Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering

In this article we describe recent progress on the design, analysis and implementation of hybrid numerical-asymptotic boundary integral methods for boundary value problems for the Helmholtz equation that model time harmonic acoustic wave scattering in domains exterior to impenetrable obstacles. These hybrid methods combine conventional piecewise polynomial approximations with high-frequency asymptotics to build basis functions suitable for representing the oscillatory solutions. They have the potential to solve scattering problems accurately in a computation time that is (almost) independent of frequency and this has been realized for many model problems. The design and analysis of this class of methods requires new results on the analysis and numerical analysis of highly oscillatory boundary integral operators and on the high-frequency asymptotics of scattering problems. The implementation requires the development of appropriate quadrature rules for highly oscillatory integrals. This article contains a historical account of the development of this currently very active field, a detailed account of recent progress and, in addition, a number of original research results on the design, analysis and implementation of these methods.

Does high-frequency repetitive transcranial magnetic stimulation produce residual and/or cumulative effects within an experimental session?

A common procedure for studying the effects on cognition of repetitive transcranial magnetic stimulation (rTMS) is to deliver rTMS concurrent with task performance, and to compare task performance on these trials versus on trials without rTMS. Recent evidence that TMS can have effects on neural activity that persist longer than the experimental session itself, however, raise questions about the assumption of the transient nature of rTMS that underlies many concurrent (or "online") rTMS designs. To our knowledge, there have been no studies in the cognitive domain examining whether the application of brief trains of rTMS during specific epochs of a complex task may have effects that spill over into subsequent task epochs, and perhaps into subsequent trials. We looked for possible immediate spill-over and longer-term cumulative effects of rTMS in data from two studies of visual short-term delayed recognition. In 54 subjects, 10-Hz rTMS trains were applied to five different brain regions during the 3-s delay period of a spatial task, and in a second group of 15 subjects, electroencephalography (EEG) was recorded while 10-Hz rTMS was applied to two brain areas during the 3-s delay period of both spatial and object tasks. No evidence for immediate effects was found in the comparison of the memory probe-evoked response on trials that were vs. were not preceded by delay-period rTMS. No evidence for cumulative effects was found in analyses of behavioral performance, and of EEG signal, as a function of task block. The implications of these findings, and their relation to the broader literature on acute vs. long-lasting effects of rTMS, are considered.

Linear criteria for gravity-wave breaking in resonant stratified flow over a ridge

Using linear theory, it is shown that, in resonant flow over a 2D mountain ridge, such as exists when a layer of uniform wind is topped by an environmental critical level, the conditions for internal gravity-wave breaking are different from those determined in previous studies for non-resonant flows. For Richardson numbers in the shear layer not exceeding 2.25, two zones of flow overturning exist, respectively below and downstream and above and upstream of the expected locations. Flow overturning occurs for values of the dimensionless height of the ridge smaller than those required for a uniform wind profile. These results may have implications for the physical understanding of high-drag states.

Resonant gravity-wave drag enhancement in linear stratified flow over mountains

High-drag states produced in stratified flow over a 2D ridge and an axisymmetric mountain are investigated using a linear, hydrostatic, analytical model. A wind profile is assumed where the background velocity is constant up to a height z1 and then decreases linearly, and the internal gravity-wave solutions are calculated exactly. In flow over a 2D ridge, the normalized surface drag is given by a closed-form analytical expression, while in flow over an axisymmetric mountain it is given by an expression involving a simple 1D integral. The drag is found to depend on two dimensionless parameters: a dimensionless height formed with z_1, and the Richardson number, Ri, in the shear layer. The drag oscillates as z_1 increases, with a period of half the hydrostatic vertical wavelength of the gravity waves. The amplitude of this modulation increases as Ri decreases. This behaviour is due to wave reflection at z_1. Drag maxima correspond to constructive interference of the upward- and downward-propagating waves in the region z < z_1, while drag minima correspond to destructive interference. The reflection coefficient at the interface z = z_1 increases as Ri decreases. The critical level, z_c, plays no role in the drag amplification. A preliminary numerical treatment of nonlinear effects is presented, where z_c appears to become more relevant, and flow over a 2D ridge qualitatively changes its character. But these effects, and their connection with linear theory, still need to be better understood.

The effects of word exposure frequency and elaboration of word processing on incidental L2 vocabulary acquisition through reading

Research on incidental second language (L2) vocabulary acquisition through reading has claimed that repeated encounters with unfamiliar words and the relative elaboration of processing these words facilitate word learning. However, so far both variables have been investigated in isolation. To help close this research gap, the current study investigates the differential effects of the variables ‘word exposure frequency’ and ‘elaboration of word processing’ on the initial word learning and subsequent word retention of advanced learners of L2 English. Whereas results showed equal effects for both variables on initial word learning, subsequent word retention was more contingent on elaborate processing of form–meaning relationships than on word frequency. These results, together with those of the studies reviewed, suggest that processing words again after reading (input–output cycles) is superior to reading-only tasks. The findings have significant implications for adaptation and development of teaching materials that enhance L2 vocabulary learning.

The signature of ENSO in the Northern Hemisphere midlatitude seasonal mean flow and high-frequency intraseasonal variability

The impact of pronounced positive and negative sea surface temperature (STT) anomalies in the tropical Pacific associated with the El Niño/Southern Oscillation (ENSO) phenomenon on the atmospheric circulation in the Northern Hemisphere extratropics during the boreal winter season is investigated. This includes both the impact on the seasonal mean flow and on the intraseasonal variability on synoptic time scales. Moreover, the interaction between the transient fluctuations on these times scales and the mean circulation is examined. Both data from an ensemble of five simulations with the ECHAM3 atmospheric general circulation model at a horizontal resolution of T42 each covering the period from 1979 through 1992 and operational analyses from ECMWF for the corresponding period are examined. In each of the simulations observed SSTs for the period of investigation are given as lower boundary forcing, but different atmospheric initial conditions are prescribed. The simulations with ECHAM3 reveal a distinct impact of the pronounced SST-anomalies in the tropical Pacific on the atmospheric circulation in the Northern Hemisphere extratropics during El Niño as well as during La Niña events. These changes in the atmospheric circulation, which are found to be highly significant in the Pacific/North American as well as in the Atlantic/European region, are consistent with the essential results obtained from the analyses. The pronounced SST-anomalies in the tropical Pacific lead to changes in the mean circulation, which are characterized by typical circulation patterns. These changes in the mean circulation are accompanied by marked variations of the activity of the transient fluctuations on synoptic time scales, that are changes in both the kinetic energy on these time scales and the atmospheric transports of momentum and heat accomplished by the short baroclinic waves. The synoptic disturbances, on the other hand, play also an important role in controlling the changes in the mean circulation associated with the ENSO phenomenon. They maintain these typical circulation patterns via barotropic, but counteract them via baroclinic processes. The hypothesis of an impact of the ENSO phenomenon in the Atlantic/European region can be supported. As the determining factor the intensification (reduction) of the Aleutian low and the simultaneous reduction (intensification) of the Icelandic low during El Niño and during La Niña events respectively, is identified. The changes in the intensity of the Aleutian low during the ENSO-events are accompanied by an alteration of the transport of momentum caused by the short baroclinic waves over the North American continent in such a way that the changes in the intensity of the Icelandic low during El Niño as well as during La Niña events are maintained.

Will greenhouse gas-induced warming over the next 50 years lead to higher frequency and greater intensity of hurricanes?

The use of a high resolution atmospheric model at T106 resolution, for studying the influence of greenhouse warming on tropical storm climatology, is investigated. The same method for identifying the storms has been used as in a previous study by Bengtsson et al. The sea surface temperature anomalies have been taken from a previous transient climate change experiment, obtained with a low resolution ocean-atmosphere coupled model. The global distribution of the storms, at the time when the CO2 concentration in the atmosphere had doubled, agrees in geographical position and seasonal variability with that of the present climate, but the number of storms is significantly reduced, particularly at the Southern Hemisphere. The main reason to this, appear to be connected to changes in the large scale circulation, such as a weaker Hadley circulation and stronger upper air westerlies. The low level vorticity in the hurricane genesis regions is generally reduced compared to the present climate, while the vertical tropospheric wind shear is somewhat increased. Most tropical storm regions indicate reduced surface windspeeds and a slightly weaker hydrological cycle.

Analytical calculation of resonant inductance for zero voltage switching in phase-shifted full-bridge converters

The phase shift full bridge (PSFB) converter allows high efficiency power conversion at high frequencies through zero voltage switching (ZVS); the parasitic drain-to-source capacitance of the MOSFET is discharged by a resonant inductance before the switch is gated resulting in near zero turn-on switching losses. Typically, an extra inductance is added to the leakage inductance of a transformer to form the resonant inductance necessary to charge and discharge the parasitic capacitances of the PSFB converter. However, many PSFB models do not consider the effects of the magnetizing inductance or dead-time in selecting the resonant inductance required to achieve ZVS. The choice of resonant inductance is crucial to the ZVS operation of the PSFB converter. Incorrectly sized resonant inductance will not achieve ZVS or will limit the load regulation ability of the converter. This paper presents a unique and accurate equation for calculating the resonant inductance required to achieve ZVS over a wide load range incorporating the effects of the magnetizing inductance and dead-time. The derived equations are validated against PSPICE simulations of a PSFB converter and extensive hardware experimentations.

Constructing the frequency and wave normal distribution of whistler-mode wave power

We introduce a new methodology that allows the construction of wave frequency distributions due to growing incoherent whistler-mode waves in the magnetosphere. The technique combines the equations of geometric optics (i.e. raytracing) with the equation of transfer of radiation in an anisotropic lossy medium to obtain spectral energy density as a function of frequency and wavenormal angle. We describe the method in detail, and then demonstrate how it could be used in an idealised magnetosphere during quiet geomagnetic conditions. For a specific set of plasma conditions, we predict that the wave power peaks off the equator at ~15 degrees magnetic latitude. The new calculations predict that wave power as a function of frequency can be adequately described using a Gaussian function, but as a function of wavenormal angle, it more closely resembles a skew normal distribution. The technique described in this paper is the first known estimate of the parallel and oblique incoherent wave spectrum as a result of growing whistler-mode waves, and provides a means to incorporate self-consistent wave-particle interactions in a kinetic model of the magnetosphere over a large volume.

Ultralow-frequency modulation of whistler-mode wave growth

Measurements from ground-based magnetometers and riometers at auroral latitudes have demonstrated that energetic (~30-300keV) electron precipitation can be modulated in the presence of magnetic field oscillations at ultra-low frequencies. It has previously been proposed that an ultra-low frequency (ULF) wave would modulate field and plasma properties near the equatorial plane, thus modifying the growth rates of whistler-mode waves. In turn, the resulting whistler-mode waves would mediate the pitch-angle scattering of electrons resulting in ionospheric precipitation. In this paper, we investigate this hypothesis by quantifying the changes to the linear growth rate expected due to a slow change in the local magnetic field strength for parameters typical of the equatorial region around 6.6RE radial distance. To constrain our study, we determine the largest possible ULF wave amplitudes from measurements of the magnetic field at geosynchronous orbit. Using nearly ten years of observations from two satellites, we demonstrate that the variation in magnetic field strength due to oscillations at 2mHz does not exceed ±10% of the background field. Modifications to the plasma density and temperature anisotropy are estimated using idealised models. For low temperature anisotropy, there is little change in the whistler-mode growth rates even for the largest ULF wave amplitude. Only for large temperature anisotropies can whistler-mode growth rates be modulated sufficiently to account for the changes in electron precipitation measured by riometers at auroral latitudes.

Optical characterization of the growth and spatial structure of a substorm onset arc

We present a detailed case study of the characteristics of auroral forms that constitute the first ionospheric signatures of substorm expansion phase onset. Analysis of the optical frequency and along-arc (azimuthal) wave number spectra provides the strongest constraint to date on the potential mechanisms and instabilities in the near-Earth magnetosphere that accompany auroral onset and which precede poleward arc expansion and auroral breakup. We evaluate the frequency and growth rates of the auroral forms as a function of azimuthal wave number to determine whether these wave characteristics are consistent with current models of the substorm onset mechanism. We find that the frequency, spatial scales, and growth rates of the auroral forms are most consistent with the cross-field current instability or a ballooning instability, most likely triggered close to the inner edge of the ion plasma sheet. This result is supportive of a near-Earth plasma sheet initiation of the substorm expansion phase. We also present evidence that the frequency and phase characteristics of the auroral undulations may be generated via resonant processes operating along the geomagnetic field. Our observations provide the most powerful constraint to date on the ionospheric manifestation of the physical processes operating during the first few minutes around auroral substorm onset.