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NASA NTRS1989

The inverse gravimetric problem in gravity modelling

One of the main purposes of geodesy is to determine the gravity field of the Earth in the space outside its physical surface. This purpose can be pursued without any particular knowledge of the internal density even if the exact shape of the physical surface of the Earth is not known, though this seems to entangle the two domains, as it was in the old Stoke's theory before the appearance of Molodensky's approach. Nevertheless, even when large, dense and homogeneous data sets are available, it was always recognized that subtracting from the gravity field the effect of the outer layer of the masses (topographic effect) yields a much smoother field. This is obviously more important when a sparse data set is bad so that any smoothing of the gravity field helps in interpolating between the data without raising the modeling error, this approach is generally followed because it has become very cheap in terms of computing time since the appearance of spectral techniques. The mathematical description of the Inverse Gravimetric Problem (IGP) is dominated mainly by two principles, which in loose terms can be formulated as follows: the knowledge of the external gravity field determines mainly the lateral variations of the density; and the deeper the density anomaly giving rise to a gravity anomaly, the more improperly posed is the problem of recovering the former from the latter. The statistical relation between rho and n (and its inverse) is also investigated in its general form, proving that degree cross-covariances have to be introduced to describe the behavior of rho. The problem of the simultaneous estimate of a spherical anomalous potential and of the external, topographic masses is addressed criticizing the choice of the mixed collection approach.

Sanso, F.↗
NASA NTRS2010

High C/O Chemistry and Weak Thermal Inversion in the Extremely Irradiated Atmosphere of Exoplanet WASP-12b

The carbon-to-oxygen ratio (C/O) in a planet provides critical information about its primordial origins and subsequent evolution. A primordial C/O greater than 0.8 causes a carbide-dominated interior as opposed to the silicate-dominated composition as found on Earth; the solar C/O is 0.54. Theory, shows that high C/O leads to a diversity of carbon-rich planets that can have very different interiors and atmospheres from those in the solar system. Here we report the detection of C/O greater than or equal to 1 in a planetary atmosphere. The transiting hot Jupiter WASP-12b has a dayside atmosphere depleted in water vapour and enhanced in methane by over two orders of magnitude compared to a solar-abundance chemical equilibrium model at the expected temperatures. The observed concentrations of the prominent molecules CO, CH4, and H2O are consistent with theoretical expectations for an atmosphere with the observed C/O = 1. The C/O ratios are not known for giant planets in the solar system, although they are expected to equal the solar value. If high C/O ratios are common, then extrasolar planets are likely very different in interior composition, and formed very differently, from expectations based on solar composition, potentially explaining the large diversity in observed radii. We also find that the extremely irradiated atmosphere (greater than 2500 K) of WASP-12b lacks a prominent thermal inversion, or a stratosphere, and has very efficient day-night energy circulation. The absence of a strong thermal inversion is in stark contrast to theoretical predictions for the most highly irradiated hot-Jupiter atmospheres.

Madhusudhan, Nikku↗
NASA NTRS2016

The Relaxation Matrix for Symmetric Tops with Inversion Symmetry. I. Effects of Line Coupling on Self-Broadened v (sub 1) and Pure Rotational Bands of NH3

The Robert-Bonamy formalism has been commonly used to calculate half-widths and shifts of spectral lines for decades. This formalism is based on several approximations. Among them, two have not been fully addressed: the isolated line approximation and the neglect of coupling between the translational and internal motions. Recently, we have shown that the isolated line approximation is not necessary in developing semi-classical line shape theories. Based on this progress, we have been able to develop a new formalism that enables not only to reduce uncertainties on calculated half-widths and shifts, but also to model line mixing effects on spectra starting from the knowledge of the intermolecular potential. In our previous studies, the new formalism had been applied to linear and asymmetric-top molecules. In the present study, the method has been extended to symmetric-top molecules with inversion symmetry. As expected, the inversion splitting induces a complete failure of the isolated line approximation. We have calculated the complex relaxation matrices of selfbroadened NH3. The half-widths and shifts in the ν1 and the pure rotational bands are reported in the present paper. When compared with measurements, the calculated half-widths match the experimental data very well, since the inapplicable isolated line approximation has been removed. With respect to the shifts, only qualitative results are obtained and discussed. Calculated off-diagonal elements of the relaxation matrix and a comparison with the observed line mixing effects are reported in the companion paper (Paper II).

Trajectory models↗
NASA NTRS1972

Errors incurred in profile reconstruction and methods for increasing inversion accuracies for occultation type measurements

A method for augmenting the occultation experiment is described for slightly refractive media. This method which permits separation of the components of the gradient of refractivity, appears applicable to most of the planets for a major portion of their atmospheres and ionospheres. The analytic theory is given, and the results of numerical tests with a radially and angularly varying model of an ionosphere are discussed.

Gross, S. H.↗
NASA NTRS1984

Hybrid Semiloof elements for plates and shells based upon a modified Hu-Washizu principle

Hybrid SemiLoof elements for plates and shells are developed based upon modified Hu-Washizu principle. In the new version of the assumed stress hybrid formulation the equilibrium equations are satisfied through the introduction of internal displacement parameters as Lagrange multipliers. The inversion of the resulting H-matrices is simplified particularly when the stresses are expressed in terms of natural coordinates. A 24-DOF triangular element and a 32-DOF quadrilateral element based on shallow shell theory are derived and evaluated.

Pian, T. H. H.↗
NASA NTRS1986

Profiling Saturn's rings by radio occultation

The development of reconstruction algorithms that correct for diffraction effects in radio occultation measurements is described. The reciprocal Fresnel transform relationship between the complex amplitude of the observed coherent signal and the complex microwave transmittance of the rings is derived using the Huygens-Fresnel formulation of the diffraction problem. The effects of the finite data segment width, the uncertainties in the Fresnel scale, systematic phase errors in the kernel of the inverse transform, reference oscillator instabilities, and random noise measurements on the resolution of the reconstructed transmittance are analyzed. Examples of reconstructed opacity profiles for some regions of Saturn's rings derived by applying the reconstruction theory to Voyager 1 at Saturn data are presented.

Marouf, Essam A.↗
NASA NTRS1993

Long-term variations of interplanetary magnetic field spectra with implications for cosmic ray modulation

The paper calculates yearly averaged power spectra of interplanetary magnetic field turbulence at 1 AU over the period 1965-1988 for fluctuations in the frequency range 5.8 x 10 exp -6 to 4.6 x 10 exp -5 Hz, corresponding to periods of 6-48 hr. The amplitudes of the spectra vary with the sunspot cycle and are inversely correlated with the intensity of about 10-GeV cosmic rays. The observed spectra are used to calculate a lower limit to the cosmic ray scattering mean free path employing resonant magnetostatic quasi-linear theory for both 'slab' and isotropic geometries of the turbulence. The mean free paths thus obtained are typically about 0.1 AU in the slab model and about 0.3 AU in the isotropic model, but they are not significantly correlated with the modulated galactic cosmic ray intensity recorded by neutron monitors. It is inferred that the scattering processes described by resonant magnetostatic theory play, at best, a very minor role in the solar modulation of about 10-GeV cosmic rays.

Bieber, John W.↗
NASA NTRS1976

Similarity theory of the buoyantly interactive planetary boundary layer with entrainment

A similarity model is developed for the vertical profiles of turbulent flow variables in an entraining turbulent boundary layer of arbitrary buoyant stability. In the general formulation the vertical profiles, internal rotation of the velocity vector, discontinuities or jumps at a capping inversion and bulk aerodynamic coefficients of the boundary layer are given by solutions to a system of ordinary differential equations in the similarity variable. To close the system, a formulation for buoyantly interactive eddy diffusivity in the boundary layer is introduced which recovers Monin-Obukhov similarity near the surface and incorporates a hypothesis accounting for the observed variation of mixing length throughout the boundary layer. The model is tested in simplified versions which depend only on roughness, surface buoyancy, and Coriolis effects by comparison with planetary-boundary-layer wind- and temperature-profile observations, measurements of flat-plate boundary layers in a thermally stratified wind tunnel and observations of profiles of terms in the turbulent kinetic-energy budget of convective planetary boundary layers. On balance, the simplified model reproduced the trend of these various observations and experiments reasonably well, suggesting that the full similarity formulation be pursued further.

Hoffert, M. I.↗
NASA NTRS1992

Calculation of fully three-dimensional separated flow with an unsteady viscous-inviscid interaction method

Three previous papers have shown that the viscous inviscid numerical methods were capable of calculating separated turbulent flows. The 'Semi-inverse method' and the models of the first author allow the computation of massive separations, stalled flows, and shock wave-boundary layer interactions, in two-dimensional or quasi-three-dimensional conditions, from low speeds to supersonic speeds. The 'Semi-implicit' method for time-consistent coupling allows for the computation of time-accurate transonic separated flow and buffer computations in two-dimensions. The present paper shows that the viscous-inviscid interaction approach is also able to compute the fully three-dimensional flow separation phenomena. The method is based on a thin-layer approximation of the theory of 'Defect-Formulation' that provides the viscous-inviscid splitting of the Navier-Stokes equations. A parametric analytical modelling of the 3D-turbulent velocity profiles is involved. Numerically, the 3D-velocity profiles are discretized in the normal z-direction and driven by parametric integral 3D-equations in direct or inverse modes in the x-direction. The viscous-inviscid coupling is fully 3D and solved the time-consistency problem with an extension of the 'Semi-implicit' method previously suggested in two-dimensions. A 3D inviscid subroutine with TSP approximation is used. Results are obtained for transonic steady flows over wings with shock-induced transonic separation. The method provides results for highly three-dimensional flow separations, such as induced by a three-dimensional through at the wall of a flat plate. The 3D viscous-inviscid coupling and the 3D model of the velocity field provide three-dimensional instantaneous skin-friction lines whose patterns exhibit the same complex topology as Navier-Stokes solvers, with foci, nodes, and saddle-points.

Leballeur, J. C.↗
NASA NTRS1978

Remote sensing of environmental particulate pollutants - Optical methods for determinations of size distribution and complex refractive index

A unifying approach, based on a generalization of Pearson's differential equation of statistical theory, is proposed for both the representation of particulate size distribution and the interpretation of radiometric measurements in terms of this parameter. A single-parameter gamma-type distribution is introduced, and it is shown that inversion can only provide the dimensionless parameter, r/ab (where r = particle radius, a = effective radius, b = effective variance), at least when the distribution vanishes at both ends. The basic inversion problem in reconstructing the particle size distribution is analyzed, and the existing methods are reviewed (with emphasis on their capabilities) and classified. A two-step strategy is proposed for simultaneously determining the complex refractive index and reconstructing the size distribution of atmospheric particulates.

Fymat, A. L.↗
NASA NTRS1994

Proton and helium cyclotron anisotropy instability thresholds in the magnetosheath

Both the protons and the helium ions of the terrestrial magnetosheath typically display T (sub perpendicular) greater than T (sub parallel), where perpendicular to and parallel to denote directions perpendicular and parallel to the background magnetic field. Observations of the highly compressed magnetosheath show an inverse correlation between these ion temperature anisotropies and the parallel proton beta. Computer simulations have demonstrated that these correlations are due to wave-particle scattering by electromagnetic ion cyclotron anisotropy instabilities. These correlations correspond to linear theory thresholds of the proton cyclotron and the helium cyclotron instabilities. This paper uses linear Vlasov theory and the assumption of a constant maximum growth rate to obtain closed-form expressions for these thresholds as a function of the relative helium density and the parallel proton beta in a parameter model of the magnetosheath.

Gary, S. Peter↗
NASA NTRS2019

Isotopologue Consistency of Semi-Empirically Computed InfraRed Line Lists and Further Improvement for Rare Isotopologues: CO2 and SO2 Case Studies.

The semi-empirical molecular rovibrational IR line lists, such as ExoMol, TheoReTs, and Ames, combine the experimental accuracy and theoretical power to reach better than 0.1 cm-1 accuracy for line positions and better than 80-90% agreement for line intensities. The quality of these existing semi-empirical IR lists allows further improvements of intensity and line positions for those unobserved minor isotopologues. This paper presents our new BTRHE (Best Theory + Reliable High-resolution Experiment) strategy implementation. For line intensity, the isotopologue consistency and the patterns of mass dependence in the Ames-296K SO2 and CO2 IR lists are quantitatively presented along the mass-inverse coordinates. The consistency and patterns are better than those in existing experimental data. The methodology proposed here can be used to identify inconsistencies, outliers, and mistakes in intensities, and help improve Effective Dipole Model (EDM) and molecular IR databases. We call for an experimental study on the 50006 and 60007 bands of CO2 628. For line position predictions, a simple approach combining the variational IR line lists with Effective Hamiltonian (EH) model may refine the effective rotational constants A0/B0/C0 and quartic centrifugal distortion constants of minor isotopologues. The prediction accuracy may be improved by two orders of magnitude, i.e. reaching 0-5 MHz prediction accuracy in the range of J<20-30, Ka<10-20, and 0.01-0.02 MHz accuracy for A0/B0/C0. Several important factors have been systematically investigated and discussed, e.g. convergence, uncertainties, higher order terms, fixing EH parameters, mass coordinates, etc. Amicrowave (MW) line set consisting of 644,636 strong transitions for all 30 isotopologues and corresponding refined EH(Ames) parameters are reported in the supplementary material. This approach may be easily extended to rovibrational bands, hot bands, and other molecular systems.

Xinchuan Huang↗
NASA NTRS1982

Applicaton of radiative transfer theory to microwave transmission medium calibrations

Precise determinations of the transmission medium loss and noise temperature contribution which are important to the performance characterization of low noise microwave receiving systems and thermal noise standards are discussed. Tropospheric loss is frequently inferred from microwave radiometer noise temperature measurements. Interpretation of these measurements requires an inversion of the radiative transfer integral equation. This is inconvenient even with computer techniques. Solutions of a rapidly convergent power series of the radiative transfer equations are presented. This solution is applicable to a low loss medium with either uniform or nonuniform loss distributions. A four layer atmosphere model is investigated to demonstrate the accuracy of the solution relative to the model. Applications include thermal noise standards and single- and dual-frequency water radiometers.

Stelzried, C. T.↗
NASA NTRS1962

Interplanetary Trajectory Optimization with Powerlimited Propulsion Systems

A trajectory-optimization process is described in which the optimum­ thrust equations are derived using the calculus of variations. The mag­nitude of the thrust is constrained within an upper and a lower bound, but the thrust direction is arbitrary. This formulation allows both the constant-thrust program and the variable-thrust program to be con­sidered. For the constant-thrust program, certain propulsion-system parameters are optimized for maximum final vehicle mass. This theory has been used to study interplanetary missions to Venus and Mars using a power-limited propulsion system. Both one-way and round­ trip rendezvous trajectories are considered. The analysis employs a two-body inverse-square force-field model of three dimensions. An iterative routine used to solve the two-point boundary-value problem is described in the Appendix.

TRAJECTORY↗
NASA NTRS1973

Quantitative observations of hydrogen-induced, slow crack growth in a low alloy steel

Hydrogen-induced slow crack growth, da/dt, was studied in AISI-SAE 4130 low alloy steel in gaseous hydrogen and distilled water environments as a function of applied stress intensity, K, at various temperatures, hydrogen pressures, and alloy strength levels. At low values of K, da/dt was found to exhibit a strong exponential K dependence (Stage 1 growth) in both hydrogen and water. At intermediate values of K, da/dt exhibited a small but finite K dependence (Stage 2), with the Stage 2 slope being greater in hydrogen than in water. In hydrogen, at a constant K, (da/dt) sub 2 varied inversely with alloy strength level and varied essentially in the same complex manner with temperature and hydrogen pressure as noted previously. The results of this study provide support for most of the qualitative predictions of the lattice decohesion theory as recently modified by Oriani. The lack of quantitative agreement between data and theory and the inability of theory to explain the observed pressure dependence of slow crack growth are mentioned and possible rationalizations to account for these differences are presented.

Nelson, H. G.↗
NASA NTRS1979

Scale covariance and G-varying cosmology. IV - The log N-log S relation

The traditional radio counts N(S) and radio source models are studied within the framework of the scale-covariant cosmology developed to investigate whether the relative strength of the gravitational and electromagnetic constants is a function of cosmological epoch. It is found that a gravitational constant G varying as the inverse of t, where t is the epoch in atomic units, is consistent with all the data analyzed. For a wide class of models the present cosmology allows a finer discrimination of the deceleration parameter than does standard theory. The results, when combined with those of previous papers, namely, those from radio and optical flux and angular-diameter data analysis, favor an open universe.

Canuto, V. M.↗
NASA NTRS1974

Solution of the radiative transfer theory problems by the Monte Carlo method

The Monte Carlo method is used for two types of problems. First, there are interpretation problems of optical observations from meteorological satellites in the short wave part of the spectrum. The sphericity of the atmosphere, the propagation function, and light polarization are considered. Second, problems dealt with the theory of spreading narrow light beams. Direct simulation of light scattering and the mathematical form of medium radiation model representation are discussed, and general integral transfer equations are calculated. The dependent tests method, derivative estimates, and solution to the inverse problem are also considered.

Marchuk, G. I.↗