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NASA NTRS1981

Numerical analysis of spectral properties of coupled oscillator Schroedinger operators. I - Single and double well anharmonic oscillators

Several methods for computing many eigenvalues and eigenfunctions of a single anharmonic oscillator Schroedinger operator whose potential may have one or two minima are described. One of the methods requires the solution of an ill-conditioned generalized eigenvalue problem. This method has the virtue of using a bounded amount of work to achieve a given accuracy in both the single and double well regions. Rigorous bounds are given, and it is proved that the approximations converge faster than any inverse power of the size of the matrices needed to compute them. The results of computations for the g:phi(4):1 theory are presented. These results indicate that the methods actually converge exponentially fast.

Isaacson, D.↗

NASA NTRS1978

Feasibility of combining linear theory and impact theory methods for the analysis and design of high speed configurations

The aerodynamic influence coefficients calculated using an existing linear theory program were used to modify the pressures calculated using impact theory. Application of the combined approach to several wing-alone configurations shows that the combined approach gives improved predictions of the local pressure and loadings over either linear theory alone or impact theory alone. The approach not only removes most of the short-comings of the individual methods, as applied in the Mach 4 to 8 range, but also provides the basis for an inverse design procedure applicable to high speed configurations.

Brooke, D.↗

NASA NTRS1979

A consistent design procedure for supercritical airfoils in free air and a wind tunnel

A computational inverse procedure for transonic airfoils in which shapes are determined supporting prescribed pressure distributions is presented. The method uses the small disturbance equation and a consistent analysis-design differencing procedure at the airfoil surface. This avoids the intermediate analysis-design-analysis iterations. The effect of any openness at the trailing edge is taken onto account by adding an effective source term in the far field. The final results from a systematic expansion procedure which models the far field for solid, ideal slotted, and free jet tunnel walls are presented along with some design results for the associated boundary conditions and those for a free flight.

Shankar, V.↗

NASA NTRS1980

Investigation of multiple scattering effects in aerosols

The results are presented of investigations on the various aspects of multiple scattering effects on visible and infrared laser beams transversing dense fog oil aerosols contained in a chamber (4' x 4' x 9'). The report briefly describes: (1) the experimental details and measurements; (2) analytical representation of the aerosol size distribution data by two analytical models (the regularized power law distribution and the inverse modified gamma distribution); (3) retrieval of aerosol size distributions from multispectral optical depth measurements by two methods (the two and three parameter fast table search methods and the nonlinear least squares method); (4) modeling of the effects of aerosol microphysical (coagulation and evaporation) and dynamical processes (gravitational settling) on the temporal behavior of aerosol size distribution, and hence on the extinction of four laser beams with wavelengths 0.44, 0.6328, 1.15, and 3.39 micrometers; and (5) the exact and approximate formulations for four methods for computing the effects of multiple scattering on the transmittance of laser beams in dense aerosols, all of which are based on the solution of the radiative transfer equation under the small angle approximation.

Deepak, A.↗

NASA NTRS1987

Measurement from satellites of land surface parameters and fluxes in the thermal infrared bands: Problems and methods

The main problems arising in the elaboration of accurate and reliable algorithms for extracting land surface parameters and flux from their measured radiances are discussed. Methods of solution in the thermal infrared spectral domain are described. Particular interest is given to the inversion of thermal models and to the problems resulting from the heterogeneity of the observed surfaces.

Becker, F.↗

NASA NTRS2010

The OMPS Limb Profiler Instrument: Two-Dimensional Retrieval Algorithm

The upcoming Ozone Mapper and Profiler Suite (OMPS), which will be launched on the NPOESS Preparatory Project (NPP) platform in early 2011, will continue monitoring the global distribution of the Earth's middle atmosphere ozone and aerosol. OMPS is composed of three instruments, namely the Total Column Mapper (heritage: TOMS, OMI), the Nadir Profiler (heritage: SBUV) and the Limb Profiler (heritage: SOLSE/LORE, OSIRIS, SCIAMACHY, SAGE III). The ultimate goal of the mission is to better understand and quantify the rate of stratospheric ozone recovery. The focus of the paper will be on the Limb Profiler (LP) instrument. The LP instrument will measure the Earth's limb radiance (which is due to the scattering of solar photons by air molecules, aerosol and Earth surface) in the ultra-violet (UV), visible and near infrared, from 285 to 1000 nm. The LP simultaneously images the whole vertical extent of the Earth's limb through three vertical slits, each covering a vertical tangent height range of 100 km and each horizontally spaced by 250 km in the cross-track direction. Measurements are made every 19 seconds along the orbit track, which corresponds to a distance of about 150km. Several data analysis tools are presently being constructed and tested to retrieve ozone and aerosol vertical distribution from limb radiance measurements. The primary NASA algorithm is based on earlier algorithms developed for the SOLSE/LORE and SAGE III limb scatter missions. All the existing retrieval algorithms rely on a spherical symmetry assumption for the atmosphere structure. While this assumption is reasonable in most of the stratosphere, it is no longer valid in regions of prime scientific interest, such as polar vortex and UTLS regions. The paper will describe a two-dimensional retrieval algorithm whereby the ozone distribution is simultaneously retrieved vertically and horizontally for a whole orbit. The retrieval code relies on (1) a forward 2D Radiative Transfer code (to model limb radiances within a non-uniform atmosphere and evaluate 2D analytical partial derivatives) and (2) an optimal estimator inversion routine. The algorithm uses the typically sparse nature of the kernel matrices as well as fast matrix inversion techniques to allow for fast inversion of limb data with efficient memory management (as was done for MIPAS data processing). While the method has so far only been developed in the context of Single Scatter, the paper will show how the CPU intensive Multiple Scatter modeling can be implemented using parallel CPU processing. Initial results will be presented in terms of retrieved ozone profiles and code performance.

Rault, Didier F.↗

NASA NTRS2015

Under-Track CFD-Based Shape Optimization for a Low-Boom Demonstrator Concept

The detailed outer mold line shaping of a Mach 1.6, demonstrator-sized low-boom concept is presented. Cruise trim is incorporated a priori as part of the shaping objective, using an equivalent-area-based approach. Design work is performed using a gradient-driven optimization framework that incorporates a three-dimensional, nonlinear flow solver, a parametric geometry modeler, and sensitivities derived using the adjoint method. The shaping effort is focused on reducing the under-track sonic boom level using an inverse design approach, while simultaneously satisfying the trim requirement. Conceptual-level geometric constraints are incorporated in the optimization process, including the internal layout of fuel tanks, landing gear, engine, and crew station. Details of the model parameterization and design process are documented for both flow-through and powered states, and the performance of these optimized vehicles presented in terms of inviscid L/D, trim state, pressures in the near-field and at the ground, and predicted sonic boom loudness.

Wintzer, Mathias↗

NASA NTRS2016

Spatial and Temporal Antarctic Ice Sheet Mass Trends, Glacio-Isostatic Adjustment, and Surface Processes from a Joint Inversion of Satellite Altimeter, Gravity, and GPS Data

We present spatiotemporal mass balance trends for the Antarctic Ice Sheet from a statistical inversion of satellite altimetry, gravimetry, and elastic-corrected GPS data for the period 2003-2013. Our method simultaneously determines annual trends in ice dynamics, surface mass balance anomalies, and a time-invariant solution for glacio-isostatic adjustment while remaining largely independent of forward models. We establish that over the period 2003-2013, Antarctica has been losing mass at a rateof -84 +/- 22 Gt per yr, with a sustained negative mean trend of dynamic imbalance of -111 +/- 13 Gt per yr. West Antarctica is the largest contributor with -112 +/- 10 Gt per yr, mainly triggered by high thinning rates of glaciers draining into the Amundsen Sea Embayment. The Antarctic Peninsula has experienced a dramatic increase in mass loss in the last decade, with a mean rate of -28 +/- 7 Gt per yr and significantly higher values for the most recent years following the destabilization of the Southern Antarctic Peninsula around 2010. The total mass loss is partly compensated by a significant mass gain of 56 +/- 18 Gt per yr in East Antarctica due to a positive trend of surface mass balance anomalies.

Martin-Espanol, Alba↗

NASA NTRS1981

A unique method to study acoustic transmission through ducts using signal synthesis and averaging of acoustic pulses

An acoustic impulse technique using a loudspeaker driver is developed to measure the acoustic properties of a duct/nozzle system. A signal synthesis method is used to generate a desired single pulse with a flat spectrum. The convolution of the desired signal and the inverse Fourier transform of the reciprocal of the driver's response are then fed to the driver. A signal averaging process eliminates the jet mixing noise from the mixture of jet noise and the internal noise, thereby allowing very low intensity signals to be measured accurately, even for high velocity jets. A theoretical analysis is carried out to predict the incident sound field; this is used to help determine the number and locations of the induct measurement points to account for the contributions due to higher order modes present in the incident tube method. The impulse technique is validated by comparing experimentally determined acoustic characteristics of a duct-nozzle system with similar results obtained by the impedance tube method. Absolute agreement in the comparisons was poor, but the overall shapes of the time histories and spectral distributions were much alike.

Salikuddin, M.↗

NASA NTRS1976

Remote probing of atmospheric particulates from radiation extinction experiments: A review of methods

The existing methodology for reconstructing the particle size distribution and inferring the refractive index of absorbing and scattering atmospheric particulates is critically reviewed. Emphasis is placed on method capabilities and shortcomings and, wherever possible, on achievable accuracy. The nature of the associated remote probing problem is analyzed with regard to the effects of the particulates on EM wave propagation in the atmosphere. The parameterization of size distribution is studied within the unifying framework of Pearson's distribution curves. The inversions of extinction measurements and their ratios are considered separately, and the potentialities of each type of measurement are identified. Work lacking in each of the methods reviewed is indicated. A method of determining both the effective complex refractive index and size distribution model parameters from the same data is also presented. Lastly, determination from extinction ratio data of the complex refractive index independent of size distribution is discussed and error analyzed.

Fymat, A. L.↗

NASA NTRS1988

A new technique for measuring extragalactic distances

A relatively direct technique of determining extragalactic distances is described. The method relies on measuring the luminosity fluctuations that arise from the counting statistics of the stars contributing the flux in each pixel of a high signal-to-noise CCD image of a galaxy. The amplitude of these fluctuations is inversely proportional to the distance of the galaxy. This approach bypasses most of the successive stages of calibration required in the traditional extragalactic distance ladder; the only serious drawback to this method is that it requires an accurate knowledge of the bright end of the luminosity function. Potentially, this method can produce accurate distances of elliptical galaxies and spiral bulges at distances out to about 20 Mpc. In this paper, it is explained how to calculate the value of the fluctuations, taking into account various sources of contamination and the effects of finite spatial resolution, and the feasibility and limitations of this technique are demonstrated via simulations and CCD images of M 32 and N 3379.

Tonry, John↗

NASA NTRS1979

Inversion of the strain-life and strain-stress relationships for use in metal fatigue analysis

The paper presents closed-form solutions (collocation method and spline-function method) for the constants of the cyclic fatigue life equation so that they can be easily incorporated into cumulative damage analysis. The collocation method involves conformity with the experimental curve at specific life values. The spline-function method is such that the basic life relation is expressed as a two-part function, one applicable at strains above the transition strain (strain at intersection of elastic and plastic lines), the other below. An illustrative example is treated by both methods. It is shown that while the collocation representation has the advantage of simplicity of form, the spline-function representation can be made more accurate over a wider life range, and is simpler to use.

Manson, S. S.↗

NASA NTRS1987

Steering Law Design for Redundant Single Gimbal Control Moment Gyro Systems

The correspondence between robotic manipulators and single gimbal Control Moment Gyro (CMG) systems was exploited to aid in the understanding and design of single gimbal CMG Steering laws. A test for null motion near a singular CMG configuration was derived which is able to distinguish between escapable and unescapable singular states. Detailed analysis of the Jacobian matrix null-space was performed and results were used to develop and test a variety of single gimbal CMG steering laws. Computer simulations showed that all existing singularity avoidance methods are unable to avoid Elliptic internal singularities. A new null motion algorithm using the Moore-Penrose pseudoinverse, however, was shown by simulation to avoid Elliptic type singularities under certain conditions. The SR-inverse, with appropriate null motion was proposed as a general approach to singularity avoidance, because of its ability to avoid singularities through limited introduction of torque error. Simulation results confirmed the superior performance of this method compared to the other available and proposed pseudoinverse-based Steering laws.

Bedrossian, Nazareth Sarkis↗

NASA NTRS1993

A novel pulse technique for thermal diffusivity determination of high-temperature levitated materials - Inverse analysis and experimental set-up

In order to determine the thermal diffusivity of materials at high temperatures, a two-step extended flash technique, which is applicable to levitated spherical samples, is proposed. The containerless flash method is modeled as an axisymmetric transient conduction heat transfer problem within the sphere subjected to a radiative boundary condition on its surface. The problem of nonlinearity which arises from the radiative heat transfer boundary condition is solved by replacing it with the measured time-dependent surface temperature data, thus giving rise to an 'Inverse Analysis'. Upon obtaining the analytic solution for the temperature field, the determination of the thermal diffusivity turns into a minimization problem, whereby the difference between the actual surface boundary condition and the analytic solution is minimized. In performing the proposed experiments, there is a need to undertake a cool-down experiment which should be governed by the lumped parameter analysis.

Shen, F.↗

NASA NTRS1981

Direct numerical simulations of turbulent shear flows

Numerical simulations of wakes of axisymmetric bodies and of turbulent mixing layers are reported. The flows were assumed to be statistically homogeneous in the mean flow direction, in concert with experimental data and the self-similarity theorem. The nonlinear Navier-Stokes equations were solved by a pseudo-spectral numerical method using a 32 x 32 x 33 point grid and an algorithm for fast Fourier transforms and inverse transforms. Leapfrog time differencing was employed on nonlinear terms and time differencing on viscous terms. Towed wakes and wakes behind a self-propelled body were simulated, showing that the towed wakes exhibited a proper temporal behavior after an initial period of adjustment, including the development of a kurtosis near the wake edge, which is experimentally verifiable. The mixing-layer simulation displayed the laboratory demonstrated presence of large scale features such as vortex cores, while the lateral coherence was weak.

Metcalfe, R. W.↗

NASA NTRS1991

Crustal structure interpreted from magnetic anomalies

This review, discusses publications during the last quadrennium (1987-1990) that used aeromagnetic data, marine magnetic data, satellite magnetic data, and rock magnetic and petrologic data to provide information on the sources of magnetic anomalies. The publications reviewed reflect increased integration of rock magnetic property and petrologic studies with magnetic anomaly interpretation studies, particularly in deep crustal magnetization, exploration for hydrocarbons, and inversion of marine magnetic anomalies. Interpretations of aeromagnetic data featuring image display techniques and using the horizontal gradient method for locating magnetization boundaries became standard.

Phillips, Jeffrey D.↗

NASA NTRS2009

A Simple and Efficient Computational Approach to Chafed Cable Time-Domain Reflectometry Signature Prediction

A method for the prediction of time-domain signatures of chafed coaxial cables is presented. The method is quasi-static in nature, and is thus efficient enough to be included in inference and inversion routines. Unlike previous models proposed, no restriction on the geometry or size of the chafe is required in the present approach. The model is validated and its speed is illustrated via comparison to simulations from a commercial, three-dimensional electromagnetic simulator.

Kowalski, Marc Edward↗

NASA NTRS2011

Geopotential Field Anomaly Continuation with Multi-Altitude Observations

Conventional gravity and magnetic anomaly continuation invokes the standard Poisson boundary condition of a zero anomaly at an infinite vertical distance from the observation surface. This simple continuation is limited, however, where multiple altitude slices of the anomaly field have been observed. Increasingly, areas are becoming available constrained by multiple boundary conditions from surface, airborne, and satellite surveys. This paper describes the implementation of continuation with multi-altitude boundary conditions in Cartesian and spherical coordinates and investigates the advantages and limitations of these applications. Continuations by EPS (Equivalent Point Source) inversion and the FT (Fourier Transform), as well as by SCHA (Spherical Cap Harmonic Analysis) are considered. These methods were selected because they are especially well suited for analyzing multi-altitude data over finite patches of the earth such as covered by the ADMAP database. In general, continuations constrained by multi-altitude data surfaces are invariably superior to those constrained by a single altitude data surface due to anomaly measurement errors and the non-uniqueness of continuation.

Kim, Jeong Woo↗