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An iterative algorithm for the solution of the Helmholtz equation is developed. The algorithm is based on a preconditioned conjugate gradient iteration for the normal equations. The preconditioning is based on an SSOR sweep for the discrete Laplacian. Numerical results are presented for a wide variety of problems of physical interest and demonstrate the effectiveness of the algorithm.
An algorithm has been developed to calculate a complete optimized set of dimensionless products of the variables associated with a physical phenomenon from any complete set of dimensionless products. The algorithm is nonexhaustive and is readily adaptable for a digital computer. Illustrative examples are also given.
The engineering development of the National Aeronautics and Space Administration's (NASA) new Space Launch System (SLS) requires cross discipline teams with extensive knowledge of launch vehicle subsystems, information theory, and autonomous algorithms dealing with all operations from pre-launch through on orbit operations. The nominal and off-nominal characteristics of SLS's elements and subsystems must be understood and matched with the autonomous algorithm monitoring and mitigation capabilities for accurate control and response to abnormal conditions throughout all vehicle mission flight phases, including precipitating safing actions and crew aborts. This presents a large and complex systems engineering challenge, which is being addressed in part by focusing on the specific subsystems involved in the handling of off-nominal mission and fault tolerance with response management. Using traditional model-based system and software engineering design principles from the Unified Modeling Language (UML) and Systems Modeling Language (SysML), the Mission and Fault Management (M&FM) algorithms for the vehicle are crafted and vetted in Integrated Development Teams (IDTs) composed of multiple development disciplines such as Systems Engineering (SE), Flight Software (FSW), Safety and Mission Assurance (S&MA) and the major subsystems and vehicle elements such as Main Propulsion Systems (MPS), boosters, avionics, Guidance, Navigation, and Control (GNC), Thrust Vector Control (TVC), and liquid engines. These model-based algorithms and their development lifecycle from inception through FSW certification are an important focus of SLS's development effort to further ensure reliable detection and response to off-nominal vehicle states during all phases of vehicle operation from pre-launch through end of flight. To test and validate these M&FM algorithms a dedicated test-bed was developed for full Vehicle Management End-to-End Testing (VMET). For addressing fault management (FM) early in the development lifecycle for the SLS program, NASA formed the M&FM team as part of the Integrated Systems Health Management and Automation Branch under the Spacecraft Vehicle Systems Department at the Marshall Space Flight Center (MSFC). To support the development of the FM algorithms, the VMET developed by the M&FM team provides the ability to integrate the algorithms, perform test cases, and integrate vendor-supplied physics-based launch vehicle (LV) subsystem models. Additionally, the team has developed processes for implementing and validating the M&FM algorithms for concept validation and risk reduction. The flexibility of the VMET capabilities enables thorough testing of the M&FM algorithms by providing configurable suites of both nominal and off-nominal test cases to validate the developed algorithms utilizing actual subsystem models such as MPS, GNC, and others. One of the principal functions of VMET is to validate the M&FM algorithms and substantiate them with performance baselines for each of the target vehicle subsystems in an independent platform exterior to the flight software test and validation processes. In any software development process there is inherent risk in the interpretation and implementation of concepts from requirements and test cases into flight software compounded with potential human errors throughout the development and regression testing lifecycle. Risk reduction is addressed by the M&FM group but in particular by the Analysis Team working with other organizations such as S&MA, Structures and Environments, GNC, Orion, Crew Office, Flight Operations, and Ground Operations by assessing performance of the M&FM algorithms in terms of their ability to reduce Loss of Mission (LOM) and Loss of Crew (LOC) probabilities. In addition, through state machine and diagnostic modeling, analysis efforts investigate a broader suite of failure effects and associated detection and responses to be tested in VMET to ensure reliable failure detection, and confirm responses do not create additional risks or cause undesired states through interactive dynamic effects with other algorithms and systems. VMET further contributes to risk reduction by prototyping and exercising the M&FM algorithms early in their implementation and without any inherent hindrances such as meeting FSW processor scheduling constraints due to their target platform - the ARINC 6535-partitioned Operating System, resource limitations, and other factors related to integration with other subsystems not directly involved with M&FM such as telemetry packing and processing. The baseline plan for use of VMET encompasses testing the original M&FM algorithms coded in the same C++ language and state machine architectural concepts as that used by FSW. This enables the development of performance standards and test cases to characterize the M&FM algorithms and sets a benchmark from which to measure their effectiveness and performance in the exterior FSW development and test processes. This paper is outlined in a systematic fashion analogous to a lifecycle process flow for engineering development of algorithms into software and testing. Section I describes the NASA SLS M&FM context, presenting the current infrastructure, leading principles, methods, and participants. Section II defines the testing philosophy of the M&FM algorithms as related to VMET followed by section III, which presents the modeling methods of the algorithms to be tested and validated in VMET. Its details are then further presented in section IV followed by Section V presenting integration, test status, and state analysis. Finally, section VI addresses the summary and forward directions followed by the appendices presenting relevant information on terminology and documentation.
Quantum computing is one of the most enticing computational paradigms with the potential to revolutionize diverse areas of future-generation computational systems. While quantum computing hardware has advanced rapidly, from tiny laboratory experiments to quantum chips that can outperform even the largest supercomputers on specialized computational tasks, these noisy-intermediate scale quantum (NISQ) processors are still too small and non-robust to be directly useful for any real-world applications. We discuss the prospects for quantum computing and AI, highlighting advances in algorithms, both near- and longer-term. Quantum error correction is critical to the realization of any such vision. The talk with touch on some recent exciting advanced in quantum error correction, particularly in dynamical codes. The talk will conclude with an example of how the combination of quantum computing and artificial intelligence can help probe fundamental aspect of quantum physics.
The Texas A&M monthly total oceanic rainfall retrieval algorithm is based on radiative transfer models and can only be modified on a physically sound basis. Within this constraint we have examined some improvements to the algorithm and it appears that it can be made significantly better. In particular, it appears that by proper use of the range of frequencies available on TMI (TRMM Microwave Imager) and AMSR that the need for the log-normal fit can be eliminated.
Recent progress in the development of implicit algorithms for the Euler equations using the flux-vector splitting method is described. Comparisons of the relative efficiency of relaxation and spatially-split approximately factored methods on a vector processor for two-dimensional flows are made. For transonic flows, the higher convergence rate per iteration of the Gauss-Seidel relaxation algorithms, which are only partially vectorizable, is amply compensated for by the faster computational rate per iteration of the approximately factored algorithm. For supersonic flows, the fully-upwind line-relaxation method is more efficient since the numerical domain of dependence is more closely matched to the physical domain of dependence. A hybrid three-dimensional algorithm using relaxation in one coordinate direction and approximate factorization in the cross-flow plane is developed and applied to a forebody shape at supersonic speeds and a swept, tapered wing at transonic speeds.
Satellite microwave radiometers have enabled us to observe the cryosphere and its changes. A variety of algorithms have been developed since the late 1970s. These convert observed microwave radiation into geophysical, glaciological properties relevant to study ice sheets’ snow accumulation and melt, terrestrial snow water equivalent and freeze/thaw state, and various sea ice cover characteristics like extent, concentration, and thickness. In spite of the continuous availability of satellite microwave radiometers for the past 40 years, potential for advancing our understanding of the relationship between microwave radiation and snow/ice properties still exists. Original empirical algorithms have matured and are becoming more physically based. This presentation offers insights into some advances made during the past 10 years in monitoring ice sheet, terrestrial snow, and sea ice. These advances made it possible to provide new, more reliable climate-related variables to the community for the satellite era using the typical 18-37 GHz frequency range (e.g., retrievals of grain size profiles in Antarctica, snow cover stratification, and therefore accumulation with applications to climate studies). Recent NASA instruments have recorded low microwave frequencies (at 1.4 GHz). These observations have a large penetration depth, they emanate from deep into the ice, where properties including temperature are very stable. Nonetheless, it has been found at both Dome C, Antarctica and Summit, Greenland that changes in surface snow properties significantly influence these observations. Compared to ice sheets, terrestrial snow and sea ice present higher spatial heterogeneities. Over land, presence of canopy and lakes, though with known locations, add ambiguities in the retrievals of snow properties. Over sea ice, ridges, leads, changes in salinity, and sea ice drift augment further the level of difficulty in obtaining robust geophysical properties. Assessing the quality of satellite retrievals, often requiring field activities, is a necessary step in designing the next generation of microwave algorithms to monitor changes in the cryosphere.
The scientific objectives of this grant are: (1) thoroughly evaluate, both theoretically and empirically, all available Special Sensor Microwave Imager (SSM/I) retrieval algorithms for column water vapor, column liquid water, and surface wind speed; (2) where both appropriate and feasible, develop, validate, and document satellite passive microwave retrieval algorithms that offer significantly improved performance compared with currently available algorithms; and (3) refine and validate a novel physical inversion scheme for retrieving rain rate over the ocean. This report summarizes work accomplished or in progress during the first year of a three year grant. The emphasis during the first year has been on the validation and refinement of the rain rate algorithm published by Petty and on the analysis of independent data sets that can be used to help evaluate the performance of rain rate algorithms over remote areas of the ocean. Two articles in the area of global oceanic precipitation are attached.
A framework is presented for developing computationally unified numerical algorithms for solving nonlinear equations that arise in modeling various problems in mathematical physics. The concept of computational unification is an attempt to encompass efficient solution procedures for computing various nonlinear phenomena that may occur in a given problem. For example, in Computational Fluid Dynamics (CFD), a unified algorithm will be one that allows for solutions to subsonic (elliptic), transonic (mixed elliptic-hyperbolic), and supersonic (hyperbolic) flows for both steady and unsteady problems. The objectives are: development of superior unified algorithms emphasizing accuracy and efficiency aspects; development of codes based on selected algorithms leading to validation; application of mature codes to realistic problems; and extension/application of CFD-based algorithms to problems in other areas of mathematical physics. The ultimate objective is to achieve integration of multidisciplinary technologies to enhance synergism in the design process through computational simulation. Specific unified algorithms for a hierarchy of gas dynamics equations and their applications to two other areas: electromagnetic scattering, and laser-materials interaction accounting for melting.
Global coronal models seek to produce an accurate physical representation of the Sun's atmosphere that can be used, for example, to drive space-weather models. Assessing their accuracy is a complex task, and there are multiple observational pathways to provide constraints and tune model parameters. Here, we combine several such independent constraints, defining a model-agnostic framework for standardized comparison. We require models to predict the distribution of coronal holes at the photosphere, and neutral line topology at the model's outer boundary. We compare these predictions to extreme-ultraviolet (EUV) observations of coronal hole locations, white-light Carrington maps of the streamer belt, and the magnetic sector structure measured in situ by Parker Solar Probe and 1 au spacecraft. We study these metrics for potential field source surface (PFSS) models as a function of source surface height and magnetogram choice, as well as comparing to the more physical Wang–Sheeley–Arge (WSA) and the Magnetohydrodynamic Algorithm outside a Sphere (MAS) models. We find that simultaneous optimization of PFSS models to all three metrics is not currently possible, implying a trade-off between the quality of representation of coronal holes and streamer belt topology. WSA and MAS results show the additional physics that they include address this by flattening the streamer belt while maintaining coronal hole sizes, with MAS also improving coronal hole representation relative to WSA. We conclude that this framework is highly useful for inter- and intra-model comparisons. Integral to the framework is the standardization of observables required of each model, evaluating different model aspects.
A hybrid statistical-physical retrieval scheme is explored which combines a statistical approach with an approach based on the development of cloud-radiation models designed to simulate precipitating atmospheres. The algorithm employs the detailed microphysical information from a cloud model as input to a radiative transfer model which generates a cloud-radiation model database. Statistical procedures are then invoked to objectively generate an initial guess composite profile data set from the database. The retrieval algorithm has been tested for a tropical typhoon case using Special Sensor Microwave/Imager (SSM/I) data and has shown satisfactory results.
The analysis of spectral signals for features that represent physical phenomenon is ubiquitous in the science and engineering communities. There are two main approaches that can be taken to extract relevant features from these high-dimensional data streams. The first set of approaches relies on extracting features using a physics-based paradigm where the underlying physical mechanism that generates the spectra is used to infer the most important features in the data stream. We focus on a complementary methodology that uses a data-driven technique that is informed by the underlying physics but also has the ability to adapt to unmodeled system attributes and dynamics. We discuss the following four algorithms: Spectral Decomposition Algorithm (SDA), Non-Negative Matrix Factorization (NMF), Independent Component Analysis (ICA) and Principal Components Analysis (PCA) and compare their performance on a spectral emulator which we use to generate artificial data with known statistical properties. This spectral emulator mimics the real-world phenomena arising from the plume of the space shuttle main engine and can be used to validate the results that arise from various spectral decomposition algorithms and is very useful for situations where real-world systems have very low probabilities of fault or failure. Our results indicate that methods like SDA and NMF provide a straightforward way of incorporating prior physical knowledge while NMF with a tuning mechanism can give superior performance on some tests. We demonstrate these algorithms to detect potential system-health issues on data from a spectral emulator with tunable health parameters.
It has been hypothesized that continuous ground-based remote sensing measurements from active and passive remote sensors combined with regular soundings of the atmospheric thermodynamic structure can be combined to describe the effects of clouds on the clear sky radiation fluxes. We critically test that hypothesis in this paper and a companion paper (Part II). Using data collected at the Southern Great Plains (SGP) Atmospheric Radiation Measurement (ARM) site sponsored by the U.S. Department of Energy, we explore an analysis methodology that results in the characterization of the physical state of the atmospheric profile at time resolutions of five minutes and vertical resolutions of 90 m. The description includes thermodynamics and water vapor profile information derived by merging radiosonde soundings with ground-based data, and continues through specification of the cloud layer occurrence and microphysical and radiative properties derived from retrieval algorithms and parameterizations. The description of the atmospheric physical state includes a calculation of the infrared and clear and cloudy sky solar flux profiles. Validation of the methodology is provided by comparing the calculated fluxes with top of atmosphere (TOA) and surface flux measurements and by comparing the total column optical depths to independently derived estimates. We find over a 1-year period of comparison in overcast uniform skies, that the calculations are strongly correlated to measurements with biases in the flux quantities at the surface and TOA of less than 10% and median fractional errors ranging from 20% to as low as 2%. In the optical depth comparison for uniform overcast skies during the year 2000 where the optical depth varies over 3 orders of magnitude we find a mean positive bias of 46% with a median bias of less than 10% and a 0.89 correlation coefficient. The slope of the linear regression line for the optical depth comparison is 0.86 with a normal deviation of 20% about this line. In addition to a case study where we examine the cloud radiative effects at the TOA, surface and atmosphere by a middle latitude synoptic-scale cyclone, we examine the cloud top pressure and optical depth retrievals of ISCCP and LBTM over a period of 1 year. Using overcast period from the year 2000, we find that the satellite algorithms tend to bias cloud tops into the middle troposphere and underestimate optical depth in high optical depth events (greater than 100) by as much as a factor of 2.
A mesh-sequencing algorithm and a conservative patched-grid-interface algorithm (hereafter Patch Algorithm ) have been incorporated into the PAB3D code, which is a computer program that solves the Navier-Stokes equations for the simulation of subsonic, transonic, or supersonic flows surrounding an aircraft or other complex aerodynamic shapes. These algorithms are efficient, flexible, and have added tremendously to the capabilities of PAB3D. The mesh-sequencing algorithm makes it possible to perform preliminary computations using only a fraction of the grid cells (provided the original cell count is divisible by an integer) along any grid coordinate axis, independently of the other axes. The patch algorithm addresses another critical need in multi-block grid situation where the cell faces of adjacent grid blocks may not coincide, leading to errors in calculating fluxes of conserved physical quantities across interfaces between the blocks. The patch algorithm, based on the Stokes integral formulation of the applicable conservation laws, effectively matches each of the interfacial cells on one side of the block interface to the corresponding fractional cell area pieces on the other side. This approach is comprehensive and unified such that all interface topology is automatically processed without user intervention. This algorithm is implemented in a preprocessing code that creates a cell-by-cell database that will maintain flux conservation at any level of full or reduced grid density as the user may choose by way of the mesh-sequencing algorithm. These two algorithms have enhanced the numerical accuracy of the code, reduced the time and effort for grid preprocessing, and provided users with the flexibility of performing computations at any desired full or reduced grid resolution to suit their specific computational requirements.
The proceedings of the Historically Black Colleges and Universities (HBCU) forum are presented. A wide range of research topics from plant science to space science and related academic areas was covered. The sessions were divided into the following subject areas: Life science; Mathematical modeling, image processing, pattern recognition, and algorithms; Microgravity processing, space utilization and application; Physical science and chemistry; Research and training programs; Space science (astronomy, planetary science, asteroids, moon); Space technology (engineering, structures and systems for application in space); Space technology (physics of materials and systems for space applications); and Technology (materials, techniques, measurements).
Results are presented of a test of the physically based total column water vapor retrieval algorithm of Wentz (1992) for sensitivity to realistic vertical distributions of temperature and water vapor. The ECMWF monthly averaged temperature and humidity fields are used to simulate the spatial pattern of systematic retrieval error of total column water vapor due to this sensitivity. The estimated systematic error is within 0.1 g/sq cm over about 70 percent of the global ocean area; systematic errors greater than 0.3 g/sq cm are expected to exist only over a few well-defined regions, about 3 percent of the global oceans, assuming that the global mean value is unbiased.
The Passive Aerodynamically Stabilized Magnetically Damped Satellite (PAMS) will be deployed from the Space Shuttle and used as a target for a Shuttle-mounted laser. It will be a cylindrical satellite with several corner cube reflectors on the ends. The center of mass of the cylinder will be near one end, and aerodynamic torques will tend to align the axis of the cylinder with the spacecraft velocity vector. Magnetic hysteresis rods will be used to provide passive despin and oscillation-damping torques on the cylinder. The behavior of the hysteresis rods depends critically on the 'B/H' curves for the combination of materials and rod length-to-diameter ratio ('l-over-d'). These curves are qualitatively described in most Physics textbooks in terms of major and minor 'hysteresis loops'. Mathematical modeling of the functional relationship between B and H is very difficult. In this paper, the physics involved is not addressed, but an algorithm is developed which provides a close approximation to empirically determined data with a few simple equations suitable for use in computer simulations.
The accurate quantification of new ice and open water areas and surface temperatures within the sea ice packs is a key to the realistic parameterization of heat, moisture, and turbulence fluxes between ocean and atmosphere in the polar regions. Multispectral NOAA advanced very high resolution radiometer/2 (AVHRR/2) satellite images are analyzed to evaluate how effectively the data can be used to characterize sea ice in the Bering and Greenland seas, both in terms of surface type and physical temperature. The basis of the classification algorithm, which is developed using a late wintertime Bering Sea ice cover data, is that frequency distributions of 10.8- micrometers radiances provide four distinct peaks, represeting open water, new ice, young ice, and thick ice with a snow cover. The results are found to be spatially and temporally consistent. Possible sources of ambiguity, especially associated with wider temporal and spatial application of the technique, are discussed. An ice surface temperature algorithm is developed for the same study area by regressing thermal infrared data from 10.8- and 12.0- micrometers channels against station air temperatures, which are assumed to approximate the skin temperatures of adjacent snow and ice. The standard deviations of the results when compared with in situ data are about 0.5 K over leads and polynyas to about 0.5-1.5 K over thick ice. This study is based upon a set of in situ data limited in scope and coverage. Cloud masks are applied using a thresholding technique that utilizes 3.74- and 10.8- micrometers channel data. The temperature maps produced show coherence with surface features like new ice and leads, and consistency with corresponding surface type maps. Further studies are needed to better understand the effects of both the spatial and temporal variability in emissivity, aerosol and precipitable atmospheric ice particle distribution, and atmospheric temperature inversions.