Search NASA⌕ Search

SEARCH · Search NASA

Results for “Cross correlation”

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 433 records · Page 24
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Constraining the scatter in the galaxy–halo connection at Milky Way masses

In this work, we develop and implement two new methods for constraining the scatter in the relationship between galaxies and dark matter haloes. These new techniques are sensitive to the scatter at low halo masses, making them complementary to previous constraints that are dependent on clustering amplitudes or rich galaxy groups, both of which are only sensitive to more massive haloes. In both of our methods, we use a galaxy group finder to locate central galaxies in the Sloan Digital Sky Survey main galaxy sample. Our first technique uses the small-scale cross-correlation of central galaxies with all lower mass galaxies. This quantity is sensitive to the satellite fraction of low-mass galaxies, which is in turn driven by the scatter between haloes and galaxies. The second technique uses the kurtosis of the distribution of line-of-sight velocities between central galaxies and neighbouring galaxies. This quantity is sensitive to the distribution of halo masses that contain the central galaxies at fixed stellar mass. Theoretical models are constructed using peak halo circular velocity, Vpeak, as our property to connect galaxies to haloes, and all comparisons between theory and observation are made after first passing the model through the group-finding algorithm. We parametrize scatter as a lognormal distribution in M* at fixed Vpeak, σ[M*|Vpeak]. The cross-correlation technique yields a constraint of σ[M*|Vpeak] = 0.27 ± 0.05 dex at a mean Vpeak of 168 km s-1, corresponding to a scatter in log M* at fixed Mh of σ[M*|Mh] = 0.38 ± 0.06 dex at $M_\text{h}=10^{11.8}\, \text{M}_\odot$. The kurtosis technique yields σ[M*|Vpeak] = 0.30 ± 0.03 at Vpeak = 209 km s-1, corresponding to σ[M*|Mh] = 0.34 ± 0.04 at $M_\text{h}=10^{12.2}\, \text{M}_\odot$. The values of σ[M*|Mh] are significantly larger than the constraints at higher masses, in agreement with the results of hydrodynamic simulations. This increase is only partly due to the scatter between Vpeak and Mh, and it represents an increase of nearly a factor of 2 relative to the values inferred from clustering and group studies at high masses.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1999

Laser Light Scattering with Multiple Scattering Suppression Used to Measure Particle Sizes

Laser light scattering is the technique of choice for noninvasively sizing particles in a fluid. The members of the Advanced Technology Development (ATD) project in laser light scattering at the NASA Lewis Research Center have invented, tested, and recently enhanced a simple and elegant way to extend the concentration range of this standard laboratory particle-sizing technique by several orders of magnitude. With this technique, particles from 3 nm to 3 mm can be measured in a solution. Recently, laser light scattering evolved to successfully size particles in both clear solutions and concentrated milky-white solutions. The enhanced technique uses the property of light that causes it to form tall interference patterns at right angles to the scattering plane (perpendicular to the laser beam) when it is scattered from a narrow laser beam. Such multiple-scattered light forms a broad fuzzy halo around the focused beam, which, in turn, forms short interference patterns. By placing two fiber optics on top of each other and perpendicular to the laser beam (see the drawing), and then cross-correlating the signals they produce, only the tall interference patterns formed by singly scattered light are detected. To restate this, unless the two fiber optics see the same interference pattern, the scattered light is not incorporated into the signal. With this technique, only singly scattered light is seen (multiple-scattered light is rejected) because only singly scattered light has an interference pattern tall enough to span both of the fiber-optic pickups. This technique is simple to use, easy to align, and works at any angle. Placing a vertical slit in front of the signal collection fibers enhanced this approach. The slit serves as an optical mask, and it significantly shortens the time needed to collect good data by selectively masking out much of the unwanted light before cross-correlation is applied.

Meyer, William V.↗
NASA NTRS2004

Rapid Chemometric Filtering of Spectral Data

A method of rapid, programmable filtering of spectral transmittance, reflectance, or fluorescence data to measure the concentrations of chemical species has been proposed. By programmable is meant that a variety of spectral analyses can readily be performed and modified in software, firmware, and/or electronic hardware, without need to change optical filters or other optical hardware of the associated spectrometers. The method is intended to enable real-time identification of single or multiple target chemical species in applications that involve high-throughput screening of multiple samples. Examples of such applications include (but are not limited to) combinatorial chemistry, flow cytometry, bead assays, testing drugs, remote sensing, and identification of targets. The basic concept of the proposed method is to perform real-time crosscorrelations of a measured spectrum with one or more analytical function(s) of wavelength that could be, for example, the known spectra of target species. Assuming that measured spectral intensities are proportional to concentrations of target species plus background spectral intensities, then after subtraction of background levels, it should be possible to determine target species concentrations from cross-correlation values. Of course, the problem of determining the concentrations is more complex when spectra of different species overlap, but the problem can be solved by use of multiple analytical functions in combination with computational techniques that have been developed previously for analyses of this type. The method is applicable to the design and operation of a spectrometer in which spectrally dispersed light is measured by means of an active-pixel sensor (APS) array. The row or column dimension of such an array is generally chosen to be aligned along the spectral-dispersion dimension, so that each pixel intercepts light in a narrow spectral band centered on a wavelength that is a known function of the pixel position. The proposed method admits of two hardware implementations for computing cross-correlations in real time.

Beaman, Gregory↗
DOE OSTI2022

Cool circumgalactic gas in galaxy clusters: connecting the DESI legacy imaging survey and SDSS DR16 Mg ιι absorbers

Herein we investigate the cool gas absorption in galaxy clusters by cross-correlating Mg II absorbers detected in quasar spectra from data release 16 of the Sloan Digital Sky Survey (SDSS) with galaxy clusters identified in the Dark Energy Spectroscopic Instrument (DESI) survey. We find significant covering fractions (⁠1–5percent within r 500 , depending on the chosen redshift interval), ~4–5 times higher than around random sightlines. While the covering fraction of cool gas in clusters decreases with increasing mass of the central galaxy, the total Mg II mass within r 500 is none the less ~10 times higher than for SDSS luminous red galaxies. The Mg II covering fraction versus impact parameter is well described by a power law in the inner regions and an exponential function at larger distances. The characteristic scale of the transition between these two regimes is smaller for large equivalent width absorbers. Cross-correlating Mg II absorption with photo–z selected cluster member galaxies from DESI reveals a statistically significant connection. The median projected distance between Mg II absorbers and the nearest cluster member is ~200 kpc, compared to ~500 kpc in random mocks with the same galaxy density profiles. We do not find a correlation between Mg II strength and the star formation rate of the closest cluster neighbour. This suggests that cool gas in clusters, as traced by Mg II absorption, is: (i) associated with satellite galaxies, (ii) dominated by cold gas clouds in the intracluster medium, rather than by the interstellar medium of galaxies, and (iii) may originate in part from gas stripped from these cluster satellites in the past.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

The imprint of cosmic voids from the DESI Legacy Survey DR9 Luminous Red Galaxies in the Planck 2018 lensing map through spectroscopically calibrated mocks

The cross-correlation of cosmic voids with the lensing convergence (κ) map of the Cosmic Microwave Background (CMB) fluctuations provides a powerful tool to refine our understanding of the current cosmological model. However, several studies have reported a moderate tension (up to ∼2σ) between the lensing imprint of cosmic voids on the observed CMB and the ΛCDM signal predicted by simulations. To address this “lensing-is-low” tension and to obtain new, precise measurements of the signal, we exploit the large DESI Legacy Survey Luminous Red Galaxy (LRG) data set, covering approximately 19 500 deg 2 of the sky and including about 10 million LRGs at z < 1.05. Our ΛCDM template was created using the Buzzard mocks, which we specifically calibrated to match the clustering properties of the observed galaxy sample by exploiting more than one million DESI spectra. We identified our catalogs of 3D voids in the range 0.35 < z < 0.95 and cross-correlated them through a stacking methodology, dividing the sample into bins according to the redshift and λv values of the voids. For the full void sample, we report a 14σ detection of the lensing signal, with A κ = 1.016 ± 0.054, which increases to 17σ when considering the void-in-void (A κ = 0.944 ± 0.064) and the void-in-cloud (A κ = 0.975 ± 0.060) populations individually, the highest detection significance for studies of this kind. We observe a full agreement between observations and ΛCDM mocks across all redshift bins, sky regions, and void populations considered. In addition to these findings, our analysis highlights the importance of accurately matching sparseness and redshift error distributions between mocks and observations, as well as the role of λ v in enhancing the signal-to-noise ratio through void population discrimination.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Simulating the Multi-epoch Direct Detection Technique to Isolate the Thermal Emission of the Non-transiting Hot Jupiter HD187123b

We report the 6.5σ detection of water from the hot Jupiter HD187123b with a Keplerian orbital velocity K {sub p} of 53 ± 13 km s{sup −1}. This high-confidence detection is made using a multi-epoch, high-resolution, cross-correlation technique, and corresponds to a planetary mass of 1.4{sub −0.3}{sup +0.5} M {sub J} and an orbital inclination of 21° ± 5°. The technique works by treating the planet/star system as a spectroscopic binary and obtaining high signal-to-noise, high-resolution observations at multiple points across the planet’s orbit to constrain the system’s binary dynamical motion. All together, seven epochs of Keck/NIRSPEC L-band observations were obtained, with five before the instrument upgrade and two after. Using high-resolution SCARLET planetary and PHOENIX stellar spectral models, we were able to drastically increase the confidence of the detection by running simulations that could reproduce, and thus remove, the nonrandom structured noise in the final likelihood space well. The ability to predict multi-epoch results will be extremely useful for furthering the technique. Here, we use these simulations to compare three different approaches to combining the cross correlations of high-resolution spectra and find that the Zucker log(L) approach is least affected by unwanted planet/star correlation for our HD187123 data set. Furthermore, we find that the same total signal-to-noise ratio (S/N) spread across an orbit in many, lower S/N epochs rather than fewer, higher S/N epochs could provide a more efficient detection. This work provides a necessary validation of multi-epoch simulations, which can be used to guide future observations and will be key to studying the atmospheres of farther separated, non-transiting exoplanets.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Systematic Effects in Galaxy-Galaxy Lensing with DESI

The Dark Energy Spectroscopic Instrument (DESI) survey will measure spectroscopic redshifts for millions of galaxies across roughly $14,000 \, \mathrm{deg}^2$ of the sky. Cross-correlating targets in the DESI survey with complementary imaging surveys allows us to measure and analyze shear distortions caused by gravitational lensing in unprecedented detail. In this work, we analyze a series of mock catalogs with ray-traced gravitational lensing and increasing sophistication to estimate systematic effects on galaxy-galaxy lensing estimators such as the tangential shear $\gamma_{\mathrm{t}}$ and the excess surface density $\Delta\Sigma$ . We employ mock catalogs tailored to the specific imaging surveys overlapping with the DESI survey: the Dark Energy Survey (DES), the Hyper Suprime-Cam (HSC) survey, and the Kilo-Degree Survey (KiDS). Among others, we find that fiber incompleteness can have significant effects on galaxy-galaxy lensing estimators but can be corrected effectively by up-weighting DESI targets with fibers by the inverse of the fiber assignment probability. Similarly, we show that intrinsic alignment and lens magnification are expected to be statistically significant given the precision forecasted for the DESI year-1 data set. Our study informs several analysis choices for upcoming cross-correlation studies of DESI with DES, HSC, and KiDS.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Dark Energy Survey Year 3 results: Cosmology from combined galaxy clustering and lensing validation on cosmological simulations

In this work, we present a validation of the Dark Energy Survey Year 3 (DES Y3) 3×2-point analysis choices by testing them on Buzzard2.0, a new suite of cosmological simulations that is tailored for the testing and validation of combined galaxy clustering and weak-lensing analyses. We show that the buzzard2.0 simulations accurately reproduce many important aspects of the DES Y3 data, including photometric redshift and magnitude distributions, and the relevant set of two-point clustering and weak-lensing statistics. We then show that our model for the 3×2-point data vector is accurate enough to recover the true cosmology in simulated surveys assuming the true redshift distributions for our source and lens samples, demonstrating robustness to uncertainties in the modeling of the nonlinear matter power spectrum, nonlinear galaxy bias, and higher-order lensing corrections. Additionally, we demonstrate for the first time that our photometric redshift calibration methodology, including information from photometry, spectroscopy, clustering cross-correlations, and galaxy–galaxy lensing ratios, is accurate enough to recover the true cosmology in simulated surveys in the presence of realistic photometric redshift uncertainties.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Dark Energy Survey Year 3 results: calibration of lens sample redshift distributions using clustering redshifts with BOSS/eBOSS

ABSTRACT We present clustering redshift measurements for Dark Energy Survey (DES) lens sample galaxies used in weak gravitational lensing and galaxy clustering studies. To perform these measurements, we cross-correlate with spectroscopic galaxies from the Baryon Acoustic Oscillation Survey (BOSS) and its extension, eBOSS. We validate our methodology in simulations, including a new technique to calibrate systematic errors that result from the galaxy clustering bias, and we find that our method is generally unbiased in calibrating the mean redshift. We apply our method to the data, and estimate the redshift distribution for 11 different photometrically selected bins. We find general agreement between clustering redshift and photometric redshift estimates, with differences on the inferred mean redshift found to be below |Δz| = 0.01 in most of the bins. We also test a method to calibrate a width parameter for redshift distributions, which we found necessary to use for some of our samples. Our typical uncertainties on the mean redshift ranged from 0.003 to 0.008, while our uncertainties on the width ranged from 4 to 9 per cent. We discuss how these results calibrate the photometric redshift distributions used in companion papers for DES Year 3 results.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1992

Integrating a local database into the StarView distributed user interface

A distributed user interface to the Space Telescope Data Archive and Distribution Service (DADS) known as StarView is being developed. The DADS architecture consists of the data archive as well as a relational database catalog describing the archive. StarView is a client/server system in which the user interface is the front-end client to the DADS catalog and archive servers. Users query the DADS catalog from the StarView interface. Query commands are transmitted via a network and evaluated by the database. The results are returned via the network and are displayed on StarView forms. Based on the results, users decide which data sets to retrieve from the DADS archive. Archive requests are packaged by StarView and sent to DADS, which returns the requested data sets to the users. The advantages of distributed client/server user interfaces over traditional one-machine systems are well known. Since users run software on machines separate from the database, the overall client response time is much faster. Also, since the server is free to process only database requests, the database response time is much faster. Disadvantages inherent in this architecture are slow overall database access time due to the network delays, lack of a 'get previous row' command, and that refinements of a previously issued query must be submitted to the database server, even though the domain of values have already been returned by the previous query. This architecture also does not allow users to cross correlate DADS catalog data with other catalogs. Clearly, a distributed user interface would be more powerful if it overcame these disadvantages. A local database is being integrated into StarView to overcome these disadvantages. When a query is made through a StarView form, which is often composed of fields from multiple tables, it is translated to an SQL query and issued to the DADS catalog. At the same time, a local database table is created to contain the resulting rows of the query. The returned rows are displayed on the form as well as inserted into the local database table. Identical results are produced by reissuing the query to either the DADS catalog or to the local table. Relational databases do not provide a 'get previous row' function because of the inherent complexity of retrieving previous rows of multiple-table joins. However, since this function is easily implemented on a single table, StarView uses the local table to retrieve the previous row. Also, StarView issues subsequent query refinements to the local table instead of the DADS catalog, eliminating the network transmission overhead. Finally, other catalogs can be imported into the local database for cross correlation with local tables. Overall, it is believe that this is a more powerful architecture for distributed, database user interfaces.

Silberberg, D. P.↗
DOE OSTI2022

Constraining the galaxy-halo connection of infrared-selected unWISE galaxies with galaxy clustering and galaxy-CMB lensing power spectra

We present the first detailed analysis of the connection between galaxies and their dark matter halos for the unWISE galaxy catalog—a full-sky, infrared-selected sample built from WISE data, containing over 500 million galaxies. Using unWISE galaxy-galaxy autocorrelation and Planck CMB lensing-galaxy cross-correlation measurements down to 10 arcmin angular scales, we constrain the halo occupation distribution (HOD), a model describing how central and satellite galaxies are distributed within dark matter halos, for three unWISE galaxy samples at mean redshifts z ¯ ≈ 0.6 , 1.1, and 1.5, assuming a fixed cosmology at the best-fit Planck Λ CDM values. We constrain the characteristic minimum halo mass to host a central galaxy, M min HOD = 1.8 3 - 1.63 + 0.41 × 10 12 M ⊙ / h , 5.22 - 4.80 + 0.34 × 10 12 M ⊙ / h , 6.60 - 1.11 + 0.30 × 10 13 M ⊙ / h and the mass scale at which one satellite galaxy per halo is found, M 1 ' = 1.1 3 - 0.70 + 0.32 × 10 13 M ⊙ / h , 1.18 - 1.11 + 0.30 × 10 13 M ⊙ / h , 1.23 - 1.17 + 0.14 × 10 14 M ⊙ / h for the unWISE samples at z ¯ ≈ 0.6 , 1.1, and 1.5, respectively. We find that all three samples are dominated by central galaxies, rather than satellites. Using our constrained HOD models, we infer the effective linear galaxy bias for each unWISE sample, and find that it does not evolve as steeply with redshift as found in previous perturbation-theory-based analyses of these galaxies. We discuss possible sources of systematic uncertainty in our results, the most significant of which is the uncertainty on the galaxy redshift distribution. Our HOD constraints provide a detailed, quantitative understanding of how the unWISE galaxies populate the underlying dark matter halo distribution. These constraints will have a direct impact on future studies employing the unWISE galaxies as a cosmological and astrophysical probe, including measurements of ionized gas thermodynamics and dark matter profiles via Sunyaev-Zel’dovich and lensing cross-correlations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Characterization of contaminants in the Lyman-alpha forest auto-correlation with DESI

Baryon Acoustic Oscillations can be measured with sub-percent precision above redshift two with the Lyman-α (Lyα) forest auto-correlation and its cross-correlation with quasar positions. This is one of the key goals of the Dark Energy Spectroscopic Instrument (DESI) which started its main survey in May 2021. We present in this paper a study of the contaminants to the Lyα forest which are mainly caused by correlated signals introduced by the spectroscopic data processing pipeline as well as astrophysical contaminants due to foreground absorption in the intergalactic medium. Notably, an excess signal caused by the sky background subtraction noise is present in the Lyα auto-correlation in the first line-of-sight separation bin. We use synthetic data to isolate this contribution, we also characterize the effect of spectro-photometric calibration noise, and propose a simple model to account for both effects in the analysis of the Lyα forest. We then measure the auto-correlation of the quasar flux transmission fraction of low redshift quasars, where there is no Lyα forest absorption but only its contaminants. We demonstrate that we can interpret the data with a two-component model: data processing noise and triply ionized Silicon and Carbon auto-correlations. This result can be used to improve the modeling of the Lyα auto-correlation function measured with DESI.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Validation of the DESI 2024 Lyα forest BAO analysis using synthetic datasets

The first year of data from the Dark Energy Spectroscopic Instrument (DESI) contains the largest set of Lyman-α (Lyα) forest spectra ever observed. This data, collected in the DESI Data Release 1 (DR1) sample, has been used to measure the Baryon Acoustic Oscillation (BAO) feature at redshift z = 2.33. In this work, we use a set of 150 synthetic realizations of DESI DR1 to validate the DESI 2024 Lyα forest BAO measurement presented in [1]. The synthetic data sets are based on Gaussian random fields using the log-normal approximation. We produce realistic synthetic DESI spectra that include all major contaminants affecting the Lyα forest. The synthetic data sets span a redshift range 1.8 < z < 3.8, and are analyzed using the same framework and pipeline used for the DESI 2024 Lyα forest BAO measurement. To measure BAO, we use both the Lyα auto-correlation and its cross-correlation with quasar positions. We use the mean of correlation functions from the set of DESI DR1 realizations to show that our model is able to recover unbiased measurements of the BAO position. We also fit each mock individually and study the population of BAO fits in order to validate BAO uncertainties and test our method for estimating the covariance matrix of the Lyα forest correlation functions. Finally, we discuss the implications of our results and identify the needs for the next generation of Lyα forest synthetic data sets, with the top priority being to simulate the effect of BAO broadening due to non-linear evolution.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Probing the limits of cosmological information from the Lyman- α forest 2-point correlation functions

The standard cosmological analysis with the Lyα forest relies on a continuum fitting procedure that suppresses information on large scales and distorts the three-dimensional correlation function on all scales. In this work, we present the first cosmological forecasts without continuum fitting distortion in the Lyα forest, focusing on the recovery of large-scale information. Using idealized synthetic data, we compare the constraining power of the full shape of the Lyα forest auto-correlation and its cross-correlation with quasars using the baseline continuum fitting analysis versus the true continuum. We find that knowledge of the true continuum enables a ∼ 10% reduction in uncertainties on the Alcock-Paczyński (AP) parameter and the matter density, Ω m . We also explore the impact of large-scale information by extending the analysis up to separations of 240 h -1 Mpc along and across the line of sight. The combination of these analysis choices can recover significant large-scale information, yielding up to a ∼ 15% improvement in AP constraints. This improvement is analogous to extending the Lyα forest survey area by ∼ 40%.

Lyman alpha forest↗
DOE OSTI2025

Self-Supervised T-GCN for Detection of Disturbance and Propagation in Power Grid

Urban power systems increasingly rely on dense sensing to monitor grid reliability, yet disturbance labels are scarce and events are rare. We present a self-supervised spatio-temporal method that detects, localizes, and characterizes grid frequency disturbances across urban areas using only unlabeled data. Our approach trains a tiny Temporal Graph Convolutional Network (T-GCN) to forecast per-site frequency residuals (deviation from 60 Hz). The sensor graph is constructed directly from signals using pre-event Pearson correlation with a cross-correlation lag penalty without geocoding. At inference, node-level anomalies are the model's forecast errors; region-level alarms arise from connected components of high-score nodes. We estimate disturbance propagation by computing per-node arrival times (first persistent exceedance), then fit a planar or time-of-arrival model to obtain direction, speed, and an epicenter proxy. With only three real events collected at decisecond resolution across U.S. cities, we evaluate the T-GCN and report time-to-detect, footprint size, and propagation consistency. We further show that short-window embeddings from the T-GCN's hidden states enable few-shot event-vs-background recognition via a simple prototypical classifier. Despite minimal data and no labels, our system yields fast, spatially coherent detection and interpretable propagation maps, offering a practical, lightweight pathway to city-scale grid resilience analytics.

Niu, Haoran [ORNL] (ORCID:0000000155228297)↗
NASA NTRS1973

Comparison of results obtained with various sensors used to measure fluctuating quantities in jets.

An experimental investigation has been conducted to compare the results obtained with six different instruments that sense fluctuating quantities in free jets. These sensors are typical of those that have recently been used by various investigators who are engaged in experimental studies of jet noise. Intensity distributions and two-point correlations with space separation and time delay were obtained. The static pressure, density, and velocity fluctuations are well correlated over the entire cross section of the jet and the cross-correlations persist for several jet diameters along the flow direction. The eddies appear to be flattened in the flow direction by a ratio of 0.4.

Parthasarathy, S. P.↗
NASA NTRS1974

Application of ultrasonic signature analysis for fatigue detection in complex structures

Ultrasonic signature analysis shows promise of being a singularly well-suited method for detecting fatigue in structures as complex as aircraft. The method employs instrumentation centered about a Fourier analyzer system, which features analog-to-digital conversion, digital data processing, and digital display of cross-correlation functions and cross-spectra. These features are essential to the analysis of ultrasonic signatures according to the procedure described here. In order to establish the feasibility of the method, the initial experiments were confined to simple plates with simulated and fatigue-induced defects respectively. In the first test the signature proved sensitive to the size of a small hole drilled into the plate. In the second test, performed on a series of fatigue-loaded plates, the signature proved capable of indicating both the initial appearance and subsequent growth of a fatigue crack. In view of these encouraging results it is concluded that the method has reached a sufficiently advanced stage of development to warrant application to small-scale structures or even actual aircraft.

Zuckerwar, A. J.↗