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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 1,387 records · Page 77
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Hybrid chemical characterization of latent images in EUV resist with 12 nm half-pitch features

With the advancement of high numerical aperture extreme ultraviolet (EUV) lithography, the new platform will enable chipmakers to achieve critical dimensions of 8 nm. However, resist materials face significant challenges in delivering increased sensitivity while managing rising stochastic variations. We aim to develop comprehensive techniques to characterize the chemical profile of latent images, stored in EUV resists after exposure and postexposure baking, which is essential for understanding the origin of stochastic effects. Infrared photo-induced force microscopy (IR PiFM) is a bimodal atomic force microscopy technique combined with an infrared light source, allowing for simultaneous sub-5 nm topographic and chemical characterization within a localized environment. Critical-dimension resonant soft X-ray scatterometry (CD-RSoXS) provides statistical data that reveal structural and chemical information for comparative analysis. For the first time, IR PiFM has been used to chemically map the latent images of EUV resists (after exposure and postexposure baking) at a record high resolution of 12 nm half-pitch, enabling nondestructive analysis of patterns prior to development. Furthermore, CD-RSoXS offers direct experimental observation and comparison of exposed, postexposure baked, and developed patterns, which align with the IR PiFM results. We demonstrate that the IR PiFM technique offers valuable insights into both high spatial resolution and local chemical information simultaneously. In addition, CD-RSoXS provides statistical results that support our main findings. This hybrid metrology approach leverages a multifaceted dataset by combining the most reliable information from each source, which is essential for a comprehensive understanding of the stochastic effects in EUV lithography processes.

O’Reilly, Padraic↗
DOE OSTI2026

Model data for infrastructure-aware simulation of compound flooding at Alligator Bayou Watershed, southeast Texas

This dataset supports infrastructure-aware hydrologic modeling and flood scenario analysis for the Alligator Bayou Watershed, a highly managed urban watershed in Southeast Texas. It includes Jupyter notebooks for figure reproduction, model configuration files, simulation outputs, and derived products used to quantify the influence of engineered stormwater infrastructure on flood behavior across multiple spatial scales. The dataset was generated using the Watershed Workflow Python package and the Advanced Terrestrial Simulator (ATS), enabling integrated surface–subsurface hydrologic simulations on a channel-aligned mesh with explicit representations of pump stations, gate structures, detention basins, and impervious surfaces. Outputs include time series of gate and pump flows, stage observations, and water balance components, as well as spatially explicit fields of peak ponded depth and flood duration across multiple infrastructure scenarios spanning a single-location detention basin expansion, distributed drainage limitations, and compound coastal flooding. These data facilitate full reproducibility of the manuscript figures and support further research on urban flood dynamics and the role of stormwater infrastructure in shaping watershed-scale flood response.

EARTH SCIENCE > OCEANS > COASTAL PROCESSES↗
DOE OSTI2021

Oxygen isotope evidence for input of magmatic fluids and precipitation of Au-Ag-tellurides in an otherwise ordinary adularia-sericite epithermal system in NE China

Abstract Tellurium-rich (Te) adularia-sericite epithermal Au-Ag deposits are an important current and future source of precious and critical metals. However, the source and evolution of ore-forming fluids in these deposits are masked by traditional bulk analysis of quartz oxygen isotope ratios that homogenize fine-scale textures and growth zones. To advance understanding of the source of Te and precious metals, herein, we use petrographic and cathodoluminescence (CL) images of such textures and growth zones to guide high spatial resolution secondary ion mass spectroscopy (SIMS) oxygen isotope analyses (10 µm spot) and spatially correlated fluid inclusion microthermometric measurements on successive quartz bands in contemporary Te-rich and Te-poor adularia-sericite (-quartz) epithermal Au-Ag vein deposits in northeastern China. The results show that large positive oxygen isotope shifts from –7.1 to +7.7‰ in quartz rims are followed by precipitation of Au-Ag telluride minerals in the Te-rich deposit, whereas small oxygen isotope shifts of only 4‰ (–2.2 to +1.6‰) were detected in quartz associated with Au-Ag minerals in the Te-poor deposits. Moreover, fluid-inclusion homogenization temperatures are higher in comb quartz rims (avg. 266.4 to 277.5 °C) followed by Au-Ag telluride minerals than in previous stages (~250 °C) in the Te-rich deposit. The Te-poor deposit has a consistent temperature (~245 °C) in quartz that pre- and postdates Au-Ag minerals. Together, the coupled increase in oxygen isotope ratios and homogenization temperatures followed by precipitation of Au-Ag tellurides strongly supports that inputs of magmatic fluid containing Au, Ag, and Te into barren meteoric water-dominated flow systems are critical to the formation of Te-rich adularia-sericite epithermal Au-Ag deposits. In contrast, Te-poor adularia-sericite epithermal Au-Ag deposits show little or no oxygen isotope or fluid-inclusion evidence for inputs of magmatic fluid.

Geochemistry & Geophysics↗
DOE OSTI2026

FY 2026 Midyear Report: Seismic Monitoring of Underground Vibration Sources Using Distributed Acoustic Sensing and Seismometers

Safeguards-relevant temporal changes in underground facilities can be observed using geophysical monitoring techniques. Seismic waves, in particular, provide valuable insights into subsurface activities and can serve as an important tool for detecting anomalous events that may indicate containment breaches at geological repositories. This midyear report summarizes ongoing efforts to automatically and rapidly detect and locate anomalous vibration signals that could be indicative of potential containment breaches. Previous work during FY25 focused on compiling continuous seismic datasets from two underground sites and developing a database of continuous waveforms and ground-truth event data derived from multiple sensing modalities. Building on this foundation, we are adapting anomaly detection and geolocation algorithms to explore methods for monitoring underground activities using two relatively low-maintenance sensing technologies: a dense surface geophone array deployed at the Pleasant Gap mine in Pennsylvania, and a three-dimensional fiber-optic cable array for distributed acoustic sensing (DAS) installed in the subsurface at the Sanford Underground Research Facility (SURF) in South Dakota. This report summarizes work conducted during the first two quarters of FY26, during which we refined a dynamic power spectral density (PSD)-based detector, applied it independently to each geophone station, and then combined the per‑station detections with density-based spatial clustering of applications with noise (DBSCAN) to cluster events and produce spatial maps over a nine‑day interval. In addition, we outline plans for a field trial at the Waste Isolation Pilot Plant (WIPP) in New Mexico to compare traditional seismic monitoring approaches with DAS techniques and to evaluate the benefits of combined data analysis. Activities during the past two quarters have included the preparation and submission of a Field Test Plan to WIPP for approval, as well as submission to headquarters for review and feedback.

58 GEOSCIENCES↗
DOE OSTI2023

The Origin of Star Formation in Early-type Galaxies Inferred from Spatially Resolved Spectroscopy

Abstract We investigate the origin of star formation activity in early-type galaxies with current star formation using spatially resolved spectroscopic data from the Mapping Nearby Galaxies at Apache Point Observatory in the Sloan Digital Sky Survey (SDSS). We first identify star-forming early-type galaxies from the SDSS sample, which are morphologically early-type but show current star formation activity in their optical spectra. We then construct comparison samples with different combinations of star formation activity and morphology, which include star-forming late-type galaxies, quiescent early-type galaxies, and quiescent late-type galaxies. Our analysis of the optical spectra reveals that the star-forming early-type galaxies have two distinctive episodes of star formation, which is similar to late-type galaxies but different from quiescent early-type galaxies with a single star formation episode. Star-forming early-type galaxies have properties in common with star-forming late-type galaxies, which include stellar population, gas and dust content, mass, and environment. However, the physical properties of star-forming early-type galaxies derived from spatially resolved spectroscopy differ from those of star-forming late-type galaxies in the sense that the gas in star-forming early-type galaxies is more concentrated than their stars, and is often kinematically misaligned with stars. The age gradient of star-forming early-type galaxies also differs from those of star-forming late-type galaxies. Our findings suggest that the current star formation in star-forming early-type galaxies has an external origin including galaxy mergers or accretion gas from the cosmic web.

Astronomy & Astrophysics↗
DOE OSTI2021

Influence of geometry on columnar to equiaxed transition during electron beam powder bed fusion of IN718

Correlation between spot-melt scan parameters (linear spot-density aka areal energy density), build geometry, and solidification microstructure evolution (columnar vs equiaxed) in a powder bed fusion technology is investigated. It is shown that to maintain the equiaxed solidification microstructure evolution in electron beam powder bed additive manufacturing (AM), the areal energy density per layer needs to be scaled with respect to the 2D cross-sectional area of the layer being melted. Samples with two different cross-sectional areas (40 × 40 mm and 20 × 20 mm) have been fabricated with varying areal energy densities. For a given square cross-section (20 × 20 mm), increasing the areal energy density (4.8 MJ/sq.m to 14.7 MJ/sq.m) transitioned the solidification microstructure from columnar to equiaxed. The observed microstructure data (Electron Back Scattered Diffraction - EBSD) is quantified by calculating the principal component (PC) score using a spatial statistics methodology. The sample with equiaxed grains is found to have a low PC score while the sample with columnar grain had a high PC score. A semi-analytical model is used to simulate the heat transfer and the local solidification conditions as a function of processing parameters (linear spot-density). The result from the heat transfer model is correlated with previously quantified microstructure data. Space-Time analysis of the melt pattern is done and correlated with the observed microstructure. In addition, from the findings, appropriate parameters have been used to additively manufacture a turbine blade with site-specific or hybrid solidification microstructure (traditional fabrication possible via a patented method of localized cold working and heat treatment).

36 MATERIALS SCIENCE↗
DOE OSTI2024

Design and Analysis of Liquid Lithium Plasma Facing Components

In this study, liquid metal (LM) on plasma-facing components (PFCs) creates a renewable protective cover enhancing power exhaust and protecting the solid substrate. Additionally, energy confinement improvement through particle pumping can be achieved in the case of liquid lithium (LL). A new variant of PFCs was recently introduced at Princeton Plasma Physics Laboratory (PPPL) where a porous wall is used to stabilize the LM surface, while using magnetohydrodynamic (MHD) drive to push the LM flow inside the component. This arrangement allows efficient heat exhaust, and enhanced control of the LM surface temperature, leading to spatial control of evaporation and condensation of LL on the plasma interface. This feature is particularly attractive when vapor shielding is introduced to allow heat flux redistribution. This system has the advantage that as the heat flux increases, the evaporation rate will increase, while decreasing heat flux will decrease the evaporation rate of lithium, ideally creating a feedback effect which could self-regulate the amount of lithium evaporated. Analytical and numerical models for LL PFCs were developed in PPPL. To calculate the target temperature distribution for the case of evaporation from the divertor, we apply an iterative process allowing two-way coupling between the fluid-kinetic analysis of plasma using SOLPS-ITER code and the flow and heat transfer analysis of the PFC using an analytical model. In the last stage, the results are validated using computational fluid dynamics (CFD) analysis with customized version of the CFX code from ANSYS. CFX was modified at PPPL to allow MHD analysis at the high magnetic field typical for fusion applications. Results of the analysis for NSTX-U tokamak conditions will be presented.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Quantifying the cooperative evolution of microphase segregation and nanostructural order in annealed polyurethanes of MDI-BDO-PTHF

Here, we quantify the relationship between microphase segregation and local structure development in thermoplastic polyurethanes. Samples were prepared with varying ratios of 4,40 -methylene diphenyl diisocyanate (MDI) and 1,4-butanediol (BDO) to polytetrahydrofuran (PTHF) and annealed at temperatures T a between RT–140 °C for 20 h each. Distinct populations of smaller and larger ordered domains are distinguished by pair distribution func tion analysis. The intermediate-range order of nanoscale hard domains in the paracrystalline state (form I) is directly extracted and characterized. The results suggest that form I of the MDI-BDO:PTHF system presents a conformational and packing order similar to the form III structure, typically obtained from stretching/annealing, but with limited spatial coherence of 3–7 nm. Heating above T g of the hard segments is necessary to achieve a substantial structural response from the annealing treatment. Increasing T a promotes purification of the soft phase via microphase segregation, coalescence of the hard blocks, and growth of paracrystalline phase, while a minority fraction of longer-range ordered domains left over from production remains relatively constant. We observe a composition-dependent decrease in the average nearest-neighbor dis tance that can be correlated with the greater number of C C, C N, and C O bonds with increased hard segment content. A non-linear deviation in the trend is observed to correlate with sample densification. The mechanical and thermal behavior of the samples is intimately tied to the segregation state.

processing-structure-properties↗
DOE OSTI2025

Robust Spectral Anomaly Detection in EELS Spectral Images via 3D Convolutional Variational Autoencoders

Abstract A 3D Convolutional Variational Autoencoder (3D‐CVAE) is introduced for automated anomaly detection in electron energy‐loss spectroscopy spectrum imaging (EELS‐SI) data. This approach leverages the full 3D structure of EELS‐SI data to detect subtle spectral anomalies while preserving both spatial and spectral correlations across the datacube. By employing cross‐entropy loss and training on bulk spectra, the model learns to reconstruct bulk features characteristic of the defect‐free material. In exploring methods for anomaly detection, both the 3D‐CVAE approach and principal component analysis (PCA) are evaluated, testing their performance using FeL‐edge ΔEpeak shifts designed to simulate material defects. These results show that 3D‐CVAE achieves superior anomaly detection and maintains consistent performance across various shift magnitudes. The method demonstrates clear bimodal separation between bulk and anomalous spectra, enabling reliable classification. Further analysis verifies that lower‐dimensional representations are robust to anomalies in the data. While performance advantages over PCA diminish with decreasing anomaly concentration, our method maintains high reconstruction quality even in challenging, noise‐dominated spectral regions. This approach provides a robust framework for unsupervised automated detection of spectral anomalies in EELS‐SI data, particularly valuable for analyzing complex material systems.

Chemistry↗
DOE OSTI2021

Quantification of Deformation-Induced Concentration Fluctuations in Polymeric Liquids by Small-Angle Neutron Scattering

This study demonstrates how the large concentration fluctuations of polymeric liquids under deformation and flow can be quantitatively studied by applying the spherical harmonic expansion technique to small-angle neutron scattering. Using a series of binary polymer blends, it is shown that the emergence of the so-called butterfly patterns is caused by the change of sign in the leading anisotropic component of the small-angle spectrum, when the scattering is dominated by intermolecular correlation associated with flow-induced demixing. The increasing spatial fluctuations of concentration are evidenced by the enhancement of the isotropic component of the scattering spectrum in the zero-angle limit and peak shift of the leading anisotropic coefficients toward low Q. Additionally, the spherical harmonic expansion framework permits real-space analysis of anisotropic scattering length density correlation in a convenient form. The methodology described in this work provides a concrete venue for quantitative studies of phase behavior of fluids under deformation and flow via small-angle scattering techniques, where mainly qualitative approaches were previously employed.

Chemical structure↗
DOE OSTI2025

Long‐Term Large‐Scale Atmospheric Forcing Data From Three‐Dimensional Constrained Variational Analysis for the ARM SGP Site

Here, this study presents a long‐term three‐dimensional large‐scale forcing data set (VARANAL3D) derived from the three‐dimensional constrained variational analysis (3DCVA) method at the Atmospheric Radiation Measurement (ARM) program Southern Great Plains (SGP) site from 2004 to 2018. Building on the same input data sets as the conventional continuous forcing data set (VARANAL), VARANAL3D maintains overall consistency in domain‐averaged fields while introducing spatial variability, offering critical insights into the influence of mesoscale synoptic systems on cloud‐related processes. Evaluations are conducted across four cloud and precipitation regimes: Clear‐sky, Shallow‐clouds, Afternoon‐precipitation, and Nocturnal‐precipitation, presenting high consistency of the domain‐mean forcing data sets while emphasizing the role of subdomain forcing variability particularly in precipitating regimes. Single column model (SCM) simulations demonstrate that subdomain VARANAL3D forcing improves cloud and precipitation representation, with the ensemble outperforming domain‐mean forcing in three cloudy and precipitating regimes. Overall, these results highlight VARANAL3D's value for investigating the impacts of spatial variability of large‐scale forcing on atmospheric processes. The VARANAL3D data set provides new opportunities for evaluating model physics, advancing the development of scale‐aware parameterizations and deepening our understanding of cloud and precipitation dynamics.

Environmental sciences↗
DOE OSTI2026

Operando microscopy for neuromorphic hardware

Microscopy techniques can uncover the physical properties and dynamic behaviours of materials, driving the discovery of emergent phenomena and guiding the design of next-generation computing hardware. As artificial intelligence becomes pervasive, the demand for high-performance materials to support sustainable information technologies is growing. Here, this Review highlights state-of-the-art imaging from electron and X-ray to optical techniques to probe the dynamics of neuromorphic materials, including operando characterization of devices. We examine design principles for neuromorphic materials, along with obstacles that hinder their development. Emphasis is placed on spatially and temporally resolved approaches that capture state changes including phase transitions, ferroic switching and spin-wave propagation that emulate biological components such as neurons, synapses and their connectivity. We discuss challenges in operando characterization and the integration of artificial intelligence-driven analysis for feedback-guided material discovery. Finally, we outline opportunities for real-time imaging of neuromorphic systems, paving the way towards adaptive, brain-inspired hardware.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Quantifying electron temperature distributions from time-integrated x-ray emission spectra

K-shell x-ray emission spectroscopy is a standard tool used to diagnose the plasma conditions created in high-energy-density physics experiments. In the simplest approach, the emissivity-weighted average temperature of the plasma can be extracted by fitting an emission spectrum to a single temperature condition. It is known, however, that a range of plasma conditions can contribute to the measured spectra due to a combination of the evolution of the sample and spatial gradients. In this work, we define a parameterized model of the temperature distribution and use Markov Chain Monte Carlo sampling of the input parameters, yielding uncertainties in the fit parameters to assess the uniqueness of the inferred temperature distribution. Here we present the analysis of time-integrated S and Fe x-ray spectroscopic data from the Orion laser facility and demonstrate that while fitting each spectral region to a single temperature yields two different temperatures, both spectra can be fit simultaneously with a single temperature distribution. We find that fitting both spectral regions together requires a maximum temperature of $1310^{+90}_{-70}$ eV with significant contributions from temperatures down to 200 eV.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

An advanced workflow for single-particle imaging with the limited data at an X-ray free-electron laser

An improved analysis for single-particle imaging (SPI) experiments, using the limited data, is presented here. Results are based on a study of bacteriophage PR772 performed at the Atomic, Molecular and Optical Science instrument at the Linac Coherent Light Source as part of the SPI initiative. Existing methods were modified to cope with the shortcomings of the experimental data: inaccessibility of information from half of the detector and a small fraction of single hits. The general SPI analysis workflow was upgraded with the expectation-maximization based classification of diffraction patterns and mode decomposition on the final virus-structure determination step. The presented processing pipeline allowed us to determine the 3D structure of bacteriophage PR772 without symmetry constraints with a spatial resolution of 6.9 nm. The obtained resolution was limited by the scattering intensity during the experiment and the relatively small number of single hits.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Spatiotemporal Variability of Electric System Reliability Metrics

As urbanization continues to grow, urban density also rises, placing significant stress on critical infrastructure. Cities often face challenges in investing in new infrastructure or upgrading existing ones. One area of infrastructure that has come under strain is the electric grid, leading to prolonged power outages. According to data from the U.S. Energy Information Administration, the average duration of power outages has steadily doubled from 2013 to 2021, primarily due to extreme weather events. The IEEE has developed a series of reliability metrics to assess the reliability of the electric system. However, these metrics are only applied at the utility level, making it challenging to comprehend the variations in these indices at finer spatial resolutions and, consequently, evaluate reliability at the non-utility level. In this study, we leveraged electric outage data collected at 15-minute intervals at the county level to estimate electric system reliability over a six-year period using a novel data analysis approach. Our findings reveal a gradual decline in reliability in the U.S. Southwest compared to national averages. Furthermore, the duration of outages per customer per event has significantly decreased in large portions of California and Florida. These discoveries can be valuable for utility companies as they seek to pinpoint regional anomalies and plan for prioritized remediation efforts.

Singh, Nagendra↗
DOE OSTI2024

Quantitative phenotyping of crop roots with spectral electrical impedance tomography: a rhizotron study with optimized measurement design

Background: Root systems are key contributors to plant health, resilience, and, ultimately, yield of agricultural crops. To optimize plant performance, phenotyping trials are conducted to breed plants with diverse root traits. However, traditional analysis methods are often labour-intensive and invasive to the root system, therefore limiting high-throughput phenotyping. Spectral electrical impedance tomography (sEIT) could help as a non-invasive and cost-efficient alternative to optical root analysis, potentially providing 2D or 3D spatio-temporal information on root development and activity. Although impedance measurements have been shown to be sensitive to root biomass, nutrient status, and diurnal activity, only few attempts have been made to employ tomographic algorithms to recover spatially resolved information on root systems. In this study, we aim to establish relationships between tomographic electrical polarization signatures and root traits of different fine root systems (maize, pinto bean, black bean, and soy bean) under hydroponic conditions. Results: Our results show that, with the use of an optimized data acquisition scheme, sEIT is capable of providing spatially resolved information on root biomass and root surface area for all investigated root systems. We found strong correlations between the total polarization strength and the root biomass (R 2 = 0.82) and root surface area (R 2 = 0.8). Our findings suggest that the captured polarization signature is dominated by cell-scale polarization processes. Additionally, we demonstrate that the resolution characteristics of the measurement scheme can have a significant impact on the tomographic reconstruction of root traits. Conclusion: Our findings showcase that sEIT is a promising tool for the tomographic reconstruction of root traits in high-throughput root phenotyping trials and should be evaluated as a substitute for traditional, often time-consuming, root characterization methods.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Confronting Dark Matter with the Multiwavelength Sky (Final Technical Report)

The existence of dark matter is a key clue to new fundamental physics, yet its nature and non-gravitational interactions remain mysterious. In the course of this five-year project (spanning July 2015 - July 2020), we have developed novel analysis techniques to separate dark matter signals from astrophysical backgrounds in the inner Galaxy, and measured hitherto-unknown properties of the Fermi Bubbles and the Galactic Center excess in gamma-rays from the inner Milky Way. We have improved predictions for the spatial distribution and energy spectra of photon signals from dark matter, and set new limits from astrophysical and cosmological datasets on dark matter inhabiting complex dark sectors, multi-particle dark matter annihilation, and tiny primordial black holes. We have successfully adapted effective field theory techniques from collider physics to make high-precision predictions for signals from heavy weakly-interacting DM, allowing us to essentially exclude the possibility that DM is a thermal wino, and have discovered novel theoretical and observational implications for dark matter bound states and self-interactions. We have developed a comprehensive public code package for modeling the effects of exotic energy injections, such as from dark matter annihilation and decay, on the ionization and temperature history of the early cosmos, and have used these tools to set robust, powerful and broadly-applicable constraints on models of light dark matter.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Verification of EvaluateFLux Utility Program

The EvaluateFlux program is a post-processing utility program for DIF3D, specifically DIF3D-VARIANT which handles Cartesian and hexagonal geometries. The EvaluateFlux program was developed to allow users to obtain flux and power traverses through the geometry domain, and its initial purpose was to facilitate foil analysis by evaluating the flux solution from DIF3D-VARIANT and combining it with foil cross section data. The EvaluateFlux program can calculate the neutron flux, as well as the reaction rates, at any user provided evaluation point. It does this by identifying the spatial mesh associated with the evaluation point and then evaluates the polynomial based neutron flux moments stored in the NHFLUX file at that point. The output of EvaluateFlux varies depending on the input setup. The maximum output includes the neutron flux and microscopic and macroscopic reaction rates at each evaluation point. The purpose of this work is to verify the outputs of EvaluateFlux. Simple models that have hand calculatable results are first defined and used to verify the EvaluateFlux outputs. More complex cases are then added where a duplicate program of EvaluateFlux that uses PrintTables outputs of the binary files is used to verify the EvaluateFlux outputs. In those complex cases, hand calculations of selected evaluation points were also displayed to confirm the software verification. For all the tests done, the hand calculations agreed well with those calculated by EvaluateFlux. For the larger complex problems, the duplicate program that can process hundreds of evaluation points was able to identify that zero points within some meshes have large errors. This aspect was attributed to the truncation error on the input provided to the duplicate program and is not a concern for the accuracy of the EvaluateFlux software.

97 MATHEMATICS AND COMPUTING↗