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Simplified detection and correction of critical data for ill-conditioned systems

Ill-conditioned systems arising in analysis and optimization can display a high sensitivity to numerical precision for changes and errors in data input. Such data may be in the form of system parameter input or desired system response. The ill-conditioning referred to generally arises from the lack of sufficient independent data to define a complex system or the weak sensitivity of response to source input parameters. It is shown how small errors in data and assumed fixed and known parameters can lead to highly erroneous results in ill-conditioned linear algebraic equations. A simplified detection and correction of critical input data arising in the coefficient matrix and desired response (i.e., right hand side) is proposed.

Ojalvo, Irving U.↗

A source-sink model of the generation of plate tectonics from non-Newtonian mantle flow

A model of mantle convection which generates plate tectonics requires strain rate- or stress-dependent rheology in order to produce strong platelike flows with weak margins as well as strike-slip deformation and plate spin (i.e., toroidal motion). Here, we employ a simple model of source-sink driven surface flow to determine the form of such a rheology that is appropriate for Earth's present-day plate motions. In this model, lithospheric motion is treated as shallow layer flow driven by sources and sinks which correspond to spreading centers and subduction zones, respectively. Two plate motion models are used to derive the source sink field. As originally implied in the simpler Cartesian version of this model, the classical power law rheologies do not generate platelike flows as well as the hypothetical Whitehead-Gans stick-slip rheology (which incorporates a simple self-lubrication mechanism). None of the fluid rheologies examined, however, produce more than approximately 60% of the original maximum shear. For either plate model, the viscosity fields produced by the power law rheologies are diffuse, and the viscosity lows over strike-slip shear zones or pseudo-margins are not as small as over the prescribed convergent-divergent margins. In contrast, the stick-slip rheology generates very platelike viscosity fields, with sharp gradients at the plate boundaries, and margins with almost uniformly low viscosity. Power law rheologies with high viscosity contrasts, however, lead to almost equally favorable comparisons, though these also yield the least platelike viscosity fields. This implies that the magnitude of toroidal flow and platelike strength distributions are not necessarily related and thus may present independent constraints on the determination of a self-consistent plate-mantle rheology.

Bercovici, David↗

Noise and Dynamical Pattern Selection in Solidification

The overall goal of this project was to understand in more detail how a pattern-forming system can adjust its spacing. "Pattern-forming systems," in this context, are nonequilibrium contina whose state is determined by experimentally adjustable control parameter. Below some critical value of the control system then has available to it a range of linearly stable, spatially periodic steady states, each characterized by a spacing which can lie anywhere within some band of values. These systems like directional solidification, where the solidification front is planar when the ratio of growth velocity to thermal gradient is below its critical value, but takes on a cellular shape above critical. They also include systems without interfaces, such as Benard convection, where it is the fluid velocity field which changes from zero to something spatially periodic as the control parameter is increased through its critical value. The basic question to be addressed was that of how the system chooses one of its myriad possible spacings when the control parameter is above critical, and in particular the role of noise in the selection process. Previous work on explosive crystallization had suggested that one spacing in the range should be preferred, in the sense that weak noise should eventually drive the system to that spacing. That work had also suggested a heuristic argument for identifying the preferred spacing. The project had three main objectives: to understand in more detail how a pattern-forming system can adjust its spacing; to investigate how noise drives a system to its preferred spacing; and to extend the heuristic argument for a preferred spacing in explosive crystallization to other pattern-forming systems.

Kurtze, Douglas A.↗

The Role of Magnetic Shear in Reconnection-driven Flare Energy Release

Using observations from the Solar Dynamics Observatory's Atmosphere Imaging Assembly and the Ramaty High Energy Solar Spectroscopic Imager, we present novel measurements of the shear of post-reconnection flare loops (PRFLs) in SOL20141218T21:40 and study its evolution with respect to magnetic reconnection and flare emission. Two quasi-parallel ribbons form adjacent to the magnetic polarity inversion line (PIL), spreading in time first parallel to the PIL and then mostly in a perpendicular direction. We measure the magnetic reconnection rate from the ribbon evolution, and also the shear angle of a large number of PRFLs observed in extreme ultraviolet passbands (≲1 MK). For the first time, the shear angle measurements are conducted using several complementary techniques allowing for cross validation of the results. In this flare, the total reconnection rate is much enhanced before a sharp increase in the hard X-ray emission, and the median shear decreases from 60°–70° to 20°, on a timescale of 10 minutes. We find a correlation between the shear-modulated total reconnection rate and the nonthermal electron flux. These results confirm the strong-to-weak shear evolution suggested in previous observational studies and reproduced in numerical models, and also confirm that, in this flare, reconnection is not an efficient producer of energetic nonthermal electrons during the first 10 minutes when the strongly sheared PRFLs are formed. We conclude that an intermediate shear angle, ≤40°, is needed for efficient particle acceleration via reconnection, and we propose a theoretical interpretation.

Solar magnetic reconnection↗

Geophysical models of Western Aphrodite-Niobe region: Venus

The new topography and gravitational field data for Venus expressed in spherical harmonics of degree and order up to 50 allow us to analyze the crust-mantle boundary relief and stress state of the Venusian lithosphere. In these models, we consider models in which convection is confined beneath a thick, buoyant lithosphere. We divide the convection regime into an upper mantle and lower mantle component. The lateral scales are smaller than on Earth. In these models, relative to Earth, convection is reflected in higher order terms of the gravitational field. On Venus geoid height and topography are highly correlated, although the topography appears to be largely compensated. We hypothesize that Venus topography for those wavelengths that correlate well with the geoid is partly compensated at the crust-mantle boundary, while for the others compensation may be distributed over the whole mantle. In turn the strong sensitivity of the stresses to parameters of the models of the external layers of Venus together with geological mapping allows us to begin investigations of the tectonics and geodynamics of the planet. For stress calculations we use a new technique of space- and time-dependent Green's response functions using Venus models with rheologically stratified lithosphere and mantle and a ductile lower crust. In the basic model of Venus the mean crust is 50-70 km thick, the density contrast across the crust-mantle boundary is in the range from 0.3 to 0.4 g/cm(exp -3). The thickness of a weak mantle zone may be from 350 to 1000 km. Strong sensitivity of calculated stress to various parameters of the layered model of Venus together with geological mapping and analysis of surface tectonic patterns allow us to investigate the tectonics and geodynamics of the planet. The results are presented in the form of maps of compression-extension and maximum shear stresses in the lithosphere and maps of crust-mantle boundary relief, which can be presented as a function of time. We have modeled the region of Western Aphrodite and the Niobe plains to get reasonable depths of compensation. Crust mantle boundary relief is calculated for Western Aphrodite-Niobe relative to a mean crustal thickness of 50 km. The calculations include the consequences of simple crust models and more complicated models with a weak, ductile lower crust, a strong upper mantle and a weak lower mantle layer.

Marchenkov, K. I.↗

Narrow radio recombination lines from ionization fronts

Model weak D-type ionization fronts are used to show that narrow H I radio recombination lines, such as those observed in the directions of several galactic H II regions, may be formed in the outermost layers of an ionization front bounding an H II region. Four model ionization fronts are computed with different values of magnetic-field strength, ionizing photon energy, and initial conditions. The recombination line strengths given by the models are compared with observed line strengths for the H II region NGC 2024, and the observed line profiles are found to be about twice as broad as the model profiles. Some likely explanations for the discrepancy are considered, particularly a variation in front velocity over the observing beam width (Stark broadening is ruled out).

Hill, J. K.↗

Doppler-radar observation of the evolution of downdrafts in convective clouds

A detailed analysis of the 20 July 1977 thunderstorm complex which formed and evolve over the South Park region in Central Colorado is presented. The storm was extensively analyzed using multiple Doppler radar and surface mesonet data, developed within an environment having very weak wind shear. The storm owed its intensification to the strength of the downdraft, which was nearly coincident with the region where the cloud had grown. The noteworthy features of this storm were its motion to the right of the cloud-level winds, its multicellular nature and discrete propagation, its north-south orientation, and its relatively large storm size and high reflectivity factor (55 dBZ). This scenario accounts for the observed mesoscale and cloud-scale event. A line of convergence was generated at the interface between the easterly upslope winds and westerly winds. During stage II, the convergence line subsequently propagated down the slopes of the Mosquito Range, and was the main forcing mechanism for the development of updraft on the west flank of the storm. The formation of downdraft on the eastern side of updraft blacked surface inflow, and created a detectable gust front. As the original downdraft intensified, the accumulation of evaporatively-chilled air caused the intensification of the mesohigh, which likely destroyed the earlier convergence line and created a stronger convergence line to the east, which forced up-lifting of the moist, westerly inflow and caused the formation of updraft to the east. An organized downdraft circulation, apparently maintained by precipitation drag and evaporational cooling, was responsible in sustaining a well-defined gust front. The storm attained its highest intensity as a consequence of merging with a neighboring cloud. The interaction of downdrafts or gust fronts from two intense cells appeared to be the primary mechanism of this merging process as suggested by Simpson et al. (1980). The merging process coincided with more rain than occurred in unmerged echoes.

Motallebi, N.↗

Human evolution in the age of the intelligent machine

A systems analysis of the future evolution of man can be conducted by analyzing the biological material of the galaxy into three subsystems: man, intelligent machines, and intelligent extraterrestrial organisms. A binomial interpretation is applied to this system wherein each of the subsystems is assigned a designation of success or failure. For man the two alternatives are, respectively, 'decline' or 'flourish', for machine they are 'become intelligent' or 'stay dumb', while for extraterrestrial intelligence the dichotomy is that of 'existence' or 'nonexistence'. The choices for each of three subsystems yield a total of eight possible states for the system. The relative lack of integration between brain components makes man a weak evolutionary contestant compared to machines. It is judged that machines should become dominant on earth within 100 years, probably by means of continuing development of existing man-machine systems. Advanced forms of extraterrestrial intelligence may exist but are too difficult to observe. The prospects for communication with extraterrestrial intelligence are reviewed.

Mclaughlin, W. I.↗

Kinematic study of flight telerobotic servicer configuration issues

Several factors, such as body size and shape, and the number of arms and their placement, will influence how well the Flight Telerobotic Servicer (FTS) is suited to its potential duties for the Space Station Program. In order to examine the implications of these configuration options, eight specific 2, 3, and 4 armed FTS configuration were simulated and used to perform a Space Station Orbital Replacement Unit (ORU) exchange. The strengths and weaknesses of each configuration were evaluated. Although most of the configurations examined were able to perform the exchange, several of the 3 and 4 arm configurations had operational advantages. The results obtained form these simulations are specific to the assumptions associated with the ORU exchange scenario examined. However, they do illustrate the general interrelationships and sensitivities which need to be understood.

Lewis, R. H.↗

Working Toward Nanotube Composites

One of the most attractive applications of single-wall carbon nanotubes (SWNT) is found in the area of structural materials. Nanotubes have a unique combination of high strength, modulus, and elongation to failure, and therefore have potential to significantly enhance the mechanical properties of today's composites. This is especially attractive for the aerospace industry looking for any chance to save weight. This is why NASA has chosen to tackle this difficult application of SWNT. Nanotube properties differ significantly from that of conventional carbon fibers, and a whole new set of problems, including adhesion and dispersion in the adhesive polymer matrix, must be resolved in order to engineer superior composite materials. From recent work on a variety of applications it is obvious that the wide range of research in nanotubes will lead to advances in physics, chemistry, and engineering. However, the possibility of ultralightweight structures is what causes dreamers to really get excited. One of the important issues in composite engineering is aspect ratio of the fibers, since it affects load transfer in composites. Nanotube length was a gray area for years, since they are formed in bundles, making it impossible to monitor individual nanotube length. Even though bundles are observed to be tens and hundreds of microns long, they can be built of relatively short tubes weakly bound by Van der Waals forces. Nanotube length can be affected by subsequent purification and ultrasound processing, which has been necessary in order to disperse nanotubes and introduce them into a polymer matrix. Some calculations show that nanotubes with 10(exp 5) aspect ratio may be necessary to achieve good load transfer. We show here that nanotubes produced in our laser system are as much as tens of microns long and get cut into lengths of hundreds of nanometers during ultrasound processing. Nanotube length was measured by AFM on pristine nanotube specimens as well, as after sonication. In each case great care was taken to measure individual nanotubes, rather than bundles. Pristine nanotubes were collected on quartz substrates placed directly in the laser oven and exposed for 0.5 s. This results in an equal mix of bundles and individual nanotubes. Nanotube length measurements were limited practically by the lateral span of the AFM scanner, but nanotube length is certainly in excess of 20 micrometers.

Arepalli, Sivaram↗

XMM-Newton Observations of the 2003 X-Ray Minimum of Eta Carinae

The XMM-Newton X-ray observatory took part in the multi-wavelength observing campaign of the massive, evolved star Eta Carinae in 2003 during its recent X-ray minimum in June 2003. This paper reports on the first results of these observations, which were performed (1) before the minimum (five times in January, 2003), (2) near the X-ray maximum just before the minimum (two times in June) and (3) during the minimum (four times in July-August). Hard X-ray emission from the point source of Eta Carinae was detected even during the minimum. The observed flux above 3 keV was approx. 3x10(exp -12) ergs cm(exp -2)/s, which is about one percent of the flux before the minimum. Light curves from the individual observations show no time variability on the scale of a few kilo-seconds. Changes in the spectral shape occurred, but these changes were smaller than expected if the minimum is produced solely by an increase of hydrogen column density. Fits of the hard X-Ray source by an absorbed 1T model show a constant plasma temperature at around 5 keV and an increase of column density from 5x10(exp 22) cm(exp -2) to 2x10(exp 23) cm(exp -2). The spectra below 6 keV significantly deviate from the models that fit the higher energy emission. The X-ray minimum seems to be dominated by an apparent decrease of the emission measure, suggesting that the brightest part of the X-ray emitting region is completely obscured during the minimum in the form of an eclipse. Partial covering plasma emission models might be considered for the spectral variation. The spectra also showed strong iron K line emission from both hot and cold gases, and weak line emission from Ni, Ca, Ar, S and Si.

Hamaguchi, K.↗

YBa2Cu3O(7-delta)/Au/Nb sandwich geometry SNS weak links on c-axis oriented YBa2Cu3O(7-delta)

Sandwich geometry superconductor/normal metal/superconductor structures have been fabricated on LaAlO3 and cubic zirconia with laser-ablated, c-axis-oriented YBa2Cu3O(7-delta) base electrodes, 100-600 A of Au, and Nb counter electrodes, all formed in situ without breaking vacuum. Junctions range in size from 5 to 50 micron on a side. Four probe I-V measurements at 4.2 K show RnA products as low as 6 x 10 to the -9th sq cm and critical current densities up to 5.2 kA/sq cm. AC Josephson steps were observed with the application of 10-GHz radiation. The temperature dependence of Jc and the observation of the AC Josephson effect suggest that true supercurrents are present and that they do indeed represent the characteristics of the YBa2Cu3O(7-delta)/Au/Nb structure. The best results were obtained when the devices were annealed at about 450 C in O2 for 30 min after Au deposition.

Foote, M. C.↗

Durability of YSZ Coated Ti2AlC in 1300 °C Mach 0.3 Burner Rig Tests

A thermal barrier coating system survived burner rig testing at 1300 °C for 500 h. A 160 µm thick yttria stabilized zirconia (YSZ) coating was applied to a Ti2AlC MAX phase bar sample by plasma spray physical vapor deposition (PS-PVD) and tested face-on in an atmospheric Mach 0.3 jet fuel burner, using 5-h thermal cycles. No thermal barrier coating (TBC) spallation or recession was observed, only a 2.4 mg/cm2 mass gain. The modest weight gain precluded severe volatility losses under high velocity burner conditions. The coating surface exhibited colonies of (111)flourite fiber-textured columns separated by craze patterns, with no visible moisture attack. The metastable tetragonal t' YSZ phase was obtained initially, transitioning to equilibrium teq and cubic YSZ, but with little detrimental monoclinic. The thickness of the alumina TGO was ~21 to 23 μm under the heated YSZ face and ~13 to 15 μm on the uncoated, cooler backside. The backside exhibited removal of initial transient TiO2 nodules and partial etching of the underlying Al2O3 scale by volatile hydroxides formed in high temperature, high velocity water vapor. Aerodynamic forces produced some bending of the cantilevered sample via creep. The test indicated exceptional stability of YSZ coatings on Ti2AlC under turbine conditions, with thermal expansion matching playing a key role. The purpose of this study was to demonstrate long term durability of YSZ/MAX phase system in aggressive high temperature burner rig testing. MAX phases have been keenly studied because of their unique crystal structure and intriguing properties (Refs. 1 and 2). Having Mn+1(Al,Si)(C,N)n general composition, they are defined as ceramics, but possess unusual desirable attributes such as high conductivity, thermal shock resistance, easy machinability, and deformation tolerance. The mechanical properties derive from weak M-(Al,Si) bonding in the basal plane that leads to sliding and kinking in preference to catastrophic crack growth. Like most ceramics they are phase stable at high temperatures, generally up to 1500 °C. High temperature oxidation resistance is excellent for alumina-forming Ti3AlC2, Ti2AlC, and Cr2AlC, as reviewed by Tallman, et al. (Ref. 3). Compatibility with α-Al2O3 scales is further enhanced in cyclic exposures by a close matching of thermal expansion coefficients, (Ref. 4) i.e., (~9.3, 10.2, 11.3×10–6/K for Al2O3, Ti2AlC, and YSZ, to be discussed). Turbine environments generally contain 10 percent water vapor in the combustion gases, therefore moisture effects can be a concern for some materials (Ref. 5). Furnace tests of MAX phases in high temperature steam generally showed little effect on Al2O3 scale growth (Ref. 6). However, high velocity and high pressure gas can influence scale losses by the formation of volatile reaction products, such as TiO(OH)2 and Al(OH)3 (Refs. 7 to 10). This phenomenon had been discussed for 1100 to 1300 °C high pressure burner rig tests of Ti2AlC (Ref. 11). A single cubic growth rate parameter kcubic was measurably lower than comparable furnace TGA data, but it could be matched reasonably well if corrected for a slight volatility term. In general, a two-parameter cubic-linear growth-volatility law was believed to apply. Corresponding scale volatility loss rates, directly measured at 1300 °C on a pre-oxidized sample, were moderate (0.012 mg/cm2/h) and largely attributed to removal of the initial TiO2 transient scale. A related CH4 burner study of high purity Cr2AlC MAX phase demonstrated 1200 °C durability after 500 rapid (5 min. heat and 2 min. cool) thermal shock cycling (29 h hot time) (Ref. 12). Heating and cooling rates were ~1000 and 500 °C per minute, with a gas velocity of 5 m/s, producing a 75 °C/mm gradient. A 7 μm Al2O3 surface scale and a 13 μm Cr7C3 depletion zone formed with no signs of failure. No evidence of scale volatility was evident, although weight change was not provided, the velocity was moderate, and the total hot time was not extensive. The same high gradient BRT was used to produce 1400 °C surface temperatures for a YSZ/Cr2AlC/IN738 system in the first study of MAX phases used as bond coats for thermal barrier coatings (TBC) (Ref. 25). Here TBC failure was reported after 745 cycles, with only a 1.5 μm Al2O3 scale entrained within a porous, Cr7C3 bondcoat depletion phase. YSZ thermal barrier coatings have been considered to be a compatible complement to Al-MAX phases because of thermal expansion matching and extremely low volatility in water vapor. Initial studies showed superior oxidative stability up to 1300 °C, for long times (at least 500 h) for Ti2AlC substrates and less (268 h) for Cr2AlC, while withstanding large alumina TGO scale thickness (~35 to 40 μm) (Refs. 13 and 14). By comparison, typical superalloy systems can only survive 1150 °C maximum interface temperatures for extended periods, with a maximum sustained TGO below 10 μm (Ref. 15). High temperature SiC based systems are known to form slow-growing SiO2 scales. But these are subject to rate enhancement and volatile Si(OH)4 products in the presence of water vapor, as described comprehensively by Opila, et al. (Refs. 5, 16 to 19). Net weight losses are generally observed in high velocity, high pressure burner rig studies (e.g., 0.084 mg/cm2/h at 1300 °C) (Ref. 20). Furthermore, the loss rates have been shown from chemical physics to scale with v1/2 and pH2O 2 (Ref. 16). Low activity, moisture-resistant environmental barrier coatings (EBC), such as rare earth silicates, are needed to prevent substrate recession under turbine conditions (Refs. 21 to 23).

Smialek, James L.↗

Formation of Amino Acids and Carboxylic Acids in Weakly Reducing Planetary Atmospheres by Solar Energetic Particles from the Young Sun

Life most likely started during the Hadean Eon; however, the environmental conditions which contributed to the complexity of its chemistry are poorly known. A better understanding of various environmental conditions, including global (heliospheric) and local (atmospheric, surface, and oceanic), along with the internal dynamic conditions of the early Earth, are required to understand the onset of abiogenesis. Herein, we examine the contributions of galactic cosmic rays (GCRs) and solar energetic particles (SEPs) associated with superflares from the young Sun to the formation of amino acids and carboxylic acids in weakly reduced gas mixtures representing the early Earth’s atmosphere. We also compare the products with those introduced by lightning events and solar ultraviolet light (UV). In a series of laboratory experiments, we detected and characterized the formation of amino acids and carboxylic acids via proton irradiation of a mixture of carbon dioxide, methane, nitrogen, and water in various mixing ratios. These experiments show the detection of amino acids after acid hydrolysis when 0.5% (v/v) of initial methane was introduced to the gas mixture. In the set of experiments with spark discharges (simulation of lightning flashes) performed for the same gas mixture, we found that at least 15% methane was required to detect the formation of amino acids, and no amino acids were detected in experiments via UV irradiation, even when 50% methane was used. Carboxylic acids were formed in non-reducing gas mixtures (0% methane) by proton irradiation and spark discharges. Hence, we suggest that GCRs and SEP events from the young Sun represent the most effective energy sources for the prebiotic formation of biologically important organic compounds from weakly reducing atmospheres. Since the energy flux of space weather, which generated frequent SEPs from the young Sun in the first 600 million years after the birth of the solar system, was expected to be much greater than that of GCRs, we conclude that SEP-driven energetic protons are the most promising energy sources for the prebiotic production of bioorganic compounds in the atmosphere of the Hadean Earth.

Kensei Kobayashi↗

Remote sensing of atomic oxygen - Some observational difficulties in the use of the forbidden O I 1173-A and O I 1641-A transitions

Recent sounding rocket and satellite studies suggest that simultaneous measurements of the O I 989-A and 1304-A resonance lines and of the forbidden 1172.6-A and 1641.3-A transitions would form the basis of a useful remote sensing technique for measuring the O I density and optical opacity of a planetary or stellar atmosphere. Because the 1172.6-A and 1641.3-A emissions are weak lines and are emitted in a wavelength region rich in spectral features, it is important to determine whether typical flight instruments can make measurements with sufficient spectral purity so that the remote sensing observations will yield accurate results. A detailed, high-resolution study of the far UV emission features in the regions surrounding the atomic oxygen transitions at 1172.6 and 1641.3 A was made. These spectra, which were excited by electron impact on O2 and N2, are presented in an attempt to display some potential sources of interference in aeronomical measurements of these O I lines. Both atomic and molecular emissions are found, and the spectral resolution necessary to make unambiguous measurements is discussed.

Erdman, P. W.↗

Methane overtone absorption by intracavity laser spectroscopy

Interpretation of planetary methane (CH4) visible-near IR spectra, used to develop models of planetary atmospheres, has been hampered by a lack of suitable laboratory spectroscopic data. The particular CH4 spectral bands are due to intrinsically weak, high overtone-combination transitions too complex for classical spectroscopic analysis. The traditional multipass cell approach to measuring spectra of weakly absorbing species is insufficiently sensitive to yield reliable results for some of the weakest CH4 absorption features and is difficult to apply at the temperatures of the planetary environments. A time modulated form of intracavity laser spectroscopy (ILS), has been shown to provide effective absorption pathlengths of 100 to 200 km with sample cells less than 1 m long. The optical physics governing this technique and the experimental parameters important for obtaining reliable, quantitative results are now well understood. Quantitative data for CH4 absorption obtained by ILS have been reported recently. Illustrative ILS data for CH4 absorption in the 619.7 nm and 681.9 nm bands are presented. New ILS facilities at UM-St. Louis will be used to measure CH4 absorption in the 700 to 1000 nm region under conditions appropriate to the planetary atmospheres.

Obrien, James J.↗

Transient/structural analysis of a combustor under explosive loads

The 8-Foot High Temperature Tunnel (HTT) at NASA Langley Research Center is a combustion-driven blow-down wind tunnel. A major potential failure mode that was considered during the combustor redesign was the possibility of a deflagration and/or detonation in the combustor. If a main burner flame-out were to occur, then unburned fuel gases could accumulate and, if reignited, an explosion could occur. An analysis has been performed to determine the safe operating limits of the combustor under transient explosive loads. The failure criteria was defined and the failure mechanisms were determined for both peak pressures and differential pressure loadings. An overview of the gas dynamics analysis was given. A finite element model was constructed to evaluate 13 transient load cases. The sensitivity of the structure to the frequency content of the transient loading was assessed. In addition, two closed form dynamic analyses were conducted to verify the finite element analysis. It was determined that the differential pressure load or thrust load was the critical load mechanism and that the nozzle is the weak link in the combustor system.

Gregory, Peyton B.↗

Dominant takeover regimes for genetic algorithms

The genetic algorithm (GA) is a machine-based optimization routine which connects evolutionary learning to natural genetic laws. The present work addresses the problem of obtaining the dominant takeover regimes in the GA dynamics. Estimated GA run times are computed for slow and fast convergence in the limits of high and low fitness ratios. Using Euler's device for obtaining partial sums in closed forms, the result relaxes the previously held requirements for long time limits. Analytical solution reveal that appropriately accelerated regimes can mark the ascendancy of the most fit solution. In virtually all cases, the weak (logarithmic) dependence of convergence time on problem size demonstrates the potential for the GA to solve large N-P complete problems.

Noever, David↗