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Accurate computation and continuation of homoclinic and heteroclinic orbits for singular perturbation problems

In earlier papers, Doedel and the authors have developed a numerical method and derived error estimates for the computation of branches of heteroclinic orbits for a system of autonomous ordinary differential equations in R(exp n). The idea of the method is to reduce a boundary value problem on the real line to a boundary value problem on a finite interval by using a local (linear or higher order) approximation of the stable and unstable manifolds. A practical limitation for the computation of homoclinic and heteroclinic orbits has been the difficulty in obtaining starting orbits. Typically these were obtained from a closed form solution or via a homotopy from a known solution. Here we consider extensions of our algorithm which allow us to obtain starting orbits on the continuation branch in a more systematic way as well as make the continuation algorithm more flexible. In applications, we use the continuation software package AUTO in combination with some initial value software. The examples considered include computation of homoclinic orbits in a singular perturbation problem and in a turbulent fluid boundary layer in the wall region problem.

Vaughan, William W.↗

Continual expansion of the active-region corona observed by the Yohkoh Soft X-ray Telescope

We have found from the observations of the Yohkoh Soft X-ray Telescope (SXT) that the corona above active regions expands occasionally, and almost continually in the cases of 'active' active regions. The key to this discovery has been a movie representation of the Yohkoh SXT data, which, for the first time, provides adequate sampling and continuity for this purpose. The movies show ubiquitous expansions above the active regions, with velocities in the range of a few to a few tens km/s. The expansion appears to preserve the overall structure of the active-region corona. This finding of almost continual expansion of the active-region corona may affect some of the basic ideas concerning active regions, as well as those of the mass-loss from the Sun and Sunlike stars.

Uchida, Yutaka↗

Structural response to discrete and continuous gusts of an airplane having wing bending flexibility and a correlation of calculated and flight results

An analysis is made of the structural response to gusts of an airplane having the degrees of freedom of vertical motion and wing bending flexibility and basic parameters are established. A convenient and accurate numerical solution of the response equations is developed for the case of discrete-gust encounter, an exact solution is made for the simpler case of continuous-sinusoidal-gust encounter, and the procedure is outlined for treating the more realistic condition of continuous random atmospheric turbulence, based on the methods of generalized harmonic analysis. Correlation studies between flight and calculated results are then given to evaluate the influence of wing bending flexibility on the structural response to gusts of two twin-engine transports and one four-engine bomber. It is shown that calculated results obtained by means of a discrete-gust approach reveal the general nature of the flexibility effects and lead to qualitative correlation with flight results. In contrast, calculations by means of the continuous-turbulence approach show good quantitative correlation with flight results and indicate a much greater degree of resolution of the flexibility effects.

Houbolt, John C↗

Pseudomaster equation for the no-count process in a continuous photodetection

The detection of cavity radiation with the detector placed outside the cavity is studied. Each leaked photon has a certain probability of propagating away without being detected. It is viewed as a continuous quantum measurement in which the density matrix is continuously revised according to the readout of the detector. The concept of pseudomaster equation for the no-count process is introduced; its solution leads to the discovery of the superoperator for the same process. It has the potential to become the key equation for continuous measurement process.

Lee, Ching-Tsung↗

Method for Fabricating Composite Structures Including Continuous Press Forming and Pultrusion Processing

A method for fabricating composite structures at a low-cost, moderate-to-high production rate is disclosed. A first embodiment of the method includes employing a continuous press forming fabrication process. A second embodiment of the method includes employing a pultrusion process for obtaining composite structures. The methods include coating yarns with matrix material, weaving the yarn into fabric to produce a continuous fabric supply, and feeding multiple layers of net-shaped fabrics having optimally oriented fibers into a debulking tool to form an undebulked preform. The continuous press forming fabrication process includes partially debulking the preform, cutting the partially debulked preform, and debulking the partially debulked preform to form a netshape. An electron-beam or similar technique then cures the structure. The pultrusion fabric process includes feeding the undebulked preform into a heated die and gradually debulking the undebulked preform. The undebulked preform in the heated die changes dimension until a desired cross-sectional dimension is achieved. This process further includes obtaining a net-shaped infiltrated uncured preform, cutting the uncured preform to a desired length, and electron-beam curing (or similar technique) the uncured preform. These fabrication methods produce superior structures formed at higher production rates, resulting in lower cost and high structural performance.

Farley, Gary L.↗

Prototype development and test results of a continuous ambient air monitoring system for hydrazine at the 10 ppb level

A Hydrazine Vapor Area Monitor (HVAM) system is currently being field tested as a detector for the presence of hydrazine in ambient air. The MDA/Polymetron Hydrazine Analyzer has been incorporated within the HVAM system as the core detector. This analyzer is a three-electrode liquid analyzer typically used in boiler feed water applications. The HVAM system incorporates a dual-phase sample collection/transport method which simultaneously pulls ambient air samples containing hydrazine and a very dilute sulfuric acid solution (0.0001 M) down a length of 1/4 inch outside diameter (OD) tubing from a remote site to the analyzer. The hydrazine-laden dilute acid stream is separated from the air and the pH is adjusted by addition of a dilute caustic solution to a pH greater than 10.2 prior to analysis. Both the dilute acid and caustic used by the HVAM are continuously generated during system operation on an "as needed" basis by mixing a metered amount of concentrated acid/base with dilution water. All of the waste water generated by the analyzer is purified for reuse by Barnstead ion-exchange cartridges so that the entire system minimizes the generation of waste materials. The pumping of all liquid streams and mixing of the caustic solution and dilution water with the incoming sample are done by a single pump motor fitted with the appropriate mix of peristaltic pump heads. The signal to noise (S/N) ratio of the analyzer has been enhanced by adding a stirrer in the MDA liquid cell to provide mixing normally generated by the high liquid flow rate designed by the manufacturer. An onboard microprocessor continuously monitors liquid levels, sample vacuum, and liquid leak sensors, as well as handles communications and other system functions (such as shut down should system malfunctions or errors occur). The overall system response of the HVAM can be automatically checked at regular intervals by measuring the analyzer response to a metered amount of calibration standard injected into the dilute acid stream. The HVAM system provides two measurement ranges (threshold limit value (TLV): 10 to 1000 parts per billion (ppb)/LEAK: 100 ppb to 10 parts per million (ppm)). The LEAK range is created by dilution of the sulfuric acid/hydrazine liquid sample with pure water. This dual range capability permits the analyzer to quantify ambient air samples whose hydrazine concentrations range from 10 ppb to as high as 10 ppm. The laboratory and field prototypes have demonstrated total system response times on the order of 10 to 12 minutes for samples ranging from 10 to 900 ppb in the lLV mode and is greater than 2 minutes for samples ranging from 100 to 1300 ppb in the LEAK mode. Service intervals of over 3 months have been demonstrated for continuous 24 hour/day, 7 day/week usage. The HVAM is made up of a purged cabinet that contains power supplies, RS422 signal transmission capabilities, a UPS, an on-site warning system, and a Line Replaceable Unit (LRU). The LRU includes all of the liquid flow system, the analyzer, the control/data system microprocessor and assorted flow and liquid-level sensors. The LRU is mounted on a track slide system so it can be serviced inplace or totally removed and quickly exchanged with another calibrated unit, thus minimizing analyzer downtime. Once an LRU is removed from an analyzer enclosure, it can be brought to a laboratory facility for complete calibration and periodic maintenance.

Meneghelli, Barry↗

Facility design consideration for continuous mix production of class 1.3 propellant

In November of 1989, NASA awarded the Advanced Solid Rocket Motor (ASRM) contract to Lockheed Missiles and Space Company (LMSC) for production of advanced solid rocket motors using the continuous mix process. Aerojet ASRM division (AAD) was selected as the facility operator and RUST International Corporation provided the engineering, procurement, and construction management services. The continuous mix process mandates that the mix and cast facilities be 'close-coupled' along with the premix facilities, creating unique and challenging requirements for the facility designer. The classical approach to handling energetic materials-division into manageable quantities, segregation, and isolation-was not available due to these process requirements and quantities involved. This paper provides a description of the physical facilities, the continuous mix process, and discusses the monitoring and detection techniques used to mitigate hazards and prevent an incident.

Williamson, K. L.↗

A Snapshot of the Continuous Emission of the Active Galactic Nucleus in NGC 3783 from Gamma-Ray to Radio Wavelengths

To better understand the physical processes that produce the continuous emission in active galactic nuclei (AGN), a snapshot of the overall continuous energy distribution of NGC 3783, from gamma ray to radio wavelengths, has been obtained within the framework of the World Astronomy Days. The data collected in this campaign are from GRO, ROSAT, Voyager 2, IUE, HST, CTIO, SAAO, and the VLA. Great care has been taken in disentangling the genuine AGN continusous emission from other contributions; depending on the waveband, the latter might be (1) unrelated contaminating sources in cases where the instrument field of view is large (2) components within which the AGN is embedded, such as the stellar bulge population which accounts for a significant fraction of the optical continuum, and free-bound and FE2 blends wich contribute to the ultraviolet flux. After correction for these other contributins, the continuous emission of the isolated AGN appears to be rather flat (i.e., approximately equal energy per unit logarithmic frequency) from soft gamma ray to infrared wavelengths. At high energies (0.1 MeV to 0.1 keV), the AGN continuum can be fitted by a power law F nu approaches Nu(exp -a) with a spectral index of alpha approximately 1. At longer wavelengths, two excesses above this power law ('bumps') appear: in the ultraviolet, the classical big blue bump, which can be interpreted as thermal emission from the accretion disc surrounding a massive black hole, and in the infrared, a second bump which can be ascribed to thermal emission from dust in the vicinity of the AGN, heated by ultraviolet radiation from the central source. By fitting accretion-disk models to the observed AGN spectral energy distribution, we find values for the accretion disk innermost temperature, accretion rate, and black hole mass, with some differences that depend on whether or not we extrapolate the high energy power law up to infrared wavelengths. A fit to the IR bump above the extended alpha equals 1 power law suggests the presence of a dust component covering the region from a distance rho approximately equals 80 light days (hot grains at a temperature of approximately equals 1500 K) to rho approximately equals 60 light years (cool grains at T approximately equals 200 K). The total mass of dust is around 60 solar masses.

Alloin, D.↗

Method for Fabricating Composite Structures Using Continuous Press Forming

A method for fabricating composite structures at a low-cost. moderate-to-high production rate. A first embodiment of the method includes employing a continuous press forming fabrication process. A second embodiment of the method includes employing a pultrusion process for obtaining composite structures. The methods include coating yarns with matrix material, weaving the yarn into fabric to produce a continuous fabric supply and feeding multiple layers of net-shaped fabrics having optimally oriented fibers into a debulking tool to form an undebulked preform. The continuous press forming fabrication process includes partially debulking the preform, cutting the partially debulked preform and debulking the partially debulked preform to form a net-shape. An electron-beam or similar technique then cures the structure. The pultrusion fabric process includes feeding the undebulked preform into a heated die and gradually debulking the undebulked preform. The undebulked preform in the heated die changes dimension until a desired cross-sectional dimension is achieved. This process further includes obtaining a net-shaped infiltrated uncured preform, cutting the uncured preform to a desired length and electron-beam curing (or similar technique) the uncured preform. These fabrication methods produce superior structures formed at higher production rates. resulting in lower cost and high structural performance.

Farley, Gary L.↗

Grant Proposal for the Continuation of the Voyager Interstellar Mission: LECP Investigation

This proposal documents the plans of the Low Energy Charged Particle (LECP) investigation team for participation in NASA's Voyager Interstellar Mission (VIM) as the Voyager 1 and 2 spacecraft explore the outer reaches of the heliosphere and search for the termination shock and the heliopause. The proposal covers the four year period from 1 January 1997 to 31 December 2000. The LECP instruments on Voyager 1 and 2 measure in situ intensities of charged particles with energies from about 30 keV to 100 MeV for ions, and about 20 keV to greater than 10 MeV for electrons. The instruments provide detailed spectral, angular, and compositional information about the particles. Composition is available for greater than 200 keV/nuc using multi-parameter measurements. Angular information is obtained by a mechanically scanned platform that rotates at various commanded rates. Measurements of low energy ion and electron intensities versus time and spatial location within the heliosphere contain an abundance of information regarding various transport and acceleration processes on both local (approx. 1 hr, approx. 0.01 AU) and global (approx. 11 yrs, approx. 100 AU) scales. The LECP instruments provide unique observations of such dynamical processes, and we anticipate that it will return critical information regarding the boundaries of the heliosphere. Several recent and exciting discoveries based on LECP measurements emphasize the important role that low energy charged particle distributions play in physical processes in the interplanetary medium. Yet, at the same time, these discoveries also underscore the fact that our understanding of processes in the outer heliosphere is, in most cases, incomplete, and in others, only rudimentary at best. Among the discoveries referred to above are the following: (1) Shocks: Examination of greater than 30 keV ion intensities have revealed: (a) a total absence of acceleration beyond only -100-200 keV at a strong transient shock in May 1991 at 35 AU, despite an enhanced level of seed particles; (b) a large transient shock in September 1991 of global scale, with intensities of shock-accelerated ions greater than or equal to 30 keV to approx. 30 MeV showing complex, highly energy-dependent spatial evolution, and small-scale (approx. few gyroradii), often anisotropic, micro-structures; (c) recurrent intensity increases in greater than or equal to 30 keV to -few MeV ions, with structures that, in some cases, show no correlation with the associated corotating shock. (2) Superthermal ion pressure: A global merged interaction region with a leading shock, downstream of which the superthermal ion (greater than or equal to 30 keV to approx. 4 MeV) pressure is comparable to that of the thermal plasma, and the total particle pressure yields a plasma beta of order unity. (3) Pickup ions: Measurements of the C/O ratio within transient structures at 35-45 AU showing the first clear evidence that transient shocks can pre-accelerate interstellar pickup ions from approx. 1 keV/nuc to at least 1 MeV/nuc. (4) Seed particles: Injection of ions for acceleration to high energies at the termination shock is unlikely to be a problem, since interplanetary transient and recurrent shocks are continually accelerating ions, of solar wind or interstellar origin, to highly superthermal energies. (5) Precursor electrons: Ambient solar electrons (greater than or equal to few tens of keV) that exist in the outer heliosphere ca form a broad precursor, several days wide, that is upstream of the termination shock and potentially observable a few months prior to the shock crossing. (6) Solar wind velocity at Voyager 1: We can use LECP ion data to obtain the solar wind velocity at Voyager 1, enabling us to provide critical measurement of the plasma flow as we approach and encounter the termination shock and other regions (necessary due to the partial failure of the Voyager 1 PLS experiment). The work of the LECP investigator team during the VIM will include: (1) Continuing operations with regard to the receipt, processing, verification, cataloging, display, and distribution of the data from the LECP instruments on Voyager 1 and 2, (2) Monitoring the health and performance of the LECP instruments, and evaluating and characterizing the response of the LECP instruments to various energetic particle and plasma environments, (3) Participating in, and supporting Voyager Project planning exercises and other coordinated activities relevant to exploration of the outer heliosphere, (4) Developing analysis techniques and operational procedures suitable for searching for and characterizing the boundaries and unique regions of the outher heliosphere, (5) Continuing the preparation of data sets appropriate for submission to the National Space Sciences Data Center (NSSDC) and, where appropriate, the Planetary Data System (PDS), (6) Maintaining direct Web access to online LECP data through the JHU/APL Voyager LECP home page, (7) Performing scientific evaluations of the Voyager 1 and 2 LECP data sets in conjunction with other data sets and other investigators, with particular focus on the outer regions of the heliosphere, and (8) Publishing the results of these evaluations in the scientific literature and presenting the results in scientific conferences.

Krimigis, Stamatios M.↗

Continuous Risk Management Course

This document includes a course plan for Continuous Risk Management taught by the Software Assurance Technology Center along with the Continuous Risk Management Guidebook of the Software Engineering Institute of Carnegie Mellon University and a description of Continuous Risk Management at NASA.

Hammer, Theodore F.↗

Effect of Combined Spaceborne Microwave and Continuous Lightning Measurements on Precipitation Forecasts of the 1998 Ground-Hog Day Storm

We evaluated the impact of several newly available sources of meteorological data on mesoscale model forecasts of precipitation produced by the extra-tropical cyclone that struck Florida on February 2, 1998. Precipitation distributions of convective rainfall events were derived from Special Sensor Microwave Imager (SSM/I) and Multi-Channel Passive Microwave Sensor (TMI) microwave radiometric data by means of the Goddard PROFiling (GPROF) algorithm. Continuous lightning distributions were obtained from sferics measurements obtained from a network of VLF radio receivers. Histograms of coincident sferics frequency distributions were matched to those of precipitation to derive bogus convective rainfall rates from the continuously available sferics measurements. SSM/I and TMI microwave data were used to derive Integrated Precipitable Water (IPW) distributions. The TMI also provided sea surface temperatures (SSTS) of the Loop Current and Gulf Stream with improved structural detail. A series of experiments assimilated IPW and latent heating from the bogus convective rainfall for six-hours in the MM5 mesoscale forecast model to produce nine-hour forecasts of all rainfall as well as other weather parameters. Although continuously assimilating latent heating only slightly improved the surface pressure distribution forecast, it significantly improved the precipitation forecasts. Correctly locating convective rainfall was found critical for assimilating latent heating in the forecast model, but measurement of the rainfall intensity proved to be less important. The improved SSTs also had a positive impact on rainfall forecasts for this case. Assimilating bogus rainfall in the model produced nine-hour forecasts of radar reflectivity distributions that agreed well with coincident observations from the TRMM spaceborne precipitation radar, ground based radar and spaceborne microwave measurements.

Weinman, James A.↗

A Compact, High-Performance Continuous Magnetic Refrigerator

We present test results of the first adiabatic demagnetization refrigerator (ADR) that can produce continuous cooling at sub-kelvin temperatures. This system uses multiple stages that operate in sequence to cascade heat from a continuous stage up to a heat sink. Continuous operation aids the usual constraints of long hold times and short recycle times that lead to the generally large mass of single-shot ADRs, and allows us to achieve much higher cooling power per unit mass. Our design goal is 10 microW of cooling at 50 mK while rejecting heat to a 6-10 K heat sink. The total cold mass is estimated to be less than 10 kg, including magnetic shielding of each stage. These parameters envelop the requirements for currently planned astronomy missions. The relatively high heat rejection capability allows it to operate with a mechanical cryocooler as part of a cryogen-free, low temperature cooling system. This has the advantages of long, mission life and reduced complexity and cost. At present, we have assembled a three-stage ADR that operates with a superfluid helium bath. Additional work is underway to develop magnetocaloric materials that can extend its heat rejection capability up to 10 K. This paper discusses the design and operation of the ADR, as well as interface requirements for cryocooler-based operation.

Shirron, Peter↗

Application of Risk Assessment Tools in the Continuous Risk Management (CRM) Process

Marshall Space Flight Center (MSFC) of the National Aeronautics and Space Administration (NASA) is currently implementing the Continuous Risk Management (CRM) Program developed by the Carnegie Mellon University and recommended by NASA as the Risk Management (RM) implementation approach. The four most frequently used risk assessment tools in the center are: (a) Failure Modes and Effects Analysis (FMEA), Hazard Analysis (HA), Fault Tree Analysis (FTA), and Probabilistic Risk Analysis (PRA). There are some guidelines for selecting the type of risk assessment tools during the project formulation phase of a project, but there is not enough guidance as to how to apply these tools in the Continuous Risk Management process (CRM). But the ways the safety and risk assessment tools are used make a significant difference in the effectiveness in the risk management function. Decisions regarding, what events are to be included in the analysis, to what level of details should the analysis be continued, make significant difference in the effectiveness of risk management program. Tools of risk analysis also depends on the phase of a project e.g. at the initial phase of a project, when not much data are available on hardware, standard FMEA cannot be applied; instead a functional FMEA may be appropriate. This study attempted to provide some directives to alleviate the difficulty in applying FTA, PRA, and FMEA in the CRM process. Hazard Analysis was not included in the scope of the study due to the short duration of the summer research project.

Paul S. Ray↗

Progress in the Development of a Continuous Adiabatic Demagnetization Refrigerator

We report on recent progress in the development of a continuous adiabatic demagnetization refrigerator (CADR). Continuous operation avoids the constraints of long hold times and short recycle times that lead to the generally large mass of single-shot ADRs, allowing us to achieve an order of magnitude larger cooling power per unit mass. Our current design goal is 10 micro W of cooling at 50 mK using a 6-10 K heat sink. The estimated mass is less than 10 kg, including magnetic shielding of each stage. The relatively high heat rejection capability allows it to operate with a mechanical cryocooler as part of a cryogen-free, low temperature cooling system. This has the advantages of long mission life and reduced complexity and cost. We have assembled a three-stage CADR and have demonstrated continuous cooling using a superfluid helium bath as the heat sink. The temperature stability is 8 micro K rms or better over the entire cycle, and the cooling power is 2.5 micro W at 60 mK rising to 10 micro W at 100 mK.

Shirron, Peter↗

A Continuous Adiabatic Demagnetization Refrigerator for Far-IR/Sub-mm Astronomy

We report on recent progress in the development of a continuous adiabatic demagnetization refrigerator (CADR). Continuous operation avoids the constraints of long hold times and short recycle times that lead to the generally large mass of single-shot ADRs, allowing us to achieve an order of magnitude larger cooling power per unit mass. Our current design goal is 10 microW of cooling at 50 mK using a 6-10 K heat sink. The estimated mass is less than 10 kg, including magnetic shielding of each stage. The relatively high heat rejection capability allows it to operate with a mechanical cryocooler as part of a cryogen-free, low temperature cooling system. This has the advantages of long mission life and reduced complexity and cost. We have assembled a three-stage CADR and have demonstrated continuous cooling using a superfluid helium bath as the heat sink. The temperature stability is 8 microK rms or better over the entire cycle, and the cooling power is 2.5 microW at 60 mK rising to 10 microW at 100 mK.

Shirron, Peter↗

Non-unity molecular heritability demonstrated by continuous evolution in vitro

INTRODUCTION: When catalytic RNA is evolved in vitro, the molecule's chemical reactivity is usually the desired selection target. Sometimes the phenotype of a particular RNA molecule cannot be unambiguously determined from its genotype, however. This can occur if a nucleotide sequence can adopt multiple folded states, an example of non-unity heritability (i.e. one genotype gives rise to more than one phenotype). In these cases, more rounds of selection are required to achieve a phenotypic shift. We tested the influence of non-unity heritability at the molecular level by selecting for variants of a ligase ribozyme via continuous evolution. RESULTS: During 20 bursts of continuous evolution of a 152-nucleotide ligase ribozyme in which the Mg2+ concentration was periodically lowered, a nine-error variant of the starting 'wild-type' molecule became dominant in the last eight bursts. This variant appears to be more active than the wild type. Kinetic analyses of the mutant suggest that it may not possess a higher first-order catalytic rate constant, however. Examination of the multiple RNA conformations present under the continuous evolution conditions suggests that the mutant is superior to the wild type because it is less likely to misfold into inactive conformers. CONCLUSIONS: The evolution of genotypes that are more likely to exhibit a particular phenotype is an epiphenomenon usually ascribed only to complex living systems. We show that this can occur at the molecular level, demonstrating that in vitro systems may have more life-like characteristics than previously thought, and providing additional support for an RNA world.

Non-NASA Center↗