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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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

The Hubble Space Telescope PanCET Program: An Optical to Infrared Transmission Spectrum of HAT-P-32Ab

We present a 0.3−5 μm transmission spectrum of the hot Jupiter HAT-P-32Ab observed with the Space Telescope Imaging Spectrograph and Wide Field Camera 3 instruments mounted on the Hubble Space Telescope, combined with Spitzer Infrared Array Camera photometry. The spectrum is composed of 51 spectrophotometric bins with widths ranging between 150 and 400 Å, measured to a median precision of 215 ppm. Comparisons of the observed transmission spectrum to a grid of 1D radiative-convective equilibrium models indicate the presence of clouds/hazes, consistent with previous transit observations and secondary eclipse measurements. To provide more robust constraints on the planet’s atmospheric properties, we perform the first full optical to infrared retrieval analysis for this planet. The retrieved spectrum is consistent with a limb temperature of 1248{sub −92}{sup +92} K, a thick cloud deck, enhanced Rayleigh scattering, and ∼10× solar H{sub 2}O abundance. We find log(Z/Z {sub ⊙}) = 2.41{sub −0.07}{sup +0.06}, and compare this measurement with the mass–metallicity relation derived for the solar system.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Crack formation in strained β-(AlxGa 1−x ) 2 O 3 films grown on (010) β-Ga 2 O 3 substrates

The cracking and local strain relaxation in (010) (Al x Ga 1−x ) 2 O 3 films grown on Ga 2 O 3 substrates are assessed in terms of film composition and thickness. We utilize x-ray diffraction and electron microscopy techniques combined with simulation and modeling to investigate that film cracking on curvature (flatness) has a directly proportional relationship with film thickness and/or aluminum content. Cross section transmission electron microscopy reveals that cracks along both the (001) and (100) cleavage planes penetrate into the substrate. The diffuse scattered intensity observed in reciprocal space maps (RSMs) is directly correlated with the tilt that is introduced due to the change in the deformation conditions near the cracks. While asymmetric RSMs show that the layers are fully strained, the diffuse scattering distribution in reciprocal space can be interpreted to show that the cracking relaxes and locally tilts the lattice ∼350 nm from the crack edges, which is consistent with the larger radius of curvature associated with the films with higher crack densities. For example, a 200 nm (Al 0.13 Ga 0.87 ) 2 O 3 thick film has an average inter-crack spacing of 3.3 µm, so most of the epitaxial layer is fully strained except near the cracks where it deforms elastically and is consistent with the gallium oxide Poisson ratio. A reciprocal space model was developed, which imports the strain and tilt distributions (based on finite element modeling) to match the features observed in the experimental maps. We also note that previous studies involving (Al x Ga 1−x ) 2 O 3 films may show evidence of cracking as observed in their symmetric and asymmetric RSMs.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Importance of viewing angle: Hotspot effect improves the ability of satellites to track terrestrial photosynthesis

The product of near-infrared reflectance of vegetation and photosynthetic active radiation (NIRvP) is a new tool for monitoring gross primary productivity (GPP) dynamics in terrestrial ecosystems, due to the discovered linear correlation between NIRvP and GPP. While remote sensing-based NIRvP is considerably influenced by sensor geometry, such geometry impacts on the NIRvP-GPP relationship remain underexplored. In this study, we calculate NIRvP using observations from the Deep Space Climate Observatory (DSCOVR) that provide unique hotspot observation geometry in which the sensor viewing angle coincides with the sun direction. We evaluated the linear correlation between NIRvP and GPP in both the common nadir direction and the special hotspot direction. The results indicate that NIRvP in the hotspot direction significantly outperforms that in the nadir direction for tracking GPP variations across different ecosystems from diurnal to daily scales. This conclusion is further supported by data from the MODerate resolution Imaging Spectroradiometer (MODIS) and simulations using the Soil Canopy Observation Photosynthesis Energy (SCOPE) model. Finally, our research highlights the value of using the unconventional hotspot-based sun-tracking satellite observations for a more accurate characterization of GPP dynamics in terrestrial ecosystems.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Inner southern magnetosphere observation of Mercury via SERENA ion sensors in BepiColombo mission

Mercury’s southern inner magnetosphere is an unexplored region as it was not observed by earlier space missions. In October 2021, BepiColombo mission has passed through this region during its first Mercury flyby. Here, we describe the observations of SERENA ion sensors nearby and inside Mercury’s magnetosphere. An intermittent high-energy signal, possibly due to an interplanetary magnetic flux rope, has been observed downstream Mercury, together with low energy solar wind. Low energy ions, possibly due to satellite outgassing, were detected outside the magnetosphere. The dayside magnetopause and bow-shock crossing were much closer to the planet than expected, signature of a highly eroded magnetosphere. Different ion populations have been observed inside the magnetosphere, like low latitude boundary layer at magnetopause inbound and partial ring current at dawn close to the planet. These observations are important for understanding the weak magnetosphere behavior so close to the Sun, revealing details never reached before.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Developing Upscaling Approach for Swarming Hydraulic Fractures Observed at Hydraulic Fracturing Test Site through Multiscale Simulations

We show that this work aims to address a challenge posed by recent observations of tightly spaced hydraulic fractures in core samples from the hydraulic fracturing test site (HFTS) in the Middle Wolfcamp Formation. Many fractures in retrieved cores have subfoot spacing, which is at odds with conventional models in which usually one hydraulic fracture is initiated per cluster. Models assuming a single fracture at each cluster, although a common practice, often predict excessive fracture propagation that is inconsistent with microseismic observation. Here, we aim to develop a numerical approach to effectively account for densely spaced hydraulic fractures in field-scale simulations. Because it is impractical to explicitly model all aforementioned fractures, we develop a new upscaling law that enables existing simulation tools to predict reservoir response to fracture swarms. The upscaling law is derived based on an energy equivalence argument and validated through multiscale simulations using a high-fidelity code, GEOS. The swarming fractures are first modeled with a spacing that is much smaller than the cluster spacing; these fractures are then approximated by an upscaled, single fracture based on the proposed upscaling law. The upscaled fracture is shown to successfully match the energy input rate and produce the total fracture aperture and average propagation length of the explicitly simulated swarm. Afterward, the upscaling approach is further implemented in 3D field-scale simulations and validated against the HFTS microseismic data of a horizontal well. Our results show that hydraulic fracture swarming can significantly affect fracture propagation behaviors compared with the propagation of single fractures as assumed by conventional modeling approaches. Under the considered situations, the conventional treatment yields fast propagation speed that far exceeds that indicated by the microseismic data. We also illustrate that this discrepancy can be reduced readily through the implementation of the upscaling law. Our results demonstrate the importance of accounting for the fracture swarming effect in field-scale simulations and the efficacy of this approach to enable realistic predictions of reservoir responses to fracture swarms, without the need to model tightly spaced fractures individually.

02 PETROLEUM↗
DOE OSTI2024

High-accuracy emulators for observables in ΛCDM, N eff, Σ m ν, and w cosmologies

ABSTRACT We use the emulation framework CosmoPower to construct and publicly release neural network emulators of cosmological observables, including the cosmic microwave background (CMB) temperature and polarization power spectra, matter power spectrum, distance-redshift relation, baryon acoustic oscillation (BAO) and redshift-space distortion (RSD) observables, and derived parameters. We train our emulators on Einstein–Boltzmann calculations obtained with high-precision numerical convergence settings, for a wide range of cosmological models including ΛCDM, wCDM, ΛCDM + Neff, and ΛCDM + Σmν. Our CMB emulators are accurate to better than 0.5 per cent out to ℓ = 104, which is sufficient for Stage-IV data analysis, and our P(k) emulators reach the same accuracy level out to $k=50 \, \, \mathrm{Mpc}^{-1}$, which is sufficient for Stage-III data analysis. We release the emulators via an online repository (CosmoPower Organisation), which will be continually updated with additional extended cosmological models. Our emulators accelerate cosmological data analysis by orders of magnitude, enabling cosmological parameter extraction analyses, using current survey data, to be performed on a laptop. We validate our emulators by comparing them to class and camb and by reproducing cosmological parameter constraints derived from Planck TT, TE, EE, and CMB lensing data, as well as from the Atacama Cosmology Telescope Data Release 4 CMB data, Dark Energy Survey Year-1 galaxy lensing and clustering data, and Baryon Oscillation Spectroscopic Survey Data Release 12 BAO and RSD data.

Astronomy & Astrophysics↗
DOE OSTI2022

HFTS-1 Natural Joint Data and Engineering Summary

This report provides an analysis of engineering and geologic data collected from the Hydraulic Fracturing Test Site #1 (HTSF-1) project in the southern Midland Basin, Reagan County, Texas. The site is being studied as part of the Science-informed Machine Learning for Accelerating Real-Time Decisions in Subsurface Applications (SMART) Initiative at the National Energy Technology Laboratory (NETL). The data collected is intended to provide a basis of understanding of the site and to construct simulation models. This report provides a summary analysis of the engineering and geologic data collected from the project to provide a basis of understanding of the site and to construct simulation models. The report examines various possible correlations in engineering properties based on natural fracture data from the program, which consisted of 11 horizontal wells, one vertical well, and one slant well. The horizontal wells are in two horizons: 1) Upper and 2) Middle Wolfcamp formations. Program data include: fracture frequency and fracture orientation data from four core runs in a slant well; fracture spacing and orientation from a vertical pilot well; laboratory triaxial testing and mineralogical determinations; and porosity results from magnetic resonance analyses from various wells, together with observations based on the data collection. In addition, available references were reviewed on the site for additional insights. As the focus of the report is on the natural system, hydraulic fracture data from the site were not examined in detail in this report. Data variability is the chief observation in examination of the database. Fracture frequency in the slant well can range from sections with values as high as five fractures per ft to sections up to 100+ ft in length with no natural observed fractures. Fracture spacing across is typically less than 10 ft, but can range up to hundreds of feet. Apparent fracturing shows the trends in two predominate orientations, E-SW and WNW-ESE, but minor variations exist. The rock units vary across the site from siliceous mudstones to calcareous mudstones, showing a general layering with depth. The laboratory properties such as strength and modulus show no apparent trend with depth, but appear to correlate with rock mineralogy with high strength and modulus values where calcium content is high. In addition, an attempt to examine variability and mineralogy on a larger scale was made using a color-coded system based on gamma ray measurements. A staged colored approach was adopted, presuming that lower gamma ray values indicate higher value of calcium content (blue scale) and that higher gamma ray values indicate higher clay mineral content (orange scale). As provided in report appendices, the system correlated well with visual examination of the slant core and the petrofabric analyses of the vertical pilot well. The results showed large variability in mineral content along the horizontal plane across the site. The change in mineral content was also rapid, on a scale less than that of the average hydraulic fracture stage length of about 180 ft.

42 ENGINEERING↗
DOE OSTI2021

Machine Learning the Sixth Dimension: Stellar Radial Velocities from 5D Phase-space Correlations

The Gaia satellite will observe the positions and velocities of over a billion Milky Way stars. In the early data releases, the majority of observed stars do not have complete 6D phase-space information. In this Letter, we demonstrate the ability to infer the missing line-of-sight velocities until more spectroscopic observations become available. Here, we utilize a novel neural network architecture that, after being trained on a subset of data with complete phase-space information, takes in a star's 5D astrometry (angular coordinates, proper motions, and parallax) and outputs a predicted line-of-sight velocity with an associated uncertainty. Working with a mock Gaia catalog, we show that the network can successfully recover the distributions and correlations of each velocity component for stars that fall within ~5 kpc of the Sun. We also demonstrate that the network can accurately reconstruct the velocity distribution of a kinematic substructure in the stellar halo that is spatially uniform, even when it comprises a small fraction of the total star count.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Ship‐Based Lidar Evaluation of Southern Ocean Low Clouds in the Storm‐Resolving General Circulation Model ICON and the ERA5 and MERRA‐2 Reanalyses

Global storm resolving models (GSRMs) represent the next generation of global climate models. One of them is a 5-km Icosahedral Nonhydrostatic Weather and Climate Model (ICON). Its high resolution means that parameterizations of convection and clouds, including subgrid-scale clouds, are omitted, relying on explicit simulation but necessarily utilizing microphysics and turbulence parameterizations. Standard-resolution (10–100 km) models, which use convection and cloud parameterizations, have substantial cloud biases over the Southern Ocean (SO), adversely affecting radiation and sea surface temperature. The SO is dominated by low clouds, which cannot be observed accurately from space due to overlapping clouds, attenuation, and ground clutter. We evaluated SO clouds in ICON and the ERA5 and MERRA-2 reanalyzes using approximately 2400 days of lidar observations and 2300 radiosonde profiles from 31 voyages and a Macquarie Island station during 2010–2021, compared to the model and reanalyzes using a ground-based lidar simulator. We found that ICON and the reanalyzes underestimate the total cloud fraction by about 10% and 20%, respectively. ICON and ERA5 overestimate the cloud occurrence peak at about 500 m, associated with underestimated lower tropospheric stability and overestimated lifting condensation level. The reanalyzes strongly underestimate fog and very low-level clouds, and MERRA-2 underestimates cloud occurrence at almost all heights. Outgoing shortwave radiation is overestimated in MERRA-2, implying a “too few, too bright” cloud problem. SO cloud and fog biases are a substantial issue in the analyzed model and reanalyzes and result in shortwave and longwave radiation biases.

Kuma, Peter [Stockholm Univ. (Sweden); Univ. of Ca↗
DOE OSTI2024

Quantum to classical parton evolution in the QGP

We study the time evolution of the density matrix of a high energy quark in the presence of a dense QCD background that is modeled as a stochastic Gaussian color field. At late times, we find that only the color singlet component of the quark’s reduced density matrix survives the in-medium evolution and that the density matrix becomes asymptotically diagonal in both transverse position and momentum spaces. In addition, we observe an accelerated entropy growth due to the larger phase space being explored by the quark and that the quantum and classical quark entropies converge at late times. We further observe that the quark state loses all memory of the initial condition. Combined with the fact that the reduced density matrix satisfies Boltzmann-diffusion transport, we conclude that the quark reduced density matrix can be interpreted as a classical phase space distribution.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Information Content of a Synergy of Ground-Based and Space-Based Infrared Sounders. Part I: Clear-Sky Environments

Abstract Profiles of atmospheric temperature and water vapor from remotely sensed platforms provide critical observations within the temporal and spatial gaps of the radiosonde network. The 2017 National Academies of Science Decadal Survey highlighted that observations of the planetary boundary layer (PBL) from the current space-based observing system are not of the necessary accuracy or resolution for monitoring and predicting high-impact weather phenomena. One possible solution to improving observations of the PBL is supplementing the existing space-based observing system with a network of ground-based profilers. A synthetic information content study is developed utilizing profiles from the Atmospheric Radiation Measurement (ARM) program sites at the Southern Great Plains (SGP), east North Atlantic (ENA), and North Slope of Alaska (NSA) to assess the benefits, in terms of degrees of freedom (DOF), vertical resolution, and uncertainties, of a synergy between the ground-based Atmospheric Emitted Radiance Interferometer (AERI) with space-based hyperspectral infrared (IR) sounders. A combination of AERI with any of the three polar-orbiting IR sounders: the Atmospheric Infrared Sounder (AIRS), the Cross-track Infrared Sounder (CrIS), or the Infrared Atmospheric Sounding Interferometer (IASI), results in a DOF increase of 30%–40% in the surface-to-700-hPa layer compared to the space-based instrument alone. Introducing AERI measurements to the observing system also results in significant improvements to vertical resolution and uncertainties in the bottom 1000 m of the atmosphere compared to CrIS measurements alone. A synergy of CrIS and AERI exceeds the 1-km-vertical-resolution goal set by the Decadal Survey in the lowest 1000 m.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Evaluation of a land-atmosphere coupling metric computed from a ground-based infrared interferometer

Land-atmosphere feedbacks are a critical component of the hydrologic cycle. Vertical profiles of boundary layer temperature and moisture, together with information about the land surface, are used to compute land-atmosphere coupling metrics. Ground based remote sensing platforms, such as the Atmospheric Emitted Radiance Interferometer (AERI), can provide high temporal resolution vertical profiles of temperature and moisture. When co-located with soil moisture, surface flux, and surface meteorological observations, such as at the Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) site, it is possible to observe both the terrestrial and atmospheric legs of land-atmosphere feedbacks. In this study, we compare a commonly used coupling metric computed from radiosonde-based data to that obtained from the AERI to characterize the accuracy and uncertainty in the metric derived from the two distinct platforms. This approach demonstrates the AERI’s utility where radiosonde observations are absent in time and/or space. Radiosonde and AERI based observations of the Convective Triggering Potential and Low-Level Humidity Index (CTP-HI low ) were computed during the 1200 UTC observation time and displayed good agreement during both 2017 and 2019 warm seasons. Furthermore, radiosonde and AERI derived metrics diagnosed the same atmospheric preconditioning based upon the CTP-HI low framework a majority of the time. When retrieval uncertainty was considered, even greater agreement was found between radiosonde and AERI derived classification. The AERI’s ability to represent this coupling metric well enabled novel exploration of temporal variability within the overnight period in CTP and HI low . Observations of CTP-HI low computed within a few hours of 1200 UTC were essentially equivalent, however with greater differences in time arose greater differences in CTP and HI low .

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Joint Survey Processing. II. Stellar Proper Motions in the COSMOS Field from Hubble Space Telescope ACS and Subaru Telescope HSC Observations

We analyze stellar proper motions in the COSMOS field to assess the presence of bulk motions. At bright magnitudes (G-band 18.5–20.76 AB), we use the proper motions of 1010 stars in the Gaia DR2 catalog. At the faint end, we compute proper motions of 11,519 pointlike objects at i-band magnitudes 19–25 AB using Hubble ACS and Subaru HSC data, which span two epochs about 11 yr apart. In order to measure these proper motions with unprecedented accuracy at faint magnitudes, we developed a foundational set of astrometric tools that will be required for joint survey processing of data from the next generation of optical/infrared surveys. The astrometric grids of Hubble ACS and Subaru HSC mosaics were corrected at the catalog level using proper motion–propagated and parallax-corrected Gaia DR2 sources. These astrometric corrections were verified using compact extragalactic sources. Upon comparison of our measured proper motions with Gaia DR2, we estimate the uncertainties in our measurements to be ~2–3 mas yr –1 axis –1 , down to 25.5 AB mag. We correct proper motions for the mean motion of the Sun, and we find that late-type main-sequence stars predominantly in the thin disk in the COSMOS field have space velocities mainly toward the Galactic center. We detect candidate high-velocity (≥220 km s –1 ) stars, six of them at ~0.4–6 kpc, from the Gaia sample, and five of them at ~20 kpc, from the faint star HSC and ACS sample. The sources from the faint star sample may be candidate halo members of the Sangarius stream.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Modelling the Alfvén eigenmode induced fast-ion flow measured by an imaging neutral particle analyzer

An imaging neutral particle analyzer (INPA) provides energy and radially resolved measurements of the confined fast-ion population ranging from the high-field side to the edge on the midplane of the DIII-D tokamak. In recent experiments, it was used to diagnose fast-ion flow in the INPA-interrogated phase-space driven by multiple, marginally unstable Alfvén eigenmodes (AEs). Here, the key features of this measured fast-ion flow are: (I) a fast-ion flow from q min and the injection energy (81 keV) towards lower energies and plasma periphery.(II) A flow from the same location towards higher energies and the plasma core, (III) a phase-space 'hole' at the injected energy and plasma core and (IV) a pile-up at the plasma core at lower energies (~60 keV). Ad hoc energetic particle diffusivity modelling of TRANSP significantly deviates from the observation. Comparably, a reduced modelling, i.e. a combination of NOVA-K and ASCOT5 code with the measured mode structure and amplitude, generally reproduce some key features of the observed phase-space flow, but largely failed to interpret fast ion depletion near the plasma axis. At last, self-consistent, first-principle multi-phase hybrid simulations that include realistic neutral beam injection and collisions are able to reproduce most features of the time-resolved phase-space flow. During consecutive hybrid phases, an RSAE consistent with the experiment grows and saturates, redistributing the injected fast ions. The resulting synthetic INPA images are in good agreement with the measurement near the injection energy. The simulations track the fast-ion redistribution within the INPA range, confirming that the measured fast-ion flow follows streamlines defined by the intersection of phase-space surfaces of constant magnetic moment μ and constant E' = nE + ωP φ , where n and ω are the instability toroidal mode number and frequency, and E and P φ the ion energy and toroidal canonical momentum. Nonperturbative effects are required to reproduce the depletion of fast ions near the magnetic axis at the injection energy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Challenges and Opportunities in Magnetospheric Space Weather Prediction

Abstract Space Weather is the study of the dynamics of the coupled Solar‐Terrestrial environment, as these dynamics impact technological systems and human activity. This paper reviews a selection of the advances, challenges, and new opportunities for magnetospheric space weather, and while the focus is on specific phenomena, many other aspects of space weather will have similar challenges and needs. As a scientific field with direct applications, the field of space weather is partly driven by imperatives from both policy and operations. We provide an introduction to some of the context in which the field exists and discuss how this might shape future developments and norms within the space weather enterprise. We briefly examine benchmarking, as a policy and operationally driven activity, as it provides immediate societal relevance and an opportunity to stretch scientific understanding. As numerical space weather prediction now becomes routine, and exascale computing is in the near future, we identify challenges relating to computational expense and big data, capturing and accounting for uncertainties, and specification of boundary conditions. Here, as with the observations supporting numerical space weather prediction, the key challenge lies in extending the lead time of predictions. We also discuss the role of data, particularly in regard to model validation and empirical modeling. Due to the growing societal impact of space weather, we also examine the relationships between space weather and its terrestrial counterpart and look at the importance of continuous evaluation, monitoring progress in predictive capability, and communication with researchers, forecasters, and end users.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Accurate shear estimation with fourth-order moments

ABSTRACT As imaging surveys progress in exploring the large-scale structure of the Universe through the use of weak gravitational lensing, achieving sub-per cent accuracy in estimating shape distortions caused by lensing, or shear, is imperative for precision cosmology. In this paper, we extend the Fourier power function shapelets (FPFS) shear estimator using fourth-order shapelet moments and combine it with the original second-order shear estimator to reduce galaxy shape noise. We calibrate this novel shear estimator analytically to a sub-per cent level-accuracy using the AnaCal framework. This higher order shear estimator is tested with realistic image simulations, and after analytical correction for the detection/selection bias and noise bias, the multiplicative shear bias $|m|$ is below $3\times 10^{-3}$ (99.7 per cent confidence interval) for both isolated and blended galaxies. Once combined with the second-order FPFS shear estimator, the shape noise is reduced by $\sim 35~{{\ \rm per\ cent}}$ for isolated galaxies in simulations with Hyper Suprime-Cam and Vera C. Rubin Observatory Legacy Survey of Space and Time observational conditions. However, for blended galaxies, the effective number density does not significantly improve with the combination of the two estimators. Based on these results, we recommend exploration of how this framework can further reduce the systematic uncertainties in shear due to point spread function leakage and modelling error, and potentially provide improved precision in shear inference in high-resolution space-based images.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Advanced Visualization for Scientific Data Analysis and Insight [Slides]

This talk will explore how we have used advanced visualization technologies to support analytical reasoning and knowledge discovery. Specifically, we will present several examples detailing some recent scientific successes using state-of-the-art immersive and high-resolution visualization at the National Renewable Energy Laboratory's Computational Science Center. On multiple occasions, we have observed scientists and engineers discover features in their data using advanced visualization technologies that they had not seen in prior investigations of their data on traditional desktop displays. We have embedded more information into our analytics tools, allowing engineers to explore complex multivariate spaces. We have observed how interactions seem to catalyze understanding.

97 MATHEMATICS AND COMPUTING↗