Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “beta”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 739 records · Page 41

Improving the chi-squared approximation for bivariate normal tolerance regions

Let X be a two-dimensional random variable distributed according to N2(mu,Sigma) and let bar-X and S be the respective sample mean and covariance matrix calculated from N observations of X. Given a containment probability beta and a level of confidence gamma, we seek a number c, depending only on N, beta, and gamma such that the ellipsoid R = (x: (x - bar-X)'S(exp -1) (x - bar-X) less than or = c) is a tolerance region of content beta and level gamma; i.e., R has probability gamma of containing at least 100 beta percent of the distribution of X. Various approximations for c exist in the literature, but one of the simplest to compute -- a multiple of the ratio of certain chi-squared percentage points -- is badly biased for small N. For the bivariate normal case, most of the bias can be removed by simple adjustment using a factor A which depends on beta and gamma. This paper provides values of A for various beta and gamma so that the simple approximation for c can be made viable for any reasonable sample size. The methodology provides an illustrative example of how a combination of Monte-Carlo simulation and simple regression modelling can be used to improve an existing approximation.

Feiveson, Alan H.↗

Long-wavelength asymptotics of unstable crossflow modes, including the effect of surface curvature

Stationary vortex instabilities with wavelengths significantly larger than the thickness of the underlying three-dimensional boundary layer are studied with asymptotic methods. The long-wavelength Rayleigh modes are locally neutral and are aligned with the direction of the local inviscid streamline. For a spanwise wave number Beta much less than 1, the spatial growth rate of these vortices is O(Beta(exp 3/2)). When Beta becomes O(R(exp -1/7)), the viscous correction associated with a thin sublayer near the surface modifies the inviscid growth rate to the leading order. As Beta is further decreased through this regime, viscous effects assume greater significance and dominate the growth-rate behavior. The spatial growth rate becomes comparable to the real part of the wave number when Beta = O(R(exp -1/4)). At this stage, the disturbance structure becomes fully viscous-inviscid interactive and is described by the triple-deck theory. For even smaller values of Beta, the vortex modes become nearly neutral again and align themselves with the direction of the wall-shear stress. Thus, the study explains the progression of the crossflow-vortex structure from the inflectional upper branch mode to nearly neutral long-wavelength modes that are aligned with the wall-shear direction.

Choudhari, Meelan↗

Infrared spectroscopy of Seyfert 2 galaxies: A look through the obscuring Torus?

We present both high-resolution (R = 1260) and low-resolution (R = 345 and 425) J-band spectra of a sample of 15 Seyfert 2 galaxies. Our goal is to look for broad Pa beta lines, indicating broad-line regions which are hidden by dust from our view at optical wavelengths. Of the 15 objects studied here, three have broad Pa beta lines: MCG-05.23.16, Mrk 463E, and NGC 2992. Mrk 176 and NGC 5728 may also have weak broad lines. In NGC 5506, previously reported to have broad Pa beta and hydrogen alpha lines, we find that the Pa beta line profile is continuous and has the same shape as the nearby line (Fe II) lambda 1.2567, which should not have a broad component. We interpret these observations as gas from the narrow-line region (NLR) with no broad component. In NGC 5506, however, the NLR profiles become broader with increasing wavelength, indicating that highly reddened wings are becoming more readily visible at the longer wavelengths. We confirm the correlation of (O I) lambda 6300/hydrogen alpha and (Fe II) lambda 1.644/Br gamma (the latter transformed to (Fe II) lambda 1.2567/Pa beta to compare with our data) found by previous authors when comparing active galactic nuclei (AGNs), supernova remnants, starbursts, and H II regions. The correlation confirms that in all of these objects both (O I) lambda 6300 and the (Fe II) lines come from partially ionized regions in which hydrogen is mostly neutral. Comparison of the infrared optical depths with column depths determined from X-ray data show a general tendency for the objects with detected broad Pa beta to have lower X-ray columns.

Goodrich, Robert W.↗

A test of the Hall-MHD model: Application to low-frequency upstream waves at Venus

Early studies suggested that in the range of parameter space where the wave angular frequency is less than the proton gyrofrequency and the plasma beta, the ratio of the thermal to magnetic pressure, is less than 1 magnetohydrodynamics provides an adequate description of the propagating modes in a plasma. However, recently, Lacombe et al. (1992) have reported significant differences between basic wave characteristics of the specific propagation modes derived from linear Vlasov and Hall-magnetohydrodynamic (MHD) theories even when the waves are only weakly damped. In this paper we compare the magnetic polarization and normalization magnetic compression ratio of ultra low frequency (ULF) upstream waves at Venus with magnetic polarization and normalized magnetic compression ratio derived from both theories. We find that while the 'kinetic' approach gives magnetic polarization and normalized magnetic compression ratio consistent with the data in the analyzed range of beta (0.5 less than beta less than 5) for the fast magnetosonic mode, the same wave characteristics derived from the Hall-MHD model strongly depend on beta and are consistent with the data only at low beta for the fast mode and at high beta for the intermediate mode.

Orlowski, D. S.↗

Relativity Parameters Determined from Lunar Laser Ranging

Analysis of 24 years of lunar laser ranging data is used to test the principle of equivalence, geodetic precession, the PPN parameters beta and gamma, and G/G. Recent data can be fitted with a rms scatter of 3 cm. (a) Using the Nordtvedt effect to test the principle of equivalence, it is found that the Moon and Earth accelerate alike in the Sun's field. The relative accelerations match to within 5 x 10(exp -13) . This limit, combined with an independent determination of y from planetary time delay, gives beta. Including the uncertainty due to compositional differences, the parameter beta differs from unity by no more than 0.0014; and, if the weak equivalence principle is satisfied, the difference is no more than 0.0006. (b) Geodetic precession matches its expected 19.2 marc sec/yr rate within 0.7%. This corresponds to a 1% test of gamma. (c) Apart from the Nordtvedt effect, beta and gamma can be tested from their influence on the lunar orbit. It is argued theoretically that the linear combination 0.8(beta) + 1.4(gamma) can be tested at the 1% level of accuracy. For solutions using numerically derived partial derivatives, higher sensitivity is found. Both 6 and y match the values of general relativity to within 0.005, and the linear combination beta+ gamma matches to within 0,003, but caution is advised due to the lack of theoretical understanding of these sensitivities. (d) No evidence for a changing gravitational constant is found, with absolute value of G/G less than or equal to 8 x lO(exp -12)/yr. There is significant sensitivity to G/G through solar perturbations on the lunar orbit.

Williams, J. G.↗

A Scale-Invariant Model of Statistical Mechanics and Modified Forms of the First and the Second Laws of Thermodynamics

A scale-invariant statistical theory of fields is presented that leads to invariant definition of density, velocity, temperature, and pressure, The definition of Boltzmann constant is introduced as k(sub k) = m(sub k)v(sub k)c = 1.381 x 10(exp -23) J x K(exp -1), suggesting that the Kelvin absolute temperature scale is equivalent to a length scale. Two new state variables called the reversible heat Q(sub rev) = TS and the reversible work W(sub rev) = PV are introduced. The modified forms of the first and second law of thermodynamics are presented. The microscopic definition of heat (work) is presented as the kinetic energy due to the random (peculiar) translational, rotational, and pulsational motions. The Gibbs free energy of an element at scale Beta is identified as the total system energy at scale (Beta-1), thus leading to an invariant form of the first law of thermodynamics U(sub Beta) = Q(sub Beta) - W(sub Beta) +N(e3)U(sub Beta-1).

Sohrab, Siavash H.↗

An XMM Study of Low-Activity Coronal Stars of 1-2 Solar Masses

The objective of these observations was to take advantage of the large collecting area and sensitivity of the European Space Agency's XMM-Newton telescope to obtain X ray grating spectra of two relatively inactive late type stars, Beta Geminorun (K0 III) and the solar analog Beta Hydri (G2 IV). The observations were carried out as scheduled, achieving exposure times of 36 kiloseconds for Beta Gem and 27 kiloseconds for Beta Hyi. Unfortunately both stars were too faint to yield spectra with enough signal-to-noise for any further analysis. Consequently, there are no scientific results to report. The following pages illustrate the very weak X ray spectra that were obtained with the two RGS grating instruments for each star, first Beta Gem and then beta Hyi.

Simon, Theodore↗

Titanium Alloys and Processing for High Speed Aircraft

Commercially available titanium alloys as well as emerging titanium alloys with limited or no production experience are being considered for a variety of applications to high speed commercial aircraft structures. A number of government and industry programs are underway to improve the performance of promising alloys by chemistry and/or processing modifications and to identify appropriate alloys and processes for specific aircraft structural applications. This paper discusses some of the results on the effects of heat treatment, service temperatures from - 54 C to +177 C, and selected processing on the mechanical properties of several candidate beta and alpha-beta titanium alloys. Included are beta alloys Timetal 21S, LCB, Beta C, Beta CEZ, and Ti-10-2-3 and alpha-beta alloys Ti-62222, Ti-6242S, Timetal 550, Ti-62S, SP-700, and Corona-X. The emphasis is on properties of rolled sheet product form and on the superplastic properties and processing of the materials.

Brewer, William D.↗

Post-translational control of collagen fibrillogenesis in mineralizing cultures of chick osteoblasts

Cultured osteoblasts from chick embryo calvaria were used as a model system to investigate the post-translational extracellular mechanisms controlling the macroassembly of collagen fibrils. The results of these studies demonstrated that cultured osteoblasts secreted a collagenous extracellular matrix that assembled and mineralized in a defined temporal and spatial sequence. The assembly of collagen occurred in a polarized fashion, such that successive orthogonal arrays of fibrils formed between successive cell layers proceeding from the culture surface toward the media. Mineralization followed in the same manner, being observed first in the deepest and oldest fibril layers. Collagen fibrillogenesis, the kinetics of cross-link formation, and collagen stability in the extracellular matrix of the cultures were examined over a 30 day culture period. Between days 8 and 12 in culture, collagen fibril diameters increased from < 30 nm to an average of 30-45 nm. Thereafter, diameters ranged in size from 20 to 200 nm. Quantitation of the collagen cross-linking residues, hydroxylysyl pyridinoline (HP) and lysyl pyridinoline (LP), showed that these mature cross-links increased from undetectable levels to concentrations found in normal chick bone. Analysis of the kinetics of their formation by pulse-chase labeling the cultures with [3H]lysine showed a doubling time of approximately 5 days. The relationships between cross-link formation, fibrillogenesis, and collagen stability were examined in cultures treated with beta-aminopropionitrile (beta-APN), a potent inhibitor of lysyl oxidase and cross-link formation. In beta-APN-treated cultures, total collagen synthesis was increased twofold, with no change in mRNA levels for type I collagen, whereas the amount of collagen accumulated in the cell layer was decreased by 50% and mineral deposition was reduced. The rate of collagen retention in the matrix was assessed by pulse-chase analysis of [3H]proline over a 16 day period in control and beta-APN-treated cultures. In control cultures, about 20% of the labeled collagen was lost from the cell layers over a 16 day period compared with > 80% in the presence of beta-APN. The beta-APN-treated cultures also showed a wider diversity of fibril diameters with a median in the > 45-60 nm range. In summary, these data suggest that cross-linking and assembly of collagen fibrils secreted by osteoblasts in vitro occur in a fashion similar to that found in vivo. The rate of cross-link formation is relatively constant and may be correlated with increasing collagen mass.(ABSTRACT TRUNCATED AT 400 WORDS).

NASA Discipline Musculoskeletal↗

Mission Analysis for LEO Microwave Power-Beaming Station in Orbital Launch of Microwave Lightcraft

A detailed mission analysis study has been performed for a 1 km diameter, rechargeable satellite solar power station (SPS) designed to boost 20m diameter, 2400 kg Micr,oWave Lightcraft (MWLC) into low earth orbit (LEO) Positioned in a 476 km daily-repeating oi.bit, the 35 GHz microwave power station is configured like a spinning, thin-film bicycle wheel covered by 30% efficient sola cells on one side and billions of solid state microwave transmitter elements on the other, At the rim of this wheel are two superconducting magnets that can stor,e 2000 G.J of energy from the 320 MW, solar array over a period of several orbits. In preparation for launch, the entire station rotates to coarsely point at the Lightcraft, and then phases up using fine-pointing information sent from a beacon on-board the Lightcraft. Upon demand, the station transmits a 10 gigawatt microwave beam to lift the MWLC from the earth surface into LEO in a flight of several minutes duration. The mission analysis study was comprised of two parts: a) Power station assessment; and b) Analysis of MWLC dynamics during the ascent to orbit including the power-beaming relationships. The power station portion addressed eight critical issues: 1) Drag force vs. station orbital altitude; 2) Solar pressure force on the station; 3) Station orbital lifetime; 4) Feasibility of geo-magnetic re-boost; 5) Beta angle (i..e., sola1 alignment) and power station effective area relationship; 6) Power station percent time in sun vs, mission elapsed time; 7) Station beta angle vs.. charge time; 8) Stresses in station structures.. The launch dynamics portion examined four issues: 1) Ascent mission/trajecto1y profile; 2) MWLC/power-station mission geometry; 3) MWLC thrust angle vs. time; 4) Power station pitch rate during power beaming. Results indicate that approximately 0 58 N of drag force acts upon the station when rotated edge-on to project the minimum frontal area of 5000 sq m. An ion engine or perhaps an electrodynamic thruster (i.e., geomagnetic re-boost) station-keeping system can maintain the orbit altitude. The rate at which the power station s superconducting magnetic energy storage system (SMES) is 'charged' directly relates to the beta angle since the station is operating in the edge-on attitude. The maximum charge rate occurs when the beta angle is at its maximum because time in the sun and projected area of the station are, too, at their maximums For the maximum charge of 2000 G.J with a maximum beta angle of 52 degrees, approximately 3 hours (2 orbital revolutions) are required to reach the full charge, while about 16 hours (10.3 revolutions) are required when the beta angle is 10 degrees. Overall, the LEO station concept appears to be a viable candidate fo1 the formidable power-beaming infrastructure needed to boost MWLC into low earth orbit.

Myrabo, L. N.↗

Solar Wind Proton Temperature Anisotropy: Linear Theory and WIND/SWE Observations

We present a comparison between WIND/SWE observations (Kasper et al., 2006) of beta parallel to p and T perpendicular to p/T parallel to p (where beta parallel to p is the proton parallel beta and T perpendicular to p and T parallel to p are the perpendicular and parallel proton are the perpendicular and parallel proton temperatures, respectively; here parallel and perpendicular indicate directions with respect to the ambient magnetic field) and predictions of the Vlasov linear theory. In the slow solar wind, the observed proton temperature anisotropy seems to be constrained by oblique instabilities, by the mirror one and the oblique fire hose, contrary to the results of the linear theory which predicts a dominance of the proton cyclotron instability and the parallel fire hose. The fast solar wind core protons exhibit an anticorrelation between beta parallel to c and T perpendicular to c/T parallel to c (where beta parallel to c is the core proton parallel beta and T perpendicular to c and T parallel to c are the perpendicular and parallel core proton temperatures, respectively) similar to that observed in the HELIOS data (Marsch et al., 2004).

Hellinger, P.↗

NASA Models of Space Radiation Induced Cancer, Circulatory Disease, and Central Nervous System Effects

The risks of late effects from galactic cosmic rays (GCR) and solar particle events (SPE) are potentially a limitation to long-term space travel. The late effects of highest concern have significant lethality including cancer, effects to the central nervous system (CNS), and circulatory diseases (CD). For cancer and CD the use of age and gender specific models with uncertainty assessments based on human epidemiology data for low LET radiation combined with relative biological effectiveness factors (RBEs) and dose- and dose-rate reduction effectiveness factors (DDREF) to extrapolate these results to space radiation exposures is considered the current "state-of-the-art". The revised NASA Space Risk Model (NSRM-2014) is based on recent radio-epidemiology data for cancer and CD, however a key feature of the NSRM-2014 is the formulation of particle fluence and track structure based radiation quality factors for solid cancer and leukemia risk estimates, which are distinct from the ICRP quality factors, and shown to lead to smaller uncertainties in risk estimates. Many persons exposed to radiation on earth as well as astronauts are life-time never-smokers, which is estimated to significantly modify radiation cancer and CD risk estimates. A key feature of the NASA radiation protection model is the classification of radiation workers by smoking history in setting dose limits. Possible qualitative differences between GCR and low LET radiation increase uncertainties and are not included in previous risk estimates. Two important qualitative differences are emerging from research studies. The first is the increased lethality of tumors observed in animal models compared to low LET radiation or background tumors. The second are Non- Targeted Effects (NTE), which include bystander effects and genomic instability, which has been observed in cell and animal models of cancer risks. NTE's could lead to significant changes in RBE and DDREF estimates for GCR particles, and the potential effectiveness of radiation mitigator's. The NSRM- 2014 approaches to model radiation quality dependent lethality and NTE's will be described. CNS effects include both early changes that may occur during long space missions and late effects such as Alzheimer's disease (AD). AD effects 50% of the population above age 80-yr, is a degenerative disease that worsens with time after initial onset leading to death, and has no known cure. AD is difficult to detect at early stages and the small number of low LET epidemiology studies undertaken have not identified an association with low dose radiation. However experimental studies in mice suggest GCR may lead to early onset AD. We discuss modeling approaches to consider mechanisms whereby radiation would lead to earlier onset of occurrence of AD. Biomarkers of AD include amyloid beta (A(Beta)) plaques, and neurofibrillary tangles (NFT) made up of aggregates of the hyperphosphorylated form of the micro-tubule associated, tau protein. Related markers include synaptic degeneration, dentritic spine loss, and neuronal cell loss through apoptosis. Radiation may affect these processes by causing oxidative stress, aberrant signaling following DNA damage, and chronic neuroinflammation. Cell types to be considered in multi-scale models are neurons, astrocytes, and microglia. We developed biochemical and cell kinetics models of DNA damage signaling related to glycogen synthase kinase-3(Beta) (GSK3(Beta)) and neuroinflammation, and considered multi-scale modeling approaches to develop computer simulations of cell interactions and their relationships to A(Beta) plaques and NFTs. Comparison of model results to experimental data for the age specific development of A(Beta) plaques in transgenic mice will be discussed.

Cucinotta, Francis A.↗

Adenovirus-mediated gene delivery to hypothalamic magnocellular neurons in mice

Vasopressin is synthesized by magnocellular neurons in supraoptic (SON) and paraventricular (PVN) hypothalamic nuclei and released by their axon terminals in the neurohypophysis (NH). With its actions as an antidiuretic hormone and vasoactive agent, vasopressin plays a pivotal role in the control of body fluids and cardiovascular homeostasis. Because of its well-defined neurobiology and functional importance, the SON/PVN-NH system is ideal to establish methods for gene transfer of genetic material into specific pathways in the mouse central nervous system. In these studies, we compared the efficiency of transferring the gene lacZ, encoding for beta-galactosidase (beta-gal), versus a gene encoding for green fluorescent protein by using replication-deficient adenovirus (Ad) vectors in adult mice. Transfection with viral concentrations up to 2 x 10(7) plaque-forming units per coverslip of NH, PVN, and SON in dissociated, cultured cells caused efficient transfection without cytotoxicity. However, over an extended period of time, higher levels (50% to 75% of the cells) of beta-gal expression were detected in comparison with green fluorescent protein (5% to 50% of the cells). With the use of a stereotaxic approach, the pituitary glands of mice were injected with Ad (4 x 10(6) plaque-forming units). In material from these animals, we were able to visualize the expression of the beta-gal gene in the NH and in magnocellular neurons of both the PVN and SON. The results of these experiments indicate that Ad-Rous sarcoma virus promoter-beta-gal is taken up by nerve terminals at the injection site (NH) and retrogradely transported to the soma of the neurons projecting to the NH. We conclude that the application of these experimental approaches will provide powerful tools for physiological studies and potential approaches to deliver therapeutic genes to treat diseases.

Non-NASA Center↗

Development of single crystal membranes

The design and construction of a high pressure crystal growth chamber was accomplished which would allow the growth of crystals under inert gas pressures of 2 MN/sq m (300 psi). A novel crystal growth technique called EFG was used to grow tubes and rods of the hollandite compounds, BaMgTi7O16, K2MgTi7O16, and tubes of sodium beta-alumina, sodium magnesium-alumina, and potassium beta-alumina. Rods and tubes grown are characterized using metallographic and X-ray diffraction techniques. The hollandite compounds are found to be two or three-phase, composed of coarse grained orientated crystallites. Single crystal c-axis tubes of sodium beta-alumina were grown from melts containing excess sodium oxide. Additional experiments demonstrated that crystals of magnesia doped beta-alumina and potassium beta-alumina also can be achieved by this EFG technique.

Stormont, R. W.↗

Effect of additions of coarse grains and fibers on the densification of a sinterable SiC

This note reports the effects on densification of independent additions of coarse equiaxed SiC grains and fibrous SiC that were mixed with fine beta-SiC to develop a duplex microstructure with improved toughness. The fine-matrix SiC did not contain excess boron and carbon. The equiaxed CVD beta-SiC was introduced in the fine beta-SiC matrix material in amounts of 5 and 10 wt%. Results indicate that the CVD beta-SiC, which is quite coarse, exhibits little indication of sinterability. The effect of these coarse-grained and fibrous additions on the sinterability of fine beta-SiC may result from a geometric type of interaction. This interpretation is reinforced by X-ray diffraction of the powders and sintered pellets via monochromatic CuK-alpha radiation; the diffraction patterns of the sintered composite structures are virtually a combination of those of the components. The addition of nonsinterable SiC to the sinterable material slightly reduces sinterability, the larger particles interacting geometrically with the fine matrix material to prevent complete densification.

Abe, H.↗

The 20 March 1980 occultation by the Uranian rings

On March 20, 1980, observations of occultations by rings alpha, beta, gamma, delta, and epsilon were observed from Cerro Tololo and Sutherland. A model ring profile was fit to the data to obtain the midtimes of the occultations and the widths of the profiles. A 14-parameter kinematic model, including J sub 2, J sub 4, and some of the orbital elements for rings 4, alpha, beta, and epsilon as free parameters, was fit to these data and previous ring occultation timings. The results yield J sub 2 = (3.396 + or - 0.020) x 10 to the -3 and a 2 sigma upper limit, absolute value of J sub 4 less than 7 x 10 to the -5th. Uniform precession models for rings alpha, beta are established and the dispersion in the values of semimajor axes and eccentricities for rings alpha, beta, and epsilon have been obtained. If self-gravity is the cause of the uniform precession, the mass of the beta ring is estimated at approximately 4 x 10 to the 16th g; the mass of the alpha ring probably is also near this value.

Elliot, J. L.↗

IUE and visual spectrophotometry of Markarian 9, Markarian 10, and 3C 390.3

Ultraviolet spectra from IUE are combined with visual spectra for the three type I Seyfert galaxies Mrk 9, Mrk 10, and 3C 390.3. The 2175 A interstellar feature is measured well enough in Mrk 9 to indicate that the extinction corresponding to E(B-V) = 0.14 + or - 0.04 is in the galaxy. Mrk 10 displays evidence for 2175 A absorption and also yields E(B-V) = 0.14 + or - 0.07, while the continuum for 3C 390.3 is too weak to positively detect the feature. It is found, after correcting for reddening, that the line-intensity ratio L(alpha)/H(beta) ranges from 8 to 18, while that for H(alpha)/H(beta) goes from 2.1 to 5.4. It is noted that the He II 1640/4686 line ratio is uncertain but appears to be consistent with the recombination value of about 8. If photoionization is assumed, a comparison of the strengths of L(alpha) and H(beta) with the UV ionizing flux suggests that H(beta) is enhanced rather than L(alpha) depressed. When a comparison is made with similar ratios in quasars, L(alpha) is found to be much stronger and H(beta) slightly stronger in Seyferts than in quasars.

Oke, J. B.↗

X-ray, optical, and radio properties of quasars

A sample of 26 low-redshift quasars was examined for relationships between X-ray luminosity and optical spectroscopic features; all quasars were observed with the Einstein Observatory and with the IDS on the Lick 3 meter telescope. Evidence is found for correlations between quasar X-ray luminosity and both optical continuum luminosity and H-beta luminosity. In the latter case, there is a smooth relationship connecting quasars, Seyfert 1, and Seyfert 2 galaxies. For the quasars in this sample, there is also a strong correlation between optical continuum luminosity and both the H-beta luminosity and equivalent width. Evidence is also found for a weak correlation between alpha-prime (ox), the mean continuum spectral index between 5000 A and 2 keV, and Fe II equivalent width, H-beta equivalent width, H-beta line width at zero intensity, and the ratio of H-beta equivalent width to its line width at zero intensity.

Blumenthal, G. R.↗