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On adaptive weighted polynomial preconditioning for Hermitian positive definite matrices

The conjugate gradient algorithm for solving Hermitian positive definite linear systems is usually combined with preconditioning in order to speed up convergence. In recent years, there has been a revival of polynomial preconditioning, motivated by the attractive features of the method on modern architectures. Standard techniques for choosing the preconditioning polynomial are based only on bounds for the extreme eigenvalues. Here a different approach is proposed, which aims at adapting the preconditioner to the eigenvalue distribution of the coefficient matrix. The technique is based on the observation that good estimates for the eigenvalue distribution can be derived after only a few steps of the Lanczos process. This information is then used to construct a weight function for a suitable Chebyshev approximation problem. The solution of this problem yields the polynomial preconditioner. In particular, we investigate the use of Bernstein-Szego weights.

Fischer, Bernd↗

Constraints on the formation history of the elliptical galaxy NGC 3923 from the colors of its globular clusters

We present a study of the colors of globular clusters associated with the elliptical galaxy NGC 3923. Our final sample consists of Wasington system C and T(sub 1) photometry for 143 globular cluster candidates with an expected contamination of no more than 10%. We find that the color distribution of the NGC 3923 globular cluster system (GCS) is broad and appears to have at least two peaks. A mixture modeling analysis of the color distribution indicates that a two-component model is favored over a single-component one at a high level of confidence (greater than 99%). This evidence for more than one population in the GCS of NGC 3923 is similar to that previously noted for the four other elliptical galaxies for which similar data have been published. Furthermore, we find that the NGC 3923 GCS is redder than the GCSs of previously studed elliptical galaxies of similar luminosity. The median metallicity inferred from our (C-(T(sub 1)))(sub 0) colors is (Fe/H)(sub med) = -0.56, with an uncertainty of 0.14 dex arising from all sources of uncertainty in the mean color. This is more metal rich than the median metallicity found for the GCS of M87 using the same method, (Fe/H)(sub med) = -0.94. Since M87 is more luminous than NGC 3923, this result points to significant scatter about any trend of higher GCS metallicity with increasing galaxy luminosity. We also show that there is a color gradient in the NGC 3923 GCS corresponding to about -0.5 dex in Delta(Fe/H)/Delta(log r). We conclude that the shape of the color distribution of individual GCSs and the variation in mean color among the GCSs of ellipticals are difficult to understand if elliptical galaxies are formed in a single protogalactic collapse. Models in which ellipticals and their globular clusters are formed in more than one event, such as a merger scenario, are more successful in accounting for these observations.

Zepf, Stephen E.↗

Refinement of Models for VLBI Analysis

Continual refinement of models and estimation methods is an integral part of improving VLBI measurements of Earth orientation and position along with advances in instrumentation and observing strategy. The modeling of the troposphere continues to be challenging with recent improvements in treating the mean gradient and gradient variations affecting the terrestrial reference frame scale and celestial declinations near the current limits of accuracy. Revised models of nutation and solid Earth tides are implemented in CALC 9.0 to conform to the latest IERS Conventions along with other changes to facilitate use by VLBI correlators. Using data since 1995 the celestial reference frame has been extended and improved consistent with the definition and 0.25 mas accuracy limit of the ICRF. The current definition of the VLBI terrestrial reference frame places a floor on the accuracy of station velocities at the 0.4 mm/yr level. The establishment of the IVS (International VLBI Service for Geodesy and Astrometry) in the past year will provide a forum for further improvements of VLBI data analysis.

Ma, C.↗

An Overview of the Tropospheric Aerosol Radiative Forcing Observational Experiment

Aerosol effects on atmospheric radiation are a leading source of uncertainty in predicting future climate. As a result, the International Global Atmospheric Chemistry Program has established a Focus on Atmospheric Aerosols (IGAC/FAA) and endorsed a series of aerosol field campaigns. TARFOX, the second in the IGAC/FAA series, was designed to reduce this uncertainty by measuring aerosol properties and effects in the US eastern seaboard, where one of the world's major plumes of industrial haze moves from the continent over the Atlantic Ocean. TARFOX's objectives are to: 1. Make simultaneous measurements of: (a) aerosol effects on radiation fields, and (b) the chemical, physical, and optical properties of the aerosols causing those effects. 2. Perform a variety of closure studies by using overdetermined data sets to test the mutual consistency of measurements and calculations of a wide range of aerosol properties and effects. 3. Use the results of the closure studies to assess and reduce uncertainties in estimates of aerosol radiative forcing, as well as to guide future field programs. An important subset of the closure studies is tests and improvements of algorithms used to derive aerosol properties and radiative effects from satellite measurements. The TARFOX Intensive Field Period (IFP) was conducted July 10-31, 1996. It included coordinated measurements from four satellites (GOES-8, NOAA-14, ERS-2, LANDSAT), four aircraft (ER-2, C-130, C-131, and a modified Cessna), land sites, and ships. A variety of aerosol conditions was sampled, ranging from relatively clean behind frontal passages to moderately polluted with aerosol optical depths exceeding 0.5 at mid-visible wavelengths. The latter conditions included separate incidents of enhancements caused primarily by anthropogenic sources and another incident of enhancement apparently influenced by recent fog processing. Spatial gradients of aerosol optical thickness were sampled to aid in isolating aerosol effects from other radiative effects and to more tightly constrain closure tests, including those of satellite retrievals. This talk gives an overview of TARFOX goals, rationale, methods, and initial key findings.

Russell, P. B.↗

A geometric deformable model for echocardiographic image segmentation

Gradient vector flow (GVF), an elegant external force for parametric deformable models, can capture object boundaries from both sides. A new geometric deformable model is proposed that combines GVF and the geodesic active contour model. The level set method is used as the numerical method of this model. The model is applied for echocardiographic image segmentation.

NASA Program Biomedical Research and Countermeasur↗

Hydrological Variations in Australia Recovered by GRACE High-Resolution Mascons Solutions

Australia represents a challenging region in which to study hydrological variations as recovered by the GRACE (Gravity Recovery And Climate Experiment) mission data. Much of Australia is characterized by relatively small hydrological signals, with large precipitation gradients between the North and the South. These signals are better recovered using innovative GRACE processing techniques such as high-resolution mascon solutions, which may help overcome the deficiencies in the standard GRACE data processing and filtering methods. We will show the power of using regional and global mas con solutions to recover hydrological variations from 2003 to 2011, as well as the oceanic mass variations in the surrounding regions. We will compare the GRACE signals with state of the art hydrology and ocean general circulation models, precipitation, soil moisture and groundwater data sets. We especially emphasize the gravity signatures observed during the decadal drought in the Murray-Darling river basin and the early 2011 floods in North-Western Australia.

Carabajal, Claudia C.↗

Exploring the Science Trade Space with the JPL Innovation Foundry A-Team

The JPL Innovation Foundry has established a new approach for exploring, developing, and evaluating early concepts with a group called the Architecture Team (A-Team). The A-Team combines innovative collaborative methods and facilitated sessions with subject matter experts and analysis tools to help mature mission concepts. Science, implementation, and programmatic elements are all considered during an ATeam study. In these studies, Concept Maturity Levels (CML) are used to group methods. These levels include idea generation and capture (CML 1), initial feasibility assessment (CML 2), and trade space exploration (CML 3). Methods used for exploring the science objectives, feasibility, and scope will be described including use of a new technique for understanding the most compelling science, called a Science Return Diagram (SRD). In the process of developing the SRD, gradients in the science trade space are uncovered along with their implications for implementation and mission architecture. Special attention is paid towards developing complete investigations, establishing a series of logical claims that lead to the natural selection of a measurement approach. Over 20 science-focused A-Team studies have used these techniques to help science teams refine their mission objectives, make implementation decisions and reveal the mission concept’s most compelling science. This paper will describe the A-Team process for exploring the mission concept's science trade space and the Science Return Diagram technique.In June of 2011 a new collaborative engineering approach forearly concept formulation began in the JPL InnovationFoundry [1], six months later becoming the “A-Team” [2].Responding to a need for exploring mission architecturelevel trades [3], the A-Team precedes Team X [4,5] in asequence of concurrent engineering teams at JPL that can beused to mature a concept from a “cocktail napkin” level ideato a complete mission point design. The A-Team efficientlyexplores the science, implementation, and programmatictrade space in early concept formulation. Small, facilitatedgroups of experts generate innovative ideas, quantitativelyassess feasibility, and discover key sensitivities in the tradespace through collaborative analysis and use of advancedmethods and tools. The A-Team process builds off theexperience within JPL and other recent approaches to earlyconcept formulation [6] including best practices of the JPLInnovation Foundry, Project Systems Engineering &Formulation Section, Team Eureka and the Rapid MissionArchitecture Team[7].The A-Team is a focal point for innovative formulationapproaches and people within JPL. It relies on a largebackground of study resources, creative thinkers and “greybeard” scrutinizers, advanced tools, and subject matterexperts with both breadth and depth in experience andexpertise that are all available at JPL. The A-Team isdesigned to be a rapid and efficient process takingapproximately 6 weeks (the entire process can be as short asjust a few days or as long as up to three months) and costingthe equivalent of a work-month of a full-time employee orless. Studies begin with detailed planning and client reviewfollowed by study sessions, analysis work, and reporting.The staffing on each study is customized to the study goalsand objectives, and it is addressed early in the A-Teamprocess. Sessions are generally half-day or whole-day eventsand conducted over a series of days with focused agendas thatare moderated by a trained facilitator. Preliminary results andknowledge capture are available within hours of each session,and a final report is generally available two weeks later.One of the biggest challenges facing early conceptdevelopment is understanding the gradient in science returnversus various available mission scenarios and payload options. Often times, major areas of scientific inquiry havealready been prioritized by science groups, including throughthe National Research Council’s Decadal Studies inAstronomy, Planetary, and Earth Science. Yet science teamscontinue to struggle, especially in competitive missionsolicitations, to capture the right amount of scope that’sachievable within the cost constraints of the opportunity.Often the desire to completely and comprehensively study ascience area in just one mission (after all, true missionopportunities are rare) drives teams to take on too much,providing requirements that are unachievable within theresources of the opportunity without inducing unacceptableimplementation risk. Alternatively, science teams can seekto reduce risk by using an established instrument, but havenot thought through the traceability and key aspects of thescience question to justify its use. Both scenarios lead to badassumptions at the beginning of the concept development thatcan then ripple through implementation option choices,potentially preventing what would have been a good scienceinvestigation from being selected.The purpose of this paper is first to provide some additionalbackground and summary of the A-Team process, tools,people, and facilities. We then focus on the A-Teammethodology for overcoming the barriers of defining thescience scope well at the early concept development stage.This includes understanding the science story andtraceability, and then examining the gradient in science returnversus key characteristics of observables, developing theright payload and mission requirement specification throughexamining the science and implementation trade space.

Ziemer, John K.↗

Comparison Between DSMC and CFD for Hypersonic Planetary Entry Simulations

Hypersonic planetary entry flows span a wide range of Knudsen numbers between rarefied and continuum flows. While computational fluid dynamics (CFD) techniques cannot provide an accurate solution for flows in the rarefied regime, the direct simulation Monte Carlo (DSMC) method is capable of providing accurate solutions for flows in both in the rarefied and continuum regimes but becomes prohibitively expensive as the Knudsen number decreases. For the purpose of thermal protection systems (TPS) design and post-flight reconstruction, various selected points along an entry trajectory are often solved using hypersonic solvers. The quantities of interest that are obtained from that exercise are generally surface quantities, such as pressure, heat flux and enthalpy. Then, material response solvers are used to either design the heat shield to an optimal thickness based on a choice of material, or to provide in-depth heating profiles through the material at various select locations, and compare with flight instrumentation such as the ones that flew on NASA’s two most recent Mars missions, MSL and Mars2020. While most of the heating is generally experienced during the continuum part of the entry, the heating within the rarefied regime is significant for some atmospheres, and hence the flow solutions need to be computed using the DSMC method. Ensuring consistency between hypersonic CFD and the DSMC is crucial so that reliable surface quantities can be passed to material response solvers. Studies were performed to compare the two methods at various select locations, for both non-reacting argon flows as well reacting CO2/N2 flows. Preliminary conclusions show that, for non-reacting flows, the agreement between the two methods for surface heating is excellent (within expected uncertainties) for a freestream Knudsen number of 0.0006, and gets progressively worse as the Knudsen number increases to 0.06. Continuum breakdown analyses were performed and showed that, in general, the Gradient Length Local Knudsen number (KnGLL) from Boyd [1] and associated criteria (KnGLL > 0.05) can be accurately used to predict zones of breakdown in the flow, and associated errors for surface quantities. Furthermore, when studying reacting flow, our studies showed that while flow quantities are highly dependent on relaxation parameters and chemistry rates, it is possible to obtain a good agreement for surface heating, as long as the continuum breakdown in minimal (see Fig. 1). Finally, we studied the impact of the grid refinement on the surface quantities in DSMC.

DSMC↗

Comparison Between DSMC and CFD for Hypersonic Planetary Entry Simulations

Hypersonic planetary entry flows span a wide range of Knudsen numbers between rarefied and continuum flows. While computational fluid dynamics (CFD) techniques cannot provide an accurate solution for flows in the rarefied regime, the direct simulation Monte Carlo (DSMC) method is capable of providing accurate solutions for flows in both in the rarefied and continuum regimes but becomes prohibitively expensive as the Knudsen number decreases. For the purpose of thermal protection systems (TPS) design and post-flight reconstruction, various selected points along an entry trajectory are often solved using hypersonic solvers. The quantities of interest that are obtained from that exercise are generally surface quantities, such as pressure, heat flux and enthalpy. Then, material response solvers are used to either design the heat shield to an optimal thickness based on a choice of material, or to provide in-depth heating profiles through the material at various select locations, and compare with flight instrumentation such as the ones that flew on NASA’s two most recent Mars missions, MSL and Mars2020. While most of the heating is generally experienced during the continuum part of the entry, the heating within the rarefied regime is significant for some atmospheres, and hence the flow solutions need to be computed using the DSMC method. Ensuring consistency between hypersonic CFD and the DSMC is crucial so that reliable surface quantities can be passed to material response solvers. Studies were performed to compare the two methods at various select locations, for both non-reacting argon flows as well reacting CO2/N2 flows. Preliminary conclusions show that, for non-reacting flows, the agreement between the two methods for surface heating is excellent (within expected uncertainties) for a freestream Knudsen number of 0.0006, and gets progressively worse as the Knudsen number increases to 0.06. Continuum breakdown analyses were performed and showed that, in general, the Gradient Length Local Knudsen number (KnGLL) from Boyd and associated criterion (KnGLL > 0.05) seems conservative in predicting zones of breakdown in the flow, and associated errors for surface quantities. Updated criteria of KnGLL = 2.0 and 0.5 appear to be more appropriate for surface and flow quantities, respectively. Furthermore, when studying reacting flows, our studies showed that while flow quantities are highly dependent on relaxation parameters and chemistry rates, it is possible to obtain a good agreement for surface heating, as long as the continuum breakdown is minimal.

DSMC↗

TRMM Microwave Radiometer Rain Rate Estimation Method with Convective and Stratiform Discrimination

Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) radiometer brightness temperature data in the 85 GHz channel (T85) reveal distinct local minima (T85min) in a regional map containing a Mesoscale Convective System (MCS). A map of surface rain rate for that region, deduced from simultaneous measurements made by the Precipitation Radar (PR) on board the TRMM satellite, reveals that these T85min, produced by scattering, correspond to local PR rain maxima. Utilizing the PR rain rate map as a guide, we have developed a TMI algorithm to retrieve convective and stratiform rain. In this algorithm, two parameters are used to classify three kinds of thunderstorms (Cbs) based on the T85 data: a) the magnitude of scattering depression deduced from local T85mi, and b) the mean horizontal gradient of T85 around such minima. Initially, the algorithm is optimized or tuned utilizing the PR and TMI data of a few MCS events. The areal distribution of light (1-10 mm/hr), moderate (10-20 mm/hr), and intense (greater than or equal to 20 mm/hr) rain rates are retrieved on the average with an accuracy of about 15%. Taking advantage of this ability of our retrieval method, one could derive the latent heat input into the atmosphere over the 760 km wide swath of the TMI radiometer in the tropics.

Prabhakara, Cuddapah↗

Application of Dorodnitsyn's Integral Method to Nonequilibrium Flows over Pointed Bodies

Dorodnitsyn's integral method is used to obtain an approximate solution to the supersonic nonequilibrium flow over pointed bodies with attached shock waves. The partial differential equations governing the flow are converted to an approximate set of ordinary equations, which are solved by numerical integration starting at the body tip. Detailed analytical and numerical results for the first approximation are presented, considering the vibrational relaxation of a diatomic gas over a wedge or cone. It is shown that the first approximation yields: (1) The exact flow-variable gradients at the wedge tip (2) Expressions for the flow-variable gradients at the cone tip which are in agreement with extrapolations of characteristics calculations (3) A good approximate algebraic solution for frozen or equilibrium conical flow (4) An approximate expression for the nonequilibrium-flow stream function which affords a means of obtaining variations across the shock layer of the temperature and vibrational energy. Numerical results for both the wedge and cone compare favorably with identical cases computed by the method of characteristics.

NONEQUILIBRIUM FLOW↗

Ocean Chlorophyll Studies from a U-2 Aircraft Platform

Chlorophyll gradient maps of large ocean areas were generated from U-2 ocean color scanner data obtained over test sites in the Pacific and Atlantic Oceans. The delineation of oceanic features using the upward radiant intensity relies on an analysis method which presupposes that radiation backscattered from the atmosphere and ocean surface can be properly modeled using a measurement made at 778 nm. An estimation of the chlorophyll concentration was performed by properly ratioing radiances measured at 472 nm and 548 nm after removing the atmospheric effects. The correlation between the remotely sensed data and in-situ surface chlorophyll measurements was validated in two sets of data. The results show that the correlation between the in-situ measured chlorophyll and the derived quantity is a negative exponential function and the correlation coefficient was calculated to be -0.965.

Kim, H. H.↗

Large Eddy Simulation of turbulent shear flows

The conceptual foundation underlying Large Eddy Simulation (LES) is summarized, and the numerical methods developed for simulation of the time-developing turbulent mixing layer and turbulent plane Poiseuille flow are discussed. Computational results show that the average Reynolds stress profile nearly attains the equilibrium shape which balances the downstream mean pressure gradient in the regions away from the walls. In the vicinity of the walls, viscous stresses are shown to be significant; together with the Reynolds stresses, these stresses balance the mean pressure gradient. It is stressed that the subgrid scale contribution to the total Reynolds stress is significant only in the vicinity of the walls. The continued development of LES is urged.

Moin, P.↗

Measurement of Seebeck coefficient using a light pulse

A high-temperature (1900 K) Seebeck coefficient apparatus is described in which small thermal gradients are generated in a sample by light pulses transmitted via light pipes. By employing an analog subtraction circuit, the Seebeck coefficient is displayed directly on an X-Y recorder. This technique presents a convenient, accurate, and rapid method for measuring the Seebeck coefficient in highly doped semiconductors as a function of temperature. The nature of the resulting display (X-Y recording) is a valuable tool in determining validity of the data. A straight line results (i.e., a minimum of hysteresis) only if all potential experimental errors are minimized. Under these conditions, the error of measurements of the Seebeck coefficient is estimated to be less than + or - 1 percent.

Wood, C.↗

Passive control plate for shock-boundary layer interactions

Computational and experimental results are presented for a passive method capable of reducing or completely eliminating the separation region in shock-boundary layer interactions of the type that can result in severe performance degradation due to flow separation in supersonic and hypersonic inlets. The method involves the placement of an embedded plate in the outer portion of the boundary layer, parallel to the wall, so that the incident shock will impinge upon, and be reflected from, its surface. This will lower the pressure gradient in the low-momentum, near-wall region. A porous control plate's effect has also been investigated.

Goodman, Wesley L.↗

Application of implicit numerical techniques to the solution of the three-dimensional diffusion equation

Implicit techniques for calculating three-dimensional, time-dependent heat diffusion in a cube are tested with emphasis on storage efficiency, accuracy, and speed of calculation. For this purpose, a tensor product technique with both Chebyshev collocation and finite differences and a generalized conjugate gradient technique with finite differences are used in conjunction with Crank-Nicolson discretization. An Euler explicit finite difference calculation is performed for use as a benchmark. The implicit techniques are found to be competitive with the Euler explicit method in terms of storage efficiency and speed of calculation and offer advantages both in accuracy and stability. Mesh stretching in the finite difference calculations is shown to markedly improve the accuracy of the solution.

Peltier, Leonard Joel↗

Further Developments of the Fringe-Imaging Skin Friction Technique

Various aspects and extensions of the Fringe-Imaging Skin Friction technique (FISF) have been explored through the use of several benchtop experiments and modeling. The technique has been extended to handle three-dimensional flow fields with mild shear gradients. The optical and imaging system has been refined and a PC-based application has been written that has made it possible to obtain high resolution skin friction field measurements in a reasonable period of time. The improved method was tested on a wingtip and compared with Navier-Stokes computations. Additionally, a general approach to interferogram-fringe spacing analysis has been developed that should have applications in other areas of interferometry. A detailed error analysis of the FISF technique is also included.

Zilliac, Gregory C.↗

The Electron Drift Instrument for Cluster

The Electron Drift Instrument (EDI) measures the drift of a weak beam of test electrons that, when emitted in certain directions, return to the spacecraft after one or more gyrations. This drift is related to the electric field and the gradient in the magnetic field, and these quantities can, by use of different electron energies, be determined separately. As a by-product, the magnetic field strength is also measured. The present paper describes the scientific objectives, the experimental method, and the technical realization of the various elements of the instrument.

Paschmann, G.↗