Efficient solution of two-stage stochastic linear programs using interior point methods

Solving deterministic equivalent formulations of two-stage stochastic linear programs using interior point methods may be computationally difficult due to the need to factorize quite dense search direction matrices (e.g., AA ^T ). Several methods for improving the algorithmic efficiency of interior point algorithms by reducing the density of these matrices have been proposed in the literature. Reformulating the program decreases the effort required to find a search direction, but at the expense of increased problem size. Using transpose product formulations (e.g., A ^T A) works well but is highly problem dependent. Schur complements may require solutions with potentially near singular matrices. Explicit factorizations of the search direction matrices eliminate these problems while only requiring the solution to several small, independent linear systems. These systems may be distributed across multiple processors. Computational experience with these methods suggests that substantial performance improvements are possible with each method and that, generally, explicit factorizations require the least computational effort.     

New equivalent step index methods for designing nonlinear fibres

Abstact The equivalent step index (ESI) framework is shown to provide a convenient approximation for evaluating the performance of different optical fibre designs for potential use in nonlinear signal processing elements. New ESI methods are presented which combine reasonable accuracy with simple expressions for the ESI parameters, allowing fast and reliable solution of fibre design problems, and straightforward comparison between theory and measurements on experimental nonlinear fibres.     

On the relation between low-dimensional models and the dynamics of coherent structures in the turbulent wall layer

In this paper we establish some rigorous connections between the dynamics of coherent structures in the wall region of the turbulent boundary layer and the low-dimensional models of the type studied by Aubry et al. (1988). An important first step is to determine what sort of connection is feasible. We choose to study the energy budget of the models in comparison with the energy budget of the real flow. This is done by comparing the respective kinetic energy equations. In the process we reexamine some of the assumptions and approximations of Aubry et al. (1988) and perform order of magnitude analyses to determine when they hold. We find that, for the models developed in that paper, involving modes which do not vary in the streamwise direction, the energy production lies within positive, experimentally determined, bounds. Moreover, the dissipation due to neglected modes may be reproduced correctly with an order 1 value of the Heisenberg parameter , as assumed by Aubry et al. This work was supported by AFOSR F49620-92-J-0287.     

Horizontal bubble flow

An experimental investigation of cocurrent bubble flow in 0.0254 m and 0.0508 m diameter horizontal pipelines has been performed. Gas and liquid mass velocities ranged from 0.00955 to 0.675 and 2720 to 6040 kg/m² sec, respectively, and gas-phase holdups or void fractions ranged from 0.13 to 7.59%.High speed motion pictures revealed that the gas, introduced into the liquid with a concentric nozzle, emerged in the form of a rough jet which was ultimately sheared into 1 times; 10^minus;3 to 3 times; 10^minus;3m diameter bubbles. Approximately 4 meters downstream from the nozzle, a well developed bubble flow was observed where bubble number density and axial velocity were constant with respect to axial position in the pipeline. Bubble velocities ranged from 0.001 to 0.57 m/sec greater than the average liquid velocities. Bubble radial and circumferential spatial distributions were found to be a strong function of the degree of turbulence in the liquid phase. Because of these turbulent flow conditions, bubble shapes were much different than those of equivalent diameter bubbles rising in stagnant liquids. A sphere-ellipsoid of revolution model was developed for characterization of bubble shape and computation of gas-liquid interfacial area and two-phase pressure drop.     

Bile UPLC-MS fingerprinting and bile acid fluxes during human liver transplantation

Bile flow restoration is a crucial step in the recovery process post transplantation of the liver. Here, metabolic trajectories based on changes in bile secretion - a known marker of functionality - have been utilised as an approach for discovering bile fluxes during transplantation. A total of ten liver transplants were monitored and from these 68 bile samples from both donors and recipients were collected and analysed using ultra-performance LC-MS in combination with multivariate statistical analysis. Based on the principal component scores constructed from the total bile fingerprint, differentiation of the bile acid concentrations before and after transplantation was detected. A trend was also observed, by constructing metabolic trajectories, whereby the post-transplant profiles approached the position of pre-transplant profiles within 30-60?min of the restoration of bile secretion function. The ten major conjugated bile acid salts were measured and a significant increase in concentrations of taurocholic acid and taurochenodeoxycholic acid were seen after transplantation. In addition, the ratios of secondary bile acids detected in gall bladder and hepatic bile were measured before and after transplantation. This study suggests that bile acid ratios in the donor liver at the pre-transplant and post-transplant stage may be important and that profiling of secreted bile after transplantation may aid clinical assessment and progress post-transplantation.     

The complex synthesis and solid state chemistry of ceria-lanthana solid solutions prepared via a hexamethylenetetramine precipitation

Mixed oxide solid solutions are becoming ever more commercially important across a range of applications. However, their synthesis can be problematical. Here, we show that ceria-lanthana solid solutions can be readily prepared via simple precipitation using hexamethylenetetramine. However, the solution chemistry can be complex, which results in the precipitated particles having a complex structure and morphology. Great care must be taken in both the synthesis and characterisation to quantify the complexity of the product. Even very high heat treatments were not able to produce highly homogeneous materials and X-ray diffractions reveals the non-equilibrium form of particles prepared in this way. Unexpected crystal structures are revealed including a new metastable cubic La₂O₃ phase.     

Selectivity in the addition reactions of organometallic reagents to aziridine-2-carboxaldehydes: the effects of protecting groups and substitution patterns

Good to excellent stereoselectivity has been found in the addition reactions of Grignard and organozinc reagents to N-protected aziridine-2-carboxaldehydes. Specifically, high syn selectivity was obtained with benzyl-protected cis, tert-butyloxycarbonyl-protected trans, and tosyl-protected 2,3-disubstituted aziridine-2-carboxaldehydes. Furthermore, rate and selectivity effects of ring substituents, temperature, solvent, and Lewis acid and base modifiers were studied. The diastereomeric preference of addition is dominated by the substrate aziridines' substitution pattern and especially the electronic character and conformational preferences of the nitrogen protecting groups. To help rationalize the observed stereochemical outcomes, conformational and electronic structural analyses of a series of model systems representing the various substitution patterns have been explored by density functional calculations at the B3LYP/6-31G* level of theory with the SM8 solvation model to account for solvent effects.     

QTAIM analysis of the HF, HCl, HBr, and HOH elimination reactions of halohydrocarbons and halohydroalcohols

The 1,2-HX elimination reaction (where X = F, Cl, Br, OH) has been established as an important reaction in the degradation of compounds introduced into the upper atmosphere, including common CFC replacement compounds. By analyzing the electron densities of the transition state geometries of these reactions using QTAIM, we see that we can divide these reactions into two types. For HF and HOH elimination, the transition state is a complete ring of bonds, and neither the C-H nor the C-X bonds have been broken at the maximum of energy. There is very little accumulation of electron density on the X atom, with the majority of charge being lost by the hydrogen atom undergoing elimination, being transferred on to the two carbon atoms. In HCl and HBr elimination, a similar loss of electron density of the hydrogen atom is accompanied by significant accumulation of electron density on the X atom and a smaller change in electron density on the carbon atoms. The C-X bond is broken in the transition state geometry, with no ring critical point being present. This may explain the relative stabilities of halohydrocarbons and haloalcohols with respect to loss of H-X.     

In vivo noninvasive detection of chlorophyll distribution in cucumber (Cucumis sativus) leaves by indices based on hyperspectral imaging

The objective of this study was to investigate the spectral behavior of the relationship between reflectance and chlorophyll content and to develop a technique for non-destructive chlorophyll estimation and distribution in leaves using hyperspectral imaging. The hyperspectral imaging data cube of cucumber (Cucumis sativus) leaves in the range of 450-850 nm was investigated and preprocessed. Sixty optical signatures or indices as a function of the associated reflectance (R(λ)) at the special wavelength (λ) nm which proposed in the literatures were used to predict the total chlorophyll content in cucumber leaves. Finally, R(710)/R(760), (R(780)-R(710))/(R(780)-R(680)), (R(750)-R(705))/(R(750)+R(705)), (R(680)-R(430))/(R(680)+R(430)), R(860)/(R(550)×R(708)), (R(695-705))(-1)-(R(750-800))(-1), and REP-LEM (a index based on red edge position and estimated with a linear extrapolation method) were identified as optimum indices. Red-edge waveband (680-780 nm) appeared in all these optimum indices, indicating the importance of REP (red edge position) in chlorophyll estimation. When (R(695-705))(-1)-(R(750-800))(-1), the best index was applied to an independent validation set, chlorophyll content (r=0.8286) were reasonably well predicted, indicating model robustness. Depending on the sample, this technique enables to identify and characterize the relative content of various chlorophyll that distribution in the cucumber leaves. The map shows a relatively low level of chlorophyll at margins. Higher level can be noticed in the regions along the main veins and in some areas exhibiting dark green tissue. Our results indicate that hyperspectral imaging has considerable promise for predicting pigments in leaves and, the pigments can be detected in situ in living plant samples non-destructively.     

Dithienothiophene (DTT)-based dyes for dye-sensitized solar cells: synthesis of 2,6-dibromo-DTT

A one-pot synthesis of 2,6-dibromodithieno[3,2-b;2',3'-d]thiophene (dibromo-DTT, 4) was developed. A key step was bromodecarboxylation of DTT-2,6-dicarboxylic acid, obtained by saponification of the diester 1. The donor-acceptor dye DAHTDTT (13), based on a central 2,6-bis[2'-(3'-hexylthienyl)]dithieno[3,2-b;2',3'-d]thiophene core (9), was prepared and incorporated in a dye-sensitized solar cell (DSC), which exhibited an energy conversion efficiency of 7.3% with V(oc) of 697 mV, J(sc) of 14.4 mA/cm(2), and ff of 0.73 at 1 sun.