Nonlinear theory for coalescing characteristics in multiphase Whitham modulation theory

The multiphase Whitham modulation equations with $N$ phases have $2N$ characteristics which may be of hyperbolic or elliptic type. In this paper a nonlinear theory is developed for coalescence, where two characteristics change from hyperbolic to elliptic via collision. Firstly, a linear theory develops the structure of colliding characteristics involving the topological sign of characteristics and multiple Jordan chains, and secondly a nonlinear modulation theory is developed for transitions. The nonlinear theory shows that coalescing characteristics morph the Whitham equations into an asymptotically valid geometric form of the two-way Boussinesq equation. That is, coalescing characteristics generate dispersion, nonlinearity and complex wave fields. For illustration, the theory is applied to coalescing characteristics associated with the modulation of two-phase travelling-wave solutions of coupled nonlinear Schr\"odinger equations, highlighting how collisions can be identified and the relevant dispersive dynamics constructed.Comment: 40 pages, 2 figure

Electronic instabilities in metal-insulator semiconductor devices

Electronic charge injection instability in silicon nitride metal-insulator-semiconductor device

SCUBA Observations of NGC 1275

Deep SCUBA observations of NGC 1275 at 450 micron and 850 micron along with the application of deconvolution algorithms have permitted us to separate the strong core emission in this galaxy from the fainter extended emission around it. The core has a steep spectral index and is likely due primarily to the AGN. The faint emission has a positive spectral index and is clearly due to extended dust in a patchy distribution out to a radius of $\sim$ 20 kpc from the nucleus. These observations have now revealed that a large quantity of dust, $\sim$ 6 $\times$ 10$^7$ $M_\odot$, 2 orders of magnitude larger than that inferred from previous optical absorption measurements, exists in this galaxy. We estimate the temperature of this dust to be $\sim$ 20 K (using an emissivity index of $\beta$ = 1.3) and the gas/dust ratio to be 360. These values are typical of spiral galaxies. The dust emission correlates spatially with the hot X-ray emitting gas which may be due to collisional heating of broadly distributed dust by electrons. Since the destruction timescale is short, the dust cannot be replenished by stellar mass loss and must be externally supplied, either via the infalling galaxy or the cooling flow itself.Comment: 13 pages, 4 figures. Figure 4 is colou

THE SPECTROSCOPY OF CRYSTAL DEFECTS - A COMPENDIUM OF DEFECT NOMENCLATURE

The authors bring together tables of current defect nomenclature and a summary of the rules actually practised (rather than idealised schemes) in choosing such labels for signals obtained with a range of spectroscopies. As well as providing a source of reference for the user lost in a maze of labels, the compilation also indicates parallels between similar defect species in very different systems (e.g. ice and quartz), even though the relationships may be far from obvious from the labels. The systems considered are all non-metals, namely ionic crystals (including oxides), silica, semiconductors (e.g. III-V and tetrahedrally coordinated II-VI), valence crystals (e.g. diamond, c-Si, a-Si) and other special hosts like ice and conducting polymers

Assessment of Current Jet Noise Prediction Capabilities

An assessment was made of the capability of jet noise prediction codes over a broad range of jet flows, with the objective of quantifying current capabilities and identifying areas requiring future research investment. Three separate codes in NASA s possession, representative of two classes of jet noise prediction codes, were evaluated, one empirical and two statistical. The empirical code is the Stone Jet Noise Module (ST2JET) contained within the ANOPP aircraft noise prediction code. It is well documented, and represents the state of the art in semi-empirical acoustic prediction codes where virtual sources are attributed to various aspects of noise generation in each jet. These sources, in combination, predict the spectral directivity of a jet plume. A total of 258 jet noise cases were examined on the ST2JET code, each run requiring only fractions of a second to complete. Two statistical jet noise prediction codes were also evaluated, JeNo v1, and Jet3D. Fewer cases were run for the statistical prediction methods because they require substantially more resources, typically a Reynolds-Averaged Navier-Stokes solution of the jet, volume integration of the source statistical models over the entire plume, and a numerical solution of the governing propagation equation within the jet. In the evaluation process, substantial justification of experimental datasets used in the evaluations was made. In the end, none of the current codes can predict jet noise within experimental uncertainty. The empirical code came within 2dB on a 1/3 octave spectral basis for a wide range of flows. The statistical code Jet3D was within experimental uncertainty at broadside angles for hot supersonic jets, but errors in peak frequency and amplitude put it out of experimental uncertainty at cooler, lower speed conditions. Jet3D did not predict changes in directivity in the downstream angles. The statistical code JeNo,v1 was within experimental uncertainty predicting noise from cold subsonic jets at all angles, but did not predict changes with heating of the jet and did not account for directivity changes at supersonic conditions. Shortcomings addressed here give direction for future work relevant to the statistical-based prediction methods. A full report will be released as a chapter in a NASA publication assessing the state of the art in aircraft noise prediction

Stardust microcrater residue compositional groups

Compositional groups are defined in residue from Stardust craters (1-9 Dc) by qualitative EDS. These compositional groups are being further studied by a FIB-SEM technique to determine representative residue compositions

Wave-coupled LiNbO_3 electrooptic modulator for microwave and millimeter-wave modulation

A new technique of phase velocity matching in electrooptic modulators was demonstrated. The results show that the phase velocity mismatch due to material dispersion in traveling-wave LiNbO_3 optical waveguide modulators can be greatly reduced by breaking the modulation transmission line into short segments and connecting each segment to its own surface dipole antenna. The array of antennas is then illuminated by the modulation signal from below at the proper angle to produce a delay from antenna to antenna that matches the optical waveguide's delay. A phase modulator 25 mm in length with five antennas and five transmission line segments was operated from 4.6 to 13 GHz with a maximum phase modulation sensitivity of over 100°/W^(1/2)

Limiting stable currents in bounded electron and ion streams

The classical static analysis of the infinite planar diode has been extended to include the effects of finite transverse beam size. Simple expressions have been found for the increase in maximum stable current density over that of an infinite stream for finite cylindrical and strip streams flowing between plates of infinite diodes. The results are also given in terms of stream perveance. The effect of a nonuniform distribution of current across the stream is shown to be relatively small. Experimental values of maximum stable current agree with those obtained from the analysis. A further extension of the static analysis has been made to include the effects of additional conducting plane boundaries parallel to the stream motion. For length-to-width ratios L/D less than 0.25 the tube is adequately described by the results for the infinite planar diode and for L/D greater than 4, the infinitely-long drift tube theory suffices. At intermediate values of L/D, the maximum amount of current that can be stably passed through the tube is greater than that predicted by either asymptotic theory

Transverse instability and its long-term development for solitary waves of the (2+1)-Boussinesq equation

The stability properties of line solitary wave solutions of the (2+1)-dimensional Boussinesq equation with respect to transverse perturbations and their consequences are considered. A geometric condition arising from a multi-symplectic formulation of this equation gives an explicit relation between the parameters for transverse instability when the transverse wavenumber is small. The Evans function is then computed explicitly, giving the eigenvalues for transverse instability for all transverse wavenumbers. To determine the nonlinear and long time implications of transverse instability, numerical simulations are performed using pseudospectral discretization. The numerics confirm the analytic results, and in all cases studied, transverse instability leads to collapse.Comment: 16 pages, 8 figures; submitted to Phys. Rev.