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At least 631 records · Page 35

Model Stellar Atmospheres and Real Stellar Atmospheres and Status of the ATLAS12 Opacity Sampling Program and of New Programs for Rosseland and for Distribution Function Opacity

I discuss errors in theory and in interpreting observations that are produced by the failure to consider resolution in space, time, and energy. I discuss convection in stellar model atmospheres and in stars. Large errors in abundances are possible such as the factor of ten error in the Li abundance for extreme Population II stars. Finally I discuss the variation of microturbulent velocity with depth, effective temperature, gravity, and abundance. These variations must be dealt with in computing models and grids and in any type of photometric calibration. I have also developed a new opacity-sampling version of my model atmosphere program called ATLAS12. It recognizes more than 1000 atomic and molecular species, each in up to 10 isotopic forms. It can treat all ions of the elements up through Zn and the first 5 ions of heavier elements up through Es. The elemental and isotopic abundances are treated as variables with depth. The fluxes predicted by ATLAS12 are not accurate in intermediate or narrow bandpass intervals because the sample size is too small. A special stripped version of the spectrum synthesis program SYNTHE is used to generate the surface flux for the converged model using the line data on CD-ROMs 1 and 15. ATLAS12 can be used to produce improved models for Am and Ap stars. It should be very useful for investigating diffusion effects in atmospheres. It can be used to model exciting stars for H II regions with abundances consistent with those of the H II region. These programs and line files will be distributed on CD-ROMs.

Kurucz, Robert L.↗

Evaluation of GOME Satellite Measurements of Tropospheric NO2 and HCHO using Regional Data from Aircraft Campaigns in the Southeastern United States

We compare tropospheric measurements of nitrogen dioxide (NO2) and formaldehyde (HCHO) from the Global Ozone Monitoring Experiment (GOME) satellite instrument with in situ measurements over eastern Texas and the southeast United States. On aveiage, the GOME and in situ measurements of tropospheric NO2 and HCHO columns are consistent despite pronounced sampling differences. The geometric mean in situ to GOME ratios over the campaign are 1.08 for NO2 and 0.84 for HCHO, with corresponding geometric standard deviations of 1.27 and 1.38. The correlation of the observed column spatial variability between the two NO2 measurement sets is encouraging before (r2 = 0.54, n = 18) and after (r2 = 0.67, n = 18) correcting for a sampling bias. Mean relative vertical profiles of HCHO and NO2 calculated with a global three-dimensional model (GEOS-CHEM) and used in the GOME retrieval are highly consistent with in situ measurements; differences would affect the retrieved NO2 and HCHO columns by a few percent. GOME HCHO columns over eastern Texas include contributions from anthropogenic volatile organic compound (VOC) emissions but are dominated by biogenic VOC emissions at the regional scale in August-September when HCHO columns are within 20% of those over the southeastern United States. In situ measurements show that during summer the lowest 1500 m (the lower mixed layer) contains 75% of the tropospheric NO2 column over Houston and Nashville, and 60% of the HCHO column over Houston. Future validation of space-based measurements of tropospheric NO2 and HCHO columns over polluted regions should include coincident in situ measurements that span the entire satellite footprint, especially in the heterogeneous mixed layer.

Martin, R. V.↗

Analyst variability in labeling of unsupervised classifications

Analyst variability in the labeling of unsupervised classifications is tested for Landsat 5 Thematic Mapper image products covering two test sites in southern California. The accuracy of results are tested using samples from a photo interpreted base map of the area. The significance of differences between analysts is indicated by comparing Kappa statistics derived from error matrices. Analyst variability is found to be statistically significant in most cases. Certain analysts provided consistently better results for a given study area or degree of training. This work demonstrates the potential influence of analyst bias on what would otherwise seem to be a fairly objective method and suggests that controls for this subjectivity should be factored into experimental designs.

Mcgwire, Kenneth C.↗

Sampling problems: The small scale structure of precipitation

The quantitative measurement of precipitation characteristics for any area on the surface of the Earth is not an easy task. Precipitation is rather variable in both space and time, and the distribution of surface rainfall data given location typically is substantially skewed. There are a number of precipitation process at work in the atmosphere, and few of them are well understood. The formal theory on sampling and estimating precipitation appears considerably deficient. Little systematic attention is given to nonsampling errors that always arise in utilizing any measurement system. Although the precipitation measurement problem is an old one, it continues to be one that is in need of systematic and careful attention. A brief history of the presently competing measurement technologies should aid us in understanding the problem inherent in this measurement task.

Crane, R. K.↗

Biogeochemistry of DMS in Surface Waters

Dimethylsulfide (DMS) is important in influencing the formation of aerosols in the troposphere over large areas of the world's oceans. Understanding the dynamics of aerosols is important to understanding the earth's radiation balance. In evaluating the factors controlling DMS in the troposphere it is vital to understand the dynamics of DMS in the surface ocean. The biogeochemical processes controlling DMS concentration in seawater are myriad; modeling and theoretical estimation are problematic. At the beginning of this project we believed that we were on the verge of simplifying the ship-track measurement of DMS, and we proposed to deploy such a system to develop a database relating high frequency DMS measurements to biological and physicochemical and optical properties of surface water that can be quantified by remote sensing techniques. We designed a system to measure DMS concomitantly with other basic chemical and biological data in a flow-through system. The project was collaborative between Woods Hole Oceanographic Institution (WHOI) and Bermuda Biological Station for Research (BBSR). The project on which we are reporting was budgeted for only one year with a one year no-cost extension. At WHOI our effort was directed towards designing traps which would be used to concentrate DMS from seawater and allow storage for subsequent analysis. At that time, GC systems were too large for easy long-term deployment on a research vessel like R/V Weatherbird, so we focused on simplifying the shipboard sampling procedure. Initial studies of sample recovery with high levels of DMS suggested that Carboxen 1000, a relatively new carbon molecular sieve, could be used as a stable storage medium. The affinity of Carboxen for DMS is several orders of magnitude higher than gold wool (another adsorbent used for DMS collection) on a weight or volume basis. Furthermore, Carboxen's affinity for DMS is also far less susceptible to humidity than gold wool. Unfortunately, further experiments with low level DMS indicated that recovery of DMS after storage was not quantitative. The material has proven to be completely acceptable for short term storage and has been incorporated into a micro-GC system. Since working on this project, we have collaborated with RVM Scientific in Santa Barbara in the design and construction of small portable micro-GC's that will make feasible at-sea measurement in moving ships, making rapid gas analysis and quantification feasible in a ship-track mode. Throughout this period at both WHOI and BBSR, we continued to analyze field data to understand that patterns of time and space variability in DMS and the processes that govern it. These insights will be crucial to determining the specifications for our automated sampling program. The data from this, the longest continuous sampling program for ocean DMS, provided insights into year to year and short-term variability.

Dacey, J. W. H.↗

High Resolution ECG for Evaluation of QT Interval Variability during Exposure to Acute Hypoxia

Ventricular repolarization instability as quantified by the index of QT interval variability (QTVI) is one of the best predictors for risk of malignant ventricular arrhythmias and sudden cardiac death. Because it is difficult to appropriately monitor early signs of organ dysfunction at high altitude, we investigated whether high resolution advanced ECG (HR-ECG) analysis might be helpful as a non-invasive and easy-to-use tool for evaluating the risk of cardiac arrhythmias during exposure to acute hypoxia. 19 non-acclimatized healthy trained alpinists (age 37, 8 plus or minus 4,7 years) participated in the study. Five-minute high-resolution 12-lead electrocardiograms (ECGs) were recorded (Cardiosoft) in each subject at rest in the supine position breathing room air and then after breathing 12.5% oxygen for 30 min. For beat-to-beat RR and QT variability, the program of Starc was utilized to derive standard time domain measures such as root mean square of the successive interval difference (rMSSD) of RRV and QTV, the corrected QT interval (QTc) and the QTVI in lead II. Changes were evaluated with paired-samples t-test with p-values less than 0.05 considered statistically significant. As expected, the RR interval and its variability both decreased with increasing altitude, with p = 0.000 and p = 0.005, respectively. Significant increases were found in both the rMSSDQT and the QTVI in lead II, with p = 0.002 and p = 0.003, respectively. There was no change in QTc interval length (p = non significant). QT variability parameters may be useful for evaluating changes in ventricular repolarization caused by hypoxia. These changes might be driven by increases in sympathetic nervous system activity at ventricular level.

Zupet, P.↗

Mathematical models of continuous flow electrophoresis: Electrophoresis technology

Two aspects of continuous flow electrophoresis were studied: (1) the structure of the flow field in continuous flow devices; and (2) the electrokinetic properties of suspended particles relevant to electrophoretic separations. Mathematical models were developed to describe flow structure and stability, with particular emphasis on effects due to buoyancy. To describe the fractionation of an arbitrary particulate sample by continuous flow electrophoresis, a general mathematical model was constructed. In this model, chamber dimensions, field strength, buffer composition, and other design variables can be altered at will to study their effects on resolution and throughput. All these mathematical models were implemented on a digital computer and the codes are available for general use. Experimental and theoretical work with particulate samples probed how particle mobility is related to buffer composition. It was found that ions on the surface of small particles are mobile, contrary to the widely accepted view. This influences particle mobility and suspension conductivity. A novel technique was used to measure the mobility of particles in concentrated suspensions.

Saville, Dudley A.↗

Miniature Variable Pressure Scanning Electron Microscope for In-Situ Imaging and Chemical Analysis

NASA Marshall Space Flight Center (MSFC) is leading an effort to develop a Miniaturized Variable Pressure Scanning Electron Microscope (MVP-SEM) for in-situ imaging and chemical analysis of uncoated samples. This instrument development will be geared towards operation on Mars and builds on a previous MSFC design of a mini-SEM for the moon (funded through the NASA Planetary Instrument Definition and Development Program). Because Mars has a dramatically different environment than the moon, modifications to the MSFC lunar mini-SEM are necessary. Mainly, the higher atmospheric pressure calls for the use of an electron gun that can operate at High Vacuum, rather than Ultra-High Vacuum. The presence of a CO2-rich atmosphere also allows for the incorporation of a variable pressure system that enables the in-situ analysis of nonconductive geological specimens. Preliminary testing of Mars meteorites in a commercial Environmental SEM(Tradmark) (FEI) confirms the usefulness of lowcurrent/low-accelerating voltage imaging and highlights the advantages of using the Mars atmosphere for environmental imaging. The unique capabilities of the MVP-SEM make it an ideal tool for pursuing key scientific goals of NASA's Flagship Mission Max-C; to perform in-situ science and collect and cache samples in preparation for sample return from Mars.

Gaskin, Jessica A.↗

Wildfire Segmentation From Remotely Sensed Data Using Quantum-Compatible Conditional Vector Quantized-Variational Autoencoders

Wildfires represent a critical environmental hazard with multifaceted implications for ecosystems, communities, and public health [1]. The escalating frequency and intensity of wildfires globally have intensified the urgency for robust segmentation methodologies to facilitate effective mitigation, response, and recovery strategies [2]. Accurate wildfire segmentation is pivotal for delineating fire boundaries, assessing progression patterns, and prioritizing resource allocation during emergency scenarios. Furthermore, precise segmentation enables stakeholders, including policymakers, environmental scientists, and emergency responders, to formulate evidence-based strategies, thereby minimizing socio-economic disruptions and ecological degradation. Consequently, advancing wildfire segmentation techniques through innovative technological interventions remains a paramount research imperative. Although foundational in wildfire segmentation, traditional deterministic models exhibit inherent limitations that compromise their efficacy in dynamic and uncertain environments. These models often operate on rigid algorithms prioritizing deterministic classifications, thereby overlooking the inherent complexities and uncertainties associated with wildfire behavior and satellite data variability. Such deterministic frameworks tend to produce oversimplified representations that fail to capture the intricate nuances of evolving fire dynamics, spatial heterogeneity, and environmental interactions [1]. Consequently, the deterministic approach’s propensity for uncertainty collapsing [1, 3] hampers the accuracy, reliability, and applicability of segmentation outcomes in real-world scenarios. Contrastingly, stochastic models offer a more nuanced and adaptable framework for wildfire segmentation. By integrating probabilistic elements into the modeling paradigm, stochastic approaches, particularly probabilistic approaches such as variational auto encoders (VAEs) [4], facilitate comprehensive uncertainty assessment, enabling researchers to quantify and incorporate uncertainties into segmentation outcomes effectively. This probabilistic nature empowers stochastic models to encapsulate variability, account for data inconsistencies, and adapt to evolving environmental conditions, enhancing segmentation accuracy, reliability, and robustness. Embracing stochastic methodologies thus catalyzes advancements in wildfire science by fostering a more holistic, adaptive, and resilient segmentation framework. Despite VAEs demonstrating significant promise in various applications, they come with inherent limitations that have garnered attention within the machine learning community. One of the primary drawbacks lies in their reliance on static priors, which essentially assume a fixed distribution for latent variables, thereby limiting the model’s flexibility to capture complex data structures effectively [5]. This static nature leads to suboptimal representations, especially when dealing with complex and high-dimensional data. Additionally, VAEs often struggle with generating sharp and realistic samples, a phenomenon commonly referred to as mode collapse [5, 7, 6]. Furthermore, the optimization process in VAEs, which involves balancing the reconstruction loss and the regularization term, can sometimes be challenging to fine-tune [7]. In recent efforts to address these shortcomings, alternative approaches like Vector Quantized Variational Auto encoders(VQ-VAEs) [7], address the challenges by incorporating discrete latent variables and leveraging techniques that enhance the quality and diversity of generated samples while maintaining efficient training dynamics. VQ-VAEs propose a dynamic prior distribution generation mechanism that diverges from the static priors commonly associated with traditional VAEs. This dynamic approach allows for more adaptive and context-aware latent variable representations, thereby potentially capturing complex data structures more effectively. Unlike autoregressive prior models such as PixelCNN, which, despite their ability to model dependencies across data dimensions, suffer from significant computational inefficiencies and lack flexibility in handling diverse datasets. In our work, we propose to use a generative quantum-compatible approach to help alleviate the shortcomings of autoregressive prior model in VQ-VAEs. Restricted Boltzmann Machines (RBMs) are a viable alternative prior model that can learn prior distributions in a faster and more flexible manner. In this research endeavor, we meticulously curate a state-of-the-art dataset leveraging satellite MODIS data in conjunction with VIIRS fire masks, derived from Fire Radiative Power (FRP), thereby encapsulating diverse wildfire scenarios and environmental contexts. We developed a conditional VQ-VAE architecture with the RBM prior model that is trained in a supervised manner for segmenting wildfire masks. This innovative approach synergistically harnesses deep learning capabilities, enabling the generation of segmentation maps characterized by heightened precision, granularity, and contextual relevance. Furthermore, replacing the autoregressive prior learning method proposed by the original VQ-VAE with a prior density approximation via quantum-compatible RBM facilitates expedited inference processes, augments flexibility in prior sampling, optimizes computational efficiency and establishes a groundbreaking benchmark in wildfire segmentation methodologies.

quantum machine learning↗

D/H ratios and H2O contents of mantle-derived amphibole megacrysts from Dish Hill, California

D/H ratios are, in principle, useful in characterizing reservoirs of mantle hydrogen and as tracers of volatile transfer processes in Earth's interior. In practice, however, interpretation of isotopic measurements on mantle derived H is complicated by surface processes such as contamination and degassing which may alter the primary D/H ratio. Although there are indications that water associated with subduction zones and certain chemically enriched basalts is enriched in D relative to 'typical' upper mantle water, the extent of isotopic heterogeneity of mantle H remains uncertain. Kaersutitic amphibole megacrysts in alkaline basalts are one of the most widespread sources of mantle water and are therefore potentially useful for large-scale regional studies of D/H variation. However, D/H ratios of these amphiboles vary widely (from plus 8 to minus 113 percent), even in samples from the same locality, so that this potential has yet to be realized. In order to investigate the origin of this variability, and to explore the possibility that primary mantle D/H ratios may be deduced from these amphiboles, we analyzed the D/H ratios and chemical compositions of a suite of 17 kaersutitic amphiboles from Dish Hill, California. This work contrasts with previous studies in which sampling is widespread, but representatives from any given locality are few. Samples were collected from a restricted area on the southern flank of the volcanic center and are associated with the basal volcanic breccia. Fourteen of the samples were large single crystals or crystal fragments (megacrysts, 0.4 to 30 grams), believed to derive from pegmatitic veins crystallized from melts in the mantle. Two were coarse-grained intergrowths of amphibole with olivine and spinel, and one was a thin (2 mm) selvage on a peridotite xenolith.

Bell, David R.↗

Technique for measuring high-temperature thermal conductivity of solids by the use of a heat pipe.

A suggested technique for accurately measuring thermal conductivity of solids in the temperature range 800-1500 C is presented. The procedure employs the sample to be tested in series combination with a high-temperature heat pipe and a heat-transfer device, which has a variable thermal conductance. By changing the thermal conductance of the heat-transfer unit and measuring the change in heat-pipe power input to maintain a constant heat-pipe temperature, one can accurately measure the heat flux through the sample in conjunction with the temperature drop across it. This steady-state technique has some inherent advantages over methods currently employed to measure thermal conductivity at elevated temperatures.

Forman, R.↗

Analysis of long term heart rate variability: methods, 1/f scaling and implications

The use of spectral techniques to quantify short term heart rate fluctuations on the order of seconds to minutes has helped define the autonomic contributions to beat-to-beat control of heart rate. We used similar techniques to quantify the entire spectrum (0.00003-1.0 Hz) of heart rate variability during 24 hour ambulatory ECG monitoring. The ECG from standard Holter monitor recordings from normal subjects was sampled with the use of a phase locked loop, and a heart rate time series was constructed at 3 Hz. Frequency analysis of the heart rate signal was performed after a nonlinear filtering algorithm was used to eliminate artifacts. A power spectrum of the entire 24 hour record revealed power that was inversely proportional to frequency, 1/f, over 4 decades from 0.00003 to 0.1 Hz (period approximately 10 hours to 10 seconds). Displaying consecutive spectra calculated at 5 minute intervals revealed marked variability in the peaks at all frequencies throughout the 24 hours, probably accounting for the lack of distinct peaks in the spectra of the entire records.

Non-NASA Center↗

Costs of measuring leaf area index of corn

The magnitude of plant-to-plant variability of leaf area of corn plants selected from uniform plots was examined and four representative methods for measuring leaf area index (LAI) were evaluated. The number of plants required and the relative costs for each sampling method were calculated to detect 10, 20, and 50% differences in LAI using 0.05 and 0.01 tests of significance and a 90% probability of success (beta = 0.1). The natural variability of leaf area per corn plant was nearly 10%. Additional variability or experimental error may be introduced by the measurement technique employed and by nonuniformity within the plot. Direct measurement of leaf area with an electronic area meter had the lowest CV, required that the fewest plants be sampled, but required approximately the same amount of time as the leaf area/weight ratio method to detect comparable differences. Indirect methods based on measurements of length and width of leaves required more plants but less total time than the direct method. Unless the coefficients for converting length and width to area are verified frequently, the indirect methods may be biased. When true differences in LAI among treatments exceed 50% of mean, all four methods are equal. The method of choice depends on the resources available, the differences to be detected, and what additional information, such as leaf weight or stalk weight, is also desired.

Daughtry, C. S. T.↗

Long term monitoring of methane in the atmosphere by multiplex gas chromatography

Methane is of interest in the study of the Earth's atmosphere because of its implication in the future global warming of the surface. This warming is produced by the absorption of infrared energy by trace gases. It has been estimated that in the next 40 to 50 years, methane could contribute 20 to 25 pct. as much atmospheric warming as that expected from carbon dioxide increases. Studies to examine sources, sinks, and cycles of methane will require analytical methods capable of continuous unattended measurement with temporal resolution of an hour or less for weeks at a time. Gas chromatography (GC) is one of the most practical methods available to conduct the analysis of air, but limitations in this technique still exist which can be alleviated with multiplex GC (MGC). MGC is a technique where many samples are pseudo-randomly introduced to the chromatograph without regard to the length of time required for an analysis. The resulting data must then be reduced using computational methods such as cross correlation. In the technique reported, a tube packed with silver oxide was used at the inlet of the GC column to create concentration pulses of methane in a sample stream of air. By using only one carrier, i.e., ambient air, an effective and accurate method to monitor the variations in concentration of methane in the atmosphere over long periods of time was developed. Methane in ambient air was monitored for an eight day period and an interesting temporal variability was found. This work has shown the utility of a relatively simple MGC for the analysis of a real environmental sample.

Valentin, Jose R.↗

The concentration and isotopic composition of carbon in basaltic glasses from the Juan de Fuca Ridge, Pacific Ocean

The abundance and C-13/C-12 ratios of carbon were analyzed in basaltic glass from twenty locations along the Juan de Fuca Ridge using a 3-step combustion/extraction technique. Carbon released during the first two combustion steps at 400-500 C and 600-650 C is interpreted to be secondary, and only the carbon recovered during a final combustion step at about 1200 C is thought to be indigenous to the samples. For carbon released at about 1200 C, glasses analyzed as 1-2 mm chips contained 23-146 ppm C with delta C-13 values of -4.8 to -9.3 per mil, whereas samples crushed to 38-63 microns or 63-90 microns yielded 56-103 ppm C with delta C-13 values of -6.1 to -9.2 per mil. The concentrations and isotopic compositions of the primary carbon dissolved in the glasses and present in the vesicles are similar to those previously reported for other ocean-ridge basalts. The Juan de Fuca basaltic magmas were not in equilibrium with respect to carbon when they erupted and quenched on the sea floor. Evidence of disequilibrium includes (1) a large range of carbon contents among glasses collected at similar depths, (2) a highly variable calculated carbon isotopic fractionation between melt and vapor determined by comparing crushed and uncrushed splits of the same sample, and (3) a lack of correlation between vesicle abundance, carbon concentration, and depth of eruption. Variations in carbon concentration and delta C-13 ratios along the ridge do not correlate with major element chemistry. The observed relationship between carbon concentrations and delta C-13 values may be explained by late-stage, variable degrees of open-system (Rayleigh-like) degassing.

Blank, Jennifer G.↗

Modeling Pore Closure in the Hot Isostatic Pressing of Additively Manufactured Inconel 718 Samples

Additive manufacturing provides opportunity for a new world of possibilities for metallic component design and fabrication; however, as-built part quality is notoriously variable, anisotropic, and degraded by porous defects. To improve quality, parts are commonly post processed using a variety of techniques including hot isostatic pressing (HIP). During HIP, high temperature and pressure is employed to improve microstructure and reduce pore volume by inducing visco-plastic deformation in the metallic substrate. Validated computational capabilities can provide predictions to guide the selection of processing condition, expected pore reduction, and the effects of varying entrapped gas in the pores. This discussion describes a micro-scale finite element structural model developed to predict pore closure due to HIP in as-built additively manufactured Inconel 718 samples produced by the laser powder bed fusion process. The model accounts for plastic deformation, creep, and internal pressure for a single pore. Pores are characterized in physical samples before and after HIP, and model predictions are compared to this measured data.

defect model prediction↗

The Measurement of Radiation Exposure of Astronauts by Radiochemical Techniques

The principal gamma-ray-omitting radioisotopes produced in the body of astronauts by cosmic-ray bombardment which have half-lives long enough to be useful for radiation dose evaluation are Be-7, Na-22, and Na-24. The sodium isotopes were measured in the preflight and postflight urine and feces, and those feces specimens collected during the manned Apollo missions, by analysis of the urine salts and the raw feces in large crystal multidimensional gamma-ray spectrometers. The Be-7 was chemically separated, and its concentration measured in an all Na(T1), anticoincidence shielded, scintillation well crystal. The overall sensitivity of the experiment was reduced by almost all variables such as low concentrations of excreted cosmogenic radionuclides, high concentrations of injected radionuclides, low sample sizes, long delay periods before analysis, and uncertain excretion rates. The astronaut radiation dose in millirads, as determined by this technique, for the Apollo 7, 8, 9, 10, 11, 12, and 13 missions was 330, 160, 315, 870 ? 550, 31, 110, and 250 respectively. In view of these limitations this technique would be best applied to cases of unusually high exposures, such as that encountered from solar flares.

R L Brodzinski↗

A computer program for two-dimensional and axisymmetric nonreacting perfect gas and equilibrium chemically reacting laminar, transitional and-or turbulent boundary layer flows

A computer program is described in detail for laminar, transitional, and/or turbulent boundary-layer flows of non-reacting (perfect gas) and reacting gas mixtures in chemical equilibrium. An implicit finite difference scheme was developed for both two dimensional and axisymmetric flows over bodies, and in rocket nozzles and hypervelocity wind tunnel nozzles. The program, program subroutines, variables, and input and output data are described. Also included is the output from a sample calculation of fully developed turbulent, perfect gas flow over a flat plate. Input data coding forms and a FORTRAN source listing of the program are included. A method is discussed for obtaining thermodynamic and transport property data which are required to perform boundary-layer calculations for reacting gases in chemical equilibrium.

Miner, E. W.↗