Error analysis of the L2 least‐squares finite element method for incompressible inviscid rotational flows

In this article we analyze the L² least‐squares finite element approximations to the incompressible inviscid rotational flow problem, which is recast into the velocity‐vorticity‐pressure formulation. The least‐squares functional is defined in terms of the sum of the squared L² norms of the residual equations over a suitable product function space. We first derive a coercivity type a priori estimate for the first‐order system problem that will play the crucial role in the error analysis. We then show that the method exhibits an optimal rate of convergence in the H¹ norm for velocity and pressure and a suboptimal rate of convergence in the L² norm for vorticity. A numerical example in two dimensions is presented, which confirms the theoretical error estimates. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004     

Mechanics of rubber shear springs

FEA calculations have been carried out for a model rubber shear spring, consisting of a block of a highly elastic material, bonded between two rigid parallel plates and sheared by displacing one of the plates parallel to the other in its own plane. The block was prevented from deforming in the perpendicular direction, and thus was deformed in plane strain. Stress distributions along the bond-line and the center-line are reported and compared with those expected from the theory of large elastic deformations. Unexpected tensile stresses were found to develop in the interior of the sheared block. They are attributed to the absence on the end surfaces of the stresses needed to maintain a simple shear, causing a pronounced change in the reference pressure—a consequence that is usually overlooked. Because the internal stresses are governed by the boundary conditions, they were strongly affected by the shape of the end surfaces. In addition, they were reduced markedly by assigning values to Poisson's ratio slightly lower than 0.5, thus allowing some volume expansion of the rubber. Strain energy release rates were also evaluated for growth of a crack along the bond-line, starting at the edges, and compared with those reported previously by Lindley and Teo [Energy for crack growth at the bonds of rubber springs, Plast. Rubber Mat. Appl. 4 (1979) 29-37], Muhr et al. [A fracture mechanics study of natural rubber-to-metal bond failure, J. Adhes. Sci. Technol. 10 (1996) 593-616], Gregory and Muhr [Stiffness and fracture analysis of bonded rubber blocks in simple shear, in: D. Boast, V.A. Coveny (Eds.), Finite Element Analysis of Elastomers, Professional Engineering Publications, Bury St. Edmunds, UK, 1999, pp. 265-274] and Gough and Muhr [Initiation of failure of rubber close to bondlines, in: Proceedings of the International Rubber Conference, Maastricht, Netherlands, June 2005, IOM Communications Ltd., London, 2005, pp. 165-174]. They confirm that a long crack at the compression edge will grow faster than one at the tension edge, but the results for short cracks were inconclusive.     

Three New Lignan Derivatives from Lindera glauca (Siebold et Zucc.) Blume

Two new aryl‐tetralin lignan glycosides, linderanosides A and B ( 1 and 2 , resp.), and a new dihydrobenzofuran neolignan glycoside, linderanoside C ( 3 ), together with five known lignan derivatives ( 4 – 8 ) were isolated from the trunk of Lindera glauca. The structures of these new compounds were determined through spectroscopic analyses, including extensive 2D‐NMR data and acid hydrolysis. The absolute configurations of the compounds were clarified by circular dichroism (CD) spectroscopic studies. Compounds 1 – 8 were evaluated for their cytotoxicity against A549 (non‐small cell lung adenocarcinoma), SK‐OV‐3 (ovarian cancer cells), A498 (human kidney epithelial cells), and HCT‐15 (colon cancer cells) human tumor cell lines using sulforhodamine B assays in vitro.     

Surface acoustic wave MEMS gyroscope

The design and performance evaluation of a surface acoustic wave (SAW) MEMS gyroscope is presented in this paper. This gyroscope is an integration of a SAW resonator and a SAW sensor. The SAW resonator is used to setup a stable reference vibration and SAW sensor is used for the detection of the secondary SAW generated by the Coriolis force. Further to this resonator, strategically positioned metallic dots that form an array along the standing wave anti-node locations are subjected to the reference vibratory motion. These vibrating dot arrays through the Coriolis effect will generate secondary SAW, which is picked up by the SAW sensor. The SAW resonator is designed and optimized using coupling-of-modes (COM) theory. In view of its one-layer planar configuration, this gyroscope can be implemented easily for applications requiring conformal mounting onto a surface of interest. This SAW gyroscope can be competitively priced inherently rugged, reliable and very sensitive. It is also capable of being wirelessly interrogated, without any sensor power source.     

Helical silica nanotubes: Nanofabrication architecture,transfer of helix and chirality to silica nanotubes

A series of neutral gelators and cationic amphiphiles derived from 1,2 diphenylethylenediamine (I) and 1,2-cyclohexanediamine (II) was synthesised. Helical silica nanotubes were prepared utilising these organic gelators through sol-gel polycondensation of tetraethoxy silane, (TEOS-silica source). Right- and left-handed helical nanotubes respectively were obtained from a 1: 1 mass mixture of optically active, (1S,2S)-III-(1S,2S)-V neutral gelator and (1S,2S)-IV-(1S,2S)-VI cationic amphiphile and a 1: 1 mass mixture of optically active, (1R,2R)-III-(1R,2R)-V neutral gelator and (1R,2R)-IV-(1R,2R)-VI cationic amphiphile, indicating that the handedness of the helical nanotubes varied with the change in the neutral gelator precursors used. The nanotubes were characterised by SEM images.     

Multiscale fabrication of multiple proteins and topographical structures by combining capillary force lithography and microscope projection photolithography

We present new methods that enable the fabrication of multiscale, multicomponent protein-patterned surfaces and multiscale topologically structured surfaces by exploiting the merits of two well-established techniques: capillary force lithography (CFL) and microscope projection photolithography (MPP) based on a protein-friendly photoresist. We further demonstrate that, when hierarchically organized micro- and nanostructures were used as a cell culture platform, human colon cancer cells (cell line SW480) preferentially adhere and migrate onto the area with nanoscale topography over the one with microscale topography. These methods will provide many exciting opportunities for the study of cellular responses to multiscale physicochemical cues.     

Fermentation of Korean Red Ginseng by Lactobacillus plantarum M-2 and Its Immunological Activities

We investigated ginsenoside transformation by fermentation of red ginseng with Lactobacillus plantarum M-2. We also examined the anti-metastasis and immune-stimulating activities of EtOH extracts of fermented red ginseng (FRG-E) in animal and human subjects. Total sugar decreased from 85.5 mg mL(-1) to 44.1 mg mL(-1) with increasing culture time during the fermentation with L. plantarum M-2. Uronic acid content reached a maximum level (534.3 μg mL(-1)) at 3 days of fermentation and decreased thereafter. Ginsenoside metabolites increased from 4,637.0 to 7,581.1 μg mL(-1) after 4 days. The prophylactic intraperitoneal injection of FRG-E (500 μg mouse(-1)) inhibited lung metastasis about 81.1%, while the inhibitory effect against tumor metastasis by treatment of EtOH extract from non-fermented red ginseng (NFRG-E) was 66.9%. Immunoglobulin A (IgA) and G (IgG) levels in the serum of healthy subjects were higher after FRG-E administration than at baseline, whereas NFRG-E induced reductions of these variables related to immunity. At 1 week, the change in IgA level by FRG-E (5.14 mg mL(-1)) was significantly higher than that by NFRG-E (-14.50 mg mL(-1); p < 0.05). It was concluded that the immunological activities of FRG-E were higher than those of NFRG-E, indicating that fermentation helped enhance the immunological activities of red ginseng.