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All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Optimal resolution in maximum entropy image reconstruction from projections with multigrid acceleration

We consider the problem of image reconstruction from a finite number of projections over the space L(sup 1)(Omega), where Omega is a compact subset of the set of Real numbers (exp 2). We prove that, given a discretization of the projection space, the function that generates the correct projection data and maximizes the Boltzmann-Shannon entropy is piecewise constant on a certain discretization of Omega, which we call the 'optimal grid'. It is on this grid that one obtains the maximum resolution given the problem setup. The size of this grid grows very quickly as the number of projections and number of cells per projection grow, indicating fast computational methods are essential to make its use feasible. We use a Fenchel duality formulation of the problem to keep the number of variables small while still using the optimal discretization, and propose a multilevel scheme to improve convergence of a simple cyclic maximization scheme applied to the dual problem.

Limber, Mark A.↗
NASA NTRS1994

Aspects of unstructured grids and finite-volume solvers for the Euler and Navier-Stokes equations

Basic algorithms for unstructured mesh generation and fluid flow calculation are discussed. In particular the following are addressed: preliminaries of graphs and meshes; duality and data structures; basic graph operations important in CFD (Computational Fluid Dynamics); triangulation methods, including Varonoi diagrams and Delaunay triangulation; maximum principle analysis; finite volume schemes for scalar conservation law equations; finite volume schemes for the Euler and Navier-Stokes equations; and convergence acceleration for steady state calculations.

Barth, T. J.↗
NASA NTRS1994

A new approach to the photon localization problem

Since wavelets form a representation of the Poincare group, it is possible to construct a localized superposition of light waves with different frequencies in a Lorentz-covariant manner. This localized wavelet satisfies a Lorentz-invariant uncertainty relation, and also the Lorentz-invariant Parseval's relation. A quantitative analysis is given for the difference between photons and localized waves. It is then shown that this localized entity corresponds to a relativistic photon with a sharply defined momentum in the non-localization limit. Waves are not particles. It is confirmed that the wave-particle duality is subject to the uncertainty principle.

Han, D.↗
NASA NTRS1995

Airborne spectrograph for the thermal IR: Broadband Array Spectrograph System

Spectroscopic studies in the 'fingerprint' region of the thermal IR from 3 to 14 microns of celestial dust components and the overall energy distribution of the sources are best served by moderate spectral resolution (R = lambda/Delta lambda approximately 30 to 200), high sensitivity observations. Spectral purity and the reproducibility of the spectral shape are critical as well, when using the spectral shape to assign temperatures to dust grains or to gas clouds based on the wavelength and shape of molecular bands. These sensor attributes are also important to the use of wavelengths and ratios of solid state features to derive compositions of dust grains in celestial sources. The advent of high quality linear arrays of blocked impurity band (BIB) detectors of Si:As permitted the development of a state-of-the-art, patented, cooled prism spectrograph. Developed at The Aerospace Corporation largely with in-house funds, the Broadband Array Spectrograph System (BASS) has been used for a variety of remote sensing applications, but especially for IR astronomical studies on the Kuiper Airborne Observatory and at the NASA Infrared Telescope Facility (IRTF). The attributes of the spectrograph, specifically having the pupil imaged onto the 2 linear 58 element detector arrays so that the effects of guiding errors are minimized, being able to maximally exploit the limited observing time by acquiring all 116 spectral channels simultaneously, and having all spectral channels imaged through the same aperture so that spectral mapping is readily and reliably accomplished, afford the scientist with a unique opportunity to conduct both surveys of examples of many different types of sources as well as in-depth studies of a given class of object by thoroughly sampling the class members. This duality was demonstrated with the BASS through a combination of KAO flights where spectral maps were obtained as part of in-depth studies of specific source regions (such as Orion and W3) and flights where up to 21 legs/flight were used to survey many different sources of different types.

Russell, Ray W.↗
NASA NTRS1997

[Advanced Development for Space Robotics With Emphasis on Fault Tolerance Technology]

This report describes work developing fault tolerant redundant robotic architectures and adaptive control strategies for robotic manipulator systems which can dynamically accommodate drastic robot manipulator mechanism, sensor or control failures and maintain stable end-point trajectory control with minimum disturbance. Kinematic designs of redundant, modular, reconfigurable arms for fault tolerance were pursued at a fundamental level. The approach developed robotic testbeds to evaluate disturbance responses of fault tolerant concepts in robotic mechanisms and controllers. The development was implemented in various fault tolerant mechanism testbeds including duality in the joint servo motor modules, parallel and serial structural architectures, and dual arms. All have real-time adaptive controller technologies to react to mechanism or controller disturbances (failures) to perform real-time reconfiguration to continue the task operations. The developments fall into three main areas: hardware, software, and theoretical.

Tesar, Delbert↗
NASA NTRS1998

Some Comments on the Status of Shell Theory at the End of the 20th Century: Complaints and Correctives

This review is divided into complaints and correctives. Complaints are directed at: sloppy refereeing and editing; authors who fail to read or acknowledge what others have done; the mis-naming or mis-crediting of results; the misunderstanding and misuse of the Kirchhoff hypothesis; inflated claims of accuracy based on overly-simplified benchmark problems; the failure to appreciate the inherent errors in various shell models; the failure to appreciate that the physical response and mathematical structure of shell theory are fundamentally different from 3-dimensional elasticity; and the irrelevance of Cosserat-type theories. Correctives include a simple, straight-forward derivation of a general nonlinear dynamic shell theory with the following features: (1) the equations of motion and kinematics (and those of thermodynamics, if desired) are exact consequences of their 3-dimensional counterparts; (2) there are no asymptotic or series expansions through the thickness; (3) all approximations (including the Kirchhoff Hypothesis) occur in the constitutive relations; (4) in static problems, there is a mixed form of the governing equations involving a mixed-energy density and exhibiting remnants of the well-known static-geometric duality of linear theory which is numerically robust because the limiting cases of nonlinear membrane theory and inextensional bending theory fall out naturally. (These latter two special cases are known to produce numerical nightmares unless treated with great care); and (5) all equations may be expressed in coordinate-free form (although, sometimes, a hybrid form is shown to be superior).

Simmonds, James G.↗
NASA NTRS2000

A Posteriori Error Estimation for Finite Volume and Finite Element Approximations Using Broken Space Approximation

We consider a posteriori error estimates for finite volume and finite element methods on arbitrary meshes subject to prescribed error functionals. Error estimates of this type are useful in a number of computational settings: (1) quantitative prediction of the numerical solution error, (2) adaptive meshing, and (3) load balancing of work on parallel computing architectures. Our analysis recasts the class of Godunov finite volumes schemes as a particular form of discontinuous Galerkin method utilizing broken space approximation obtained via reconstruction of cell-averaged data. In this general framework, weighted residual error bounds are readily obtained using duality arguments and Galerkin orthogonality. Additional consideration is given to issues such as nonlinearity, efficiency, and the relationship to other existing methods. Numerical examples are given throughout the talk to demonstrate the sharpness of the estimates and efficiency of the techniques. Additional information is contained in the original.

Barth, Timothy J.↗
NASA NTRS1998

An Astronomical Test of CCD Photometric Precision

This article considers a posteriori error estimation of specified functionals for first-order systems of conservation laws discretized using the discontinuous Galerkin (DG) finite element method. Using duality techniques. we derive exact error representation formulas for both linear and nonlinear functionals given an associated bilinear or nonlinear variational form. Weighted residual approximations of the exact error representation formula are then proposed and numerically evaluated for Ringleb flow, an exact solution of the 2-D Euler equations.

Koch, David↗
NASA NTRS1999

A Posteriori Error Estimation for Discontinuous Galerkin Approximations of Hyperbolic Systems

This article considers a posteriori error estimation of specified functionals for first-order systems of conservation laws discretized using the discontinuous Galerkin (DG) finite element method. Using duality techniques, we derive exact error representation formulas for both linear and nonlinear functionals given an associated bilinear or nonlinear variational form. Weighted residual approximations of the exact error representation formula are then proposed and numerically evaluated for Ringleb flow, an exact solution of the 2-D Euler equations.

Larson, Mats G.↗
NASA NTRS2003

Questions Revisited: A Close Examination of Calculus of Inference and Inquiry

In this paper I examine more closely the way in which probability theory, the calculus of inference, is derived from the Boolean lattice structure of logical assertions ordered by implication. I demonstrate how the duality between the logical conjunction and disjunction in Boolean algebra is lost when deriving the probability calculus. In addition, I look more closely at the other lattice identities to verify that they are satisfied by the probability calculus. Last, I look towards developing the calculus of inquiry demonstrating that there is a sum and product rule for the relevance measure as well as a Bayes theorem. Current difficulties in deriving the complete inquiry calculus will also be discussed.

Knuth, Kevin H.↗
NASA NTRS2004

A-Posteriori Error Estimation for Hyperbolic Conservation Laws with Constraint

This lecture considers a-posteriori error estimates for the numerical solution of conservation laws with time invariant constraints such as those arising in magnetohydrodynamics (MHD) and gravitational physics. Using standard duality arguments, a-posteriori error estimates for the discontinuous Galerkin finite element method are then presented for MHD with solenoidal constraint. From these estimates, a procedure for adaptive discretization is outlined. A taxonomy of Green's functions for the linearized MHD operator is given which characterizes the domain of dependence for pointwise errors. The extension to other constrained systems such as the Einstein equations of gravitational physics are then considered. Finally, future directions and open problems are discussed.

Barth, Timothy↗
NASA NTRS2006

Various Ambiguities in Re-constructing Laser Pulse Parameters

We think that mode lock laser pulses are generated by the summation process that take place between the monochromatic EM filed frequencies as if they interact with each other as shown in equation 1. In reality, the pulse generation is a collaborative interaction process between EM fields and various material medium. When we carry out the actual mode lock analysis, we do take into account of interpaly between all the temporal dynamics of the cavity gain medium, cavity round trip time and the response time of the intra cavity element (saturable absorber, Kerr medium, etc.). that really enforces the locking of the phase of the cavity spontaneous emissions. On a conceptual level, this simplistic representation of the mode locking by Eq.1 ignores all these critical physical processes. When we try to analyze a pulsed field, again we start by representing it very much like this equation, even though we can only detect the square modulus of this complex field and loose a lot of phase related information to the detectors quantum whims and their time constants. The key parameters for a light pulse are as follows. Foremost is the (i) carrier frequency, which cannot be described or imagined without its state of undulation expressed as its (ii) phase. Next is our imagined time finite (iii) carrier envelope that provides the temporal boundary of the field amplitude strength of the undulating E-field. The final parameter is the (iv) state of polarization or the unique plane along which the strength of the E-field gradient undulates. None of these filed characteristics are made self-evident to us by the fields themselves. We do not see light. Light does not see light. Light beams pass through each other without altering each others energy distribution unless there are interacting material molecules (dipoles) within the physical volume of superposition of the beams. In contrast, we can sense the material particles. Material particles sense each other and they cannot pass through each other without interacting with (scattering from) each other. Thus the interpretation of the superposition phenomenon of multiple fields on detectors should not be lumped under the mysterious "wave-particle duality" philosophy. The phenomenon of superposition can be understood better when we focus on the actual process experienced by the detecting dipoles when allowed by QM rules, they respond to and sum all the induced stimulations due to all the superposed fields followed by the proportionate energy absorption giving rise to the fringes we observe. We will present various experimental results to illustrate our arguments. Our position is that such detector behavior driven interpretations rather than the generally implied field-field interaction driven explanations, will help us better understand the ultimate nature of light and hence invent better and newer devices and instruments.

Roychoudhuri, Chandrasekhar↗
NASA NTRS2006

Smoke and Pollution Aerosol Effect on Cloud Cover

Pollution and smoke aerosols can increase or decrease the cloud cover. This duality in the effects of aerosols forms one of the largest uncertainties in climate research. Using solar measurements from Aerosol Robotic Network sites around the globe, we show an increase in cloud cover with an increase in the aerosol column concentration and an inverse dependence on the aerosol absorption of sunlight. The emerging rule appears to be independent of geographical location or aerosol type, thus increasing our confidence in the understanding of these aerosol effects on the clouds and climate. Preliminary estimates suggest an increase of 5% in cloud cover.

Kaufman, Yoram J.↗
NASA NTRS2007

Multijunction Solar Cell Development and Production at Spectrolab

Development of multijunction space solar cells is much like that for any high technology product. New products face two major pressures from the market: improving performance while maintaining heritage. This duality of purpose is not new and has been represented since ancient times by the Roman god Janus.[1] This deity was typically represented as two faces on a single head: one facing forward and the other to the rear. The image of Janus has been used as symbolism for many combined forces of dual purpose, such as the balance in life between beginnings and endings, or between art and science. For our purposes, Janus represents our design philosophy balance between looking to the future for improvement while simultaneously blending past heritage. In the space photovoltaics industry there are good reasons for both purposes. Looking to the past, a product must have a space flight heritage to gain widespread use. The main reason being that this is an unforgiving business. Spacecraft are expensive to build, launch and operate. Typically once a satellite is launched, in-field service for a power systems problem is near impossible.[2Balanced with this is looking forward. New missions typically require more power than previous programs or attempt new objectives such as a new orbit. And there is always the cost pressure for both the satellite itself as well as the launch costs. Both of which push solar technology to improve power density at a lower cost. The consequence of this balance in a high-risk environment is that space PV develops as a series of infrequent large technology steps or generational changes interspersed with more frequent small technology steps or evolutionary changes. Figure 1 gives a bit of clarification on this point. It depicts the historical progress in space solar cells tracked by efficiency against first launch date for most major products introduced by Spectrolab. The first generation is the Si-based technology reaching a peak values near 15% AM0 (herein denoted for max. power, AM0, 1.353 W/cm2, 28 C). The GaAs single junction device generation supplanted this technology with first flight of GaAs on GaAs substrate in 1982.[3] More recently this generation has been supplanted by the multijunction solar cell GaInP/GaAs/Ge generation. The first launch of a commercial satellite powered by multijunction technology was in 1997 (Hughes HS 601HP) using solar arrays based on Spectrolab s dual junction (DJ) cells. The cells at that time were an impressive 21.5% efficient at beginning-of-life (BOL).[4] Eight years later, the multijunction device has evolved through several versions. The incorporation of an active Ge subcell formed the Triple Junction (TJ) product line at 25.1% efficient, on orbit since November 2001. The evolution of the TJ into the Improved Triple Junction (ITJ) at 26.8% efficient has been on orbit since June of 2002.[5]

Fetzer, Chris↗
NASA NTRS2009

Atlantic Tropical Cyclogenetic Processes During SOP-3 NAMMA in the GEOS-5 Global Data Assimilation and Forecast System

This article investigates the role of the Saharan air layer (SAL) in tropical cyclogenetic processes associated with a nondeveloping and a developing African easterly wave observed during the Special Observation Period (SOP-3) phase of the 2006 NASA African. Monsoon Multidisciplinary Analyses (NAMMA). The two waves are chosen because they both interact heavily with Saharan air. A glottal data assimilation and forecast system, the NASA Goddard Earth Observing System. version 5 (GEOS-5), is being run to produce a set of high-9 uality global analyses, inclusive of all observations used operationally but with additional satellite information. In particular, following previous works by the same authors, the duality-controlled data from the Atmospheric Infrared Sounder (AIRS) used to produce these analyses have a better coverage than the one adopted by operational centers. From these improved analyses, two sets of 31 five-day high-resolution forecasts, at horizontal resolutions of both half and quarter degrees, are produced. Results indicate that very steep moisture gradients are associated with the SAL in forecasts and analyses, even at great distances from their source over the Sahara. In addition, a thermal dipole in the vertiieat (warm above, cool below) is present in the nondeveloping case. The Moderate Resolution Imaging Spoctroradiometer (MODIS) aboard NASA's Terra and Aqua satellites shows that aerosol optical thickness, indicative of more dust as opposed to other factors, is higher in the nondeveloping case. Altogether, results suggest that the radiative effect of dust may play some role in producing a thermal structure less favorable to cyclogenesis. Results also indicate that only global horizontal resolutions on the order of 20-30 km can capture the large-scale transport and the tine thermal structure of the SAL, inclusive of the sharp moisture gradients, reproducing the effect of tropical cyclone suppression that has been hypothesized by previous authors from observational and regional modeling perspectives. Thcse effects cannot be fully represented at lower resolutions, therefore global resolution of a quarter of a degree is a minimum critical threshold necessary to investigate Atlantic tropical cyclogenesis from a global modeling perspective

Reale, Oreste↗
NASA NTRS2011

Entanglement in Self-Supervised Dynamics

A new type of correlation has been developed similar to quantum entanglement in self-supervised dynamics (SSD). SSDs have been introduced as a quantum-classical hybrid based upon the Madelung equation in which the quantum potential is replaced by an information potential. As a result, SSD preserves the quantum topology along with superposition, entanglement, and wave-particle duality. At the same time, it can be implemented in any scale including the Newtonian scale. The main properties of SSD associated with simulating intelligence have been formulated. The attention with this innovation is focused on intelligent agents interaction based upon the new fundamental non-New tonian effect; namely, entanglement.

Zak, Michail↗
NASA NTRS2012

Atom Interferometry for Fundamental Physics and Gravity Measurements in Space

Laser-cooled atoms are used as freefall test masses. The gravitational acceleration on atoms is measured by atom-wave interferometry. The fundamental concept behind atom interferometry is the quantum mechanical particle-wave duality. One can exploit the wave-like nature of atoms to construct an atom interferometer based on matter waves analogous to laser interferometers.

atom interferometry↗
NASA NTRS2013

Downscaling Satellite Precipitation with Emphasis on Extremes: A Variational 1-Norm Regularization in the Derivative Domain

The increasing availability of precipitation observations from space, e.g., from the Tropical Rainfall Measuring Mission (TRMM) and the forthcoming Global Precipitation Measuring (GPM) Mission, has fueled renewed interest in developing frameworks for downscaling and multi-sensor data fusion that can handle large data sets in computationally efficient ways while optimally reproducing desired properties of the underlying rainfall fields. Of special interest is the reproduction of extreme precipitation intensities and gradients, as these are directly relevant to hazard prediction. In this paper, we present a new formalism for downscaling satellite precipitation observations, which explicitly allows for the preservation of some key geometrical and statistical properties of spatial precipitation. These include sharp intensity gradients (due to high-intensity regions embedded within lower-intensity areas), coherent spatial structures (due to regions of slowly varying rainfall),and thicker-than-Gaussian tails of precipitation gradients and intensities. Specifically, we pose the downscaling problem as a discrete inverse problem and solve it via a regularized variational approach (variational downscaling) where the regularization term is selected to impose the desired smoothness in the solution while allowing for some steep gradients(called 1-norm or total variation regularization). We demonstrate the duality between this geometrically inspired solution and its Bayesian statistical interpretation, which is equivalent to assuming a Laplace prior distribution for the precipitation intensities in the derivative (wavelet) space. When the observation operator is not known, we discuss the effect of its misspecification and explore a previously proposed dictionary-based sparse inverse downscaling methodology to indirectly learn the observation operator from a database of coincidental high- and low-resolution observations. The proposed method and ideas are illustrated in case studies featuring the downscaling of a hurricane precipitation field.

Hurricanes↗