Comparisons between model equations for long waves

Summary Considered here are model equations for weakly nonlinear and dispersive long waves, which feature general forms of dispersion and pure power nonlinearity. Two variants of such equations are introduced, one of Korteweg-de Vries type and one of regularized long-wave type. It is proven that solutions of the pure initial-value problem for these two types of model equations are the same, to within the order of accuracy attributable to either, on the long time scale during which nonlinear and dispersive effects may accumulate to make an order-one relative difference to the wave profiles.This research was supported in part by the National Science Foundation. A considerable portion of the project was completed while the first author was resident at the Institute for Mathematics and Its Applications, University of Minnesota.     

The determination of the past and the future of a physical system in quantum mechanics

The determination of the past and the future of a physical system are complementary aims of measurements. An optimal determination of the past of a system can be achieved by an informationally complete set of physical quantities. Such a set is always strongly noncommutative. An optimal determination of the future of a physical system can be obtained by a Boolean complete set of quantities. The two aims can be reconciled to a reasonable degree with using unsharp measurements.This work was partly supported by the Bundesministerium für Forschung und Technologie, Bonn, the Research Institute for Theoretical Physics, Helsinki, and the University of Turku Foundation, Turku.     

Electron traps and positive DLTS signals in VPE GaAs MESFETs

Capacitance DLTS measurements have been performed in VPE GaAs MESFETs prepared on Bridgman Cr-doped and LEC undoped semi-insulating substrates. A band of electron traps not intrinsically related to the VPE growth process and accumulating near the metal (gate) — semiconductor interface was detected in all the samples. Deeper regions into the channel were free from any detectable trap. Near pinch-off conditions, a positive capacitance signal was found to dominate the DLTS spectra only in the case of samples prepared on Cr-doped substrates. The hypothesis of this positive transient being related to changes in the occupation of surface states in the ungated surface access regions has been checked by comparing experimental and calculated dependencies of the signal amplitude on reverse gate voltage. Unexplained discrepancies, together with the absence of positive signal in MESFETs prepared on LEC undoped substrates, suggest the possibility of hole emission from hole traps within the bulk of the device.     

OPTIMAL INVESTMENT IN THE PROTECTION OF A VULNERABLE BIOLOGICAL RESOURCE

It is assumed that the probability of destruction of a biological asset by natural hazards can be reduced through investment in protection. Specifically a model, in which the hazard rate depends on both the age of the asset and the accumulated invested protection capital, is assumed. The protection capital depreciates through time and its effectiveness in reducing the hazard rate is subject to diminishing returns. It is shown how the investment schedule to maximize the expected net present value of the asset can be determined using the methods of deterministic optimal control, with the survival probability regarded as a state variable. The optimal investment pattern involves “bang-bang-singular” control. A numerical scheme for determining jointly the optimal investment policy and the optimal harvest (or replacement) age is outlined and a numerical example involving forest fire protection is given.     

Correlation between time functions of sound pressure, masking, and OAE suppression

Periodic sound-pressure time functions with frequency components below 50 Hz were used to measure within their period (a) the temporal course of masking, called a masking-period pattern (MPP), and (b) the temporal course of suppression of delayed evoked otoacoustic emissions, called a suppression-period pattern (SPP). Three different time functions were used: an alternating Gaussian impulse, its first integral, and its second integral. In each case, the course of the SPP is a mirror image of that of the MPP: Small masking corresponds to small suppression, while strong masking coincides with almost total suppression. Since otoacoustic emissions are assumed to have their origin in the inner ear, it can be argued that simultaneous masking, an effect including central processing, is very strongly based on peripheral processes located in the cochlea. Both MPP and SPP are closely related to the second derivative of the sound-pressure time function.     

Exact soliton solutions of spinor Bose-Einstein condensates

We study matter-wave solitons in Bose-Einstein condensates of ultracold gaseous atoms with spin degrees of freedom and present a class of exact solutions based on the inverse scattering method. The one-soliton solutions are classified with respect to the spin states. We analyze collisional effects between solitons in the same or different spin state(s), which reveals a very interesting possibility: we can manipulate the spin dynamics by controlling the parameters of colliding solitons.     

Global fit analysis including the ν9 + ν4 − ν4 hot band of ethane: Evidence of an interaction with the ν12 fundamental

The ν₉ fundamental band of ethane occurs in the 12 μm region. It is the strongest band of ethane in a terrestrial window and is commonly used for the identification of ethane in the Jovian planets. The ν₉ + ν₄ − ν₄ band occurs in the same region; neither can be analysed as an isolated band, since both are embedded in the torsional bath of the ground vibrational state. We report here two global fit models including data from both of these bands as well as the ν₃ fundamental and the ν₄, 2ν₄ − ν₄, and 3ν₄ torsional transitions. The first is restricted to −5 ? KΔK ? 15 in the hot band and gives an excellent fit to the included data. Three resonant interactions are identified in this fit—a Coriolis interaction with two resonant cases between the ν₉ torsional stack and that of the ground vibrational state (gs) and a resonant Fermi interaction between the ν₃ fundamental and the gs. Hot band lines with KΔK < −5 are influenced by a fourth perturbation, with a crossing at −11 < KΔK < −10, which has been attributed to an interaction with the ν₁₂ fundamental. A second fit, demonstrating a promising treatment of this interaction, is also presented.     

INFLUENCE OF A LEVELNESS DEFECT IN A THRUST BEARING ON THE DYNAMIC BEHAVIOUR OF AN ELASTIC SHAFT

This paper examines the non-linear dynamic behaviour of a flexible shaft. The shaft is mounted on two journal bearings and the axial load is supported by a defective hydrodynamic thrust bearing at one end. The defect is a levelness defect of the rotor. The thrust bearing behaviour must be considered to be non-linear because of the effects of the defect. The shaft is modelled with typical beam finite elements including effects such as the gyroscopic effects. A modal technique is used to reduce the number of degrees of freedom. Results show that the thrust bearing defects introduce supplementary critical speeds. The linear approach is unable to show the supplementary critical speeds which are obtained only by using non-linear analysis.     

Effect of hydrogen on the photoelectronic properties of GaAs/InGaAs quantum-well heterostructures with an island palladium layer on the surface

The effect of hydrogen on the photoluminescence and planar conductivity of GaAs/InGaAs quantum-well heterostructures with an island Pd layer at the anodically oxidized surface was studied. Unlike continuous deposited Pd layers, island layers do not cause the formation of defects in the GaAs surface region and yet the Pd layer maintains high catalytic activity with respect to hydrogen. It is found that the thermal treatment of such a structure in a hydrogen atmosphere causes atomic-hydrogen passivation of the defects in quantum wells. Studies of the characteristics of planar photoresistors with an island Pd layer acting as hydrogen sensors show that their hydrogen detectivity is approximately two orders of magnitude higher than that of diode structures with continuous Pd layers.     

Electrooptical anharmonicity parameters of the strong hydrogen bond

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 54, No. 4, pp. 581–587, April, 1991.