trabeculae selection and accurate measurement of distance traveled by the ultrasonic wave, thus yielding a good degree of confidence in the acoustic velocity measured. For all the three principal anatomical directions, the measured acoustic speeds ranged from 2,115 to 3,077 m/s, giving an average of 2,505 m/s. Average wave velocities in the superior–inferior, medial–lateral and anterior–posterior anatomical directions were found to be 2,295, 2,469 and 2,754 m/s, respectively; the differences corresponding to the three directions do not appear to be significant. Subsequently, the modulus was then determined using elastic wave propagation theory.     

A ligand-free copper(I) oxide catalyzed strategy for the N-arylation of azoles in water

A simple and practical protocol has been developed for the cross-coupling of azoles and aryl iodides under ligand-free copper(I) oxide catalyzed conditions in water. The protocol uses tetrabutylammonium bromide (TBAB) as the phase-transfer catalyst, and water as the solvent, and shows good tolerance towards various functional groups.     

Biomimetic anchors for antifouling and antibacterial polymer brushes on stainless steel

Barnacle cement (BC) was beneficially applied on stainless steel (SS) to serve as the initiator anchor for surface-initiated polymerization. The amine and hydroxyl moieties of barnacle cement reacted with 2-bromoisobutyryl bromide to provide the alkyl halide initiator for the surface-initiated atom transfer radical polymerization (ATRP) of 2-hydroxyethyl methacrylate (HEMA). The hydroxyl groups of HEMA polymer (PHEMA) were then converted to carboxyl groups for coupling of chitosan (CS) to impart the SS surface with both antifouling and antibacterial properties. The surface-functionalized SS reduced bovine serum albumin adsorption, bacterial adhesion, and exhibited antibacterial efficacy against Escherichia coli (E. coli). The effectiveness of barnacle cement as an initiator anchor was compared to that of dopamine, a marine mussel inspired biomimetic anchor previously used in surface-initiated polymerization. The results indicate that the barnacle cement is a stable and effective anchor for functional surface coatings and polymer brushes.