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Two variable expansion method applied to ordinary differential equation and two wave propagation problems, comparing results with matched asymptotic expansions and coordinate stretching methods
NASA created the Supersonics Project as part of the NASA Fundamental Aeronautics Program to advance technology that will make a supersonic flight over land viable. Computational flow solvers have lacked the ability to accurately predict sonic boom from the near to far field. The focus of this investigation was to establish gridding and adaptation techniques to predict near-to-mid-field (<10 body lengths below the aircraft) boom signatures at supersonic speeds using the USM3D unstructured grid flow solver. The study began by examining sources along the body the aircraft, far field sourcing and far field boundaries. The study then examined several techniques for grid adaptation. During the course of the study, volume sourcing was introduced as a new way to source grids using the grid generation code VGRID. Two different methods of using the volume sources were examined. The first method, based on manual insertion of the numerous volume sources, made great improvements in the prediction capability of USM3D for boom signatures. The second method (SSGRID), which uses an a priori adaptation approach to stretch and shear the original unstructured grid to align the grid and pressure waves, showed similar results with a more automated approach. Due to SSGRID s results and ease of use, the rest of the study focused on developing a best practice using SSGRID. The best practice created by this study for boom predictions using the CFD code USM3D involved: 1) creating a small cylindrical outer boundary either 1 or 2 body lengths in diameter (depending on how far below the aircraft the boom prediction is required), 2) using a single volume source under the aircraft, and 3) using SSGRID to stretch and shear the grid to the desired length.
During SOLVE, the bulk of the in-situ observations of PSCs are of large scale extended structures associated with synoptic scale cooling. The nature of these structures is also determined by layers of high relative NOy that have been stretched into thin layers by advective processes. Some of the in situ observations, however, are clearly correlated with gravity wave signatures. The first goal of this work is to examine these cases and evaluate gravity wave parameters. In particular, we are interested in the intrinsic periods of the waves and their temperature amplitude, which are key ingredients in the nucleation process. Secondly, we will examine some rudimentary properties of the particle size distributions and composition, comparing these with in situ observations of the more extended PSC features. Finally, we will attempt to ascertain the mechanism which generates the gravity waves.
It was previously shown that the strong vorticity in isotropic turbulence is organized into tubular vortices ('worms') whose properties were characterized through the use of full numerical simulations at several Reynolds numbers. At the time most of the observations were kinematic, and several scaling laws were discovered for which there was no theoretical explanation. In the meantime, further analysis of the same fields yielded new information on the generation of the vortices, and it was realized that even if they had to be formed by stretching, they were at any given moment actually compressed at many points of their axes. This apparent contradiction was partially explained by postulating axial inertial waves induced by the nonuniformity of the vortex cores, which helped to 'spread' the axial strain and allowed the vortices to remain compact even if not uniformly stretched. The existence of such solutions was recently proved numerically. The present report discusses a set of new numerical simulations of isotropic turbulence, and a reanalysis of the old ones, in an effort to prove or disprove the presence of these waves in actual turbulent flows and to understand the dynamics, as opposed to the kinematics, of the vortices.
An experimental technique for absolute measurement of ultrasonic wave particle displacement amplitudes in liquids is reported. The technique is capable of measurements over a frequency range of two decades with a sensitivity less than one angstrom. The technique utilizes a previously reported submersible electrostatic acoustic transducer (ESAT) featuring a conductive membrane stretched over a recessed electrode. An uncertainty analysis shows that the displacement amplitude of an ultrasonic plane wave incident on the ESAT can be experimentally determined to better than 2.3-4 percent, depending on frequency, in the frequency range of 0.5-15 MHz. Membranes with lower and more uniform areal densities can improve the accuracy and extend the operation to higher frequencies.
High-resolution laboratory spectrophotometer and Airborne Imaging Spectrometer (AIS) data were used to analyze forest leaf and canopy chemistry. Fundamental stretching frequencies of organic bonds in the visible, near infrared and short-wave infrared are indicative of concentrations and total content of nitrogen, phosphorous, starch and sugar. Laboratory spectrophotometer measurements showed very strong negative correlations with nitrogen (measured using wet chemistry) in the visible wavelengths. Strong correlations with green wet canopy weight in the atmospheric water absorption windows were observed in the AIS data. A fairly strong negative correlation between the AIS data at 1500 nm and total nitrogen and nitrogen concentration was evident. This relationship corresponds very closely to protein absorption features near 1500 nm.
Gravitational waves are produced by a wide variety of sources throughout the cosmos, including the mergers of black hole and neutron star binaries/compact objects spiraling into central black holes in galactic nuclei, close compact binaries/and phase transitions and quantum fluctuations in the early universe. Observing these signals can bring new, and often very precise, information about their sources across vast stretches of cosmic time. In this talk we will focus on thee opening of this gravitational-wave window on the universe, highlighting new opportunities for discovery and multi-messenger astronomy.
The conference presents papers on the shape, dynamics, and thermal structure of the plasmasphere and plasmapause; the ionosphere as a supplier of plasma to the earth's magnetosphere; the modeling and remote sensing of thermal plasma in the earth's magnetosphere; and magnetospheric cold plasmas as a medium for wave generation and propagation. Particular attention is given to whistler studies of plasmasphere shape and dynamics, plasmasphere thermal structure as measured by ISEE-1 and DE-1, low-energy ion flows into the magnetosphere, field-aligned flows of ionospheric plasma in the magnetosphere, and field-aligned plasmaspheric flows at moderate latitudes. Papers are also presented on the effects of a tailward stretching geomagnetic field on the drift motion of plasma particles in the magnetospheric equatorial plane, ion cyclotron waves observed near the plasmapause, and the response of energetic particles to nightside magnetic pulsations as seen by AMPTE/CCE.
DE 1 satellite radio observations were conducted in the 1525-5925 Hz range during a pass over an ionospheric heating facility; the waves were detected during a 2-min period, and the measurements indicated pulse-stretching by a few hundred msec, in conjunction with spectral broadening of about 10 Hz. The observed signal delays and pulse distortion are not consistent with expectations assuming propagation in a smooth magnetosphere between the assumed 'polar electrojet antenna' in the ionospheric D/E region and the 11,000-km altitude of the satellite. Scattering by density irregularities is judged the likely sources of the spectral broadening and delays.
Full configuration-interaction (FCI) calculations are performed at selected geometries for the (sup 1)Sigma(+) state of HCF and the (sup 2)B(sub 1) and (sup 3)A(sub 1) states NH2 using both DZ and DZP Gaussian basis sets. Higher excitations become more important when the bonds are stretched and the SCF reference becomes a poorer zeroth-order description of the wave function. The CASSCF-MRCI procedure gives excellent agreement with the FCI potentials, especially when corrected with a multireference analog of the Davidson correction.
Eleven stationary geometries of quartet O4(+) have been studied by ab initio methods. The geometries were optimized at the Complete Active Space Self-Consistent Field (CASSCF) level of theory and the energies were calculated by the multiconfigurational second order pertubation method (CASPT2), using Double-Zeta Plus polarization (DZP), Triple-Zeta Plus Double Polarization (TZ2P), average Atomic Natural Orbital (ANO) (5s4p2d) and average ANO (6s5p3d2f) basis sets. The rectangular and trans-planar structures are found to be the most stable, with an energy barrier to conversion between the two at the threshold of dissociation. Both have a delocalized hole and are stable relative to separated 02 and 02(+)by 11.0 and 11.5 kcal/mol for the rectangular and the 2 trans-planar structure, respectively, compared with the experimentally deduced energy in the range of 9.2 to 10.8 kcal/mol. The adiabatic ionization potentials of 04 and 02 are computed to be 11.67 and 12.21 eV, while experimental values are 11.66 and 12.07 eV, respectively. The vibrational frequencies have been computed for all degrees of freedom at the CASSCF level of theory. Symmetry breaking is found to be a particular problem in the computation of the antisymmetric stretch frequency for the delocalized structures at the CASSCF level of theory. Attempts to rectify these problems using the restricted active space self-consistent field (RASSCF) method leads to additional difficulties, but further analysis yields insight into the symmetry breaking and problems with earlier calculations. Finally, a nonorthogonal configuration interaction (CI) calculation based on the interaction of localized CASSCF wave functions using the Complete Active Space State Interation (CASSI) method leads to a balanced treatment of the antisymmetric stretch which is free from symmetry breaking. The study explains the four most prominent absorption frequencies observed in the partially unassigned IR spectrum of O4(+) isolated in solid neon as the antisymmetric OO stretch, and the combination band of the symmetric and antisymmetric 00 stretch of both the rectangular and trans-planar structures.
The paper summarizes the four general double-adiabatic invariants governing ideal MHD flow in a narrow tube and renders them in a form suitable for the calculation of flow in tubes of nonconstant cross-sectional area. Results for converging-diverging flux tubes are developed and compared to single-adiabatic results which are identical to those for ordinary gasdynamic flow. It is found that in certain parameter regimes the governing equation for the vector potential is elliptic and can be reduced to Laplace's equation by simple stretching of one coordinate. In other regimes the equation is hyperbolic, indicating the presence of wave patterns. The relevance of these results to flow over magnetopause undulations, including flux transfer events, is discussed.
Analysis of the dynamical stability of a large flux tube suggests that the field of a sunspot must divide into many separate tubes within the first 1000 km below the surface. Buoyancy of the Wilson depression at the visible surface and probably also a downdraft beneath the sunspot hold the separate tubes in a loose cluster. Convective generation of Alfven waves, which are emitted preferentially downward, cools the tubes. Aerodynamic drag on a slender flux tube stretched vertically across a convective cell is also studied. Since the drag is approximately proportional to the local kinetic energy density, the density stratification weights the drag in favor of the upper layers. Horizontal motions concentrated in the bottom of the convective cell may reverse this density effect. A downdraft of about two km/sec through the flux tubes beneath the sunspot is hypothesized.
Computations of two-dimensional solutions of the Navier-Stokes equations are carried out for finite-amplitude waves on steady unidirectional flow. Several cases are considered. The numerical method employs pseudospectral techniques in the streamwise direction and finite differences on a stretched grid in the transverse direction, with matching to asymptotic solutions when unbounded. Earlier results for Poiseuille flow in a channel are re-obtained, except that attention is drawn to the dependence of the minimum Reynolds number on the physical constraint of constant flux or constant pressure gradient. Attempts to calculate waves in Couette flow by continuation in the velocity of a channel wall fail. The asymptotic suction boundary layer is shown to possess finite-amplitude waves at Reynolds numbers orders of magnitude less than the critical Reynolds number for linear instability. Waves in the Blasius boundary layer and unsteady Rayleigh profile are calculated by employing the artifice of adding a body force to cancel the spatial or temporal growth. The results are verified by comparison with perturbation analysis in the vicinity of the linear-instability critical Reynolds numbers.
Low-pass (long-wave transmitting) interference filters, suitable for broadband photometric observations, previously have been constructed from series of capacitive grids stretched on thin Mylar. These filters have the desired optical properties of high transmission, sharp cut-ons, and good blocking at short wavelengths. Their designs, however, do not scale from one wavelength to another and their performance can deteriorate at low temperatures due to differential contraction of the dielectric backing and the supporting structure. The deviation of these early filters from the predicted scaling was due primarily to the difference in refractive index between the backing material and the medium between the grids. In the present paper, filters are described in which dielectric spacers are used, instead of air, as the medium between the grids. This technique has improved the scaling and has reduced the distortion from differential contraction.
In the present paper, it is suggested that the observation of cavities near Ganymede can be explained by a model which postulates that Ganymede continuously creates a cavity that is stretched out into a sheet along X by rotation and is spatially distorted by a spectrum of Alfven waves with perturbations along Y and with wavelengths comparable to the size of the field lines passing through Ganymede. Possible causes of the cavities are examined.
Full configuration-interaction (FCI) calculations are performed at selected geometries for the 1-sigma(+) state of HF and the 2-B(1) and 2-A(1) states of NH2 using both DZ and DZP gaussian basis sets. Higher excitations become more important when the bonds are stretched and the self-consistent field (SCF) reference becomes a poorer zeroth-order description of the wave function. The complete active space SCF - multireference configuration-interaction (CASSCF-MRCI) procedure gives excellent agreement with the FCI potentials, especially when corrected with a multi-reference analog of the Davidson correction.
Full configuration-interaction (FCI) calculations are performed at selected geometries for the 1-sigma(+) state of HF and the 2-B(1) and 2-A(1) states of NH2 using both DZ and DZP gaussian basis sets. Higher excitations become more important when the bonds are stretched and the self-consistent field (SCF) reference becomes a poorer zeroth-order description of the wave function. The complete active space SCF - multireference configuration-interaction (CASSCF-MRCI) procedure gives excellent agreement with the FCI potentials, especially when corrected with a multi-reference analog of the Davidson correction.