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On the existence and stability conditions for mixed-hybrid finite element solutions based on Reissner's variational principle

The extensions of Reissner's two-field (stress and displacement) principle to the cases wherein the displacement field is discontinuous and/or the stress field results in unreciprocated tractions, at a finite number of surfaces ('interelement boundaries') in a domain (as, for instance, when the domain is discretized into finite elements), is considered. The conditions for the existence, uniqueness, and stability of mixed-hybrid finite element solutions based on such discontinuous fields, are summarized. The reduction of these global conditions to local ('element') level, and the attendant conditions on the ranks of element matrices, are discussed. Two examples of stable, invariant, least-order elements - a four-node square planar element and an eight-node cubic element - are discussed in detail.

Karlovitz, L. A.

Performance of Heterostructural TaC/AlGaN Schottky Diodes Based on First Principles Electronic Structure Properties

Advances in ultra-wide bandgap materials, such as high Al-content AlxGa1-xN (AlGaN), are essential for next generation power electronics, but the requirement for lattice matched substrates is currently a significant obstacle. Recently, conductive TaC has emerged as a promising virtual substrate for AlGaN heteroepitaxy, with wurtzite (0001) AlxGa1-xN lattice-matched to rocksalt (111) TaC at x ~ 0.5. Thus, understanding and controlling the electronic properties of the TaC/AlGaN interface is key for developing technological applications based on TaC/AlGaN devices. Using density functional theory and electronic structure calculations, we here investigate TaC/Al0.5Ga0.5N interfaces, where we include explicit alloy models in the slab calculations. We predict the Schottky barrier height and the electric field discontinuity resulting from interface charges. Considering all possible combinations of (Ta, C) substrate termination, (Al/Ga, N) nucleation, and (Al/Ga, N) polarity, we construct a chemical potential phase diagram to identify the stable interfaces that can be accessed through variation of the synthesis conditions. The predicted interface electronic properties are implemented in device performance simulations to demonstrate a practical design for a strain-free, high-efficiency TaC/AlGaN Schottky diode with a low barrier height and without interface charges, underscoring the potential of TaC as a substrate for ultra-wide bandgap devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC

Transport of cosmic rays in the solar corona

A method by which energetic cosmic ray particles in the interplanetary medium can diffuse in solar longitude. The method consists of particle motion occurring along current sheets separating discontinuous field structures in the corona. These sheets can serve as pathways along which energetic particles drift at nearly their propagation speed. A model of the coronal magnetic field and the large scale field behavior are analyzed. A mechanism by which particles can travel across the coronal magnetic field and arrive at the earth is suggested.

Schatten, K. H.

Post-shock spikes: A new feature of proton and alpha enhancements associated with an interplanetary shock wave

Abrupt and prolonged enhancements in the intensities of 100 to approximately 2000 keV nucleon protons and alpha particles observed in interplanetary space are interpreted as particle populations confined between an interplanetary shock front and a magnetic field discontinuity. Prominent intensity spikes observed only below approximately 400 keV per charge for both protons and alpha particles several hours behind the shock front suggest that some fraction of the confined particles is accelerated by an energy per charge dependent process.

Gloeckler, G.

Modulation of low-energy cosmic rays

The relation between the diffusion coefficient of cosmic rays in the solar wind and the power spectrum of interplanetary magnetic field fluctuations, established in recent theories, is tested directly for low energy protons (below 80 MeV). In addition, an attempt is made to determine whether the particles are scattered by magnetic field discontinuities or by fluctuations between discontinuities. Predictions of a perturbation solution of the Fokker-Planck equation are compared with observations of the cosmic ray radial gradient. It is found that at energies between 40 and 80 MeV, galactic cosmic ray protons respond to changes in the predicted diffusion coefficients (i.e., the relationship under consideration holds at these low energies). The relation between changes in the proton flux and modulation parameters is best when the contribution of discontinuities is subtracted, which means that scattering is caused by fluctuations between discontinuities. There appears to be no distinct relation between changes in the modulation parameters and changes in the intensity of 20 to 40 MeV protons.

Sari, J. W.

Electromagnetic sounding of the moon using Apollo 16 and Lunokhod 2 surface magnetometer observations /preliminary results/

A technique of deep electromagnetic sounding of the moon using simultaneous magnetic-field measurements at two lunar surface sites is described. The method, used with the assumption that deep electrical conductivity is a function only of lunar radius, has the advantage of allowing calculation of the external driving field from two surface-site measurements only and therefore does not require data from a lunar orbiting satellite. A transient-response calculation is presented for the example of a magnetic-field discontinuity, measured simultaneously by Apollo 16 and Lunokhod 2 surface magnetometers.

Vanian, L. L.

Plasma electron observations in the wake of Venus

Two plasma regimes were observed in the Venus wake, one characterized by negative-going anisotropies accompanied by high bulk speeds and low magnetic variance, and the other characterized by positive-going anisotropies accompanied by low bulk speeds and high magnetic variance. The two modes alternate in time in a stochastic bimodal fashion as interplanetary magnetic field discontinuities propagate past Venus and switch on the positive anisotropies. The positive mode probably represents enhanced planetary ion pickup which results in instabilities, the damping of which energizes the electrons in the distant wake.

Yeates, C. M.

High-altitude observations of an intense inverted V event

Inverted-V events which generally occur in the pre-midnight sector over the auroral zone are frequently associated with reversals in the convection electric field. Such a reversal is observed by the University of Iowa quasispherical LEPEDEA on board ISEE 1 at an altitude of 13 RE on May 1, 1978. The bulk of the plasma shows a large shear over a five-minute interval. The associated change in the convection electric field is 5.1 mV/m. Large values of the field-aligned current are simultaneously detected. The potential structure appears to extend to the satellite location. Using a theoretical model, the field-aligned current due to the electric field discontinuity has been calculated. The magnitude of the parallel potential drop and width of the inverted-V region agree well with observation.

Huang, C. Y.

A two-dimensional radial outflow model of plasma at Jupiter

An analytic solution illustrating the behavior of incompressible irrotational plasma outflow in two dimensions is given for application to the Jovian magnetosphere. Plasma is assumed to emanate from the Alfven surface and is channeled downtail by the confining magnetopause surface. Conformal transformation methods are used to map this complex magnetotail geometry into a rectangular box for which the solution to Laplace's equation is expressed in simple form. The model suggests that a dipole layer is formed on the dawn side in the vicinity of the Alfven surface where the flow bifurcates into clockwise and counterclockwise motion. An electric field discontinuity of this type fixed in local time may be able to account for several anomalous spin-periodic phenomena, namely, the modulation of Io-independent radio emissions and the injection of energetic electrons into interplanetary space.

Barbosa, D. D.

Two Algorithms For Hypersonic Computations

Two new algorithms developed containing several desirable features for computation of viscous, hypersonic flows about three-dimensional geometries. Employ upwind-differencing methods, having unsurpassed abiltiy to capture flow-field discontinuities without need for any user-specified smoothing terms. Particularly important in hypersonic computations where many complicated wave structures exist. Both algorithms based on finite-volume formulation to ensure schemes, including boundary conditions, fully conservative.

Molvik, G. A.

Electromagnetic Sounding of the Moon Using Apollo 16 and Lunokhod 2 Surface Magnetometer Observations (Preliminary Results)

A new technique of deep electromagnetic sounding of the Moon using simultaneous magnetic field measurements at two lunar surface sites is described. The method, used with the assumption that deep electrical conductivity is a function only of lunar radius, has the advantage of allowing calculation of the external driving field from two surface site measurements only, and therefore does not require data from a lunar orbiting satellite. A transient response calculation is presented for the example of a magnetic field discontinuity of February 13, 1973, measured simultaneously by Apollo 16 and Lunokhod 2 surface magnetometers.

Vanyan, L. L.

Magnetosheath Flow Anomalies in 3-D

Measurements of the plasma and magnetic field with high temporal resolution on the Interball Tail probe reveal many flow anomalies in the magnetosheath. They are usually seen as flow direction and number density variations, accompanied by magnetic field discontinuities. Large flow anomalies with number density variations of factor of 2 or more and velocity variations of 100 km/s or more are seen with periodicity of about I per hour. The cases of flow anomalies following in succession are also observed, and suggest their decay while propagating through the magnetosheath. Some magnetospheric disturbances observed in the outer magnetosphere after the satellite has crossed the magnetopause on the inbound orbit suggest their association with magnetosheath flow anomalies observed in the magnetosheath prior to magnetopause crossing.

Vaisberg, O. L.

Some Experiences with High Order Discretization Schemes for Compressible Fluid Flow

It is widely recognized that the structure and complexity of compressible fluid flow places high demands on numerical discretization techniques for the fluid flow equations. Fluid flows arising in external aerodynamics often contain both flow field discontinuities and fluid boundary-layers. Both must be accurately resolved to provide useful information to aerodynamic design and analysis engineers. These accuracy requirements motivated the present author to examine a class of finite-volume techniques on arbitrary triangulated domains based on linear or quadratic reconstruction of integral-averaged data followed by upwind flux function evaluation and small time evolution. More recently, we have considered some new upwind techniques which yield compact discretizations while maintaining higher order accuracy. In the mini-symposium talk we will discuss both of these techniques as well as demonstrate the relative merits of each method by computing a number of aerodynamic flows containing shock waves and boundary-layers.

Barth, Timothy J.

Structure and Composition of the Distant Lunar Exosphere: Constraints from ARTEMIS Observations of Ion Acceleration in Time-Varying Fields

By analyzing the trajectories of ionized constituents of the lunar exosphere in time-varying electromagnetic fields, we can place constraints on the composition, structure, and dynamics of the lunar exosphere. Heavy ions travel slower than light ions in the same fields, so by observing the lag between field rotations and the response of ions from the lunar exosphere, we can place constraints on the composition of the ions. Acceleration, Reconnection, Turbulence, and Electrodynamics of Moon's Interaction with the Sun (ARTEMIS) provides an ideal platform to utilize such an analysis, since its two-probe vantage allows precise timing of the propagation of field discontinuities in the solar wind, and its sensitive plasma instruments can detect the ion response. We demonstrate the utility of this technique by using fully time-dependent charged particle tracing to analyze several minutes of ion observations taken by the two ARTEMIS probes ~3000-5000 km above the dusk terminator on 25 January 2014. The observations from this time period allow us to reach several interesting conclusions. The ion production at altitudes of a few hundred kilometers above the sunlit surface of the Moon has an unexpectedly significant contribution from species with masses of 40 amu or greater. The inferred distribution of the neutral source population has a large scale height, suggesting that micrometeorite impact vaporization and/or sputtering play an important role in the production of neutrals from the surface. Our observations also suggest an asymmetry in ion production, consistent with either a compositional variation in neutral vapor production or a local reduction in solar wind sputtering in magnetic regions of the surface.

Moon

Spontaneous Hot Flow Anomalies at Mars and Venus

We report the first observations of Spontaneous Hot Flow Anomalies (SHFAs) at Venus and Mars, demonstrating their existence in the foreshocks of other planets beyond Earth. Using data from the ESA Venus Express and the NASA Mars Atmosphere and Volatile EvolutioN (MAVEN) spacecraft, we present magnetic and plasma observations from events at both planets, exhibiting properties similar to “classical” Hot Flow Anomalies, with bounding shock-like compressive regions and a hot and diffuse core. However, these explosive foreshock transients were observed without any attendant interplanetary magnetic field discontinuity, consistent with SHFAs observed at Earth and our hybrid simulations.

Collinson, Glyn A.

An introduction to generalized functions with some applications in aerodynamics and aeroacoustics

In this paper, we start with the definition of generalized functions as continuous linear functionals on the space of infinitely differentiable functions with compact support. The concept of generalization differentiation is introduced next. This is the most important concept in generalized function theory and the applications we present utilize mainly this concept. First, some of the results of classical analysis, such as Leibniz rule of differentiation under the integral sign and the divergence theorem, are derived using the generalized function theory. It is shown that the divergence theorem remains valid for discontinuous vector fields provided that the derivatives are all viewed as generalized derivatives. This implies that all conservation laws of fluid mechanics are valid as they stand for discontinuous fields with all derivatives treated as generalized deriatives. Once these derivatives are written as ordinary derivatives and jumps in the field parameters across discontinuities, the jump conditions can be easily found. For example, the unsteady shock jump conditions can be derived from mass and momentum conservation laws. By using a generalized function theory, this derivative becomes trivial. Other applications of the generalized function theory in aerodynamics discussed in this paper are derivation of general transport theorems for deriving governing equations of fluid mechanics, the interpretation of finite part of divergent integrals, derivation of Oswatiitsch integral equation of transonic flow, and analysis of velocity field discontinuities as sources of vorticity. Applications in aeroacoustics presented here include the derivation of the Kirchoff formula for moving surfaces,the noise from moving surfaces, and shock noise source strength based on the Ffowcs Williams-Hawkings equation.

Farassat, F.

The magnetopause as a tangential discontinuity for large field rotation angles

Three passes of the ISEE 1 and 2 satellites through the dayside terrestrial magnetopause are discussed where the magnetopause is identified as a tangential discontinuity. This identification is based primarily on the failure of the plasma and magnetic field data to satisfy the conditions for a rotational discontinuity. In all these cases the interplanetary magnetic field was directed strongly southward and the angles between the fields on the two sides of the magnetopause ranged between 136 deg and 170 deg. As this is precisely the field geometry thought to be most conducive for reconnection, the magnetopause would be expected to be a rotational discontinuity. The simplest explanation of this result would appear to be that the magnetic field orientation is not the only factor controlling the onset of reconnection. However, as the identification of the discontinuity applies only locally, it cannot be excluded that for the magnetic field conditions investigated here, different portions of the magnetopause can be described as tangential and rotational discontinuities simultaneously.

Papamastorakis, I.

Plasma field characteristics of directional discontinuities in the interplanetary medium

The paper examines plasma and magnetic-field changes occurring across 1359 directional discontinuities taken from interplanetary data spanning almost four solar rotations. The plasma field characteristics of these events exhibit a distinct variation with large-scale solar-wind velocity. At low velocities, tangential discontinuities appear to predominate. At higher velocities, a substantial and increasing fraction of directional discontinuities exhibits the plasma field properties expected of outwardly propagating rotational discontinuities. The results of Sari (1972, 1975) and of the present study suggest that in the calculation of propagation diffusion coefficients for low-energy cosmic rays, the effects of directional discontinuities should be subtracted from the magnetic fluctuation spectrum during relatively quiet wind conditions. It is not clear that such subtraction is necessary during more disturbed periods.

Solodyna, C. V.