A new approximation method for scattering by long finite arrays

The scattering of water waves by a long array of evenly spaced,rigid, vertical circular cylinders is analysed under the usualassumptions of linear theory. These assumptions permit the reductionof the problem to that of solving the Helmholtz equation intwo dimensions, with appropriate circular boundaries. Our primarygoal is to show how solutions obtained for semi-infinite arrayscan be combined to provide accurate and numerically efficientsolutions to problems involving long, but finite, arrays. Theparticular diffraction problem considered here has been chosenboth for its theoretical interest and for its applicability.The design of offshore structures supported by cylindrical columnsis commonplace and understanding how the multiple interactionsbetween the waves and the supports affect the field is clearlyimportant. The theoretical interest comes from the fact that,for wavelengths greater than twice the geometric periodicity,the associated infinite array can support Rayleigh–Blochsurface waves that propagate along the array without attenuation.For a long finite array, we expect to see these surface wavestravelling back and forth along the array and interacting withthe ends. For particular sets of parameters, near-trapping haspreviously been observed and we provide a quantitative explanationof this phenomenon based on the excitation and reflection ofsurface waves by the ends of the finite array.     

Nuclear radii of thorium isotopes from laser spectroscopy of stored ions

Isotope shifts and hyperfine splittings in optical transitions for atomic ions of the thorium isotopes²²⁷Th to²³⁰Th and²³²Th have been measured by laser spectroscopy on stored ions. From the isotope shift data, changes of the mean square charge radii are determined. A continuous increase of the charge radius with mass numberA is observed, in agreement with droplet model calculations. The results indicate that the odd-even staggering for Th is different from that one of the neighbouring isotones of Fr and Ra. There is some empirical evidence from systematics for an inversion of the staggering and the appearance of an octupole deformation atN ≦137. The hyperfine splitting for²²⁹Th for 3 electronic levels is given.     

CGC using a programmable electronic pressure controller

Capillary gas chromatographic separations were performed with an electronic pressure control system developed to provide precise closed-loop control of inlet pressure through the use of a solid state micro-machined pressure sensor and electronically controlled proportional valve. The closed-loop control of the electronic system provided better precision than the open-loop control achieved by manual pressure regulation. Closed-loop control can perform pressure programming, which can be combined with temperature programming to optimize separations. The pressure sensor monitors the integrity of the flow system and singals the controller to reduce flow in the presence of a sudden loss of system pressure.     

A processing method enabling the use of peak height for accurate and precise proton NMR quantitation

In NMR, peak area quantitation is the most common method used because the area under a peak or peak group is proportional to the number of nuclei at those frequencies. Peak height quantitation has not enjoyed as much utility because of poor precision and linearity as a result of inconsistent shapes and peak widths (measured at half height). By using a post‐acquisition processing method employing a Gaussian or line‐broadening (exponential decay) apodization (i.e. weighting function) to normalize the shape and width of the internal standard (ISTD) peak, the heights of an analyte calibration spectrum can be compared to the analyte peaks in a sample spectrum resulting in accurate and precise quantitative results. Peak height results compared favorably with ‘clean’ peak area results for several hundred illicit samples of methamphetamine HCl, cocaine HCl, and heroin HCl, of varying composition and purity. Using peak height and peak area results together can enhance the confidence in the reported purity value; a major advantage in high throughput, automated quantitative analyses. Published in 2009 by John Wiley & Sons, Ltd.     

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