Scrambled Geometric Net Integration Over General Product Spaces

Quasi-Monte Carlo (QMC) sampling has been developed for integration over \([0,1]^s\) where it has superior accuracy to Monte Carlo (MC) for integrands of bounded variation. Scrambled net quadrature allows replication-based error estimation for QMC with at least the same accuracy and for smooth enough integrands even better accuracy than plain QMC. Integration over triangles, spheres, disks and Cartesian products of such spaces is more difficult for QMC because the induced integrand on a unit cube may fail to have the desired regularity. In this paper, we present a construction of point sets for numerical integration over Cartesian products of s spaces of dimension d, with triangles (\(d=2\)) being of special interest. The point sets are transformations of randomized (t, m, s)-nets using recursive geometric partitions. The resulting integral estimates are unbiased, and their variance is o(1 / n) for any integrand in \(L^2\) of the product space. Under smoothness assumptions on the integrand, our randomized QMC algorithm has variance \(O(n^{-1 - 2/d} (\log n)^{s-1})\), for integration over s-fold Cartesian products of d-dimensional domains, compared to \(O(n^{-1})\) for ordinary MC.     

Air-cooled gas-turbine discs: a review of recent research

The flow between corotating compressor or turbine discs and the flow between a turbine disc and an adjacent stationary casing can be respectively modelled by a rotating cavity and by a rotor-stator system. This paper reviews some of the recent experimental and theoretical work on flow and heat transfer in these two classes of rotating-disc systems. Comparisons between the theoretical and measured distributions of velocity, pressure, and Nusselt numbers are made for the rotating cavity with a superimposed radial flow of cooling air. For the rotor-stator system, some recent work on the fluid dynamics is outlined, and particular mention is made of the so-called “ingress problem” and of the use of pre-swirl air to improve the blade-cooling effectiveness.     

The automatic control of boundary-layer transition — Experiments and computation

In recent years there has been an increasing interest in the control of boundary-layer transition through the use of wall suction. In the current work suction is provided through one or more suction panels situated close to the leading edge of a plate. Experiments show that boundary-layer pressure fluctuation measurements can be used to identify the position of transition. Transition can be maintained at a desired location with minimum power consumption by employing an automatic adaptive feedback control loop which regulates the suction flow rates of two independent suction panels. This can be expressed as a constrained optimization problem. To allow the suction flow rates to be updated, a modified least mean squares algorithm is used within the control loop. Experimental measurements show that the control algorithm allows fast and stable convergence towards the optimum suction distribution for a double suction panel configuration. Numerical simulations have also been performed. The two-dimensional boundary layer was calculated allowing the viscous boundary layer to interact with the inviscid outer flow. Following linear stability theory the spatial growth rates are calculated by solving an Orr-Sommerfeld type eigenvalue problem, with the streamwise location of transition predicted via thee ^N -method. Applying the same optimization strategy as in the experiments, good qualitative agreement between computations and experiments was found. The optimization algorithm has been applied to computer models where the relation between suction flow rates and transition location is described by an empirical analytical function. This shows that the controller can in principle be applied to systems with more than two suction panels.Nomenclature b transition location with zero suction - d desired transition location - e(k) error signal - k iteration index - p rms pressure - p _ref reference rms pressure - r sum of the reference pressure - u streamwise velocity - u _e external velocity - inviscid external velocity - A wave amplitude - F( ) cost function - I identity matrix - N maximum amplification factor - P projection matrix - R Reynolds number - Re Reynolds number based on the boundary-layer thickness - R matrix of weights - Tu turbulence level - vector of suction flow rates - v normal velocity - v _wall suction velocity at the surface - x streamwise coordinates - x _m microphone location - x _T(k) measured transition location - y normal coordinate - y(k) sum of the measured pressures - w(k) noise - plate length - r +i _i - free stream velocity - * displacement thickness - gradient vector - Lagrange multiplier - controller gain - disturbance stream function - disturbance amplitude - wave frequency = complex wave number     

The interrelation between void fraction fluctuations and flow patterns in two-phase flow

A fast response, linearized X-ray void measurement system has been used to obtain statistical measurements in normally fluctuating air-water flow in a rectangular channel. It is demonstrated that the probability density function (PDF) of the fluctuations in void fraction may be used as an objective and quantitative flow pattern discriminator for the three dominant patterns of bubbly, slug, and annular flow. This concept is applied to data over the range of 0.0 to 37 m/sec mixture velocities to show that slug flow is simply a transitional, periodic time combination of bubbly and annular flows. Film thicknesses calculated from the PDF data are similar in magnitude in both slug and annular flows. Calculation of slug length and residence time ratios along with bubble lengths in slug flow are also readily obtainable from the statistical measurements. Spectral density measurements showed bubbly flow to be stochastic while slug and annular flows showed periodicities correlatable in terms of the liquid volume flux.     

Aryl-aryl bond formation by the fluoride-free cross-coupling of aryldisiloxanes with aryl bromides

The prevalence of the biaryl structural motif in biologically interesting and synthetically important molecules has inspired considerable interest in the development of methods for aryl-aryl bond formation. Herein we describe a novel strategy for this process involving the fluoride-free, palladium-catalysed cross-coupling of readily accessible aryldisiloxanes and aryl bromides. Using a statistical-based optimisation process, preparatively useful reaction conditions were formulated to allow the cross-coupling of a wide range of different substrates. This methodology represents an attractive, cost-efficient, flexible and robust alternative to the traditional transition-metal-catalysed routes typically used to generate molecules containing the privileged biaryl scaffold.     

Differentiation of Regioisomeric Aromatic Ketocarboxylic Acids by Positive Mode Atmospheric Pressure Chemical Ionization Collision-Activated Dissociation Tandem Mass Spectrometry in a Linear Quadrupole Ion Trap Mass Spectrometer

Positive-mode atmospheric pressure chemical ionization tandem mass spectrometry (APCI-MS ⁿ ) was tested for the differentiation of regioisomeric aromatic ketocarboxylic acids. Each analyte forms exclusively an abundant protonated molecule upon ionization via positive-mode APCI in a commercial linear quadrupole ion trap (LQIT) mass spectrometer. Energy-resolved collision-activated dissociation (CAD) experiments carried out on the protonated analytes revealed fragmentation patterns that varied based on the location of the functional groups. Unambiguous differentiation between the regioisomers was achieved in each case by observing different fragmentation patterns, different relative abundances of ion-molecule reaction products, or different relative abundances of fragment ions formed at different collision energies. The mechanisms of some of the reactions were examined by H/D exchange reactions and molecular orbital calculations.     

Recent progress in biopolymer nanoparticle and microparticle formation by heat-treating electrostatic protein-polysaccharide complexes

Functional biopolymer nanoparticles or microparticles can be formed by heat treatment of globular protein-ionic polysaccharide electrostatic complexes under appropriate solution conditions. These biopolymer particles can be used as encapsulation and delivery systems, fat mimetics, lightening agents, or texture modifiers. This review highlights recent progress in the design and fabrication of biopolymer particles based on heating globular protein-ionic polysaccharide complexes above the thermal denaturation temperature of the proteins. The influence of biopolymer type, protein-polysaccharide ratio, pH, ionic strength, and thermal history on the characteristics of the biopolymer particles formed is reviewed. Our current understanding of the underlying physicochemical mechanisms of particle formation and properties is given. The information provided in this review should facilitate the rational design of biopolymer particles with specific physicochemical and functional attributes, as well as stimulate further research in identifying the physicochemical origin of particle formation.     

Metallosurfactants of bioinorganic interest: Coordination-induced self assembly

This review covers selected surfactant ligands that undergo a change in aggregate morphology upon coordination of a metal ion, with a particular focus on coordination-induced micelle-to-vesicle transitions. The surfactants include microbially produced amphiphilic siderophores, as well as synthetic amphiphilic ligands. The mechanism of the metal-induced phase change is considered in light of the coordination chemistry of the metal ions, the nature of the ligands, and changes in molecular geometry that result from metal coordination. Of particular interest are biologically produced amphiphiles that coordinate transition metal ions and amphiphilic ligands of relevance to bioinorganic chemistry.     

Double addition of H2 to transition metal-borane complexes: a 'hydride shuttle' process between boron and transition metal centres

The addition of H(2) across a transition metal-borane bond is reported for the first time providing a mechanism for recharging borane functional groups to borohydride.