Measurements of the curves-of-growth of hot water vapor
Hot water vapor curve of growth, using statistical band model with exponential line intensity distribution yielding spectral absorption coefficients
Ludwig, C. B.↗
SEARCH · Engineering Papers
Results for “exponential growth”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Gaseous hydrogen-induced cracking of Ti-5Al-2.5Sn.
Study of the kinetics of hydrogen-induced cracking in the Ti-5Al-2.5Sn titanium alloy, which has a structure of acicular alpha platelets in a beta matrix. The crack-growth rate at low stress-intensity levels was found to be exponentially dependent on stress intensity but essentially independent of temperature. The crack-growth rate at intermediate stress-intensity levels was found to be independent of stress intensity but dependent on temperature in such a way that crack-growth rate was controlled by a thermally activated mechanism having an activation energy of 5500 cal/mole and varied as the square root of the hydrogen pressure. The crack-growth rate at stress-intensity levels very near the fracture toughness is presumed to be independent of environment. The results are interpreted to suggest that crack growth at high stress intensities is controlled by normal, bulk failure mechanisms such as void coalescence and the like. At intermediate stress-intensity levels the transport of hydrogen to some interaction site along the alpha-beta boundary is the rate-controlling mechanism. The crack-growth behavior at low stress intensities suggests that the hydrogen interacts at this site to produce a strain-induced hydride which, in turn, induces crack growth by restricting plastic flow at the crack tip.
Williams, D. P.↗
Slow crack growth in glass in combined mode I and mode II loading
Slow crack growth in soda-lime glass under combined mode I and mode II loading was investigated in precracked disk specimens in which pure mode I, pure mode II, and various combinations of mode I and mode II were achieved by loading in diametral compression at selected angles with respect to symmetric radial cracks. It is shown that slow crack growth under these conditions can be described by a simple exponential relationship with elastic strain energy release rate as the effective crack-driving force parameter. It is possible to interpret this equation in terms of theoretical models that treat subcritical crack growth as a thermally activated bond-rupture process with an activation energy dependent on the environment, and the elastic energy release rate as the crack-driving force parameter.
Shetty, D. K.↗
Exact solution of the Lifshitz equations governing the growth of fluctuations in cosmology
The exact solution of the Lifshitz equations governing the cosmological evolution of an initial fluctuation is presented. Lifshitz results valid for squares of the sound velocity equal to zero and 1/3 are extended in closed form to any equation of state where the pressure equals the total energy density times the square of the sound velocity. The solutions embody all the results found previously for special cases of the square of the sound velocity. It is found that the growth of any initial fluctuation is only an exponential function of time with an exponent of not more than 4/3 and is insufficient to produce galaxies unless the initial fluctuation is very large. A possible way to produce very large initial fluctuations by modifying the equation of state by including gravitational interactions is also examined. It is found that a phase transition can occur at baryonic density of 1 nucleon per cubic Planck length or equivalently, at a time of about 10 to the -43rd power sec. At those early times, the masses allowed by causality requirements are too small to be of interest in galaxy formation.
Adams, P. J.↗
Size effects in models for mechanically-stressed protein crystals and aggregates
As protein aggregates increase in size, they become easier to disrupt mechanically. Using the scaling properties of models proposed to govern protein aggregation, the effect of thermal vibrations and gravity are investigated as deforming forces. For typical protein assemblies made of 30 A proteins, the assembled diameter must remain less than 100-10,000 times the molecular radius to survive in finite thermal and gravity fields. The analysis predicts the following experimental outcomes: (1) reductions in gravitational strain should favor larger protein aggregates; (2) in comparing the aggregate stability of different proteins, the addition of peptide chains should stabilize against thermal strain, but should not affect gravitational strain; (3) critical aggregate sizes should show significant (exponential) sensitivity to cluster geometry, solution preparation and growth conditions. The analysis is extended to consider qualitative size effects in crystal damage during X-ray exposure.
Noever, David A.↗
Observations of stratospheric hydrogen fluoride by halogen occultation experiment (HALOE)
The Halogen Occultation Experiment (HALOE) Hydrogen Fluoride (HF) channel on the Upper Atmospheric Research Satellite (UARS) is providing the first global measurements of stratospheric HF, the dominant flourine reservoir in the atmosphere. This paper describes the latitudinal and seasonal variations of HALOE-observed HF in terms of vertical profiles, altitude/latitude cross sections, and column abundances. The HF global distribution shows a 'tracerlike' structure and its column amount increases with latitude, in agreement with previous aircraft measurements of the HF column amount. A comparison between the HALOE HF column above 20 km and the ATMOS 1985 measurements is used to estimate the annual rate of increase of stratospheric HF. Exponential rates of 4.9-6.6%/yr and linear growth rates of 6-8.6%/yr in 1985 and 4.3-5.5%/yr in 1992-1993 are found. HALOE HF measurements during the 1993 Antarctic spring are briefly described. This species behaves like a conserved tracer and its distribution shows an area of enhanced mixing ratios correlated with the polar vortex that has a clear latitude boundary. Finally, simulated HF distributions by the National Center for Atmospheric Research (NCAR) two-dimensional model are used to compare with HALOE observations of HF. Reasonable agreements in the global structure and the absolute amount of HF are found. The differences between the model and the observed results indicate the need for improving treatment of atmospheric dynamics and fluorine-related chemical parameters in the model simulations.
Luo, M.↗
Multiple gravity-wave breaking levels
Gravity waves for which the expression /u(bar)-c/, where u(bar) = mean flow speed and c = wave phase speed, exhibits a sharp minimum in the upper troposphere or lower stratosphere, have decaying amplitudes above this level despite their exponentially decreasing mean density; this decay then ceases and growth resumes. If a gravity wave breaks below the level of /u(bar)-c/min, it will cease breaking above this level, while resuming breaking at some higher, second level which is a lower bound for the level of breaking in the mesosphere. Explicit calculations show the second breaking levels to be close to observed levels of mesospheric gravity wave breaking.
Lindzen, R. S.↗
Comparison of U.S. and Russian Slow Crack Growth Data and Models
Both the US and Russian space programs use similar predictive models for design of fused silica windows on the International space station. The Russian model can be derived from the power expression for slow crack growth (SCG) or “static fatigue.” The US uses both power and exponential models. Despite the similarity of models and data fitting approach (linear regression and right censoring), different SCG parameters have been derived by US and Russian parties for the same material (Russian fused silica) tested in a similar manner. The difference appears to be related to the use of short-term strength data along with the longer-term static fatigue data, with the power law parameter n being very sensitive to the conversion of strength data into equivalent static data. This hybrid approach is feasible if strength data is measured with a constant stress rate and is appropriately converted to a static equivalent. More research into the approach is needed. However, because of the nonlinear behavior of fused silica in log(v) – log(K(I) ) space and the sensitivity of parameter estimation to fit range, the exponential model is a better choice regardless of test method. Functions are given to convert parameters from the Russian model to those in the US model. However, accurate conversion is hampered by the lack of inert strength data. When the same test technique is used, US and Russian materials exhibit very similar parameters.
Silica, strength, impact, crack growth, windows, I↗
Evaluation of alpha-SiC sintering using statistical methods
The effect of time and temperature on the density and strength of alpha-SiC was studied and mathematically modeled using a central composite experimental design. A sintering temperature of 2150 C for 1.7 h maximized the flexural strength and densification values. However, temperatures above 2200 C promoted abnormal grain growth, with resulting appreciable decreases in strength. Flexural strength increased exponentially with increasing density for specimens with densities less than or equal to 92 percent of theoretical.
Hurst, J. B.↗
Software Design Improvements: Software Benefits and Limitations - Part 1
Computer hardware and associated software have been used for many years to process accounting information, to analyze test data and to perform engineering analysis. Now computers and software also control everything from automobiles to washing machines and the number and type of applications are growing at an exponential rate. The size of individual program has shown similar growth. Furthermore, software and hardware are used to monitor and/or control potentially dangerous products and safety-critical systems. These uses include everything from airplanes and braking systems to medical devices and nuclear plants. The question is: how can this hardware and software be made more reliable? Also, how can software quality be improved? What methodology needs to be provided on large and small software products to improve the design and how can software be verified?
Lalli, Vincent R.↗
Shear-induced instability and arch filament eruption - A magnetohydrodynamic (MHD) numerical simulation
A situation wherein a bipolar magnetic field embedded in a stratified solar atmosphere undergoes symmetrical shear motion at the footpoints is investigated via a 2D (nonplanar) MHD simulation. It was found that the vertical plasma flow velocities grow exponentially, leading to a new type of global MHD instability. The growth rate increases almost linearly until it reaches the same order of magnitude as the Alfven speed. Then a nonlinear MHD instability occurs beyond this point. It was found that the central loops are pinched by opposing Lorentz forces, and the outer closed loops stretch upward with the vertically-rising mass flow. The nonlinear dynamical shearing instability is illustrated by a numerical example that is given for three different values of the plasma beta that span several orders of magnitude.
Wu, S. T.↗
Age as a diagnostic of stratospheric transport
Estimates of stratospheric age from observations of long-lived trace gases with increasing tropospheric concentrations invoke the implicit assumption that an air parcel has been transported intact from the tropopical tropopause. However, because of rapid and irreversible mixing in the stratosphere, a particular air parcel cannot be identified with one that left the troposphere at some prior time. The parcel contains a mix of air with a range of transit times, and the mean value over this range is the most appropriate definition of age. The measured tracer concentration is also a mean over the parcel, but its value depends both on the transit time distribution and the past history of the tracer in the troposphere. In principle, only if the tropospheric concentration is increasing linearly can the age be directly inferred. We illustrate these points by employing both a one-dimensional diffusive analog of stratospheric transport, and the general circulation model (GCM) of the Goddard Institute for Space Studies (GISS). Within the limits of the GCM, we estimate the time over which tropospheric tracer concentrations must be approximately linear in order to determine stratospheric age unambiguously; the concentration of an exponentially increasing tracer is a function only of age if the growth time constant is greater than about 7 years, which is true for all the chlorofluorocarbons. More rapid source variations (for example, the annual cycle in CO2) have no such direct relationship with age.
Hall, Timothy M.↗
Thermal and solutal conditions at the tips of a directional dendritic growth front
The line-of-sight averaged, time-dependent dendrite tip concentrations for the diffusion dominated vertical directional solidification of a metal model (ammonium chloride and water) were obtained by extrapolating exponentially fit diffusion layer profiles measured using a laser interferometer. The tip concentrations were shown to increase linearly with time throughout the diffusion dominated growth process for an initially stagnant dendritic array. The process was terminated for the cases chosen by convective breakdown suffered when the conditionally stable diffusion layer exceeded the critical Rayleigh criteria. The transient tip concentrations were determined to significantly exceed the values predicted for steady state, thus producing much larger constitutional undercoolings. This has ramifications for growth speeds, arm spacings and the dendritic structure itself.
Mccay, T. D.↗
Growth-phase thinning of the near-Earth current sheet during the CDAW 6 substorm
The thinning of the near-Earth current sheet during the growth phase of the Coordinated Data Analysis Workshop (CDAW) 6 magnetospheric substorm is studied. The expansion onset of the substorm occurred at 1054 UT, March 22, 1979. During the growth phase, two spacecraft, International Sun Earth Explorer (ISEE) 1 and ISEE 2, were within the current sheet approximately 13 R(sub E) from the Earth and obtained simultaneous high-resolution magnetic data at two points in the current sheet. Plasma data were also provided by the ISEE spacecraft and solar wind data by IMP 8. To facilitate the analysis, the GSM magnetic field data are transformed to a 'neutral sheet coordinate system' in which the new x axis is parallel to the average magnetic field above and below the neutral sheet and the new y axis lies in the GSM equatorial plane. A model based on the assumption that the current sheet is a time-invariant structure fails to predict neutral sheet crossing times. Consequently, the Harris sheet model, which allows one to remove the restriction of time invariancy, is used instead. It is found that during the growth phase, a model parameter corresponding to the thickness of the current sheet decreased exponentially from about 5 R(sub E) to 1 R(sub E) with a time constant of about 14 min. In addition, the ISEE 1 and ISEE 2 neutral sheet crossings after expansion onset indicate that the neutral sheet was moving upward at 7 km/s relative to the spacecraft. Since both crossings occurred in approximately 80 s, the current sheet thickness is estimated to be about 500 km. These results demonstrate that the near-Earth current sheet undergoes dramatic thinning during the substorm growth phase and expansion onset.
Sanny, Jeff↗
Expression of Genes Associated with DNA Damage Sensing in Human Fibroblasts Exposed to Low-dose-rate Gamma Rays
Understanding of the molecular response to low-dose and low-dose-rate radiation exposure is essential for the extrapolation of high-dose radiation risks to those at dose levels relevant to space and other environmental concerns. Most of the reported studies of gene expressions induced by low-dose or low-dose-rate radiation were carried out on exponentially growing cells. In the present study, we analyzed expressions of 84 genes associated with DNA damage sensing using real time PCR in human fibroblasts in mostly G1 phase of the cell cycle. The cells were exposed continuously to gamma rays at a dose rate of 0.8 cGy/hr for 1, 2, 6 or 24 hrs at 37 C throughout the exposure. The total RNA was isolated immediately after the exposure was terminated. Of the 84 genes, only a few showed significant changes of the expression level. Some of the genes (e.g. DDit3 and BTG2) were found to be up or down regulated only after a short period of exposure, while other genes (e.g. PRKDC) displayed a highest expression level at the 24 hr time point. The expression profiles for the exposed cells which had a smaller portion of G1 cells indicated more cell cycle signaling and DNA repair genes either up or down regulated. Interestingly, the panel of genes changed from radiation exposure in G1 cells is different from the panel in cells having less G1 arrest cells. The gene expression profile of the cells responding to low-dose-radiation insult apparently depends on the cell growth stage. The response pathway in G1 cells may differ from that in exponentially growing cells.
Zhang, Ye↗
Time development of a perturbed-spherical nucleus in a pure supercooled liquid. I - Power-law growth of morphological instabilities. II - Nonlinear development
The linear growth stage of the morphological instabilities developing at the liquid-solid interface during crystal growth from an axisymmetric spherical nucleus is analyzed. The corresponding growth rate parameters are calculated numerically, and it is shown that morphological instabilities for free growth evolve according to a power law in agreement with WKB results and contrary to an exponential law found in a quasi-stationary approximation. The time evolution of an arbitrary perturbed liquid-solid interface from a linear into the nonlinear stage is studied. The initial perturbations include the eigenfunctions for the linear problem, localized perturbations of the grain-boundary type, and a stochastic noise. It is shown that the perturbations grow and spread in a wavelike manner. The formation of a predendritic growth stage is characterized by establishment of constant values of tip radius and velocity.
Pines, V.↗
DE-1 observations of hole electron distribution functions and the cyclotron maser resonance
The hole electron distribution functions observed by the DE-1 satellite within inverted-V events at altitudes of between 9000 km and 15,000 km are examined as a possible free energy source for exciting Z-mode radiation through cyclotron maser resonance. In the DE-1 observations the hole distribution function had center velocities varying between 8000 km/s and 20,000 km/s, with the radii varying between 2000 km/s and 10,000 km/s. The observed distribution function is fitted by an exponential function around the center of the hole, and is used to calculate growth rates of Z-mode radiation. Growth rates as high as 0.001 of the electron gyrofrequency are obtained. It is also shown that the observed hole distribution functions can excite Z-mode radiation at wave frequencies slightly above the gyrofrequency, and wave propagation angles slightly below 90 deg in the source region. The results suggest that the hole distribution function could provide additional amplification for Z-mode waves in the auroral zone.
Lin, C. S.↗
Random Lorentz band model with exponential- tailed S super -1 line-intensity distribution function.
1/s line intensity distribution function for molecular spectra representation using growth curves calculated for Lorentz lines
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