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Solving Upwind-Biased Discretizations: Multigrid Solver Using Semicoarsening - 2

This paper studies a novel multigrid approach to the solution for a second order upwind biased discretization of the convection equation in two dimensions. This approach is based on semi-coarsening and well balanced explicit correction terms added to coarse-grid operators to maintain on coarse-grid the same cross-characteristic interaction as on the target (fine) grid. Colored relaxation schemes are used on all the levels allowing a very efficient parallel implementation. The results of the numerical tests can be summarized as follows: 1) The residual asymptotic convergence rate of the proposed V(0, 2) multigrid cycle is about 3 per cycle. This convergence rate far surpasses the theoretical limit (4/3) predicted for standard multigrid algorithms using full coarsening. The reported efficiency does not deteriorate with increasing the cycle, depth (number of levels) and/or refining the target-grid mesh spacing. 2) The full multi-grid algorithm (FMG) with two V(0, 2) cycles on the target grid and just one V(0, 2) cycle on all the coarse grids always provides an approximate solution with the algebraic error less than the discretization error. Estimates of the total work in the FMG algorithm are ranged between 18 and 30 minimal work units (depending on the target (discretizatioin). Thus, the overall efficiency of the FMG solver closely approaches (if does not achieve) the goal of the textbook multigrid efficiency. 3) A novel approach to deriving a discrete solution approximating the true continuous solution with a relative accuracy given in advance is developed. An adaptive multigrid algorithm (AMA) using comparison of the solutions on two successive target grids to estimate the accuracy of the current target-grid solution is defined. A desired relative accuracy is accepted as an input parameter. The final target grid on which this accuracy can be achieved is chosen automatically in the solution process. the actual relative accuracy of the discrete solution approximation obtained by AMA is always better than the required accuracy; the computational complexity of the AMA algorithm is (nearly) optimal (comparable with the complexity of the FMG algorithm applied to solve the problem on the optimally spaced target grid).

Diskin, Boris↗

Applicability of the single equivalent point dipole model to represent a spatially distributed bio-electrical source

Although the single equivalent point dipole model has been used to represent well-localised bio-electrical sources, in realistic situations the source is distributed. Consequently, position estimates of point dipoles determined by inverse algorithms suffer from systematic error due to the non-exact applicability of the inverse model. In realistic situations, this systematic error cannot be avoided, a limitation that is independent of the complexity of the torso model used. This study quantitatively investigates the intrinsic limitations in the assignment of a location to the equivalent dipole due to distributed electrical source. To simulate arrhythmic activity in the heart, a model of a wave of depolarisation spreading from a focal source over the surface of a spherical shell is used. The activity is represented by a sequence of concentric belt sources (obtained by slicing the shell with a sequence of parallel plane pairs), with constant dipole moment per unit length (circumferentially) directed parallel to the propagation direction. The distributed source is represented by N dipoles at equal arc lengths along the belt. The sum of the dipole potentials is calculated at predefined electrode locations. The inverse problem involves finding a single equivalent point dipole that best reproduces the electrode potentials due to the distributed source. The inverse problem is implemented by minimising the chi2 per degree of freedom. It is found that the trajectory traced by the equivalent dipole is sensitive to the location of the spherical shell relative to the fixed electrodes. It is shown that this trajectory does not coincide with the sequence of geometrical centres of the consecutive belt sources. For distributed sources within a bounded spherical medium, displaced from the sphere's centre by 40% of the sphere's radius, it is found that the error in the equivalent dipole location varies from 3 to 20% for sources with size between 5 and 50% of the sphere's radius. Finally, a method is devised to obtain the size of the distributed source during the cardiac cycle.

NASA Discipline Cardiopulmonary↗

Statistics of Cloud Optical Properties from Airborne Lidar Measurements

Cloud optical properties, such as extinction-to-backscatter ratio and depolarization ratio, have a significant impact on the accuracy of cloud extinction retrievals from lidar systems because parameterizations of these variables are often used in non-ideal conditions to determine cloud type and optical depth. Statistics and trends of these optical parameters were analyzed for four years, 2003-2007, of Cloud Physics Lidar data during five projects of varying geographic locations. Extinction-to-backscatter ratio (at 532 nm) was derived by calculating the transmission loss through the cloud layer, while depolarization ratio was computed using the parallel and perpendicular polarized 1064 nm channels. The majority of the cloud layers yielded an S-ratio between 10 and 40 sr with the S-ratio frequency distribution centered at 25 sr for ice clouds, 21 sr for mixed phase clouds, and 11 sr for water clouds. On average for ice clouds, S ratio slightly decreased with decreasing temperature, while depolarization ratio increased significantly as temperatures decreased. Trends for water and mixed phase clouds were also observed. Ultimately, these observed trends in optical properties as a function of temperature and geographic location will improve current parameterizations of extinction-to-backscatter ratio, which consequently increases accuracy in cloud optical depth and radiative forcing estimates.

Yorks, John E.↗

Constraints on Porosity and Mass Loss in O-star Winds from the Modeling of X-ray Emission Line Profile Shapes

We fit X-ray emission line profiles in high resolution XMM-Newton and Chandra grating spectra of the early O supergiant Zeta Pup with models that include the effects of porosity in the stellar wind. We explore the effects of porosity due to both spherical and flattened clumps. We find that porosity models with flattened clumps oriented parallel to the photosphere provide poor fits to observed line shapes. However, porosity models with isotropic clumps can provide acceptable fits to observed line shapes, but only if the porosity effect is moderate. We quantify the degeneracy between porosity effects from isotropic clumps and the mass-loss rate inferred from the X-ray line shapes, and we show that only modest increases in the mass-loss rate (40%) are allowed if moderate porosity effects (h(sub infinity) less than approximately R(sub ∗)) are assumed to be important. Large porosity lengths, and thus strong porosity effects, are ruled out regardless of assumptions about clump shape. Thus, X-ray mass-loss rate estimates are relatively insensitive to both optically thin and optically thick clumping. This supports the use of X-ray spectroscopy as a mass-loss rate calibration for bright, nearby O stars

porosity↗

EDIN design study alternate space shuttle booster replacement concepts. Volume 1: Engineering analysis

The use of a recoverable liquid rocket booster (LRB) system to replace the existing solid rocket booster (SRB) system for the shuttle was studied. Historical weight estimating relationships were developed for the LRB using Saturn technology and modified as required. Mission performance was computed using February 1975 shuttle configuration groundrules to allow reasonable comparison of the existing shuttle with the study designs. The launch trajectory was constrained to pass through both the RTLS/AOA and main engine cut off points of the shuttle reference mission 1. Performance analysis is based on a point design trajectory model which optimizes initial tilt rate and exoatmospheric pitch profile. A gravity turn was employed during the boost phase in place of the shuttle angle of attack profile. Engine throttling add/or shutdown was used to constrain dynamic pressure and/or longitudinal acceleration where necessary. Four basic configurations were investigated: a parallel burn vehicle with an F-1 engine powered LRB; a parallel burn vehicle with a high pressure engine powered LRB; a series burn vehicle with a high pressure engine powered LRB. The relative sizes of the LRB and the ET are optimized to minimize GLOW in most cases.

Demakes, P. T.↗

A multi-domain method for subsonic viscous flows

We have developed a Schwarz type domain decomposition method for a pressure base, two- and three-dimensional Navier-Stokes solver. This technique allows one to partition a flow path, which can be characterized by complex geometry and/or complicated flow physics, into smaller sub-domains according to the local geometric simplicity or estimated flow scales. We can, then, sweep the sub-domains in some order and solve the Navier-Stokes equations using as boundary conditions, along the domain interfaces, the Dirichlet conditions which are taken from the most recent update of the solution in the adjacent neighboring domains. With this technique, one can minimize the adverse effects caused by grid skewness and the stiffness problem caused by disparate flow scales. Here, we report the results of a few fundamental flow cases to demonstrate that a judicious use of the multi-domain method can offer a significant convergence acceleration over the traditional one-domain method. This method can be extended to exploit the architecture of a parallel computer to further improve the speed.

Chan, Daniel C.↗

Introduction: Neuromorphic Materials

The explosive growth in data collection and the need to process it efficiently, as well as the desire to automate increasingly complex tasks in transportation, medical care, manufacturing, security and many other fields have motivated a growing interest in neuromorphic computing. Unlike the binary, transistorbased ON/OFF logic gates and separate logic and memory functionalities employed in digital computing, neuromorphic computing is inspired by animal brains that use interconnected synapses and neurons to perform processing, storage and transmission of information at the same location, while only consuming ~20 W or less of power. Motivated by the brain’s efficiency, adaptability, self-learning and resiliency qualities, neuromorphic computing can be broadly defined as an approach to processing and storing information using hardware and algorithms inspired by models of biological neural systems. Present research in neuromorphic computing encompasses approaches that vary significantly in their degree of neuro-inspiration, from systems that only incorporate features such as asynchronous, event-driven operation or use crossbar arrays of non-volatile memory (NVM) elements to accelerate deep neural networks (DNNs), to designs that embrace the extreme parallelism, sparsity, reconfigurability, adaptability, complexity and stochasticity observed in nervous systems. The term ‘neuromorphic’ computing is often credited to Carver Mead, who in the 1980s investigated Si-based analog electronics to replicate functions of the animal retina. Earlier important advances in this field include the work of Frank Rosenblatt, who proposed the concept of the perceptron, Bernard Widrow, who used this concept to build one of the first analog neural networks, the Adaline and many other researchers (see ref. 6 for an historical perspective on neuromorphic computing). With the recent increase in the use of artificial intelligence and large language models, and rising concerns over the associated energy costs, interest in neuromorphic hardware has expanded rapidly. According to some estimates, driven largely by the drastic growth in the training use of artificial intelligence (AI) models using the current computing architectures, the energy cost of computing is projected to reach the energy supply worldwide by 2045. Furthermore, while this is not a realistic outcome, it means that, if more efficient computing technologies are not developed -- soon -- the world will soon become one where demand for energy and market constraints limit the continued increase of societal access to AI and cloud services from data centers. Data centers used for training and use of these models consume hundreds of terawatt hours of electricity, already past 4% of the US electricity demand.

Circuits↗

Necessary and Sufficient Conditions for Attitude Estimation in Fractionated Spacecraft Systems

This paper addresses the problem of attitude estimation in fractionated spacecraft clusters. Each module in the cluster may have either a star-tracker, a relative attitude sensor, or both. Using results in nonlinear ob- servability theory, we provide graph-theoretic sufficient conditions for the attitude of every module to be observable. In particular we show that the attitude of every module in the cluster can be observed if every module has either a star tracker with non-collinear stars, or there is a path through the sensing network from a module with a star tracker to the module without a star tracker, and each of the relative measurements along the path has either multiple non-collinear beacons or a single beacon that is not parallel to the rotation vector of the target module.

Blackmore, Lars↗

The drag coefficient of cylindrical spacecraft in orbit at altitudes greater than 150 km

The spacecraft of the Geopotential Research Mission (GRM) are cylindrical in form and designed to fly with their longitudinal axes parallel to their direction of flight. The ratio of length to diameter of these spacecraft is roughly equal to 5.0. Other spacecraft previously flown had corresponding ratios roughly equal to 1.0, and therefore the drag produced by impacts on the lateral surfaces of those spacecraft was not as large as it will be on the GRM spacecraft. Since the drag coefficient is essentially the drag force divided by the frontal area in flight, lateral impacts, when taken into account make the GRM drag coefficient significantly larger than the coefficients used before for shorter spacecraft. A simple formula is derived for the drag coefficient of a cylindrical body flying with its long axis along the direction of flight, and it is used to estimate the drag for the GRM. The formula shows that the drag due to lateral surface impacts depends on the ratio of length-to-diameter and on a coefficient C sub LS (lateral surface impact coefficient) which can be determined from previous cylindrical spacecraft flown with the same attitude, or can be obtained from laboratory measurements of momentum accommodation coefficients.

Herrero, F. A.↗

Large-scale structure after COBE: Peculiar velocities and correlations of cold dark matter halos

Large N-body simulations on parallel supercomputers allow one to simultaneously investigate large-scale structure and the formation of galactic halos with unprecedented resolution. Our study shows that the masses as well as the spatial distribution of halos on scales of tens of megaparsecs in a cold dark matter (CDM) universe with the spectrum normalized to the anisotropies detected by Cosmic Background Explorer (COBE) is compatible with the observations. We also show that the average value of the relative pairwise velocity dispersion sigma(sub v) - used as a principal argument against COBE-normalized CDM models-is significantly lower for halos than for individual particles. When the observational methods of extracting sigma(sub v) are applied to the redshift catalogs obtained from the numerical experiments, estimates differ significantly between different observation-sized samples and overlap observational estimates obtained following the same procedure.

Zurek, Wojciech H.↗

An Efficient Objective Analysis System for Parallel Computers

A new atmospheric objective analysis system designed for parallel computers will be described. The system can produce a global analysis (on a 1 X 1 lat-lon grid with 18 levels of heights and winds and 10 levels of moisture) using 120,000 observations in 17 minutes on 32 CPUs (SGI Origin 2000). No special parallel code is needed (e.g. MPI or multitasking) and the 32 CPUs do not have to be on the same platform. The system is totally portable and can run on several different architectures at once. In addition, the system can easily scale up to 100 or more CPUS. This will allow for much higher resolution and significant increases in input data. The system scales linearly as the number of observations and the number of grid points. The cost overhead in going from 1 to 32 CPUs is 18%. In addition, the analysis results are identical regardless of the number of processors used. This system has all the characteristics of optimal interpolation, combining detailed instrument and first guess error statistics to produce the best estimate of the atmospheric state. Static tests with a 2 X 2.5 resolution version of this system showed it's analysis increments are comparable to the latest NASA operational system including maintenance of mass-wind balance. Results from several months of cycling test in the Goddard EOS Data Assimilation System (GEOS DAS) show this new analysis retains the same level of agreement between the first guess and observations (O-F statistics) as the current operational system.

Stobie, J.↗

An Efficient Objective Analysis System for Parallel Computers

A new objective analysis system designed for parallel computers will be described. The system can produce a global analysis (on a 2 x 2.5 lat-lon grid with 20 levels of heights and winds and 10 levels of moisture) using 120,000 observations in less than 3 minutes on 32 CPUs (SGI Origin 2000). No special parallel code is needed (e.g. MPI or multitasking) and the 32 CPUs do not have to be on the same platform. The system Ls totally portable and can run on -several different architectures at once. In addition, the system can easily scale up to 100 or more CPUS. This will allow for much higher resolution and significant increases in input data. The system scales linearly as the number of observations and the number of grid points. The cost overhead in going from I to 32 CPus is 18%. in addition, the analysis results are identical regardless of the number of processors used. T'his system has all the characteristics of optimal interpolation, combining detailed instrument and first guess error statistics to produce the best estimate of the atmospheric state. It also includes a new quality control (buddy check) system. Static tests with the system showed it's analysis increments are comparable to the latest NASA operational system including maintenance of mass-wind balance. Results from a 2-month cycling test in the Goddard EOS Data Assimilation System (GEOS DAS) show this new analysis retains the same level of agreement between the first guess and observations (0-F statistics) throughout the entire two months.

Stobie, James G.↗

GOES-R Active Vibration Damping Controller Design, Implementation, and On-Orbit Performance

GOES-R series spacecraft feature a number of flexible appendages with modal frequencies below 3.0 Hz which, if excited by spacecraft disturbances, can be sources of undesirable jitter perturbing spacecraft pointing. In order to meet GOES-R pointing stability requirements, the spacecraft flight software implements an Active Vibration Damping (AVD) rate control law which acts in parallel with the nadir point attitude control law. The AVD controller commands spacecraft reaction wheel actuators based upon Inertial Measurement Unit (IMU) inputs to provide additional damping for spacecraft structural modes below 3.0 Hz which vary with solar wing angle. A GOES-R spacecraft dynamics and attitude control system identified model is constructed from pseudo-random reaction wheel torque commands and IMU angular rate response measurements occurring over a single orbit during spacecraft post-deployment activities. The identified Fourier model is computed on the ground, uplinked to the spacecraft flight computer, and the AVD controller filter coefficients are periodically computed on-board from the Fourier model. Consequently, the AVD controller formulation is based not upon pre-launch simulation model estimates but upon on-orbit nadir point attitude control and time-varying spacecraft dynamics. GOES-R high-fidelity time domain simulation results herein demonstrate the accuracy of the AVD identified Fourier model relative to the pre-launch spacecraft dynamics and control truth model. The AVD controller on-board the GOES-16 spacecraft achieves more than a ten-fold increase in structural mode damping of the fundamental solar wing mode while maintaining controller stability margins and ensuring that the nadir point attitude control bandwidth does not fall below 0.02 Hz. On-orbit GOES-16 spacecraft appendage modal frequencies and damping ratios are quantified based upon the AVD system identification, and the increase in modal damping provided by the AVD controller for each structural mode is presented. The GOES-16 spacecraft AVD controller frequency domain stability margins and nadir point attitude control bandwidth are presented along with on-orbit time domain disturbance response performance.

Active Vibration Damping↗

Parallel-in-time quantum simulation via Page and Wootters quantum time

In the past few decades, researchers have created a veritable zoo of quantum algorithms by drawing inspiration from classical computing, information theory, and even from physical phenomena. Here, we present quantum algorithms for parallel-in-time simulations that are inspired by the Page and Wootters formalism. In this framework, and thus in our algorithms, the classical time variable of quantum mechanics is promoted to the quantum realm by introducing a Hilbert space of “clock” qubits that are then entangled with the “system” qubits. We show that our algorithms can compute temporal properties over 𝑁 different times of many-body systems by only using log⁡(𝑁) clock qubits. As such, we achieve an exponential trade-off between time and spatial complexities. In addition, we rigorously prove that the entanglement created between the system qubits and the clock qubits has operational meaning, as it encodes valuable information about the system’s dynamics. We also provide a circuit depth estimation of all the protocols, showing a running time advantage in computation times over traditional sequential-in-time algorithms. In particular, for the case when the dynamics are determined by the Aubry-Andre model, we present a hybrid method for which our algorithms have a depth that only scales as 𝒪⁡(log⁡(𝑁)⁢𝑛). As a by-product, we can relate the previous schemes to the problem of equilibration of an isolated quantum system, thus indicating that our framework enables a new dimension for studying dynamical properties of many-body systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Definition of International GPM GV Research Program

The Global Precipitation Measurement (GPM) Mission will consist of a constellation of rain-measuring satellites, the main member of which (the core satellite) will serve as the measurement reference to the other members of the constellation. The core satellite is being developed jointly by the National Aeronautics and Space Administration (NASA) and the newly-named Japan Aerospace Exploration Agency (JAXA -- previously NASDA) along with its government partner, the Communications Research Laboratory (CRL). The GPM mission was proposed as a follow-up mission to the Tropical Rainfall Measuring Mission (TRMM) by both NASA and NASDA based on the unparalleled scientific success of TRMM, and has recently been joined by the European Space Agency (ESA) via its formulation of the European GPM mission (i.e., EGPM). GPM is an ambitious mission designed to produce accurate and frequent global observations of precipitation (both rain and snow) made possible by replacing the TRMM satellite with the new core satellite carrying an advanced radar-radiometer system, and serving as the centerpiece for the constellation of some eight (8) additional satellites being provided through international cooperation. The core satellite is to be flown up to high latitudes (inclined some 65-70 degrees), and will carry a Ku/Ka-band, nadir-scanning, dual-frequency precipitation radar (DPR) that is being developed by JAXA and CRL, along with a large aperture, extended frequency-range, conically-scanning passive microwave radiometer being developed by NASA and its industrial partners. Each constellation satellite will also carry some type of multi-channel passive microwave radiometer (as well as a multi-beam Ka-band radar in the case of EGPM) whose rain estimates will be calibrated and referenced to those made by the core satellite, producing for the first time fully-global, continuous, and bias-free precipitation datasets. GPM data will be delivered in near-realtime, taking a major step toward the operational use of precipitation information for model initialization and data assimilation in a number of application areas such as hazardous weather forecasting, flood warning, fresh water resource assessment, and crop growth prediction. In addition, GPM data will complement the now-existing global temperature record, allowing for improved assessments of climate change, particularly those processes in which the global water cycle both forces and responds to climatic drifts in global temperature conditions. A foremost element of this international constellation mission is a parallel international ground validation (GV) network. This GV network is needed to determine uncertainties in the rain retrievals, critical for application of the retrieval information in weather and hydrometeorological modeling and climate diagnostics, as well as assurances that the satellite retrievals of surface rainfall are consistent with those actually measured at the surface. The key aspects of this network is that it must be worldwide and created through the GPM partnership process. Therefore the network will consist of a confederation of government agencies, academic organizations, private institutions, and individual scientists from a collection of nations who have initiated the process by gathering in Abingdon to develop the fundamentals of the international GPM GV research programme. Therefore in keeping with our responsibilities as the front-runners of the programme, the main objectives of this workshop are: (1) to present and share opinions on interests, perspectives, and concerns about GPM GV research; (2) to examine the conceptual and/or planned GPM GV site templates from NASA, NASDA, ESA, and other partners; (3) to define the main scientific objectives of the international GPM GV research programme; (4) to formulate a preliminary set of international GPM GV science and measurement requirements; and (5) to convene a Steering Committee to aid the organization of the GPM GV program, to document its science implementation plans, and to aid planning for follow-up GPM GV meetings.

Smith, Eric A.↗

Evaluation of the Terminal Area Precision Scheduling and Spacing System for Performance-Based Navigation Arrivals

The growth of global demand for air transportation has put increasing strain on the nation's air traffic management system. To relieve this strain, the International Civil Aviation Organization has urged all nations to adopt Performance-Based Navigation (PBN), which can help to reduce air traffic congestion, decrease aviation fuel consumption, and protect the environment. NASA has developed a Terminal Area Precision Scheduling and Spacing (TAPSS) system that can support increased use of PBN during periods of high traffic, while supporting fuel-efficient, continuous descent approaches. In the original development of this system, arrival aircraft are assigned fuel-efficient Area Navigation (RNAV) Standard Terminal Arrival Routes before their initial descent from cruise, with routing defined to a specific runway. The system also determines precise schedules for these aircraft that facilitate continuous descent through the assigned routes. To meet these schedules, controllers are given a set of advisory tools to precisely control aircraft. The TAPSS system has been evaluated in a series of human-in-the-loop (HITL) air traffic simulations during 2010 and 2011. Results indicated increased airport arrival throughput up to 10 over current operations, and maintained fuel-efficient aircraft decent profiles from the initial descent to landing with reduced controller workload. This paper focuses on results from a joint NASA and FAA HITL simulation conducted in 2012. Due to the FAA rollout of the advance terminal area PBN procedures at mid-sized airports first, the TAPSS system was modified to manage arrival aircraft as they entered Terminal Radar Approach Control (TRACON). Dallas-Love Field airport (DAL) was selected by the FAA as a representative mid-sized airport within a constrained TRACON airspace due to the close proximity of a major airport, in this case Dallas-Ft Worth International Airport, one of the busiest in the world. To address this constraint, RNAV routes and Required Navigation Performance with the particular capability known as Radius-to-Fix (RNP-RF) approaches to a short final were used. The purpose of this simulation was to get feedback on how current operations could benefit with the TAPSS system and also to evaluate the efficacy of the advisory tools to support the broader use of PBN in the US National Airspace System. For this NASA-FAA joint experiment, an Air Traffic Control laboratory at NASA Ames was arranged to simulate arrivals into DAL in Instrument Meteorological Conditions utilizing parallel dependent approaches, with two feeder positions that handed off traffic to one final position. Four FAA controllers participated, alternately covering these three positions. All participants were Full-Performance Level terminal controllers and members of the National Air Traffic Controllers Association. During the simulation, PBN arrival operations were compared and contrasted in three conditions. They were the Baseline, where none of the TAPSS systems TRACON controller decision support advisories were provided, the Limited Advisories, reflecting the existing but dormant capabilities of the current terminal automation equipment with providing a subset of the TAPSS systems advisories; numerical delay, landing sequence, and runway assignment information, and the Full Advisories, with providing the following in addition to the ones in the Limited condition; trajectory slot markers, timelines of estimated times of arrivals and sched

Performance based navigation↗

Radiative magnetized thermal conduction fronts

The evolution of plane-parallel magnetized thermal conduction fronts in the interstellar medium (ISM) was studied. Separating the coronal ISM phase and interstellar clouds, these fronts have been thought to be the site of the intermediate-temperature regions whose presence was inferred from O VI absorption-line studies. The front evolution was followed numerically, starting from the initial discontinuous temperature distribution between the hot and cold medium, and ending in the final cooling stage of the hot medium. It was found that, for the typical ISM pressure of 4000 K/cu cm and the hot medium temperature of 10 to the 6th K, the transition from evaporation to condensation in a nonmagnetized front occurs when the front thickness is 15 pc. This thickness is a factor of 5 smaller than previously estimated. The O VI column densities in both evaporative and condensation stages agree with observations if the initial hot medium temperature Th exceeds 750,000 K. Condensing conduction fronts give better agreement with observed O VI line profiles because of lower gas temperatures.

Borkowski, Kazimierz J.↗

Spinning Spacecraft Attitude Estimation Using Markley Variables: Filter Implementation And Results

Attitude estimation is often more difficult for spinning spacecraft than for three-axis stabilized platforms due to the need to follow rapidly-varying state vector elements and the lack of three-axis rate measurements from gyros. The estimation problem simplifies when torques are negligible and nutation has damped out, but the general case requires a sequential filter with dynamics propagation. This paper describes the implementation and test results for an extended Kalman filter for spinning spacecraft attitude and rate estimation based on a novel set of variables suggested in a paper by Markley [AAS93-3301 (referred to hereafter as Markley variables). Markley has demonstrated that the new set of variables provides a superior parameterization for numerical integration of the attitude dynamics for spinning or momentum-biased spacecraft. The advantage is that the Markley variables have fewer rapidly-varying elements than other representations such as the attitude quaternion and rate vector. A filter based on these variables was expected to show improved performance due to the more accurate numerical state propagation. However, for a variety of test cases, it has been found that the new filter, as currently implemented, does not perform significantly better than a quaternion-based filter that was developed and tested in parallel. This paper reviews the mathematical background for a filter based on Markley variables. It also describes some features of the implementation and presents test results. The test cases are based on a mission using magnetometer and Sun sensor data and gyro measurements on two axes normal to the spin axis. The orbit and attitude scenarios and spacecraft parameters are modeled after one of the THEMIS (Time History of Events and Macroscale Interactions during Substorms) probes. Several tests are presented that demonstrate the filter accuracy and convergence properties. The tests include torque-free motion with various nutation angles, large constant-torque attitude slews, sensor misalignments, large initial attitude and rate errors, and cases with low data frequency. It is found that the convergence is rapid, the radius of convergence is large, and the results are reasonably accurate even in the presence of unmodeled perturbations.

Sedlak, Joseph E.↗