Spatial Stability for Mixed Convection Boundary Layer over a Heated Horizontal Plate

The spatial stability properties of a mixed convection boundary layer developing over a heated horizontal plate is studied here under linear and quasi-parallel flow assumption. The main aim of the present work is to find out if there is a critical buoyancy parameter that would indicate the importance of heat transfer in destabilizing mixed convection boundary layers, when the buoyancy effect is given by Boussinesq approximation. The undisturbed flow used here is that given by the similarity solution of [ 1 ] that implies the wall temperature to vary as the inverse square root of the distance from the leading edge of the plate. The stability of this flow has been investigated by using the compound matrix method (CMM)—that allows finding all the modes in the chosen range in the complex wave number plane for spatial stability analysis. Presented neutral curves for mixed convection boundary layer show the existence of two types of disturbances present simultaneously, for large buoyancy parameter. One notices very unstable high-frequency mode when the buoyancy parameter exceeds the above-mentioned critical value. This unstable thermal mode is in addition to the hydrodynamic mode of isothermal flow given by corresponding similarity profile. The calculated critical buoyancy parameter is shown to qualitatively match with experimental results.     

On a wave equation with a cubic convolution

We study the well-posedness of the Cauchy problem and the asymptotic behavior of solutions of the nonlinear wave equation $\text{u}{}_{\mathrm{tt}}\text{? Δu + m}{}^2\text{+ u(V 1 u}{}^2\text{) = 0}$ in Euclidean space.     

Shape sensitivity analysis of a quasi‐electrostatic piezoelectric system in multilayered media

The optimization of shape and topology of piezo‐patches or layered piezo‐electrical material attached to structural parts, such as elastic bodies, plates and shells, plays a major role in the design of smart structures, as piezo‐mechanic‐acoustic devices in loudspeakers or energy harvesters. While the design for time‐harmonic motions is genuinely frequency‐dependent, as has been reported in the literature in the context of density optimization with the SIMP‐method, time‐varying piezoelectric material has not been investigated with respect to the optimal design so far. Therefore, shape sensitivities for layered piezoelectric material and time‐varying loads and charges are derived in this paper. In particular, we provide the shape‐derivatives for nested piezo‐layers associated with a class of shape functional. More general layers can be dealt with similar approach. Copyright © 2010 John Wiley & Sons, Ltd.     

Mobile geometric graphs: detection, coverage and percolation

We consider the following dynamic Boolean model introduced by van den Berg et al. (Stoch. Process. Appl. 69:247–257, 1997). At time 0, let the nodes of the graph be a Poisson point process in ${\mathbb{R}^d}$ with constant intensity and let each node move independently according to Brownian motion. At any time t, we put an edge between every pair of nodes whose distance is at most r. We study three fundamental problems in this model: detection (the time until a target point—fixed or moving—is within distance r of some node of the graph); coverage (the time until all points inside a finite box are detected by the graph); and percolation (the time until a given node belongs to the infinite connected component of the graph). We obtain precise asymptotics for these quantities by combining ideas from stochastic geometry, coupling and multi-scale analysis.     

Effects of water and electric field on atomic oxygen adsorption on Pt–Co alloys

Density functional theory is used to study the effect of atomic oxygen adsorption at various coverages with and without the presence of water on ordered and Pt-segregated PtCo surfaces. The strength of O adsorption, as well as surface reconstruction effects due to the adsorbate are strongly influenced by the presence of the oxygen-philic transition metal on the surface or subsurface. At high O coverage, buckling of the Co atom on PtCo surfaces is much smaller than that of Pt on Pt(1 1 1) surfaces, and buckling of Pt atoms on Pt-skin surfaces is negligible. Also, the effect of an electric field perpendicular to the surface on adsorbed water and atomic oxygen is investigated. Spontaneous water dissociation is not found on the ordered and segregated alloy surfaces within the entire applied electric field range (−0.51 to 0.51 V/Å). Water changes orientation under strong negative fields, switching from a metal–O to a metal–H interaction, and the effect is much more pronounced in the low-coordination sites of cluster models.     

A multi-analytical approach to studying binding media in oil paintings

This article presents a multi-analytical approach to investigating the drying, polymerisation and oxidative degradation of linseed oil, which had undergone various treatments known to be undertaken during the nineteenth century in preparation for painting. The oil was mechanically extracted from the same seed lot then processed by different methods: water washing, heat treatments, and the addition of driers, with and without heat. The oil was prepared in 1999 within the framework of the MOLART project. We compared thermogravimetric analysis (TG), which yields macromolecular information, with gas-chromatography mass-spectrometry (GC/MS) and direct exposure mass spectrometry (DE-MS), which provide molecular information. This comparison enabled us to elucidate the role of pre-treatment on the composition of the oil. TG and oxygen uptake curves registered at a constant temperature helped us to identify the different physical behaviour of the oil samples, thus highlighting the presence of hydrolysed, oxidised and crosslinked fractions, as a consequence of the different pre-treatments. GC/MS was used to characterise the soluble and non-polymeric fraction of the oil, to calculate the ratios of palmitic to stearic acid (P/S), and azelaic to palmitic acid (A/P), and to further evaluate the effects of oil pre-treatments. DE-MS using chemical ionisation with CH₄, enabled us to establish the chemical composition of the oil in different stages of ageing. DE-MS proved to be a useful tool for a simultaneous semi-quantitative characterisation of the free fatty acids, monoglycerids, diglycerides and triglycerides present in each sample. The combination of thermal analysis with GC/MS and DE-MS enabled a model to be developed, which unravelled how oil pre-treatments produce binders with different physical–chemical qualities.     

Simultaneous Exact Control of Quasi-Electrostatic Piezoelectric Systems in Multilayered Media

We consider two quasi-electrostatic models in a multilayered piezoelectric structure. Both models only differ on the boundary conditions. For each one of them we prove a boundary observability inequality which together with the Hilbert Uniqueness Method introduced by J.L. Lions allow us to drive both systems to rest at time T with the same control function. We require suitable geometric conditions on the region and the interfaces as well as monotonicity assumptions on the coefficients of the model.     

Antioxidant and antibacterial activities of bark extracts from Commiphora berryi and Commiphora caudata

This study investigates the in vitro antioxidant and antimicrobial activities of eight extracts obtained from the dried barks of Commiphora berryi and Commiphora caudata (Burseraceae). The radical scavenging activity was assessed by 1,1-diphenyl-2-picryl hydrazyl (DPPH) and nitric oxide assays. The methanolic extracts of C. berryi and C. caudata showed significant DPPH radical scavenging activity, with IC?? values of 26.92 and 21.16?μg?mL?1, respectively, and low radical scavenging activity against the nitric oxide assay. The antimicrobial activity of the plants was tested against the Gram-positive and Gram-negative bacteria. The ethyl acetate, chloroform and petroleum ether extracts of C. berryi showed good antibacterial activity against Pseudomonas aeruginosa, with a minimum inhibitory concentration (MIC) of 0.26?mg?mL?1, whereas the ethyl acetate and methanol extracts of C. caudata showed moderate antimicrobial activity with an MIC of more than 2.0?mg?mL?1 against P. aeruginosa compared to the petroleum ether and chloroform extracts, which showed an MIC of 1.1?mg?mL?1. The methanolic extracts of C. berryi and C. caudata also showed moderate cytotoxic activity against a human mammary carcinoma cell line (MCF-7), with values IC?? of 82.6 and 88.4?μg?mL?1, respectively.     

Aromatic resin characterisation by gas chromatography-mass spectrometry. Raw and archaeological materials

An analytical procedure based on alkaline hydrolysis, solvent extraction and trimethyl-silylation followed by gas chromatography-mass spectrometry (GC-MS) analysis was used to study the chemical composition of benzoe and storax resins, water-insoluble exudates of trees of the Styrax and Liquidambar genus. They are chemically characterised by having aromatic acids, alcohols and esters as their main components and are thus known as aromatic and/or balsamic resins. This analytical procedure allowed us to characterise the main components of the two resins and, even though cinnamic acid is the main component of both the resins, the presence of other characteristic aromatic compounds and triterpenes permitted us to distinguish between the two materials. All the compounds identified in benzoe resin were detected in an archaeological organic residue from an Egyptian ceramic censer (fifth to seventh centuries a.d.), thus proving that this resin was used as one of the components of the mixture of organic materials burned as incense. These results provide the first chemical evidence of the presence of benzoe resin in an archaeological material from Mediterranean area.