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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 181 records · Page 10

Dynamics and control of a continuum model for a solar power system

An approach for modeling dynamic equations of motion of a plate attached with rigid bodies is presented. The equations of motion are developed using the principle of virtual work. Lagrange multipliers are used as interaction forces and/or moments to maintain prescribed constraints which is the basis of the interconnection between the plate and rigid bodies. The overall approach is unique in the sense that a continuous model described by a family of partial differential equations is established. An approximate formulation by using variational method is established yielding a solution compatible with the assumed degree of approximation. The formulation is useful particularly when parametric study of dynamic response for a satellite power system is desired. As an example, an approximate governing equation of algebraic eigenvalue problem is given for a dual microwave power transmission system. Controller design is discussed.

Juang, J. N.↗

Advanced Algorithms and High-Performance Testbed for Large-Scale Site Characterization and Subsurface Target Detecting Using Airborne Ground Penetrating SAR

A team of US Army Corps of Engineers, Omaha District and Engineering and Support Center, Huntsville, let Propulsion Laboratory (JPL), Stanford Research Institute (SRI), and Montgomery Watson is currently in the process of planning and conducting the largest ever survey at the Former Buckley Field (60,000 acres), in Colorado, by using SRI airborne, ground penetrating, Synthetic Aperture Radar (SAR). The purpose of this survey is the detection of surface and subsurface Unexploded Ordnance (UXO) and in a broader sense the site characterization for identification of contaminated as well as clear areas. In preparation for such a large-scale survey, JPL has been developing advanced algorithms and a high-performance restbed for processing of massive amount of expected SAR data from this site. Two key requirements of this project are the accuracy (in terms of UXO detection) and speed of SAR data processing. The first key feature of this testbed is a large degree of automation and a minimum degree of the need for human perception in the processing to achieve an acceptable processing rate of several hundred acres per day. For accurate UXO detection, novel algorithms have been developed and implemented. These algorithms analyze dual polarized (HH and VV) SAR data. They are based on the correlation of HH and VV SAR data and involve a rather large set of parameters for accurate detection of UXO. For each specific site, this set of parameters can be optimized by using ground truth data (i.e., known surface and subsurface UXOs). In this paper, we discuss these algorithms and their successful application for detection of surface and subsurface anti-tank mines by using a data set from Yuma proving Ground, A7, acquired by SRI SAR.

Fijany, Amir↗

Carbon and Oxygen Isotope Measurements of Ordinary Chondrite (OC) Meteorites from Antarctica Indicate Distinct Carbonate Species Using a Stepped Acid Extraction Procedure

The purpose of this study is to characterize the stable isotope values of terrestrial, secondary carbonate minerals from five Ordinary Chondrite (OC) meteorites collected in Antarctica. These samples were identified and requested from NASA based upon their size, alteration history, and collection proximity to known Martian meteorites. They are also assumed to be carbonate-free before falling to Earth. This research addresses two questions involving Mars carbonates: 1) characterize terrestrial, secondary carbonate isotope values to apply to Martian meteorites for isolating in-situ carbonates, and 2) increase understanding of carbonates formed in cold and arid environments with Antarctica as an analog for Mars. Two samples from each meteorite, each approximately 0.5 grams, were crushed and dissolved in pure phosphoric acid for 3 sequential reactions: a) R times 0 for 1 hour at 30 degrees Centigrade (fine calcite extraction), b) R times 1 for 18 hours at 30 degrees Centigrade (course calcite extraction), and c) R times 2 for 3 hours at 150 degrees Centigrade (siderite and/or magnesite extraction). CO (sub 2) was distilled by freezing with liquid nitrogen from each sample tube, then separated from organics and sulfides with a TRACE GC using a Restek HayeSep Q 80/100 6 foot 2 millimeter stainless column, and then analyzed on a Thermo MAT 253 Isotope Ratio Mass Spectrometer (IRMS) in Dual Inlet mode. This system was built at NASA/JSC over the past 3 years and proof-tested with known carbonate standards to develop procedures, assess yield, and quantify expected error bands. Two distinct species of carbonates are found: 1) calcite, and 2) non-calcite carbonate (future testing will attempt to differentiate siderite from magnesite). Preliminary results indicate the terrestrial carbonates are formed at approximately sigma (sup 13) C equal to plus 5 per mille, which is consistent with atmospheric CO (sub 2) sigma (sup 13) C equal to minus 7 per mille and fractionation of plus12 per mille based upon polar temperature of -20 degrees Centigrade. The oxygen values fractionate sigma (sup 18) O equal to minus 10-20 per mille lighter between the R times 0 and R times 1 reactions at 30 degrees Centigrade. The carbonate oxygen isotope measurements are consistently heavier than expected with meteoric water and temperatures from Antarctica, perhaps due to secondary carbonate formation during curation in Houston, TX.

Evans, Michael E.↗

The timbre of Hawking gravitons: an effective description of energy transport from holography

Planar black holes in AdS, which are holographically dual to compressible relativistic fluids, have a long-lived phonon mode that captures the physics of attenuated sound propagation and transports energy in the plasma. We describe the open effective field theory of this fluctuating phonon degree of freedom. The dynamics of the phonon is encoded in a single scalar field whose gravitational coupling has non-trivial spatial momentum dependence. This description fits neatly into the paradigm of classifying gravitational modes by their Markovianity index, depending on whether they are long-lived. The sound scalar is a non-Markovian field with index 3 - d for a d-dimensional fluid. We reproduce (and extend) the dispersion relation of the holographic sound mode to quartic order in derivatives, constructing in the process the effective field theory governing its attenuated dynamics and associated stochastic fluctuations. We also remark on the presence of additional spatially homogeneous zero modes in the gravitational problem, which remain disconnected from the phonon Goldstone mode.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Optimizing Orbit-Instrument Configuration for Global Precipitation Mission (GPM) Satellite Fleet

Following the scientific success of the Tropical Rainfall Measuring Mission (TRMM) spearheaded by a group of NASA and NASDA scientists, their external scientific collaborators, and additional investigators within the European Union's TRMM Research Program (EUROTRMM), there has been substantial progress towards the development of a new internationally organized, global scale, and satellite-based precipitation measuring mission. The highlights of this newly developing mission are a greatly expanded scope of measuring capability and a more diversified set of science objectives. The mission is called the Global Precipitation Mission (GPM). Notionally, GPM will be a constellation-type mission involving a fleet of nine satellites. In this fleet, one member is referred to as the "core" spacecraft flown in an approximately 70 degree inclined non-sun-synchronous orbit, somewhat similar to TRMM in that it carries both a multi-channel polarized passive microwave radiometer (PMW) and a radar system, but in this case it will be a dual frequency Ku-Ka band radar system enabling explicit measurements of microphysical DSD properties. The remainder of fleet members are eight orbit-synchronized, sun-synchronous "constellation" spacecraft each carrying some type of multi-channel PMW radiometer, enabling no worse than 3-hour diurnal sampling over the entire globe. In this configuration the "core" spacecraft serves as a high quality reference platform for training and calibrating the PMW rain retrieval algorithms used with the "constellation" radiometers. Within NASA, GPM has advanced to the pre-formulation phase which has enabled the initiation of a set of science and technology studies which will help lead to the final mission design some time in the 2003 period. This presentation first provides an overview of the notional GPM program and mission design, including its organizational and programmatic concepts, scientific agenda, expected instrument package, and basic flight architecture. Following this introduction, we focus specifically on the last topic, that being an analysis which leads to an optimal flight architecture dictated in part by science requirements but constrained by allowable orbital mechanics, instrument scan patterns, and antenna aperture properties. Because the optimal architecture involves an interplay between orbit mechanics and instrument specifications, it is important to recognize that in attempting to serve various scientific themes, the final optimal architecture will represent a compromise concerning dynamic range, spatial resolution, sampling interval, pointing, beam coincidence, and measurement uncertainty. Moreover, cost becomes a major factor in seeking the optimal architecture through the pathways of antenna and instrument scan designs, as well as propulsion requirements associated with the orbit heights of various "constellation" members. Although the results presented at the IGARSS-2001 meeting will likely not be the fully refined flight architecture specifications, they are expected to be nearly complete.

Smith, Eric A.↗

The Magnetospheric Multiscale Missions Fast Plasma Investigations Dual Electron Spectrometer Development

The Magnetospheric Multiscale mission (MMS) is designed to examine magnetic reconnection that occurs on both the Earths dayside magnetopause and in the magnetotail region on Earths night side. In order to resolve fine structures of the three dimensional electron distributions in both regions, the Fast Plasma Investigation's (FPI) Dual Electron Spectrometer (DES) is designed to measure electron distributions with a time resolution of 30 ms. In order to achieve this unprecedented sampling rate, the DES will have eight individual spectrometers each sampling 180 x 45 degree sections of the sky. Because of the field of view limitations of top hat analyzers, each spectrometer will use electro-static deflectors to change its look direction. The engineering model of the DES has been fabricated and tested. We will present the results of measurements for fields of view, angular FVVHM responses, dE/E, analyzer constant, and geometric factors for all deflection states. We will compare these results to simulation results and discuss causes of the response variations.

Shappirio, M.↗

Shocks, superconvergence, and a stringy equivalence principle

We study propagation of a probe particle through a series of closely situated gravitational shocks. We argue that in any UV-complete theory of gravity the result does not depend on the shock ordering — in other words, coincident gravitational shocks commute. Shock commutativity leads to nontrivial constraints on low-energy effective theories. In particular, it excludes non-minimal gravitational couplings unless extra degrees of freedom are judiciously added. In flat space, these constraints are encoded in the vanishing of a certain “superconvergence sum rule.” In AdS, shock commutativity becomes the statement that average null energy (ANEC) operators commute in the dual CFT. We prove commutativity of ANEC operators in any unitary CFT and establish sufficient conditions for commutativity of more general light-ray operators. Superconvergence sum rules on CFT data can be obtained by inserting complete sets of states between light-ray operators.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Impact of low reactivity fuel type on low load combustion, emissions, and cyclic variations of diesel-ignited dual fuel combustion

In this study, cyclic variations in dual fuel combustion with diesel ignition of three different low reactivity fuels (methane, propane, and gasoline) are examined under identical operating conditions. Experiments were performed on a single cylinder research engine (SCRE) at a low load of 3.3 bar brake mean effective pressure (BMEP). The start of injection (SOI) of diesel was varied from 280 to 330 absolute crank angle degrees (CAD). Engine speed, rail pressure, and boost pressure were held constant at 1500 rpm, 500 bar, and 1.5 bar, respectively. The energy substituted by the low reactivity fuel was fixed at 80% of the total energy input. It was found that diesel-methane (DM) and diesel-propane (DP) combustion were affected by diesel mixing to a greater extent than diesel-gasoline (DG) combustion due to the higher reactivity of gasoline. The magnitude of low temperature heat release was greatest for DG combustion followed by DM and DP combustion for all SOIs. The ignition delay for DG combustion was the shortest, followed by DM and DP combustion. DM and DP combustion exhibited more cyclic variations than DG combustion. Cyclic variations decreased for DM and DP combustion when SOI was advanced; however, DG combustion cyclic variations remained essentially constant for all SOIs. Earlier SOIs (280, 290, 300, and 310 CAD) for DM and (280, 290, and 300 CAD) for DP combustion indicated some prior-cycle effects on the combustion and IMEP (i.e. some level of determinism).

Engineering↗

High‐Entropy Lithium Argyrodite Solid Electrolytes Enabling Stable All‐Solid‐State Batteries

Abstract Superionic solid electrolytes (SEs) are essential for bulk‐type solid‐state battery (SSB) applications. Multicomponent SEs are recently attracting attention for their favorable charge‐transport properties, however a thorough understanding of how configurational entropy (ΔS conf ) affects ionic conductivity is lacking. Here, we successfully synthesized a series of halogen‐rich lithium argyrodites with the general formula Li 5.5 PS 4.5 Cl x Br 1.5‐x (0≤x≤1.5). Using neutron powder diffraction and 31 P magic‐angle spinning nuclear magnetic resonance spectroscopy, the S 2− /Cl − /Br − occupancy on the anion sublattice was quantitatively analyzed. We show that disorder positively affects Li‐ion dynamics, leading to a room‐temperature ionic conductivity of 22.7 mS cm −1 (9.6 mS cm −1 in cold‐pressed state) for Li 5.5 PS 4.5 Cl 0.8 Br 0.7 (ΔS conf =1.98R). To the best of our knowledge, this is the first experimental evidence that configurational entropy of the anion sublattice correlates with ion mobility. Our results indicate the possibility of improving ionic conductivity in ceramic ion conductors by tailoring the degree of compositional complexity. Moreover, the Li 5.5 PS 4.5 Cl 0.8 Br 0.7 SE allowed for stable cycling of single‐crystal LiNi 0.9 Co 0.06 Mn 0.04 O 2 (s‐NCM90) composite cathodes in SSB cells, emphasizing that dual‐substituted lithium argyrodites hold great promise in enabling high‐performance electrochemical energy storage.

Chemistry↗

Limited proteolysis of pea protein to promote aggregation/gelation: role of enzyme concentration and molecular characteristics

Limited proteolysis promotes aggregation/gelation of plant proteins, but its relationship with the molecular characteristics of hydrolysates remains poorly understood. In here, response surface methodology was employed to evaluate the effects of protein concentration, Alcalase level, and hydrolysis time on the storage modulus (G′) of pea protein hydrolysates (PPH). 7.5% protein, 1.65% Alcalase, and a 6-min reaction time resulted in the highest relative increase in G′ upon heating PPH, whereas both higher (3.55%) and lower (0.3%) Alcalase levels led to less increment. Increasing the Alcalase level increased the degree of hydrolysis while decreasing the molecular weight, surface hydrophobicity, and total sulfhydryl and disulfide bond contents of PPH. Confocal laser scanning microscopy and X-ray scattering analyses found PPH produced with 1.65% Alcalase formed interconnected aggregates with dual structural domains, but not at other Alcalase conditions. These results demonstrate the role of controlled proteolysis in governing the aggregation/gelation behavior of PPH.

X-ray scattering↗

Phase diagram and spectroscopic signatures of a supersolid in the quantum ising magnet K 2 Co(SeO 3 ) 2

Supersolid phases are quantum-entangled states of matter exhibiting the dual characteristics of superfluidity and solidity. Theory predicts that hard-core bosons on a triangular lattice can form such phases at half filling and near complete filling. Leveraging an exact mapping between bosons and spin-$\frac{1}{2}$ degrees of freedom, here we show that these phases are realized in the triangular-lattice antiferromagnet K 2 Co(SeO 3 ) 2 . At zero field, neutron diffraction reveals the development of quasi-two-dimensional $\sqrt3$ x $\sqrt3$ magnetic order with Z 3 translational symmetry breaking (solidity), though with reduced amplitude indicating strong quantum fluctuations. These fluctuations manifest as equidistant bands of continuum neutron scattering, where the lowest-energy mode is gapless at K ($\frac{1}{3}$ $\frac{1}{3}$), consistent with broken U(1) spin rotational symmetry (superfluidity). For c-axis-oriented magnetic fields near saturation, we find a second phase consistent with a high-field supersolid. These two supersolids are separated by a pronounced 1/3 magnetization plateau phase that supports coherent spin waves, from which we determine the underlying spin Hamiltonian.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

The FRB-searching Pipeline of the Tianlai Cylinder Pathfinder Array

This paper presents the design, calibration, and survey strategy of the Fast Radio Burst (FRB) digital backend and its real-time data processing pipeline employed in the Tianlai Cylinder Pathfinder Array. The array, consisting of three parallel cylindrical reflectors and equipped with 96 dual-polarization feeds, is a radio interferometer array designed for conducting drift scans of the northern celestial semi-sphere. The FRB digital backend enables the formation of 96 digital beams, effectively covering an area of approximately 40 square degrees with the 3 dB beam. Our pipeline demonstrates the capability to conduct an automatic search of FRBs, detecting at quasi-real-time and classifying FRB candidates automatically. The current FRB searching pipeline has an overall recall rate of 88%. During the commissioning phase, we successfully detected signals emitted by four well-known pulsars: PSR B0329+54, B2021+51, B0823+26, and B2020+28. We report the first discovery of an FRB by our array, designated as FRB 20220414A. We also investigate the optimal arrangement for the digitally formed beams to achieve maximum detection rate by numerical simulation.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Quadratic strong coupling in AlN Kerr cavity solitons

Photonic platforms with χ (2) nonlinearity offer new degrees of freedom for Kerr frequency comb development. Here, we demonstrate Kerr soliton generation at 1550 nm with phase-matched quadratic coupling to the 775 nm harmonic band in a single AlN microring and thus the formation of dual-band mode-locked combs. In the strong quadratic coupling regime where the χ (2) phase-matching window overlaps the pump mode, the pump-to-harmonic-comb conversion efficiency is optimized. However, the strong quadratic coupling also drastically modifies the Kerr comb generation dynamics and decreases the probability of soliton generation. By engineering the χ (2) phase-matching wavelength, we are able to achieve a balance between high conversion efficiency and high soliton formation rate under the available pump power and microring quality factors. Our numerical simulations confirm the experimental observations. These findings provide guidance on tailoring single-cavity dual-band coherent comb sources.

Gong, Zheng (ORCID:0000000301704870)↗

Experimental analyses of trailing edge flows

An experimental study of several of the trailing edge and wake turbulence properties for a NACA 64A010 airfoil section was completed. The experiment was conducted at the Ohio State University Aeronautical and Astronautical Research Laboratory in the 6 inch X 22 inch transonic wind tunnel facility. The data were obtained at a free stream Mach number of 0.80 and a flow Reynolds number (based on chord length) of 5 million. The principle diagnostic tool was a dual-component laser Doppler velocimeter. The experimental data included surface static pressures, chordwise and vertical mean velocities, RMS turbulence intensities, local flow angles, and a determination of turbulence kinetic energy in the wake. Two angles of attack (0 and 2 degrees) were investigated. At these incidence angles, four flow field surveys were obtained ranging in position from the surface of the airfoil, between the transonic shock and the trailing edge, to the far-wake. At both angles of attack, the turbulence intensities and turbulence kinetic energy were observed to decay in the streamwise direction. In the far wake, for the non-lifting case, the turbulence intensities were nearly isotropic. For the two degree case, the horizontal component of the turbulence intensity was observed to be substantially higher than the vertical component.

Petrie, S. L.↗

GPM Mission Overview

The Global Precipitation Measurement (GPM) Mission is an international satellite mission to unify and advance precipitation measurements from a constellation of research and operational sensors to provide "next-generation" precipitation products. Relative to current global rainfall products, GPM data products will be characterized by: (1) more accurate instantaneous precipitation measurements (especially for light rain and cold-season solid/snow precipitation), (2) more frequent sampling by an expanded constellation of microwave radiometers that include operational humidity sounders over land, (3) inter-calibrated microwave brightness temperatures from constellation radiometers within a unified framework, and (4) physical-based precipitation retrievals from constellation radiometers using a common a priori cloud hydrometeor database derived from GPM Core sensor measurements. The cornerstone of the GPM mission is the deployment of a Core Observatory in a unique 65 degree non-Sun-synchronous orbit to serve as a physics observatory and a calibration reference to improve precipitation measurements by a constellation of dedicated and operational passive microwave sensors. The Core Observatory will carry a KulKa-band Dual-frequency Precipitation Radar (DPR) and a multi-channel (10-183 GHz) GPM Microwave Radiometer (GMI). The combined use ofDPR and GMI measurements will place greater constraints on possible solutions to radiometer retrievals to improve the accuracy and consistency of precipitation retrievals from all constellation radiometers. As a science mission with integrated application goals, GPM is designed to (1) advance precipitation measurement capability from space through combined use of active and passive microwave sensors, (2) advance the knowledge of the global water/energy cycle and freshwater availability through better description of the space-time variability of global precipitation, and (3) improve weather, climate, and hydrological prediction capabilities through more accurate and frequent measurements of instantaneous precipitation rates and time-integrated rainfall accumulation. An overview of the GPM mission concept and science activities in the United States, together with an update on international collaborations in radiometer intercalibration and ground validation, will be presented.

Hou, Arthur Y.↗

Transition Modeling Based on the Dual N-factor Method for the CRM-NLF Wind Tunnel Configuration

The dual N-factor method is used to model the boundary-layer transition over the common research model with natural laminar flow (CRM-NLF) aircraft configuration. The flow conditions match selected test conditions from a wind tunnel experiment in the National Transonic Facility at the NASA Langley Research Center. The paper presents a systematic methodology for transition prediction in the presence of a dual shock system and extends the prior capability for iteratively coupled computational fluid dynamics (CFD) predictions to incorporate three-dimensional, transonic wings. The method employs stability computations based on the linear parabolized stability equations (PSE), along with a dual N-factor criterion. The iterative process begins with the fully turbulent Reynolds-averaged-Navier-Stokes (RANS) mean flow solution. For the first iteration, a mean flow solution is calculated with an imposed transition front that aligns with the shock front from the fully turbulent solution. Subsequently, stability computations are performed along a set of streamlines across the wing to calculate the amplification of planar Tollmien-Schlichting (TS) and stationary crossflow (CF) modes. The transition criterion based on the dual N-factor method is used to infer the updated transition front and the process is successively repeated until convergence of the solution. Within three iterations, the predicted fronts for angles of attack of 1.45, 1.98, 2.46 and 2.94 degrees and a mean-aerodynamic-chord Reynolds number equal to 15 million, approach visual convergence in most regions of the studied cases, and the resulting predictions are in good agreement with the transition fronts deduced from measurements of temperature-sensitive paint. Even though surface pressure measurements based on fully-turbulent flow agree well with the measured pressure coefficient distributions, strong viscous-inviscid interaction effects cause significant shifts in the shock locations based on the imposed transition front, underscoring the intrusive nature of static pressure measurements using surface mounted ports on the CRM-NLF configuration.

Boundary Layer Transition↗

fcc lattice, checkerboards, fractons, and quantum field theory

In this work, we consider XY-spin degrees of freedom on an FCC lattice, such that the system respects some subsystem global symmetry. We then gauge this global symmetry and study the corresponding $U(1)$ gauge theory on the FCC lattice. Surprisingly, this $U(1)$ gauge theory is dual to the original spin system. We also analyze a similar $\mathbb{Z}_N$ gauge theory on that lattice. All these systems are fractonic. The $U(1)$ theories are gapless and the $\mathbb{Z}_N$ theories are gapped. We analyze the continuum limits of all these systems and present free continuum Lagrangians for their low-energy physics. Our $\mathbb{Z}_2$ FCC gauge theory is the continuum limit of the well known checkerboard model of fractons. Our continuum analysis leads to a straightforward proof of the known fact that this theory is dual to two copies of the $\mathbb{Z}_2$ X-cube model. We find new models and new relations between known models. The $\mathbb{Z}_N$ FCC gauge theory can be realized by coupling three copies of an anisotropic model of lineons and planons to a certain exotic $\mathbb{Z}_2$ gauge theory. Also, although for $N=2$ this model is dual to two copies of the $\mathbb{Z}_2$ X-cube model, a similar statement is not true for higher $N$.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Dual-Use Aspects of System Health Management

System Health Management functionality is an essential part of any space launch system. Health management functionality is an integral part of mission reliability, since it is needed to verify the reliability before the mission starts. Health Management is also a key factor in life cycle cost reduction and in increasing system availability. The degree of coverage needed by the system and the degree of coverage made available at a reasonable cost are critical parameters of a successful design. These problems are not unique to the launch vehicle world. In particular, the Intelligent Vehicle Highway System, commercial aircraft systems, train systems, and many types of industrial production facilities require various degrees of system health management. In all of these applications, too, the designers must balance the benefits and costs of health management in order to optimize costs. The importance of an integrated system is emphasized. That is, we present the case for considering health management as an integral part of system design, rather than functionality to be added on at the end of the design process. The importance of maintaining the system viewpoint is discussed in making hardware and software tradeoffs and in arriving at design decisions. We describe an approach to determine the parameters to be monitored in any system health management application. This approach is based on Design of Experiments (DOE), prototyping, failure modes and effects analyses, cost modeling and discrete event simulation. The various computer-based tools that facilitate the approach are discussed. The approach described originally was used to develop a fault tolerant avionics architecture for launch vehicles that incorporated health management as an integral part of the system. Finally, we discuss generalizing the technique to apply it to other domains. Several illustrations are presented.

Owens, P. R.↗