Three-level Decomposition Approach for Solving Feedstock Problems on Microcomputers

Many decision support systems for feedstock companies include an option for the solution of large linear programming problems. A three-level decomposition algorithm is presented which substantially improves the solution times for such linear programming problems. When decisions must be made on the addition of new raw materials or extra quantities of existing raw materials to feed mixes, the usual approach is to use parametric linear programming. A new approach to this decision problem, based on the results of the three-level decomposition algorithm, is presented in the paper. Finally, implementation issues and the computational performance of the new approaches on real-world problems are discussed.     

Integrated optical components on atom chips

We report on the integration of small-scale optical components into silicon wafers for use in atom chips. We present an on-chip fibre-optic atom detection scheme that can probe clouds with small atom numbers. The fibres can also be used to generate microscopic dipole traps. We describe our most recent results with optical microcavities and show that a sufficiently high finesse can be achieved to enable single-atom detection on an atom chip. The key components have been fabricated by etching directly into the atom chip silicon substrate.     

On the stress singularities in the plane elasticity of the composite wedge

This paper examines the composite, two-dimensional, linear elastic wedge for singular stresses at its vertex. A full range of wedge boundary and matching conditions is considered. Using separation of variables on the Airy stress function, the usual determinant conditions for singularities of the formO(r ^-) asr 0 are established and further conditions are derived for singularities of the formO(r ^- lnr) asr 0. The order of the determinant involved in these conditions depends upon the number of materials comprising the wedge. Two systematic methods of expanding the determinant for theN-material wedge are presented.

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Résumé Ce papier examine le coin composé, linéaire et élastique, en deux dimensions, pour déterminer les contraintes singulières à son sommet. On va considérer la rangée totale des conditions aux limites du coin, et les conditions correspondantes dans le coin. On se sert de la séparation des variables de la fonction de contrainte d'Airy, pour déterminer les conditions usuelles sur le déterminant pour les singularités de la formeO(r ^-) quandr 0, et on dérive des conditions additionnelles pour les singularités de la formeO(r ^- lnr) quandr 0. L'ordre du déterminant impliqué dans ces conditions dépend du nombre des matériaux dans le coin. D'abord on propose deux méthodes systématiques de développer le déterminant du coin deN-matériaux.

     

Ten-deg off-axis test for shear properties in fiber composites

A combined theoretical and experimental investigation was conducted to assess the suitability of the 10-deg off-axis tensile-test specimen for the intralaminar-shear characterization of unidirectional composites. Composite mechanics, a combined-stress failure criterion and a finiteelement analysis were used to determine theoretically the stress-strain variation across the specimen width and the relative stress and strain magnitudes at the 10-deg plane. Strain gages were used to measure the strain variation across the specimen width at specimen midlength and near the end tabs. Specimens from Mod-I/epoxy. T-300/epoxy, and S-glass/epoxy were used in the experimental program. It was found that the 10-deg off-axis tensile-test specimen is suitable for intralaminar-shear characterization and it, is recommended that it should be considered as a possible standard test specimen for such a characterization.     

Peptide coated gold nanoparticles that bind lanthanide ions

Water soluble gold nanoparticles are coated with peptides bearing a dithiol surface active group for studies of lanthanide binding; characteristic red luminescence is observed upon europium binding to the nanoparticles.     

Inelastic neutron scattering from amorphous solids

Utilization of the inelastic neutron scattering technique for the study of the dynamics of amorphous solids is discussed. Excitation energies of interest range from a fraction of a milli-electron-volt (meV) to several hundred meV. For coherent scatterers, the scattering-vector dependence of the cross section gives information on the correlation between the motions of different atoms. Progress in the application of the technique to several classes of materials is reviewed, and the possibilities offered by the new generation of pulsed-spallation neutron sources are considered. Existing instrumentation on presently operating sources should already be able to measure wide-ranging scattering functions for comparison to model predictions for several types of amorphous solids. Higher flux sources, now at the proposal stage, would allow greater detail in the scattering to be observed and thus aid in discriminating between models.     

A study of three-nucleon transfer reactions on 17O

The reactions ¹⁷O(¹¹B, ⁸Li)²⁰Ne, ¹⁷O(¹²C, ⁹Be)²⁰Ne and ¹⁷O(¹³C, ¹⁰B)²⁰F have been studied using beams of 115 MeV ¹¹B and ¹²C and 105 MeV ¹³C incident on a gas target. Shell-model calculations have been performed for ²⁰Ne and ²⁰F, for comparison with the experimental data. It is found that the data can be interpreted using the shell model spectroscopic factors and a semi-classical reaction theory. We justify the use of the latter by applying it to the cases of three-nucleon transfer on ¹⁶O. Spin assignments are suggested for previously unidentified states in ²⁰F.     

A new strategy for the stereoselective synthesis of unnatural α-amino acids

A new method for the synthesis of racemic non-proteinogenic α-amino acids has been developed, which involves (i) hetero-Diels-Alder addition of ethyl 2-nitrosoacrylate to electron rich alkenes such as enol ethers, enamines and allylsilanes, (ii) NaCNBH₃ reduction of the CN bond in the oxazines thus generated, the stereochemistry of the products being controlled by epimerisation of the thermodynamically less stable isomer to the more stable one, (iii) protection of the N-H group as N-Boc and (iv) finally, N-O bond cleavage of both free and protected products to give proline or bis-homoserine derivatives, respectively. An example with concomitant reduction of the carboxylate group, resulting in the formation of the respective amino alcohol is reported. Applying this methodology to a homochiral enol ether, the protected parent d-proline was prepared in enantiomerically pure form, whereas the asymmetric synthesis of the respective bis-homoserine was unsuccessful.     

Quasisymmetric embeddings, the observable diameter, and expansion properties of graphs

It is shown that the edges of any n-point vertex expander can be replaced by new edges so that the resulting graph is an edge expander, and such that any two vertices that are joined by a new edge are at distance in the original graph. This result is optimal, and is shown to have various geometric consequences. In particular, it is used to obtain an alternative perspective on the recent algorithm of Arora et al. [Proceedings of the 36th Annual ACM Symposium on the Theory of Computing, 2004, pp. 222-231.] for approximating the edge expansion of a graph, and to give a nearly optimal lower bound on the ratio between the observable diameter and the diameter of doubling metric measure spaces which are quasisymmetrically embeddable in Hilbert space.