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The ratio of rotational discontinuities (RD's) to tangential discontinuities (TD's) in the solar wind at 1 AU is considered, along with some of its major implications. In particular, the ratio of the number of RD's to TD's in an interval typical of the solar wind is searched. Some of the involved difficulties are discussed, and several alternate questions are raised.
The Harang discontinuity, the area separating the positive and negative bay regions in the midnight sector of the auroral zone, is a focal point for changes in behavior of many phenomena. Through this region the electric field, in a frame corotating with the earth, rotates through the west from a basically northward field in the positive bay region to a basically southward field in the negative bay region, appearing as a reversal in a single-axis measurement of the north-south component. Thirty-two of these reversals have been identified in the Ogo 6 data from November and December 1969. The discontinuity is dynamic in nature, moving southward and steepening its latitudinal profile as magnetic activity is increased. As activity decreases, it relaxes poleward and spreads out in latitudinal width. It occurs over several hours of magnetic local time.
The properties of directional discontinuities occurring in selected periods of interplanetary magnetic field data are investigated. Microscale fluctuations in these selected periods have previously been identified as being predominantly Alfvenic on time scales ranging from 5 min to a few hours. We argue that the majority of directional discontinuities in such periods are rotational and outwardly propagating.
A complete analysis of an interplanetary disturbance of Nov. 19, 1970 using the Apollo 12-SIDE (Suprathermal Ion Detector Experiment) is presented. The SIDE detectors were pointing at 26.3 degrees from the normal solar-wind direction during the observations. The data were least-squares fitted (using a parabolic hypersurface approximation) to a convected Maxwell-Boltzmann distribution function. The results of the fit combined with two other experiments showed a drastic change in the wind speed (from an steady 352 km/sec down to 219 km/sec), direction, and temperature. Except for a delta-function increase at the onset, the density remained constant. There was a considerable enhancement in the abundance of He and probably of heavier elements. The interplanetary magnetic field exhibited a jump of 21 gamma with a change in latitude from -56 to -76 degrees in solar ecliptic coordinates. It is concluded that the disturbance was due to the driver gas-tangential discontinuity of a solar flare-induced shock wave. The characteristic of the tangential discontinuity fit well with theoretical prediction.
The main difficulty in perturbing a discontinuous transonic flow is in the representation of the shift in the location of the discontinuity (shock wave). Herein presented is a method of overcoming this difficulty by using a distorted airfoil as the initial case rather than the real physical airfoil; the distortion is chosen such that the shock location is unchanged by the perturbation. The distorted airfoil is obtained by the use of a strained coordinate system. A direct consequence of the theory is the derivation of an algebraic similarity relation between related airfoils with shock waves at differing locations. Results for simple examples are shown.
The probability of triggering of polar substorms by a large-scale magnetospheric compression associated with a discontinuity in the solar wind has been examined statistically using ground magnetogram data, AE index data and satellite geomagnetic data on 125 sudden storm commencements observed during 1967-1970. The triggering probability was found to depend on the amplitude of the sudden storm commencement and on the degree of preceding AE activity. In almost all cases the triggering occurred when the B-Z component of the interplanetary magnetic field was negative or decreasing during the 30 min before the passage of the discontinuity. Transient geomagnetic responses with a time scale of Alfven wave propagation in the polar cap also depend on interplanetary magnetic field conditions.
An investigation of Nichrome/tungsten laminar composites showed that intentionally introduced discontinuities, such as perforations through or grooves on the surface of the matrix laminae, improved thermal expansion mismatch damage resistance. It was found that specimens having smooth matrix laminate surfaces were virtually destroyed by delamination in 21 or fewer fast cool cycles in which they were water quenched from 981 C. Specimens having interior matrix laminae with discontinuities and relatively thin, nondiscontinuous, surface matrix laminae resisted 50 similar cycles without evident delamination damage.
Using discrete time state variable representation, a generalized computer-aided modeling and analysis of dc-dc converters is presented. The methodology provides exact modeling and is applicable to all types of power stages and duty-cycle control, including continuous and discontinuous inductor current operation. Converter stability, transient behavior and audio susceptibility can be analytically evaluated and predicted. The generalized theory of the proposed approach to converter modeling and analysis is presented first, followed by a demonstrative example applying the theory to a constant frequency buck converter operating in continuous and discontinuous inductor current mode. Excellent agreement with laboratory test data has been observed.
A method for modelling switching converters in the discontinuous conduction mode is developed, whose starting point is the unified state-space representation, and whose end result is a complete linear circuit model which correctly represents all essential features, namely, the input, output, and transfer properties (static dc as well as dynamic ac small signal). While the method is generally applicable to any switching converter operating in the discontinuous conduction mode, it is extensively illustrated for the three common power stages (buck, boost, and buck-boost). The results for these converters are then easily tabulated owing to the fixed equivalent circuit topology of their canonical circuit model.
The radial distribution of the Jovian sulfur plasma is discussed. Spectra of the ionized sulfur in the Jovian magnetosphere indicate a sharp discontinuity in visible sulfur emission at a radial distance of six Jupiter radii (Io orbit), outside of which emission is greatly reduced and the plasma is observed not to be in corotation with the planet. Possible explanations of this phenomenon include an effect of Io on the electron temperature outside its orbit, leading to the suppression of S II emission by second ionization, and a current system in Jupiter's ionosphere which prevents plasma from diffusing outward and decouples it from the corotation field. This discontinuity also requires reconciliation with Pioneer observations of the radial and pitch-angle diffusion of energetic charged particles.
Spline based techniques for estimating spatially varying parameters that appear in parabolic distributed systems (typical of those found in reservoir simulation problems) are presented. The problem of determining discontinuous coefficients, estimating both the functional shape and points of discontinuity for such parameters is discussed. Convergence results and a summary of numerical performance of the resulting algorithms are given.
Photoluminescence studies at 4 K on Ga(0.47)In(0.53)As/Al(0.48)In(0.52)As single quantum wells exhibit emission ranging from 1.318 eV for a 15-A well to 0.82 eV for thick wells. The emission energy of each single quantum well is compared to theoretical curves which are generated from a finite potential square well model. The closest agreement between the experimental curves and the theoretical curves occurs when the conduction band discontinuity is taken to be 70 percent of the bandgap discontinuity or 0.52 eV.
The pointwise values of a function, f(x), can be accurately recovered either from its spectral or pseudospectral approximations, so that the accuracy solely depends on the local smoothness of f in the neighborhood of the point x. Most notably, given the equidistant function grid values, its intermediate point values are recovered within spectral accuracy, despite the possible presence of discontinuities scattered in the domain. (Recall that the usual spectral convergence rate decelerates otherwise to first order, throughout). To this end, a highly oscillatory smoothing kernel is employed in contrast to the more standard positive unit-mass mollifiers. In particular, post-processing of a stable Fourier method applied to hyperbolic equations with discontinuous data, recovers the exact solution modulo a spectrally small error. Numerical examples are presented.
Computations on zonal grids - in particular, grids with metric discontinuities resulting from the interspersion of highly clustered regions with coarse regions - are possible using a fully conservative form of the Osher upwind scheme. These zonal grids can result from an abrupt clustering of points near solution discontinuities or near other flow features that require improved resolution. The zonal approach is shown to capture shocks with almost 'shock-fitting' quality but with minimal effort. Results for inviscid flow, including quasi-one-dimensional nozzle flow, supersonic flow over a cylinder, and blast-wave diffraction by a ramp, are presented. These calculations demonstrate the powerful capabilities of the Osher scheme used in conjunction with zonal grids in simulating flow fields with complex shock patterns.
The problem of estimating discontinuous coefficients, including locations of discontinuities, that occur in second order hyperbolic systems typical of those arising in I-D surface seismic problems is discussed. In addition, the problem of identifying unknown parameters that appear in boundary conditions for the system is treated. A spline-based approximation theory is presented, together with related convergence findings and representative numerical examples.
The surfaces of discontinuity (SDs) identified by Parker (1986) in the torsion of a force-free magnetic field in an infinitely conducting fluid contained betweeen two fixed boundary planes are characterized analytically. It is shown that field discontinuities (current sheets) occur whenever an SD terminates within the fluid or intersects with another SD, that intersections occur in most cases, and that the resulting current sheets are responsible for most field dissipation in highly conducting fluids. The astrophysical implications of these findings and a number of unresolved problems are discussed.
The pointwise values of a function, f(x), can be accurately recovered either from its spectral or pseudospectral approximations, so that the accuracy solely depends on the local smoothness of f in the neighborhood of the point x. Most notably, given the equidistant function grid values, its intermediate point values are recovered within spectral accuracy, despite the possible presence of discontinuities scattered in the domain. (Recall that the usual spectral convergence rate decelerates otherwise to first order, throughout). To this end, a highly oscillatory smoothing kernel is employed in contrast to the more standard positive unit-mass mollifiers. In particular, post-processing of a stable Fourier method applied to hyperbolic equations with discontinuous data, recovers the exact solution modulo a spectrally small error. Numerical examples are presented.
The aim of this study is to find a reliable numerical algorithm to calculate thermal design sensitivities of a transient problem with discontinuous derivatives. The thermal system of interest is a transient heat conduction problem related to the curing process of a composite laminate. A logical function which can smoothly approximate the discontinuity is introduced to modify the system equation. Two commonly used methods, the adjoint variable method and the direct differentiation method, are then applied to find the design derivatives of the modified system. The comparisons of numerical results obtained by these two methods demonstrate that the direct differentiation method is a better choice to be used in calculating thermal design sensitivity.