W1{infty}-convergence of the discrete free boundary for obstacle problems

We examine the discrete free boundaries arising from a finiteelement discretization of a variational inequality. We giveL error bounds for the Hausdorff distance of the discrete andtrue free boundary, as well as for the normals. The theoreticalresults are confirmed by numerical experiments in two and threedimensions.     

A novel peristaltic micropump with low compression ratios

It is common for peristaltic micropumps to have large compression ratios. In the limit, the chamber of the pump is completely blocked by the membrane to prevent back flow. Different from this kind of pump, a micropump with small compression ratios is proposed in this study. With small oscillation amplitudes the membrane of the pump can reciprocate at high frequencies to improve its pumping flow. Both the multidimensional method and the lumped‐element method are employed for analysis. For this kind of peristaltic micropump the working fluid is allowed to flow freely in the forward and backward directions. Therefore, the operating sequences for the high‐compression ratio type of pumps are not appropriate. It is shown that the theoretical net flow rate is zero for the four‐phase and six‐phase modes of sequence and becomes negative for the three‐phase mode unless regulators, such as the nozzle/diffusers, are incorporated to rectify the flow. However, this pump becomes very attractive by reversing the operating sequence of the three‐phase mode because positive net flow is yielded. It is seen that with the reversed three‐phase mode and the nozzle/diffuser as connecting channels, the pumping effectiveness is greatly enhanced. The pumps with both two chambers and three chambers are under consideration in the study. Copyright ©2011 John Wiley & Sons, Ltd.     

Nonlinearly coupled vibrations of thin-walled elastic beams of open section

An account of certain subharmonic vibrations as observed during a resonant testing of thin-walled beams of monosymmetric open section for coupled torsional and bending vibrations is presented. The phenomenon can be described in terms of the vibrational modes of the beam. When the beam is excited at the resonant frequency of a higher mode, there is a tendency for the lowest mode to be excited, resulting in a high-order subharmonic oscillation. It is found that when such phenomenon occurs, the high-mode frequency is a multiple or near multiple of the fundamental frequency of the beam. Under such condition, the response of the beam consists of a superposition of the response of the high mode (harmonic response) and that of the fundamental mode (subharmonic response). The amplitude of the subharmonic motion is generally much larger than that of the harmonic response.     

Melt crystalfization and crystal morphology of two low molecular weight linear polyethylene fractions

Melt-crystallization behavior and single-crystal morphology of two low molecular weight (LMW) linear polyethylene (PE) fractions of 3900 and 5800 have been investigated. Linear growth rates along the b axis (G _b) of these fractions were measured via polarized light microscopy (PLM). The two fractions show a growth rate change at an undercooling of 17°C (at 117°C and 120°C, respectively, for these two fractions), which may be identified as the regime I/II transition. This transition does not correspond to a single-crystal morphological change from a truncated lozenge with curved (200) and (110) planes to a lenticular crystal as proposed previously. However, this morphological change can be observed at a temperature higher than the regime transition (at 122°C and 124°C), at which the cusps of the G _b data can be observed for these two fractions. Based on our morphological study via PLM, transmission electron microscopy, electron diffraction, small-angle x-ray scattering (SAXS), and differential scanning calorimetry (DSC) experiments, it is found that within a 2°C temperature region, the G _b change is accompanied by a sharp long period increase and a drastic change in single-crystal morphology from a truncated lozenge with curved (200) and (110) planes to a lenticular-shape crystal. The morphological change may result from a sudden increase in the G _b coupled with a smaller change in the growth rate along the a axis with undercooling. This implies that, within this temperature region (2°C), the crystals may undergo substantial changes in the geometry of the (110) and (200) crystal growth fronts and chain folding behavior.     

Photooxidation of Methane over TiO2

Fourier‐transform infrared spectroscopy has been employed to investigate the adsorption and photo‐oxidation of CH₄ over powdered TiO₂. The interaction between the CH₄ and TiO₂ surface is weak. It is found that no CH₄ molecules are adsorbed on the surface at 35 °C in a vacuum. Under UV irradiation, CH₄ decomposes to form CO_(a), CO_2(g), H20_(a), and HCOO_(a) in the presence of O₂. The photoreaction rate is retarded and only small amounts of CO_(a) and HCOO_(a) are formed in the absence of O₂. It is observed that the oxygen atoms of O₂ are incorporated into these photoproducts as ¹⁸O₂ is used. The major ¹⁸O‐containing products are C¹⁸O_(a), C¹⁸O_2(g), H₂ ¹⁸O_(a), HC¹⁶O¹⁸O_(a), and HC¹⁸O¹⁸O_(a) after 180 min UV irradiation. However, the extent of ¹⁸O incorporating into the adsorbed formate is dependent on UV irradiation time. In the early stage of UV irradiation HC¹⁶O¹⁶O_(a) is the major formate form indicating the involvement of TiO₂ lattice oxygens for its formation, but HC¹⁸O¹⁸O_(a) becomes the major one after 180 min indicating the involvement of ¹⁸O₂. Formate on TiO₂ further photodecomposes to CO_2(g), but not to CO_(a). CO_(a) formation is directly from CH₄ photodecomposition with the participation of TiO₂ lattice oxygens and O₂.     

Intermolecular structural homogeneity of metallocene polyethylene copolymers

Direct proof of intermolecular compositional inhomogeneity of a metallocene polyethylene copolymer has been obtained using a cross-fractionation (CF) technique. The ethylene/1-hexene copolymer sample was synthesized using a Zr-based homogeneous metallocene catalyst. A solvent gradient fractionation (SGF) applied to the whole polymer material has produced nearly monodispersed molecular weight distribution fractions. The component molecules of a representative SGF fraction are then further sorted out, using a temperature gradient fractionation technique, according to their short-chain branching (SCB) differences. Molecular characterization of the resulting CF fractions reveals the presence of significant intermolecular SCB content differences among the components of the sample material.     

Control of thermoresponsive property of urea end‐functionalized poly(N‐isopropylacrylamide) based on the hydrogen bond‐assisted self‐assembly in water

The precise synthesis and variation in the thermoresponsive property based on the supramolecular assembly of a novel urea end‐functionalized poly(N‐isopropylacrylamide) (PNIPAM) were studied. A series of PNIPAMs with different diphenylurea groups at the chain end (X? Ph? NH? CO? NH? Ph? trz? PNIPAM: X = H, OCH₃, CH₃, NO₂, Cl, and CF₃) were synthesized by using a combination of the atom transfer radical polymerization and the copper(I)‐catalyzed azide‐alkyne cycloaddition. The cloud point of the obtained polymers depended on the hydrogen‐bonding ability of the introduced urea group. The ¹H NMR measurement suggested that the obtained PNIPAM assembled in water via the intermolecular hydrogen bonding by the terminal urea group. From the dynamic light scattering and transmission electron microscopy measurements, the aggregated nanoparticles of the resulting polymer were directly observed in water at a temperature below its cloud point. The hydrogen‐bonding property of the chain end urea group was concluded to be involved in the aggregation of the PNIPAM in water, leading to the variation in its cloud point. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 6259–6268, 2009