Backlund transformations and exact solutions for a nonlinear elliptic equation modelling isothermal magnetostatic atmosphere

The equations of magnetostatic equilibria for a plasma in agravitational field are investigated analytically. For equilibriawith an ignorable spatial coordinate, the equations reduce toa single nonlinear elliptic equation for the magnetic potentialu known as the Grad-Shafranov equation. By specifying the arbitraryfunctions in this equation, a Liouville equation is obtained.Bäcklund transformations are described and applied to obtainexact solutions for the Liouville equation modelling an isothermalmagnetostatic atmosphere, in which the current density J isproportional to the exponential of the magnetic potential andmoveover falls off exponentially with distance vertical to thebase with an e-folding distance equal to the gravitational scaleheight.     

Highly directional acoustic receivers

The theoretical directivity of a single combined acoustic receiver, a device that can measure many quantities of an acoustic field at a collocated point, is presented here. The formulation is developed using a Taylor series expansion of acoustic pressure about the origin of a Cartesian coordinate system. For example, the quantities measured by a second-order combined receiver, denoted a dyadic sensor, are acoustic pressure, the three orthogonal components of acoustic particle velocity, and the nine spatial gradients of the velocity vector. The power series expansion, which can be of any order, is cast into an expression that defines the directivity of a single receiving element. It is shown that a single highly directional dyadic sensor can have a directivity index of up to 9.5 dB. However, there is a price to pay with highly directive sensors; these sensors can be significantly more sensitive to nonacoustic noise sources.     

Solid state effects in the Auger spectrum of zinc and oxidised zinc

Measurements of the zinc L_2,3M_4,5M_4,5 Auger spectra are reported. The line shapes in solid zinc are similar to those in zinc vapour but the Auger energies have increased by about 15 eV and the line breadths have broadened from 0.5 eV to 1.0 eV fwhm. The ratio of the L₂:L₃ groups differ from the vapour suggesting that L₂L₃M_4,5 Coster-Kronig transitions occur in the solid but not in the vapour. Changes in the spectra with oxidation have been observed. The Auger lines broaden on oxidation and a line breadth of 3.2 eV fwhm gives the best fit to the spectrum of almost fully oxidised zinc. The oxide L₃M_4,5M_4,5¹G₄ peak progressively shifts from 2.6 eV to 4.2 eV below the metal peak as the oxide thickness increases, the latter value being close to the measured shift in crystalline zinc oxide. Similar energy variation is reported for solid Argon condensed onto clean silver and the shifts are explained in terms of variation in “extra electron relaxation” with film thickness.     

Structure and bonding in the metal complexes of ethylenediaminetetra-acetic acid

The metal-ion complexes of ethylenediaminetetra-acetic acid (EDTA) find widespread use not only in analysis, but also in foodstuffs, pharmacy, and medicine. A review of the structures of the solid complexes illustrates the considerable variation in co-ordination number of the metal-ion, and the possible denticities of EDTA. These data are relevant to the solid-state properties and also to the structures of the complexes in solution, which cannot be directly determined.     

Basilar-membrane responses to multicomponent (Schroeder-phase) signals: understanding intensity effects

Harmonic complexes comprised of the same spectral components in either positive-Schroeder (+Schr) or negative-Schroeder (-Schr) phase [see Schroeder, IEEE Trans. Inf. Theory 16, 85-89 (1970)] have identical long-term spectra and similar waveform envelopes. However, localized patterns of basilar-membrane (BM) excitation can be quite different in response to these two stimuli. Measurements in chinchillas showed more modulated (peakier) BM excitation for +Schr than -Schr complexes [Recio and Rhode, J. Acoust. Soc. Am. 108, 2281-2298 (2000)]. In the current study, laser velocimetry was used to examine BM responses at a location tuned to approximately 17 kHz in the basal turn of the guinea-pig cochlea, for +Schr and -Schr complexes with a 203-Hz fundamental frequency and including 101 equal-amplitude components from 2031 to 22,344 Hz. At 35-dB SPL, +Schr response waveforms showed greater amplitude modulation than -Schr responses. With increasing stimulation level, internal modulation decreased for both complexes. To understand the observed phenomena quantitatively, responses were predicted on the basis of a linearized model of the cochlea. Prediction was based on an "indirect impulse response" measured in the same animal. Response waveforms for Schroeder-phase signals were accurately predicted, provided that the level of the indirect impulse used in prediction closely matched the level of the Schroeder-phase stimulus. This result confirms that the underlying model, which originally was developed for noise stimuli, is valid for stimuli that produce completely different response waveforms. Moreover, it justifies explanation of cochlear filtering (i.e., differential treatment of different frequencies) in terms of a linear system.     

Wave propagation patterns in a "classical" three-dimensional model of the cochlea

The generation mechanisms of cochlear waves, in particular those that give rise to otoacoustic emissions (OAEs), are often complex. This makes it difficult to analyze wave propagation. In this paper two unusual excitation methods are applied to a three-dimensional stylized classical nonlinear model of the cochlea. The model used is constructed on the basis of data from an experimental animal selected to yield a smooth basilar-membrane impedance function. Waves going in two directions can be elicited by exciting the model locally instead of via the stapes. Production of DPOAEs was simulated by presenting the model with two relatively strong primary tones, with frequencies f1 and f2, estimating the driving pressure for the distortion product (DP) with frequency 2f1 - f2, and computing the resulting DP response pattern - as a function of distance along the basilar membrane. For wide as well as narrow frequency separations the resulting DP wave pattern in the model invariably showed that a reverse wave is dominant in nearly the entire region from the peak of the f2-tone to the stapes. The computed DP wave pattern was further analyzed as to its constituent components with the aim to isolate their properties.     

The user and terrain-machine system research

Designing off-road equipment to meet user requirements assumes that research results are brought to bear on real design problems, that the user has been identified, and that the user's needs are communicated to the designer. In the area of military vehicles, these conditions are met. The U.S. Army Mobility Model is an example of how this is done.The Army Mobility Model, a computer simulation technique, allows terrain, vehicle, and driver characteristics to be combined to predict the performance of vehicles according to various criteria such as speed, fuel consumption, etc. The results of the computer analysis appear in map form, and there are also special techniques for finding the optimum route between two points. The data base has been validated by actual vehicle performance measurements.Several recent applications of the Army Mobility Model are discussed. These applications demonstrate that the need for a systematic application of terrain-vehicle research results to vehicle design has been at least partly fulfilled. This simulation technique has developed a stronger communication link between the vehicle designer and user. Establishing this link has created a new demand for a wide variety of vehicle performance predictions for which many predictive relations are not yet fully developed and validated. Adequate research will be necessary to ensure further progress in this direction.     

Crystal and magnetic structures of afeIIFeIII(C2O4)3 (A = organic cation): two-dimensional honeycomb ferrimagnets

Ferrimagnetic tris-oxalato-ferrate(II,III) salts with general formula AFeIIFeIII(C2O4)3 (A = quaternary ammonium, phosphonium) all crystallise in two-dimensional hexagonal honeycomb lattices but while some show conventional Néel type Q magnetisation at low temperature others show negative Néet type N magnetisation below a compensation temperature Tcomp. The compounds having negative magnetisation show a discontinuity in the magnetisation at a temperature between Tcomp and Tc suggesting a magneto-strictive transition. For the type Q compounds, hysteresis and frequency dependent AC susceptibility show that the low temperature magnetic state is glassy, either because of frustration of random anisotropy domains below a blocking temperature, or imbalance in the fractions of FeII and FeIII.     

Double-hole aluminum center in α-quartz

EPR studies at ca. 25 K of a single crystal of α-quartz, which had been X-irradiated at 77 K, have disclosed the presence of a new type of impurity center. This is thought to consist of a substitutional aluminum 3+ ion with electron holes at two neighboring oxygen ions, forming a triplet system. The two primary ²⁷Al hyperfine multiples as well as the half-field spectrum have been observed, and have led to an approximate spin-Hamiltonian.