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NASA NTRS1993

New limb-darkening coefficients for modeling binary star light curves

We present monochromatic, passband-specific, and bolometric limb-darkening coefficients for a linear as well as nonlinear logarithmic and square root limb-darkening laws. These coefficients, including the bolometric ones, are needed when modeling binary star light curves with the latest version of the Wilson-Devinney light curve progam. We base our calculations on the most recent ATLAS stellar atmosphere models for solar chemical composition stars with a wide range of effective temperatures and surface gravitites. We examine how well various limb-darkening approximations represent the variation of the emerging specific intensity across a stellar surface as computed according to the model. For binary star light curve modeling purposes, we propose the use of a logarithmic or a square root law. We design our tables in such a manner that the relative quality of either law with respect to another can be easily compared. Since the computation of bolometric limb-darkening coefficients first requires monochromatic coefficients, we also offer tables of these coefficients (at 1221 wavelength values between 9.09 nm and 160 micrometer) and tables of passband-specific coefficients for commonly used photometric filters.

Van Hamme, W.↗

NASA NTRS1995

Large-eddy simulations with wall models

The near-wall viscous and buffer regions of wall-bounded flows generally require a large expenditure of computational resources to be resolved adequately, even in large-eddy simulation (LES). Often as much as 50% of the grid points in a computational domain are devoted to these regions. The dense grids that this implies also generally require small time steps for numerical stability and/or accuracy. It is commonly assumed that the inner wall layers are near equilibrium, so that the standard logarithmic law can be applied as the boundary condition for the wall stress well away from the wall, for example, in the logarithmic region, obviating the need to expend large amounts of grid points and computational time in this region. This approach is commonly employed in LES of planetary boundary layers, and it has also been used for some simple engineering flows. In order to calculate accurately a wall-bounded flow with coarse wall resolution, one requires the wall stress as a boundary condition. The goal of this work is to determine the extent to which equilibrium and boundary layer assumptions are valid in the near-wall regions, to develop models for the inner layer based on such assumptions, and to test these modeling ideas in some relatively simple flows with different pressure gradients, such as channel flow and flow over a backward-facing step. Ultimately, models that perform adequately in these situations will be applied to more complex flow configurations, such as an airfoil.

Cabot, W.↗

NASA NTRS1995

High-temperature oxidation behavior of reaction-formed silicon carbide ceramics

The oxidation behavior of reaction-formed silicon carbide (RFSC) ceramics was investigated in the temperature range of 1100 to 1400 C. The oxidation weight change was recorded by TGA; the oxidized materials were examined by light and electron microscopy, and the oxidation product by x-ray diffraction analysis (XRD). The materials exhibited initial weight loss, followed by passive weight gain (with enhanced parabolic rates, k(sub p)), and ending with a negative (logarithmic) deviation from the parabolic law. The weight loss arose from the oxidation of residual carbon, and the enhanced k(sub p) values from internal oxidation and the oxidation of residual silicon, while the logarithmic kinetics is thought to have resulted from crystallization of the oxide. The presence of a small amount of MoSi, in the RFSC material caused a further increase in the oxidation rate. The only solid oxidation product for all temperatures studied was silica.

Ogbuji, Linus U. J. T.↗

NASA NTRS1996

Symmetries in Turbulent Boundary Layer Flows

The objective is the development of a new theory which enables the algorithmic computation of all self-similar mean velocity profiles. The theory is based on Liegroup analysis and unifies a large set of self-similar solutions for the mean velocity of stationary parallel turbulent shear flows. The results include the logarithmic law of the wall, an algebraic law, the viscous sublayer, the linear region in the middle of a Couette flow and in the middle of a rotating channel flow, and a new exponential mean velocity profile not previously reported. Experimental results taken in the outer parts of a high Reynolds number flat-plate boundary layer, strongly support the exponential profile. From experimental as well as from DNS data of a turbulent channel flow the algebraic scaling law could be confirmed in both the center region and in the near wall region. In the case of the logarithmic law of the wall, the scaling with the wall distance arises as a result of the analysis and has not been assumed in the derivation. The crucial part of the derivation of all the different mean velocity profiles is to consider the invariance of the equation for the velocity fluctuations at the same time as the invariance of the equation for the velocity product equations. The latter is the dyad product of the velocity fluctuations with the equation for the velocity fluctuations. It has been proven that all the invariant solutions are also consistent with similarity of all velocity moment equations up to any arbitrary order.

Oberlack, M.↗

NASA NTRS1999

Double Resonances and Spectral Scaling in the Weak Turbulence Theory of Rotating and Stratified Turbulence

In rotating turbulence, stably stratified turbulence, and in rotating stratified turbulence, heuristic arguments concerning the turbulent time scale suggest that the inertial range energy spectrum scales as k(exp -2). From the viewpoint of weak turbulence theory, there are three possibilities which might invalidate these arguments: four-wave interactions could dominate three-wave interactions leading to a modified inertial range energy balance, double resonances could alter the time scale, and the energy flux integral might not converge. It is shown that although double resonances exist in all of these problems, they do not influence overall energy transfer. However, the resonance conditions cause the flux integral for rotating turbulence to diverge logarithmically when evaluated for a k(exp -2) energy spectrum; therefore, this spectrum requires logarithmic corrections. Finally, the role of four-wave interactions is briefly discussed.

Rubinstein, Robert↗

NASA NTRS1994

Nonlinear Optical Image Processing with Bacteriorhodopsin Films

The transmission properties of some bacteriorhodopsin film spatial light modulators are uniquely suited to allow nonlinear optical image processing operations to be applied to images with multiplicative noise characteristics. A logarithmic amplitude transmission feature of the film permits the conversion of multiplicative noise to additive noise, which may then be linearly filtered out in the Fourier plane of the transformed image. The bacteriorhodopsin film displays the logarithmic amplitude response for write beam intensities spanning a dynamic range greater than 2.0 orders of magnitude. We present experimental results demonstrating the principle and capability for several different image and noise situations, including deterministic noise and speckle. Using the bacteriorhodopsin film, we successfully filter out image noise from the transformed image that cannot be removed from the original image.

Downie, John D.↗

NASA NTRS2002

Optimal Design of Functionally Graded Metallic Foam Insulations

The focus of our work has been on developing an insight into the physics that govern the optimum design of thermal insulation for use in thermal protection systems of launch vehicle. Of particular interest was to obtain optimality criteria for designing foam insulations that have density (or porosity) distributions through the thickness for optimum thermal performance. We investigate the optimum design of functionally graded thermal insulation for steady state heat transfer through the foam. We showed that the heat transfer in the foam has competing modes, of radiation and conduction. The problem assumed a fixed inside temperature of 400 K and varied the aerodynamic surface heating on the outside surface from 0.2 to 1.0 MW/sq m. The thermal insulation develops a high temperature gradient through the thickness. Investigation of the model developed for heat conduction in foams showed that at high temperatures (as on outside wall) intracellular radiation dominates the heat transfer in the foam. Minimizing radiation requires reducing the pore size, which increases the density of the foam. At low temperatures (as on the inside wall), intracellular conduction (of the metal and air) dominates the heat transfer. Minimizing conduction requires increasing the pore size. This indicated that for every temperature there was an optimum value of density that minimized the heat transfer coefficient. Two optimization studies were performed. One was to minimize the heat transmitted though a fixed thickness insulation by varying density profiles. The second was to obtain the minimum mass insulation for specified thickness. Analytical optimality criteria were derived for the cases considered. The optimality condition for minimum heat transfer required that at each temperature we find the density that minimizes the heat transfer coefficient. Once a relationship between the optimum heat transfer coefficient and the temperature was found, the design problem reduced to the solution of a simple nonlinear differential equation. Preliminary results of this work were presented at the American Society of Composites meeting, and the final version was submitted for publication in the AIAA Journal. In addition to minimizing the transmitted heat, we investigated the optimum design for minimum weight given an acceptable level of heat transmission through the insulation. The optimality criterion developed was different from that obtained for minimizing beat transfer coefficient. For minimum mass design, we had to find for a given temperature the optimum density, which minimized the logarithmic derivative of the insulation thermal conductivity with respect to its density. The logarithmic derivative is defined as the ratio of relative change in the dependent response (thermal conductivity) to the relative change in the independent variable (density). The results have been documented as a conference paper that will be presented at the upcoming AIAA.

Haftka, Raphael T.↗

NASA NTRS2003

On the Use of the Log-Normal Particle Size Distribution to Characterize Global Rain

Although most parameterizations of the drop size distributions (DSD) use the gamma function, there are several advantages to the log-normal form, particularly if we want to characterize the large scale space-time variability of the DSD and rain rate. The advantages of the distribution are twofold: the logarithm of any moment can be expressed as a linear combination of the individual parameters of the distribution; the parameters of the distribution are approximately normally distributed. Since all radar and rainfall-related parameters can be written approximately as a moment of the DSD, the first property allows us to express the logarithm of any radar/rainfall variable as a linear combination of the individual DSD parameters. Another consequence is that any power law relationship between rain rate, reflectivity factor, specific attenuation or water content can be expressed in terms of the covariance matrix of the DSD parameters. The joint-normal property of the DSD parameters has applications to the description of the space-time variation of rainfall in the sense that any radar-rainfall quantity can be specified by the covariance matrix associated with the DSD parameters at two arbitrary space-time points. As such, the parameterization provides a means by which we can use the spaceborne radar-derived DSD parameters to specify in part the covariance matrices globally. However, since satellite observations have coarse temporal sampling, the specification of the temporal covariance must be derived from ancillary measurements and models. Work is presently underway to determine whether the use of instantaneous rain rate data from the TRMM Precipitation Radar can provide good estimates of the spatial correlation in rain rate from data collected in 5(sup 0)x 5(sup 0) x 1 month space-time boxes. To characterize the temporal characteristics of the DSD parameters, disdrometer data are being used from the Wallops Flight Facility site where as many as 4 disdrometers have been used to acquire data over a 2 km path. These data should help quantify the temporal form of the covariance matrix at this site.

Meneghini, Robert↗

NASA NTRS1996

Changes in autonomic activity preceding onset of nonsustained ventricular tachycardia

Background: The triggering role of the autonomic nervous system in the initiation of ventricular tachycardia has not been established. To investigate the relationship between changes in autonomic activity and the occurrence of nonsustained ventricular tachycardia (NSVT) we examined heart rate variability (HRV) during the 2-hour period preceding spontaneous episodes of NSVT. Twenty-four subjects were identified retrospectively as having had one episode of NSVT during 24-hour Holter ECC recording. Methods: We measured the mean interval between normal heats (meanRR), the standard deviation of the intervals between beats (SD), the percentage of counts of sequential intervals between normal beats with a change of >50 ms (%RR50), the logarithms of low- and high-frequency spectral components (lnLF, lnHF) of HRV for sequential 10-minute segments preceding NSVT. The correlation dimension (CDim) of HRV was calculated similarly for sequential 20-minute segments. We assessed the significance of the time-course change of each marker over the 120-minute period prior to NSVT onset. Results: MeanRR (P < 0.05), lnLF (P < 0.0001), lnHF (P < 0.0001), the natural logarithm of the ratio of LF to HF (ln[LF/HF]; P < 0.05), and CDim (P < 0.05) showed significant time-course changes during that period, while SD and %RR50 did not. MeanRR, lnLF, lnHF, and CDim all decreased prior to the onset of NSVT, whereas ln(LF/HF) increased. We divided the subjects into two groups: one consisting of 12 patients with coronary artery disease; and the second group of 12 patients without known coronary artery disease. Both groups showed significant changes (P < 0.05) of CDim, lnLF, and lnHF preceding the episodes of NSVT. Conclusions: Changes in the pattern of HRV prior to the onset of episodes of NSVT suggest that changes in autonomic activity may commonly play a role in the triggering of spontaneous episodes of NSVT in susceptible patients. The measured changes suggest a reduction in parasympathetic activity, perhaps in conjunction with an increase in sympathetic activity, may trigger NSVT.

Non-NASA Center↗

NASA NTRS1991

The oxygen content of ocean bottom waters, the burial efficiency of organic carbon, and the regulation of atmospheric oxygen

Data for the burial efficiency of organic carbon with marine sediments have been compiled for 69 locations. The burial efficiency as here defined is the ratio of the quantity of organic carbon which is ultimately buried to that which reaches the sediment-water interface. As noted previously, the sedimentation rate exerts a dominant influence on the burial efficiency. The logarithm of the burial efficiency is linearly related to the logarithm of the sedimentation rate at low sedimentation rates. At high sedimentation rates the burial efficiency can exceed 50% and becomes nearly independent of the sedimentation rate. The residual of the burial efficiency after the effect of the sedimentation rate has been subtracted is a weak function of the O2 concentration in bottom waters. The scatter is sufficiently large, so that the effect of the O2 concentration in bottom waters on the burial efficiency of organic matter could be either negligible or a minor but significant part of the mechanism that controls the level of O2 in the atmosphere.

Non-NASA Center↗

NASA NTRS1997

Natural Strain

Logarithmic strain is the preferred measure of strain used by materials scientists, who typically refer to it as the "true strain." It was Nadai who gave it the name "natural strain," which seems more appropriate. This strain measure was proposed by Ludwik for the one-dimensional extension of a rod with length l. It was defined via the integral of dl/l to which Ludwik gave the name "effective specific strain." Today, it is after Hencky, who extended Ludwik's measure to three-dimensional analysis by defining logarithmic strains for the three principal directions.

Freed, Alan D.↗

NASA NTRS2006

Assessment of Postflight Locomotor Performance Utilizing a Test of Functional Mobility: Strategic and Adaptive Responses

Space flight induces adaptive modification in sensorimotor function, allowing crewmembers to operate in the unique microgravity environment. This adaptive state, however, is inappropriate for a terrestrial environment. During a re-adaptation period upon their return to Earth, crewmembers experience alterations in sensorimotor function, causing various disturbances in perception, spatial orientation, posture, gait, and eye-head coordination. Following long duration space flight, sensorimotor dysfunction would prevent or extend the time required to make an emergency egress from the vehicle; compromising crew safety and mission objectives. We are investigating two types of motor learning that may interact with each other and influence a crewmember's ability to re-adapt to Earth's gravity environment. In strategic learning, crewmembers make rapid modifications in their motor control strategy emphasizing error reduction. This type of learning may be critical during the first minutes and hours after landing. In adaptive learning, long-term plastic transformations occur, involving morphological changes and synaptic modification. In recent literature these two behavioral components have been associated with separate brain structures that control the execution of motor strategies: the strategic component was linked to the posterior parietal cortex and the adaptive component was linked to the cerebellum (Pisella, et al. 2004). The goal of this paper was to demonstrate the relative contributions of the strategic and adaptive components to the re-adaptation process in locomotor control after long duration space flight missions on the International Space Station (ISS). The Functional Mobility Test (FMT) was developed to assess crewmember s ability to ambulate postflight from an operational and functional perspective. Sixteen crewmembers were tested preflight (3 sessions) and postflight (days 1, 2, 4, 7, 25) following a long duration space flight (approx 6 months) on the ISS. We have further analyzed the FMT data to characterize strategic and adaptive components during the postflight readaptation period. Crewmembers walked at a preferred pace through an obstacle course set up on a base of 10 cm thick medium density foam (Sunmate Foam, Dynamic Systems, Inc., Leicester, NC). The 6.0m X 4.0m course consisted of several pylons made of foam; a Styrofoam barrier 46.0cm high that crewmembers stepped over; and a portal constructed of two Styrofoam blocks, each 31cm high, with a horizontal bar covered by foam and suspended from the ceiling which was adjusted to the height of the crewmember s shoulder. The portal required crewmembers to bend at the waist and step over a barrier simultaneously. All obstacles were lightweight, soft and easily knocked over. Crewmembers were instructed to walk through the course as quickly and as safely as possible without touching any of the objects on the course. This task was performed three times in the clockwise direction and three times in the counterclockwise direction that was randomly chosen. The dependent measures for each trial were: time to complete the course (seconds) and the number of obstacles touched or knocked down. For each crewmember, the time to complete each FMT trial from postflight days 1, 2, 4, 7 and 25 were further analyzed. A single logarithmic curve using a least squares calculation was fit through these data to produce a single comprehensive curve (macro). This macro curve composed of data spanning 25 days, illustrates the re-adaptive learning function over the longer time scale term. Additionally, logarithmic curves were fit to the 6 data trials within each individual post flight test day to produce 5 separate daily curves. These micro curves, produced from data obtained over the course of minutes, illustrates the strategic learning function exhibited over a relative shorter time scale. The macro curve for all subjects exhibited adaptive motor learning patterns over the 25 day period. Howev, 9/16 crewmembers exhibited significant strategic motor learning patterns in their micro curves, as defined by m > 1 in the equation of the line y=m*LN(x) +b. These data indicate that postflight recovery in locomotor function involves both strategic and adaptive mechanisms. Future countermeasures will be designed to enhance both recovery processes.

Warren, L. E.↗

NASA NTRS2007

Characterizing the Superconducting-to-Normal Transition in Mo/Au Transition-Edge Sensor Bilayers

We are developing arrays of Mo/Au bilayer transition-edge sensors (TES's) for applications in future X-ray astronomy missions such as NASA's Constellation-X. The physical properties of the superconducting-to-normal transition in our TES bilayers, while often reproducible and characterized, are not well understood. The addition of normal metal features on top of the bilayer are found to change the shape and temperature of the transition, and they typically reduce the unexplained 'excess' noise. In order to understand and potentially optimize the properties of the transition, we have been studying the temperature, widths and current dependence of these transitions. We report on the characterization of devices both deposited on silicon substrates and suspended on thin silicon nitride membranes. This includes key device parameters such as the logarithmic resistance sensitivity with temperature alpha, and the logarithmic resistance sensitivity with current beta, of the phase-transition. We investigate alpha and beta as a function of current, both at fixed and varying bias points in the transition. Using Ginzburg-Landau theory for the current dependence of the superconducting transition temperature, we investigate the relationship between alpha and beta and compare our measured and theoretical estimates.

Smith, Stephen J.↗

NASA NTRS2011

An Estimate of Low-Cloud Feedbacks from Variations of Cloud Radiative and Physical Properties with Sea Surface Temperature on Interannual Time Scales

Simulations of climate change have yet to reach a consensus on the sign and magnitude of the changes in physical properties of marine boundary layer clouds. In this study, the authors analyze how cloud and radiative properties vary with SST anomaly in low-cloud regions, based on five years (March 2000 - February 2005) of Clouds and the Earth s Radiant Energy System (CERES) -- Terra monthly gridded data and matched European Centre for Medium-Range Weather Forecasts (ECMWF) meteorological reanalaysis data. In particular, this study focuses on the changes in cloud radiative effect, cloud fraction, and cloud optical depth with SST anomaly. The major findings are as follows. First, the low-cloud amount (-1.9% to -3.4% /K) and the logarithm of low-cloud optical depth (-0.085 to -0.100/K) tend to decrease while the net cloud radiative effect (3.86 W/m(exp 2)/ K) becomes less negative as SST anomalies increase. These results are broadly consistent with previous observational studies. Second, after the changes in cloud and radiative properties with SST anomaly are separated into dynamic, thermodynamic, and residual components, changes in the dynamic component (taken as the vertical velocity at 700 hPa) have relatively little effect on cloud and radiative properties. However, the estimated inversion strength decreases with increasing SST, accounting for a large portion of the measured decreases in cloud fraction and cloud optical depth. The residual positive change in net cloud radiative effect (1.48 W/m(exp 2)/ K) and small changes in low-cloud amount (-0.81% to 0.22% /K) and decrease in the logarithm of optical depth (-0.035 to -0.046/ K) with SST are interpreted as a positive cloud feedback, with cloud optical depth feedback being the dominant contributor. Last, the magnitudes of the residual changes differ greatly among the six low-cloud regions examined in this study, with the largest positive feedbacks (approximately 4 W/m(exp 2)/ K) in the southeast and northeast Atlantic regions and a slightly negative feedback (-0.2 W/m(exp 2)/ K) in the south-central Pacific region. Because the retrievals of cloud optical depth and/or cloud fraction are difficult in the presence of aerosols, the transport of heavy African continental aerosols may contribute to the large magnitudes of estimated cloud feedback in the two Atlantic regions.

Eitzen, Zachary A.↗

NASA NTRS2010

Climatological Aspects of the Optical Properties of Fine/Coarse Mode Aerosol Mixtures

Aerosol mixtures composed of coarse mode desert dust combined with fine mode combustion generated aerosols (from fossil fuel and biomass burning sources) were investigated at three locations that are in and/or downwind of major global aerosol emission source regions. Multiyear monitoring data at Aerosol Robotic Network sites in Beijing (central eastern China), Kanpur (Indo-Gangetic Plain, northern India), and Ilorin (Nigeria, Sudanian zone of West Africa) were utilized to study the climatological characteristics of aerosol optical properties. Multiyear climatological averages of spectral single scattering albedo (SSA) versus fine mode fraction (FMF) of aerosol optical depth at 675 nm at all three sites exhibited relatively linear trends up to 50% FMF. This suggests the possibility that external linear mixing of both fine and coarse mode components (weighted by FMF) dominates the SSA variation, where the SSA of each component remains relatively constant for this range of FMF only. However, it is likely that a combination of other factors is also involved in determining the dynamics of SSA as a function of FMF, such as fine mode particles adhering to coarse mode dust. The spectral variation of the climatological averaged aerosol absorption optical depth (AAOD) was nearly linear in logarithmic coordinates over the wavelength range of 440-870 nm for both the Kanpur and Ilorin sites. However, at two sites in China (Beijing and Xianghe), a distinct nonlinearity in spectral AAOD in logarithmic space was observed, suggesting the possibility of anomalously strong absorption in coarse mode aerosols increasing the 870 nm AAOD.

Eck, T. F.↗

NASA NTRS2012

Stellar Populations of Lyman Break Galaxies at z approx. to 1-3 in the HST/WFC3 Early Release Science Observations

We analyze the spectral energy distributions (SEDs) of Lyman break galaxies . (LBGs) at z approx = 1-3 selected using the Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3) UVIS channel filters. These HST /WFC3 obse,rvations cover about 50 arcmin2 in the GOODS-South field as a part of the WFC3 Early Release Science program. These LBGs at z approx = 1-3 are selected using dropout selection criteria similar to high redshift LBGs. The deep multi-band photometry in this field is used to identify best-fit SED models, from which we infer the following results: (1) the photometric redshift estimate of these dropout selected LBGs is accurate to within few percent; (2) the UV spectral slope f3 is redder than at high redshift (z > 3), where LBGs are less dusty; (3) on average, LBGs at .z approx = 1-3 are massive, dustier and more highly star-forming, compared to LBGs at higher redshifts with similar luminosities, though their median values are similar within 1a uncertainties. This could imply that identical dropout selection technique, at all. redshifts, find physically similar galaxies; and (4) the stellar masses of these LBGs are directly proportional to their UV luminosities with a logarithmic slope of approx 0.46, and star-formation rates are proportional to their stellar masses with a logarithmic slope of approx 0.90. These relations hold true - within luminosities probed in this study - for LBGs from z approx = 1.5 to 5. The star-forming galaxies selected using other color-based techniques show similar correlations at z approx = 2, but to avoid any selection biases, and for direct comparison with LBGs at z > 3, a true Lyman break selection at z approx = 2 is essential. The future HST UV surveys,. both wider and deeper, covering a large luminosity range are important to better understand LBG properties, and their evolution.

Hathi, N. P.↗

NASA NTRSDate not supplied

Parallelized Quadrupole Simulations of Thermographic Responses of Composites

Thermography has been shown to be a viable technique for inspection of composites. Model inversion of the thermography data requires a fast method for performing the forward problem. Viable numerical methods for the thermal response forward problem are finite element, finite difference and the quadrupole method. Normally both the finite element and finite difference methods solve for the thermal response in the time domain which limits one’s ability to increase the speed of the simulation by parallelization. In contrast, the quadrupole method solves for the Laplace transform of the thermal response. One of the features of the Laplace transform methodology is the solution at any discrete time is independent of the solution at all other times. Therefore, it is easy to separate into a set of independent calculations with each of the times of interest being performed in parallel. Additionally, the numeric inversion of the Laplace transform typically involves numerically solving for the Laplace transform at multiple Laplace frequencies. Each of those solutions are also independent of solutions at other frequencies and can be calculated in parallel. By parallelization of this method, it is possible to perform the simulations of three-dimensional configurations in seconds. When the input stimulus for thermal response is a delta function heat flux (a reasonable approximation for flash heating), the thermal response is smooth. For this case, it is possible to accurately estimate the thermal response at any time within a given time interval from a set of simulations separated by exponentially increasing time steps. From these simulations, it is possible to accurately interpolate to find the response at intermediate times by a spline interpolation of the logarithm of time versus logarithm of temperature. The thermal response with exponential time stepping is shown to produce values for the thermal response which are within 1% of values within the time interval. The simulations are compared to finite element simulations of the same inspection configurations. The simulations are also compared to the thermographic measurements on composites where shape and depth of the delaminations are obtained from other inspection methods.

Thermography↗

NASA NTRSDate not supplied

Parallelized Quadrupole Simulations of Thermographic Responses of Composites

Thermography↗