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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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At least 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Effects of CO2 Addition on the Turbulent Flame Front Dynamics and Propagation Speeds of Methane/Air Mixtures

Exhaust gas recirculation (EGR) is one of the most promising methods of improving the performance of power-generating gas turbines. CO2 is known to have the largest impact on flame behavior of any major exhaust species, but few studies have specified its thermal, kinetic, and transport effects on turbulent flames. Therefore, in this study, methane/air mixtures diluted with CO2 are experimentally investigated in a reactor-assisted turbulent slot (RATS) burner using OH planar laser-induced fluorescence (PLIF) measurements. CO2 addition is tested under both constant adiabatic flame temperature and variable adiabatic flame temperature conditions in order to elucidate its thermal, kinetic, and transport effects. Particular attention is paid to CO2's effects on the flame surface density, progress variable, turbulent burning velocity, and flame wrinkling. The experimental measurements reveal that CO2's thermal effects are the dominant factor in elongating the turbulent flame brush and decreasing the turbulent burning velocity. When thermal effects are removed by holding the adiabatic flame temperature constant, CO2's kinetic effects are the next most important factor, producing an approximately 5% decrease in the global consumption speed for each 5% of CO2 addition. The transport effects of CO2, however, tend to increase the global consumption speed, counteracting 30–50% of the kinetic effects when the adiabatic flame temperature is fixed. It is also seen that CO2 addition increases the normalized global consumption speed primarily through an enhancement of the stretch factor.

Engineering↗
NASA NTRS2016

Low Ozone over Europe Doesn't Mean the Sky Is Falling, Its Actually Rising

Data Sources: NASA Aura Microwave Limb Sounder (MLS) (O3 profiles and columns), NASA Global Modeling Initiative (GMI) Chemistry and Transport Model (calculated O3depletion), and MERRA Tropopause Heights. Technical Description of Figures: The left graphics show MLS northern hemisphere stratospheric column ozone on Feb. 1, 2016. Very low columns are seen over the UK and Europe (<225 DU, inside dashed circle). The lower graphic shows the GMI-calculated O3 depletion. It's very small, suggesting the low O3 does not indicate significant depletion. The right graphics show how the high tropopause height in this region explains the observed low ozone. The lower panel shows that the high tropopause on Feb. 1 lifts the O3 profile compared to a typical profile found earlier in winter. This motion lifts the profile to lower pressures thus reducing the total column. The GMI Model shows only 4 Dobson Units (DU) of O3 depletion even though the column is more than 100 DU lower than one month earlier. Scientific significant and societal relevance: To quantitatively understand anthropogenic impacts to the stratospheric ozone layer, we must be able to distinguish between low ozone caused by ozone depleting substances and that caused by natural dynamical variability in the atmosphere. Observations and realistic simulations of atmospheric composition are both required in order to separate natural and anthropogenic ozone variability.

Stratospheric↗
NASA NTRS2007

Simulation of Boundary-Layer Cumulus and Stratocumulus Clouds using a Cloud-Resolving Model With Low- and Third-Order Turbulence Closures

The effects of subgrid-scale condensation and transport become more important as the grid spacings increase from those typically used in large-eddy simulation (LES) to those typically used in cloud-resolving models (CRMs). Incorporation of these effects can be achieved by a joint probability density function approach that utilizes higher-order moments of thermodynamic and dynamic variables. This study examines how well shallow cumulus and stratocumulus clouds are simulated by two versions of a CRM that is implemented with low-order and third-order turbulence closures (LOC and TOC) when a typical CRM horizontal resolution is used and what roles the subgrid-scale and resolved-scale processes play as the horizontal grid spacing of the CRM becomes finer. Cumulus clouds were mostly produced through subgrid-scale transport processes while stratocumulus clouds were produced through both subgrid-scale and resolved-scale processes in the TOC version of the CRM when a typical CRM grid spacing is used. The LOC version of the CRM relied upon resolved-scale circulations to produce both cumulus and stratocumulus clouds, due to small subgrid-scale transports. The mean profiles of thermodynamic variables, cloud fraction and liquid water content exhibit significant differences between the two versions of the CRM, with the TOC results agreeing better with the LES than the LOC results. The characteristics, temporal evolution and mean profiles of shallow cumulus and stratocumulus clouds are weakly dependent upon the horizontal grid spacing used in the TOC CRM. However, the ratio of the subgrid-scale to resolved-scale fluxes becomes smaller as the horizontal grid spacing decreases. The subcloud-layer fluxes are mostly due to the resolved scales when a grid spacing less than or equal to 1 km is used. The overall results of the TOC simulations suggest that a 1-km grid spacing is a good choice for CRM simulation of shallow cumulus and stratocumulus.

Xu, Kuan-Man↗
DOE OSTI2018

Quantizations of the classical time of arrival and their dynamics

The classical time of arrival in the interacting case is quantized by way of quantizing its expansion about the free time of arrival. The quantization is formulated in coordinate representation which represents ordering rules in terms of two variable polynomial functions. This leads to representations of the quantized time of arrival operators as integral operators whose kernels are determined by the chosen ordering rule. The formulation lends itself to generalization which allows construction of time of arrival operators that cannot be obtained by direct quantization using particular ordering rules. Weyl, symmetric and Born–Jordan quantizations are specifically studied. The dynamics of the eigenfunctions of the different time of arrival operators are investigated. The eigenfunctions exhibit unitary arrival at the intended arrival point at their respective eigenvalues.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2005

Data Assimilation and Data Fusion for Planetary Atmospheres

The overarching goal of this Cooperative Agreement was to develop a model and procedures for the data assimilation of planetary spacecraft atmospheric observations. Data assimilation - in its application to weather analysis and prediction - is the process of finding an initial state of the meteorological variables (winds, temperatures, pressures, etc.) of an atmosphere, which, when propagated forward in time using a deterministic general circulation model, reproduces all of the available observations over that time to within the measurement and computational errors. With this definition, data assimilation is seen to be a natural extension of well-known least-squares minimization techniques. The primary complication arises from the scale of the problem: For the Martian atmosphere with the available nadir-viewing Thermal Emission Spectrometer data from Mars Global Surveyor, approximately 1,000,000 individual measurements of channel radiances (in the 15-micrometer region, where these radiances relate directly to the surface and atmospheric temperature) were made per day. A suitable general circulation model for dealing with this data set has on the order of 20,000 independent variables. After some spatial and temporal averaging of the data - which provides a necessary statistical estimate of the representativeness of the measurements, a crucial issue in data assimilation - the problem reduces in scale to the solution of approximately 50,000 equations for the 20,000 variables.

Houben, Howard↗
NASA NTRS1997

Parameterizing Grid-Averaged Longwave Fluxes for Inhomogeneous Marine Boundary Layer Clouds

This paper examines the relative impacts on grid-averaged longwave flux transmittance (emittance) for Marine Boundary Layer (MBL) cloud fields arising from horizontal variability of optical depth tau and cloud sides, First, using fields of Landsat-inferred tau and a Monte Carlo photon transport algorithm, it is demonstrated that mean all-sky transmittances for 3D variable MBL clouds can be computed accurately by the conventional method of linearly weighting clear and cloudy transmittances by their respective sky fractions. Then, the approximations of decoupling cloud and radiative properties and assuming independent columns are shown to be adequate for computation of mean flux transmittance. Since real clouds have nonzero geometric thicknesses, cloud fractions A'(sub c) presented to isotropic beams usually exceed the more familiar vertically projected cloud fractions A(sub c). It is shown, however, that when A(sub c)less than or equal to 0.9, biases for all-sky transmittance stemming from use of A(sub c) as opposed to A'(sub c) are roughly 2-5 times smaller than, and opposite in sign to, biases due to neglect of horizontal variability of tau. By neglecting variable tau, all-sky transmittances are underestimated often by more than 0.1 for A(sub c) near 0.75 and this translates into relative errors that can exceed 40% (corresponding errors for all-sky emittance are about 20% for most values of A(sub c). Thus, priority should be given to development of General Circulation Model (GCM) parameterizations that account for the effects of horizontal variations in unresolved tau, effects of cloud sides are of secondary importance. On this note, an efficient stochastic model for computing grid-averaged cloudy-sky flux transmittances is furnished that assumes that distributions of tau, for regions comparable in size to GCM grid cells, can be described adequately by gamma distribution functions. While the plane-parallel, homogeneous model underestimates cloud transmittance by about an order of magnitude when 3D variable cloud transmittances are less than or equal to 0.2 and by approx. 20% to 100% otherwise, the stochastic model reduces these biases often by more than 80%.

Barker, Howard W.↗
NASA NTRS2017

Program to Optimize Simulated Trajectories II (POST2) Surrogate Models for Mars Ascent Vehicle (MAV) Performance Assessment

The primary purpose of the multiPOST tool is to enable the execution of much larger sets of vehicle cases to allow for broader trade space exploration. However, this exploration is not achieved solely with the increased case throughput. The multiPOST tool is applied to carry out a Design of Experiments (DOE), which is a set of cases that have been structured to capture a maximum amount of information about the design space with minimal computational effort. The results of the DOE are then used to fit a surrogate model, ultimately enabling parametric design space exploration. The approach used for the MAV study includes both DOE and surrogate modeling. First, the primary design considerations for the vehicle were used to develop the variables and ranges for the multiPOST DOE. The final set of DOE variables were carefully selected in order to capture the desired vehicle trades and take into account any special considerations for surrogate modeling. Next, the DOE sets were executed through multiPOST. Following successful completion of the DOE cases, a manual verification trial was performed. The trial involved randomly selecting cases from the DOE set and running them by hand. The results from the human analyst's run and multiPOST were then compared to ensure that the automated runs were being executed properly. Completion of the verification trials was then followed by surrogate model fitting. After fits to the multiPOST data were successfully created, the surrogate models were used as a stand-in for POST2 to carry out the desired MAV trades. Using the surrogate models in lieu of POST2 allowed for visualization of vehicle sensitivities to the input variables as well as rapid evaluation of vehicle performance. Although the models introduce some error into the output of the trade study, they were very effective at identifying areas of interest within the trade space for further refinement by human analysts. The next section will cover all of the ground rules and assumptions associated with DOE setup and multiPOST execution. Section 3.1 gives the final DOE variables and ranges, while section 3.2 addresses the POST2 specific assumptions. The results of the verification trials are given in section 4. Section 5 gives the surrogate model fitting results, including the goodness-of-fit metrics for each fit. Finally, the MAV specific results are discussed in section 6.

Zwack, M. R.↗
NASA NTRS2013

A Suzaku X-ray Observation of One Orbit of the Supergiant Fast X-ray Transient IGR J16479-4514

We report on a 250 ks long X-ray observation of the supergiant fast X-ray transient (SFXT) IGR J16479-4514 performed with Suzaku in 2012 February. During this observation, about 80% of the short orbital period (P(sub orb) approximates 3.32 days) was covered as continuously as possible for the first time. The source light curve displays variability of more than two orders of magnitude, starting with a very low emission state (10(exp −13) erg / sq cm/s; 1-10 keV) lasting the first 46 ks, consistent with being due to the X-ray eclipse by the supergiant companion. The transition to the uneclipsed X-ray emission is energy dependent. Outside the eclipse, the source spends most of the time at a level of 6-7X10)(exp−12) erg/sq. cm/s) punctuated by two structured faint flares with a duration of about 10 and 15 ks, respectively, reaching a peak flux of 3-4X10(exp −11) erg/sq. cm./S, separated by about 0.2 in orbital phase. Remarkably, the first faint flare occurs at a similar orbital phase of the bright flares previously observed in the system. This indicates the presence of a phase-locked large scale structure in the supergiant wind, driving a higher accretion rate onto the compact object. The average X-ray spectrum is hard and highly absorbed, with a column density, NH, of 10*exp 23)/sq cm, clearly in excess of the interstellar absorption. There is no evidence for variability of the absorbing column density, except that during the eclipse, where a less absorbed X-ray spectrum is observed. A narrow Fe K-alpha emission line at 6.4 keV is viewed along the whole orbit, with an intensity which correlates with the continuum emission above 7 keV. The scattered component visible during the X-ray eclipse allowed us to directly probe the wind density at the orbital separation, resulting in rho(sub w)=7X10(exp −14) g/cubic cm. Assuming a spherical geometry for the supergiant wind, the derived wind density translates into a ratio M(sub w)/v(sub infinity) = 7X10(exp −17) Solar M/km which, assuming terminal velocities in a large range 500-3000 km/s, implies an accretion luminosity two orders of magnitude higher than that observed. As a consequence, a mechanism should be at work reducing the mass accretion rate. Different possibilities are discussed.

J164794514↗
DOE OSTI2022

The Milky Way Revealed by Variable Stars. I. Sample Selection of RR Lyrae Stars and Evidence for Merger History

In order to study the Milky Way, RR Lyrae (RRL) variable stars identified by Gaia, ASAS-SN, and ZTF sky survey projects have been analyzed as tracers in this work. Photometric and spectroscopic information of 3417 RRLs including proper motions, radial velocity, and metallcity are obtained from observational data of Gaia, LAMOST, GALAH, APOGEE, and RAVE. Precise distances of RRLs with typical uncertainties less than 3% are derived by using a recent comprehensive period–luminosity–metallicity relation. Our results from kinematical and chemical analysis provide important clues for the assembly history of the Milky Way, especially for the Gaia–Sausage ancient merger. The kinematical and chemical trends found in this work are consistent with those of recent simulations that indicated that the Gaia–Sausage merger had a dual origin in the Galactic thick disk and halo. As recent similar works have found, the halo RRL sample in this work contains a subset of radially biased orbits besides a more isotropic component. This higher orbital anisotropy component amounts to β ≃ 0.8, and it contributes between 42% and 83% of the halo RRLs at 4 < R( kpc) < 20.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1995

Response of the upper atmosphere to variations in the solar soft x-ray irradiance

Terrestrial far ultraviolet (FUV) airglow emissions have been suggested as a means for remote sensing the structure of the upper atmosphere. The energy which leads to the excitation of FUV airglow emissions is solar irradiance at extreme ultraviolet (EUV) and soft x-ray wavelengths. Solar irradiance at these wavelengths is known to be highly variable; studies of nitric oxide (NO) in the lower thermosphere have suggested a variability of more than an order of magnitude in the solar soft x-ray irradiance. To properly interpret the FUV airflow, the magnitude of the solar energy deposition must be known. Previous analyses have used the electron impact excited Lyman-Birge-Hopfield (LBH) bands of N2 to infer the flux of photoelectrons in the atmosphere and thus to infer the magnitude of the solar irradiance. This dissertation presents the first simultaneous measurements of the FUV airglow, the major atmospheric constituent densities, and the solar EUV and soft x-ray irradiances. The measurements were made on three flights of an identical sounding rocket payload at different levels of solar activity. The linear response in brightness of the LBH bands to variations in solar irradiance is demonstrated. In addition to the N2 LBH bands, atomic oxygen lines at 135.6 and 130.4 nm are also studied. Unlike the LBH bands, these emissions undergo radiative transfer effects in the atmosphere. The OI emission at 135.6 nm is found to be well modeled using a radiative transfer calculation and the known excitation processes. Unfortunately, the assumed processes leading to OI 130.4 nm excitation are found to be insufficient to reproduce the observed variability of this emission. Production of NO in the atmosphere is examined; it is shown that a lower than previously reported variability in the solar soft x-ray irradiance is required to explain the variability of NO.

Bailey, Scott Martin↗
NASA NTRS1994

Numerical Wave Propagation 211 Based on Wave Primitives

Compact higher order finite difference equations are applied to a sequence of problems in wave propagation and aeroacoustics. Systems of PDE's are reduced to a sequence of simple wave primitives using a local eigenvector decomposition. The wave primitives are first order PDE's in two independent variable and allow natural boundary conditions to be imposed for both single- and multidimensional problems. The method uses a "discrete dispersion relation" approach to obtain high order approximations to the wave primitives on a 3 spatial point / 2 time level computational molecule. The scheme is fourth order accurate for the class of system with constant coefficients, e.g., those that support exponential solutions. Weakly non-linear PDE's are solved in a similar manner using a variant of the "method of frozen coefficients." Experience with the new algorithm for linear, non-linear, and multi-dimensional test problems will be described.

Davis, Sanford S.↗
NASA NTRS2010

On the Temporal Variability of Low-Mode Internal Tides in the Deep Ocean

In situ measurements of internal tides are typically characterized by high temporal variability, with strong dependence on stratification, mesoscale eddies, and background currents commonly observed. Thus, it is surprising to find phase-locked internal tides detectable by satellite altimetry. An important question is how much tidal variability is missed by altimetry. We address this question in several ways. We subset the altimetry by season and find only very small changes -- an important exception being internal tides in the South China Sea where we observe strong seasonal dependence. A wavenumber-domain analysis confirms that throughout most of the global ocean there is little temporal variability in altimetric internal-tide signals, at least in the first baroclinic mode, which is the mode that dominates surface elevation. The analysis shows higher order modes to be significantly more variable. The results of this study have important practical implications for the anticipated SWOT wide-swath altimeter mission, for which removal of internal tide signals is critical for observing non-tidal submesoscale phenomena.

Ray, Richard D.↗
NASA NTRS1988

Dynamic variability of column ozone

A first-order, analytic estimate of the dynamical change in column ozone density is given as a function of temperature change in the lower stratosphere. It is found that, for each 1 percent (about 2 C) cooling averaged over the lower stratosphere, the column ozone density can be expected to decrease by approximately 7 percent, if it can be assumed that such a temperature change is induced by changes in wave transports.

Tung, Ka Kit↗
NASA NTRS1992

Computation of ephemerides for long-period variable stars for the Hipparcos mission

In order to predict the luminosities of LPVs observed by Hipparcos, many visual light curves, characterized by irregularly spaced data, were analyzed using original and complementary methods. The obtained power spectra, including amplitudes and phases, are utilized in the computation of the ephemerides. The predictions are regularly checked with observations. In this paper we present the methods and suggest some physical implications that are evoked.

Mennessier, M. O.↗
NASA NTRS2019

Informing Algorithms from Ground Validation: The GPM Combined Algorithm

Ground validation (GV) for the Global Precipitation Measurement (GPM) mission encompasses in-situ (e.g., gauge, disdrometer) measurements, ground radar products, and comprehensive datasets from dedicated airborne field campaigns. These datasets are used for direct validation of the precipitation products from GPM as well as to inform assumptions used by the algorithms that produce these products. This presentation will focus on current and potential such uses of GV data in the GPM combined radar-radiometer algorithm.The GPM combined algorithm, by virtue of using data from the Dual-frequency Precipitation Radar (DPR) and GPM Microwave Imager (GMI), is the most well-constrained instantaneous precipitation product from GPM. It also plays an important in role the passive microwave algorithms as a basis for the construction of brightness temperature-precipitation profile databases and is a calibrator for the multi- satellite gridded product IMERG. Since both radar and radiometer data are used as observational inputs, and even with these data the retrievals are underconstrained, microphysical properties of the hydrometeor profile that are relevant over the range of GMI and DPR wavelengths and incidence angles need to be assumed by the algorithm forward models. Such properties include the normalized intercept parameter (N w ) and shape parameter () of the particle size distribution, ice size-density relationship, and particle size-aspect ratio relationships. The sub-beam variability must also be prescribed in order to accurately simulate the observed radar reflectivity profiles without introducing significant biases. The sensitivity of the algorithm to these parameters, along with their mean values and variability, will be discussed. Examples of future directions include refinement with new data (particularly the assumptions related to ice), and seeking relationships between assumptions and observable or environmental data.

Munchak, Joe.↗
DOE OSTI2018

Spatial analysis of concentrations of multiple air pollutants using NASA DISCOVER-AQ aircraft measurements: Implications for exposure assessment

Highlights: • Aircraft measurements showed spatially varying relations of multiple air pollutants. • NO{sub x}, toluene, and xylenes/ethylbenzene were reasonable proxies of traffic and urban air pollution. • Between-pollutant concentration correlations and ratios varied by space. • Multiple pollutant relations provided insights for exposure assessment and multipollutant epidemiology. In recent years, multipollutant approaches have been employed to investigate the association with health outcomes to better represent real-world conditions than more traditional analysis that considers a single pollutant. With regard to the exposure assessment of a mixture of air pollutants, it is critical to understand the spatial variability in multipollutant relations in order to assess their potential health implications. In this study, we investigated the spatial relations of multiple pollutant concentrations (i.e., NO{sub x}, NO{sub y}, black carbon, carbon monoxide, acetaldehyde, formaldehyde, toluene, xylenes/ethylbenzene, ozone, water-soluble organic carbon, and aerosol extinction) observed from the P-3B aircraft in the 2011 NASA field campaign in Baltimore/Washington D.C. areas during July 2011. The between-pollutant Pearson correlations and Z-scores (calculated from log-transformed concentrations) between near-highways and non-highways and between near-urban centers and non-urban centers varied by pollutant pair and space. We found generally lower correlations between NO{sub x} and other pollutants for near-highways (average r = 0.36) than for non-highways (average r = 0.41) and also for non-urban centers (average r = 0.37) than for near-urban centers (average r = 0.41). This indicated that the temporal associations between NO{sub x} and health outcomes might be less affected by other pollutants, which were also related to same health outcomes, for near-highways and non-urban centers. The analysis of between-pollutant Z-scores showed varying spatial relations for popular traffic-related pollutants with the Z-score differences of 0.43 (NO{sub x}-carbon monoxide), 0.29 (NO{sub x}-black carbon), and 0.17 (black carbon-carbon monoxide) between near-highways and non-highways. This result exhibited heterogeneous traffic-related pollutant mixtures with the proximity to highways, potentially leading to the diverse extent of health associations. Furthermore, a mixed effects model presented pollutant-specific associations between the concentrations and the proximity to highways and urban centers, showing larger declines for NO{sub x}, xylenes/ethylbenzene, toluene, and NO{sub y} than those for the pollutants related to secondary pollutant formation. The model also demonstrated the different sensitivity of each pollutant to meteorological parameters, which may modify the spatial and temporal variability in the relations between the pollutants. Our findings provide insights for exposure assessment studies to better understand the cumulative health consequences associated with multiple air pollutants simultaneously.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Variance-Reduced Accelerated First-Order Methods: Central Limit Theorems and Confidence Statements

In this paper, we consider a strongly convex stochastic optimization problem and propose three classes of variable sample-size stochastic first-order methods: (i) the standard stochastic gradient descent method, (ii) its accelerated variant, and (iii) the stochastic heavy-ball method. In each scheme, the exact gradients are approximated by averaging across an increasing batch size of sampled gradients. We prove that when the sample size increases at a geometric rate, the generated estimates converge in mean to the optimal solution at an analogous geometric rate for schemes (i)–(iii). Based on this result, we provide central limit statements, whereby it is shown that the rescaled estimation errors converge in distribution to a normal distribution with the associated covariance matrix dependent on the Hessian matrix, the covariance of the gradient noise, and the step length. If the sample size increases at a polynomial rate, we show that the estimation errors decay at a corresponding polynomial rate and establish the associated central limit theorems (CLTs). Under certain conditions, we discuss how both the algorithms and the associated limit theorems may be extended to constrained and nonsmooth regimes. As a result, we provide an avenue to construct confidence regions for the optimal solution based on the established CLTs and test the theoretical findings on a stochastic parameter estimation problem.

Lei, Jinlong↗
NASA NTRS2009

Graphical User Interface for Simulink Integrated Performance Analysis Model

The J-2X Engine (built by Pratt & Whitney Rocketdyne,) in the Upper Stage of the Ares I Crew Launch Vehicle, will only start within a certain range of temperature and pressure for Liquid Hydrogen and Liquid Oxygen propellants. The purpose of the Simulink Integrated Performance Analysis Model is to verify that in all reasonable conditions the temperature and pressure of the propellants are within the required J-2X engine start boxes. In order to run the simulation, test variables must be entered at all reasonable values of parameters such as heat leak and mass flow rate. To make this testing process as efficient as possible in order to save the maximum amount of time and money, and to show that the J-2X engine will start when it is required to do so, a graphical user interface (GUI) was created to allow the input of values to be used as parameters in the Simulink Model, without opening or altering the contents of the model. The GUI must allow for test data to come from Microsoft Excel files, allow those values to be edited before testing, place those values into the Simulink Model, and get the output from the Simulink Model. The GUI was built using MATLAB, and will run the Simulink simulation when the Simulate option is activated. After running the simulation, the GUI will construct a new Microsoft Excel file, as well as a MATLAB matrix file, using the output values for each test of the simulation so that they may graphed and compared to other values.

Durham, R. Caitlyn↗