An alternating direction Galerkin method for elliptic problems with gradient nonlinearity

Several problems in many applications involve the solution of partial differential equations with gradient dependent nonlinearity. The numerical solution of the resulting nonlinear system is rather expensive. We present an alternating direction Galerkin method that allows much faster solution of the nonlinear system. The alternating direction formulation help reduce the problem into a sequence of nonlinear systems that may be solved very efficiently. Theoretical study of the convergence of the method will also be presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The role of excited state molecular association in photoreactions of dibenzoylmethanatoboron difluoride with conjugated enones and en-esters: An anomalous excimer reaction

The singlet excited state of the title borofluoride, *DBMBF₂, reacted efficiently with acyclic enones and en-esters but only feebly with the corresponding excimer in analogy to simple acyclic olefins to give cycloaddition products, in spite of substantially different electronic character of the double bonds. Cyclic enones, on the contrary, reacted with both *DBMBF₂ and the excimer with increasing fluorescence quenching constants and adduct quantum yields as the rigidity of enone rings relaxes. They interacted with the excimer to cause the enone stimulated excimer dissociation which occurred most likely by the intermediary of the enone exciplexes. The interaction of 2-cyclopentenone (CP) by this process caused strong increases in *DBMBF₂ fluorescence intensity, that was interpreted to arise from a fast reverse step (k_x) from the exciplex as shown by increasing *DBMBF₂ fluorescence intensities upon addition of CP. Apparently the exciplexes from 2-cyclohexenone, 2-cyclootenone and 2-cyclododecenone had a decreasing degree of reversibility (i.e., relatively smaller reverse reaction rates): this trend caused Φ_a increases and, correspondingly, lesser enhancement of *DBMBF₂ fluorescence in the same order. The last enone, while mainly reacted with excimer, showed almost the same reactivity and Φ_a pattern of acyclic enones. In contrast to cyclic olefins, the last three enones reacted to show decreased Φ_a on increasing initial [DBMBF₂] (i.e., higher excimer concentrations); and hidden deactivation step was implicated in the excimer reaction with these enones. The anomalous reaction patterns were assumed to be caused by differences in the geometrical orientation of an enone within exciplexes and of enone attack on the excimer.     

Application of N-PLS calibration to the simultaneous determination of Cu(2+), Cd(2+) and Pb(2+) using peptide modified electrochemical sensors

The simultaneous determination of Cu(2+), Cd(2+) and Pb(2+) is demonstrated at four modified gold electrodes using N-PLS calibration. Three of the electrodes were modified with the peptides Gly-Gly-His, gamma-Glu-Cys Gly and human angiotensin I which were covalently attached to thioctic acid self-assembled monolayers and the fourth electrode was modified with thioctic acid only. Voltammetry at the modified electrodes in the presence of the three metal ions revealed one peak due to the reduction of copper and another due to the overlapping peaks of cadmium and lead which made quantification using conventional methods difficult. N-PLS was used to calibrate and predict trace concentrations (100 nM to 10 microM) of mixtures of Cu(2+), Cd(2+) and Pb(2+).     

Effects of Ellipticity Angle on Modulation Instabilities in Birefringent Optical Fibers

Previous studies on modulation instabilities(MIs) in birefringent optical fibers focus on the ordinary linearly and circularly ones. This paper reports an analysis of MIs in the general elliptically birefringent fibers with the emphasis on investigating the effects of ellipticity angle(0? ≤θ≤ 90?). Both symmetric and antisymmetric CW states are considered. In the anomalous dispersion regime, for the symmetric(antisymmetric) CW states, we show that MI gain increases dramatically(reduces first and then enhances greatly) as the increment of θ. In the normal dispersion regime, for the both CW states, the distinctive feature is that the gain of the MI bands reduces first, vanishes at θ = 45?,reappears across this ellipticity angle, and quickly increases after then.     

Novel cuticular hydrocarbons from the cane beetle Antitrogus parvulus--4,6,8,10,16-penta- and 4,6,8,10,16,18-hexamethyldocosanes-unprecedented anti-anti-anti-stereochemistry in the 4,6,8,10-methyltetrad

The major cuticular hydrocarbons from the cane beetle species Antitrogus parvulus are 4,6,8,10,16-penta- and 4,6,8,10,16,18-hexamethyldocosanes, 1 and 2, respectively. Stereoisomers of 2,4,6,8-tetramethylundecanal of established relative stereochemistry were derived from 2,4,6-trimethylphenol and were then coupled with appropriate methyl-substituted phosphoranes 62 and 25 to furnish alkenes, which on reduction provided diastereomers of 1 and 2, respectively. Capillary gas chromatography, mass spectrometry, and high resolution 13C NMR spectroscopy confirmed 1 as either 84a or 84b and 2 as either 15a or 15b. The novelty of these structures and their relative stereochemistry is briefly related to polyketide assembly.     

The zwitterion effect in proton exchange membranes as synthesised by polymerisation of bicontinuous microemulsions

The bicontinuous microemulsions consisting of a polymerisable zwitterionic surfactant 3-((11-acryloyloxyundecyl)imidazolyl) propyl sulfonate (AIPS) and other monomers can be cross-polymerised to form good proton conductive membranes.     

Low-loss, wide-angle Y splitter at approximately ~1.6- mum wavelengths built with a two-dimensional photonic crystal

We report a successful experimental realization of a photonic-crystal Y splitter operating at lambda~1.6 mum . Our device has a large splitting angle of 120 degrees and a miniature size of ~3 mumx3 mum . Furthermore, the Y-splitter loss is measured to be 0.5-1 dB at lambda=1640-1680 nm, making the Y splitter promising for integrated photonic-circuit applications. These unique properties are attributed to the new guiding principle made possible by the photonic bandgap.     

A heuristic for sea-freight container selection,cargo allocation and cargo orientation

A model is proposed to generate solutions for container selection, for the allocation of cargo to containers, and for cargo orientation within a container. The model is in the form of a mixed integer program with the objective of minimizing the total shipping cost. The practical requirements of loading priority and weight distribution along the main dimension of the container are incorporated into the model. A heuristic solution strategy is proposed and used to control the computation time by pre-setting the search increments. Three case examples are presented. The first and third examples show that the proposed model can produce a better solution than the manual schedulers. The second example is taken from the literature and is compared with the solution generated by the proposed model, demonstrating that the practical considerations incorporated into the model do not necessarily lead to increased shipping costs.