An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy

Using the approach of Rulla (1996 SIAM J. Numer. Anal. 33, 68-87)for analysing the time discretization error and assuming moreregularity on the initial data, we improve on the error boundderived by Barrett and Blowey (1996 IMA J. Numer. Anal. 16,257-287) for a fully practical piecewise linear finite elementapproximation with a backward Euler time discretization of amodel for phase separation of a multi-component alloy.     

Prediction of temperature-insensitive molecular absorption lines in laser-assisted combustion diagnostics

In laser-assisted combustion diagnostics it is a recurring task to predict molecular transitions whose signal strength depends only weakly on variations in temperature. The signal strength is proportional to the Boltzmann fraction of the level probed and the amplitude of the absorption line profile. In the past investigations have been presented in which this task was attack by detailed numerical calculations of the temperature dependence of pertinent physical properties of the molecule. Another widely applied approach relies on an analytical formula for the Boltzmann fraction of hetero-nuclear diatomic molecules and the neglect of line shape effects. The analytical approach experiences a continuing popularity in laser-assisted combustion diagnostics, which is why we compared both approaches with each other. The objective of this comparison was to assess the accuracy of the analytical approach and to reveal its potential pitfalls. Our comparison revealed that the analytical approach suffers from mediocre accuracy, which makes it unfit for practical applications. One cause is the neglect of higher lying vibrational levels, which show a non-negligible population for typical flame temperatures. Another reason is the neglect of fine structure splitting in molecules with non-zero orbit angular momentum in the ground state. Another reason for the observed inaccuracy is the neglect of line shape effects quenching, which were found to have a significant effect on the temperature sensitivity of a line. Because of its insufficient accuracy due to both oversimplified models of the molecular energy levels and the neglect of line shape effects and quenching we discourage from applying the analytical approach and recommend the use of detailed numerical approaches that are free of the above limitations.     

Generation of ultraviolet broadband light in a single-mode fiber

Ultraviolet broadband light spanning 337–405 nm was produced in a single-mode optical fiber primarily by stimulated Raman scattering. Pulses of 4 ns duration at 337 nm were coupled into a 50 m long ultraviolet-grade fiber featuring single-mode operation in the 320–450 nm range. Significant spectral broadening was achieved with pulses of only ∼10 W peak power. Our experiments demonstrate the potential for a source with ∼10⁴ times the spectral radiance of a quartz tungsten halogen lamp, which is currently used for many applications in this wavelength range. PACS 42.65.Ky; 42.81.Wg     

Reaction of bis[bis(tri-tert-butoxysilanethiolato) cadmium(II)] with 3,5-dimethylpyridine - 113Cd NMR solution study

NMR studies on the reaction of bis[bis(tri-tert-butoxysilanethiolato)cadmium(II)] with 3,5-dimethylpyridine in benzene-d(6) and toluene-d(8) solutions provide clear evidence for the equilibrium character of formation of mixed S,N-ligand cadmium complex.     

Atomic hydrogen concentration mapping in thermal plasma chemical vapour deposition

Two-dimensional maps of atomic hydrogen concentration in reactive gas layers were measured using two-photon laser-induced fluorescence. The measurements were made in conditions of diamond-film chemical vapour deposition using a thermal inductively coupled plasma. Their purpose was to investigate the influence of the atomic hydrogen concentration in the reactive gas layer on the diamond growth. Concentration maps were obtained under parametric variation of the plasma flow conditions. Axial profiles were extracted from the measured maps and compared to temperature profiles measured by Rayleigh scattering to determine the degree of chemical non-equilibrium in the reactive layer. The non-uniform quenching over the measured area was accounted for with an iterative calculation of the species concentrations. For small differences of the atomic hydrogen concentration in the reactive layer a large variation in quality of the grown diamond was observed. Received: 28 June 2000 / Revised version: 6 October 2000 / Published online: 21 February 2001     

Standard single-mode fibers as convenient means for the generation of ultrafast high-pulse-energy super-continua

High-pulse-energy super-continua featuring an M² of one were generated in standard single-mode fibers. The highest pulse energy achieved was ∼600 nJ and the pulse duration was ∼1 ps. The spectral width of the generated continua extended over up to 35% of the pump wavelength. PACS 42.65.-k; 42.81.-i; 42.79.Nv