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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 1,207 records · Page 67
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Benchmarking Cylindrical Blast Wave Theory Against the OSIRIS-REx Sample Return Capsule Reentry

Weak shock theory based on cylindrical blast waves has been used to interpret meteor infrasound, but it has not been systematically benchmarked against a non-ablating hypersonic source with independently known parameters. The objective of this study is not to propose a new theoretical framework, but to evaluate the operational validity of the existing suite of blast radius formulations against a high-fidelity ground truth dataset. The OSIRIS-REx Sample Return Capsule reentry on 24 September 2023 provides such a benchmark because the capsule geometry, trajectory, and infrasound emission points are constrained from mission data and ray tracing, reducing source-side uncertainty associated with ablation. Using observations from 39 infrasound stations, this benchmarking study evaluates six published blast radius (${R}_{0}$ ) formulations and three weak-shock transition coefficients ( C ) within a stratified atmospheric propagation model to predict signal period and peak overpressure. The benchmarking identifies the Sakurai formulation as the best-performing formulation for non-ablating bodies, with the Jones/Plooster formulation performing comparably when a physically appropriate C is adopted. Sakurai and Jones/Plooster yield linear-period median absolute percentage residuals of 9% and 11%, respectively. The period predictions show only weak sensitivity to C at these propagation distances. The Mach-diameter approximation commonly used in meteor studies overestimates ${R}_{0}$ by more than a factor of 3 in the absence of ablation. Finally, these results establish a performance baseline for applying cylindrical blast wave theory to effectively non-ablating hypersonic bodies and demonstrate that the signal period is a robust observable for constraining ${R}_{0}$.

atmospheric entry↗
DOE OSTI2023

High-throughput exploration of the WMoVTaNbAl refractory multi-principal-element alloys under multiple-property constraints

Development of next-generation gas turbines requires the design and fabrication of novel high-temperature structural materials capable of operating beyond 1300°C. Here, we propose a high-throughput alloy design framework under multiple-property constraints to discover new refractory multi-principal element alloys (MPEAs) for high-temperature applications. The framework treats the development of MPEAs as a composition-agnostic constraint satisfaction problem, i.e., no prescriptions are made concerning the design space before performing investigatory calculations. We target alloys in the WMoVTaNbAl chemistry space that are predicted to meet constraints on the following properties simultaneously: single-phase stability, density, solidus temperature, yield strength at 1300°C, and ductile-to-brittle-transition temperature. These properties are relevant to both applications in gas turbines and manufacturability. A set of 214 MoNbV-rich alloys meet these relevant constraints. These feasible alloys are investigated with density functional theory (DFT) to provide a fundamental electronic basis for their superior properties. Three compositionally representative alloys from the feasible design space (Mo 45 Nb 35 Ta 5 V 15 , Mo 25 Nb 50 V 20 W 5 , and Mo 30 Nb 35 Ta 5 V 25 W 5 ) are selected with a k-medoids-based design scheme for detailed DFT analysis and experimental characterization. The DFT analysis predicted a single-phase BCC at high temperatures with a high yield strength for all three MPEAs, in agreement with CALPHAD (CALculation of PHAse Diagrams) and experiments, respectively. These three alloys are benchmarked against a public database of 1546 MPEAs. Concerning the aforementioned constraints, the Mo 30 Nb 35 Ta 5 V 25 W 5 alloy outperforms these 1546 MPEAs. The present work demonstrates the ability of the proposed design methodology to identify candidate alloys for a given application under multiple property constraints in a combinatorically vast design space.

36 MATERIALS SCIENCE↗
NASA NTRS2011

Investigating Some Technical Issues on Cohesive Zone Modeling of Fracture

This study investigates some technical issues related to the use of cohesive zone models (CZMs) in modeling fracture processes. These issues include: why cohesive laws of different shapes can produce similar fracture predictions; under what conditions CZM predictions have a high degree of agreement with linear elastic fracture mechanics (LEFM) analysis results; when the shape of cohesive laws becomes important in the fracture predictions; and why the opening profile along the cohesive zone length needs to be accurately predicted. Two cohesive models were used in this study to address these technical issues. They are the linear softening cohesive model and the Dugdale perfectly plastic cohesive model. Each cohesive model constitutes five cohesive laws of different maximum tractions. All cohesive laws have the same cohesive work rate (CWR) which is defined by the area under the traction-separation curve. The effects of the maximum traction on the cohesive zone length and the critical remote applied stress are investigated for both models. For a CZM to predict a fracture load similar to that obtained by an LEFM analysis, the cohesive zone length needs to be much smaller than the crack length, which reflects the small scale yielding condition requirement for LEFM analysis to be valid. For large-scale cohesive zone cases, the predicted critical remote applied stresses depend on the shape of cohesive models used and can significantly deviate from LEFM results. Furthermore, this study also reveals the importance of accurately predicting the cohesive zone profile in determining the critical remote applied load.

Wang, John T.↗
NASA NTRS2015

How the Assumed Size Distribution of Dust Minerals Affects the Predicted Ice Forming Nuclei

The formation of ice in clouds depends on the availability of ice forming nuclei (IFN). Dust aerosol particles are considered the most important source of IFN at a global scale. Recent laboratory studies have demonstrated that the mineral feldspar provides the most efficient dust IFN for immersion freezing and together with kaolinite for deposition ice nucleation, and that the phyllosilicates illite and montmorillonite (a member of the smectite group) are of secondary importance.A few studies have applied global models that simulate mineral specific dust to predict the number and geographical distribution of IFN. These studies have been based on the simple assumption that the mineral composition of soil as provided in data sets from the literature translates directly into the mineral composition of the dust aerosols. However, these tables are based on measurements of wet-sieved soil where dust aggregates are destroyed to a large degree. In consequence, the size distribution of dust is shifted to smaller sizes, and phyllosilicates like illite, kaolinite, and smectite are only found in the size range 2 m. In contrast, in measurements of the mineral composition of dust aerosols, the largest mass fraction of these phyllosilicates is found in the size range 2 m as part of dust aggregates. Conversely, the mass fraction of feldspar is smaller in this size range, varying with the geographical location. This may have a significant effect on the predicted IFN number and its geographical distribution.An improved mineral specific dust aerosol module has been recently implemented in the NASA GISS Earth System ModelE2. The dust module takes into consideration the disaggregated state of wet-sieved soil, on which the tables of soil mineral fractions are based. To simulate the atmospheric cycle of the minerals, the mass size distribution of each mineral in aggregates that are emitted from undispersed parent soil is reconstructed. In the current study, we test the null-hypothesis that simulating the presence of a large mass fraction of phyllosilicates in dust aerosols in the size range 2 m, in comparison to a simple model assumption where this is neglected, does not yield a significant effect on the magnitude and geographical distribution of the predicted IFN number. Results from sensitivity experiments are presented as well.

Dust↗
DOE OSTI2023

Genomic prediction of switchgrass winter survivorship across diverse lowland populations

Abstract In the North-Central United States, lowland ecotype switchgrass can increase yield by up to 50% compared with locally adapted but early flowering cultivars. However, lowland ecotypes are not winter tolerant. The mechanism for winter damage is unknown but previously has been associated with late flowering time. This study investigated heading date (measured for two years) and winter survivorship (measured for three years) in a multi-generation population generated from two winter-hardy lowland individuals and diverse southern lowland populations. Sequencing data (311,776 markers) from 1,306 individuals were used to evaluate genome-wide trait prediction through cross-validation and progeny prediction (n = 52). Genetic variance for heading date and winter survivorship was additive with high narrow-sense heritability (0.64 and 0.71, respectively) and reliability (0.68 and 0.76, respectively). The initial negative correlation between winter survivorship and heading date degraded across generations (F1 r = −0.43, pseudo-F2 r = −0.28, pseudo-F2 progeny r = −0.15). Within-family predictive ability was moderately high for heading date and winter survivorship (0.53 and 0.52, respectively). A multi-trait model did not improve predictive ability for either trait. Progeny predictive ability was 0.71 for winter survivorship and 0.53 for heading date. These results suggest that lowland ecotype populations can obtain sufficient survival rates in the northern United States with two or three cycles of effective selection. Despite accurate genomic prediction, naturally occurring winter mortality successfully isolated winter tolerant genotypes and appears to be an efficient method to develop high-yielding, cold-tolerant switchgrass cultivars.

60 APPLIED LIFE SCIENCES↗
NASA NTRS1991

Orbit determination support for Hiten's aerobraking in the Earth's atmosphere

Two passes of the ISAS (Japan's Institute of Space and Astronautical Science) Hiten spacecraft through the Earth's atmosphere, at perigee altitudes of 125 km and 120 km, during Mar. 1991 marked the first aerobraking technology demonstrations for an object in cis-lunar orbit traveling at near Earth escape velocity. Prediction and control of perigee altitude to better than 1 km was desired to assure spacecraft survival. Covariance analysis provided confidence that prediction accuracy better than 200 m for support of final trim maneuver design was achievable with NASA DSN (Deep Space Network) tracking support. ISAS used orbit determination results in their decisions to cancel final trim maneuvers. Post flight reconstructions, marking the first combined use of DSN and ISAS tracking data, yielded perigee altitude solutions which agree with the near real time mission operations support predictions to better than 50 m.

Efron, L.↗
NASA NTRSDate not supplied

Early Information Parameter-Set Analysis for Satellite Close Approaches using Machine Learning

Understanding orbital mechanics is essential in space flight and navigation applications, and leveraging modern force models for flight path projection remains an important aspect in space mission design and operation. However, force models do not capture all the dynamics or perturbations in the space environment and thus are subject to errors in predicting the state vectors. The further out the predicted miss distance between spacecraft is from the time of closest approach (TCA), the larger the propagated errors in the predicted miss distance at TCA is. The dependency on these force models for spacecraft flight state prediction calls for a more reliable method that can quantify, or even reduce, these propagated errors. With recent advances in the field artificial intelligence, specifically in machine and deep learning algorithms, a model that implements these approaches can improve on the modern force model approach. The goal for this work is to provide an early-information decision-making threshold, in order to prioritize risk assessment implementation, given the ongoing increase of space objects. In analyzing the relationship of several parameters from conjunction data messages(CDMs) and solar information, early information becomes viable in miss distance prediction with unsupervised learning techniques, which learn the parameters that are linked together with miss distance and probability of collision (Pc) variables. Another approach implemented for identifying relationships within CDMs is supervised learning, in which a shallow neural network binary classifier learns to distinguish events with Pc values¡108. These parameters detected in the unsupervised process are then applied to a regression neural network, which predicts the miss distance at TCA for a specific event within a given uncertainty bound. For the regression neural network, a Long Short Term Memory (LSTM) neural network is implemented, which yields memory about each time step in an event. Using an LSTM network, the model learns to predict miss distance within 0.2km of the value measured at TCA. Although there is a limited amount of "close miss" data to train a network, the network learns to associate parameters, like large energy dissipation rates with the secondary object, with an elevated Pc

Brianna I. Robertson↗
DOE OSTI2022

Graph neural networks for efficient learning of mechanical properties of polycrystals

Herein we present graph neural networks (GNNs) as an efficient and accurate machine learning approach to predict mechanical properties of polycrystalline materials. Here, a GNN was developed based on graph representation of polycrystals incorporating only fundamental features of grains including their crystallographic orientation, size, and grain neighbor connectivity information. We tested our method on modeling stiffness and yield strength of α -Ti microstructures, varying in their crystallographic texture. We find the GNN predicts both properties with high accuracy with mean relative errors of ~1% for unseen microstructures from a given set of textures and < 2% for microstructures of unseen texture, even when presented with limited training data. This accuracy is comparable to methods that require high-resolution three-dimensional (3D) microstructure data, such as 3D convolutional neural networks (3D-CNNs) and models that depend on the computation of spatial statistics. The present results show that graph-based deep learning is a promising framework for property prediction, especially considering the high cost associated with obtaining high-resolution 3D microstructure data and the general scarcity of experimental materials datasets.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Scalar-induced neutrinoless double beta decay in SU(5)

We discuss the role of heavy scalar fields in mediating neutrinoless double beta decay (0νββ) within the SU(5) Grand Unified Theory framework, extended suitably to include neutrino mass. In such a minimal realistic SU(5) setup for fermion masses, the scalar contributions to 0νββ are extremely suppressed as a consequence of the proton decay bound. We circumvent this problem by imposing a discrete Z 3 symmetry. However, the scalar contributions to 0νββ remain suppressed in this SU(5) x Z 3 model due to the neutrino mass constraint. We find that the 0νββ contribution can be enhanced by extending the scalar sector with an additional 15-dimensional scalar representation with suitable Z 3 charge. Such an extension not only yields realistic fermion mass spectra but also leads to experimentally testable predictions in upcoming ton-scale 0νββ searches, which can be used as a sensitive probe of the new scalars across a broad range, from LHC-accessible scales up to ∼ 10 10 GeV.

Baryon/Lepton Number Violation↗
DOE OSTI2020

Interpenetration and kinetic effects in converging, high-energy plasma jets

In this work, we report on numerical simulations of laser-driven convergent plasma fusion targets. These “inverted corona” fusion targets are useful for the study of counter-streaming and converging rarefied plasma flows, and previous experiments have demonstrated their potential as neutron sources. The scheme consists of a fuel layer lined along the interior surface of a hollow plastic shell that is laser-ablated and expands inward towards the target center. The plasma streams generated in these targets are initially nearly collisionless as they converge, leading to wide interaction length scales and long interaction time scales as the jets interpenetrate. Such kinetic effects impact mixing of constituent ions - a phenomenon not properly captured by single-fluid hydrodynamic simulations. Here we conduct numerical simulations using two different methods: (1) single-fluid simulations in HYDRA, and (2) kinetic-ion, fluid-electron hybrid particle-in-cell (PIC) simulations in the code Chicago. It is shown that the initially nearly collisionless plasma fronts interpenetrate deeply and lead to broader interaction regions in space and time resulting in significant beam-beam fusion. The two approaches make different, testable predictions for the effect of fuel-layer thickness on neutron yield.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Measurement of 3 Λ H production in Pb–Pb collisions at √ s NN = 5.02 TeV

The first measurement of 3 Λ H and $^{3}_{\overline{Λ}}$$\overline{H}$ differential production with respect to transverse momentum and centrality in Pb–Pb collisions at √ s NN = 5.02 TeV is presented. The 3 Λ H has been reconstructed via its two-charged-body decay channel, i.e., 3 Λ H → 3 He → π - . A Blast-Wave model fit of the p T -differential spectra of all nuclear species measured by the ALICE collaboration suggests that the kinetic freeze-out surface is consistent with that of other nuclei. The ratio between the integrated yields of 3 Λ H and 3 He is compared to predictions from the statistical hadronisation model and the coalescence model, with the latter being favoured by the presented measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Synthesis and Structural Study of Substituted Ternary Nitrides for Ammonia Production

Over the past few decades, inorganic nitride materials have grown in importance in part due to their potential as catalysts for the synthesis of NH 3 , a key ingredient in fertilizer and precursor to industrial chemicals. Of particular interest are the ternary (ABN) or higher-order nitrides with high metal-to-nitrogen ratios that show promise in enhancing NH 3 synthesis reaction rates and yields via heterogeneous catalysis or chemical looping. Although metal nitrides are predicted to be numerous, the stability of nitrogen triple bonds found in N 2 , especially in comparison to the metal–nitrogen bonds, has considerably hindered synthetic efforts to produce complex nitride compounds. In this study, we present an exhaustive down-selection process to identify ternary nitrides for a promising chemical looping NH 3 production mechanism. We also report on a facile and efficient two-step synthesis method that can produce well-characterized η-carbide Co 3 Mo 3 N/Fe 3 Mo 3 N or filled β-manganese Ni 2 Mo 3 N ternaries, as well as their associated quaternary, (Co,Fe) 3 Mo 3 N, (Fe,Ni) 2 Mo 3 N, and (Co,Ni) 2 Mo 3 N, solid solutions. To further explore the quaternary space, syntheses of (Co,Ni) 3 Mo 3 N (Ni ≤ 10 mol %) and Co 3 (Mo,W) 3 N (W ≤ 10 mol %) were also investigated. The structures of the nitrides were characterized via X-ray powder diffraction. The morphology and compositions were characterized with scanning electron microscopy. In conclusion, the multitude of chemically unique, but structurally related, nitrides suggests that properties such as nitrogen activity may be tunable, making the materials of great interest for NH 3 synthesis schemes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Ab initio molecular dynamics free energy study of enhanced copper (II) dimerization on mineral surfaces

Understanding the adsorption of isolated metal cations from water on to mineral surfaces is critical for toxic waste retention and cleanup in the environment. Heterogeneous nucleation of metal oxyhydroxides and other minerals on material surfaces is key to crystal growth and dissolution. The link connecting these two areas, namely cation dimerization and polymerization, is far less understood. In this work we apply ab initio molecular dynamics calculations to examine the coordination structure of hydroxide-bridged Cu(II) dimers, and the free energy changes associated with Cu(II) dimerization on silica surfaces. The dimer dissociation pathway involves sequential breaking of two Cu 2+ -OH – bonds, yielding three local minima in the free energy profiles associated with 0-2 OH – bridges between the metal cations, and requires the design of a (to our knowledge) novel reaction coordinate for the simulations. Cu(II) adsorbed on silica surfaces are found to exhibit stronger tendency towards dimerization than when residing in water. Cluster-plus-implicit-solvent methods yield incorrect trends if OH – hydration is not correctly depicted. The predicted free energy landscapes are consistent with fast equilibrium times (seconds) among adsorbed structures, and favor Cu 2+ dimer formation on silica surfaces over monomer adsorption.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Seismoacoustic analysis of underground explosions using the Rayleigh integral

SUMMARY A coupled seismoacoustic model is developed for the analysis of acoustic signals produced by underground explosive events with an aim to develop a means of improving estimated depth and yield for explosion monitoring. A ground spall model is used to predict surface motion characteristics produced by an underground explosion and the Rayleigh integral is applied to relate the surface motion to the acoustic signal some distance from surface ground zero. The low-frequency component of the ground motion associated with the prolonged free fall of lofted material during spall is found to dominate the acoustic signal propagating away from surface ground zero at shallow angles. The model is applied to observed ground motion and acoustic signals recorded during the Source Physics Experiment (SPE) with promising results. In addition to accurately predicting characteristics of the observed acoustic signals from several of the SPE events, the model provides a means of explaining the lack of signals observed during several events in the SPE due to the directionality of the higher frequency acoustic signals associated with the uplift and closure components as well as the lack of a spatially localized, longer duration dwell.

58 GEOSCIENCES↗
DOE OSTI2025

Mixing by internal gravity waves in stars: assessing numerical simulations against theory

ABSTRACT Here we present a study of radial chemical mixing in non-rotating massive main-sequence stars driven by internal gravity waves (IGWs), based on multidimensional hydrodynamical simulations with the fully compressible code MUSIC. We examine two proposed mechanisms of material mixing in stars by IGWs that are commonly quoted, relating to thermal diffusion and sub-wavelength shearing. Thermal diffusion provides a non-restorative effect to the waves, leaving material displaced from its previous equilibrium, while shearing arising within the waves drives weak localized flows, mixing the fluid there. Using IGW spectra from the simulations, we evaluate theoretical predictions of mixing rates due to these mechanisms. We show, for $20\, \mathrm{M}_\odot$ main-sequence stars, that neither of these mechanisms are likely to create mixing sufficient to correct inaccuracies in current stellar evolution models. Furthermore, we compare these predictions to results obtained from Lagrangian tracer particles, following a method recently used for global simulations of stellar interiors to measure mixing by IGWs in their radiative zones. We demonstrate that tracer particle methods face significant numerical challenges in measuring the small diffusion coefficients predicted by the aforementioned theories, for which they are prone to yielding artificially enhanced coefficients. Diffusion coefficients based on such methods are currently used with stellar evolution codes for asteroseismic studies, but should be viewed with caution. Finally, in a case where tracer particles do not suffer from numerical artefacts, we suggest that a diffusion model is not suitable for time-scales typically considered by 2D numerical simulations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Influence of nonstatistical properties in nuclear structure on emission of prompt fission neutrons

We report the Hauser-Feshbach fission-fragment decay (HF 3 D) model is extended to calculate the prompt fission neutron spectrum (PFNS) for the thermal-neutron-induced fission on 235 U, where the evaporated neutrons from all possible fission-fragment pairs are aggregated. By studying model parameter sensitivities on the calculated PFNS as well as nonstatistical behavior of low-lying discrete level spin distribution, we conclude that discrepancies between the aggregation calculation and the experimental PFNS seen at higher neutron emission energies can be attributed to both the primary fission-fragment yield distribution and the possible high spin states that are not predicted by the statistical theory of nuclear structure.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Energy filtering–induced ultrahigh thermoelectric power factors in Ni 3 Ge

Traditional thermoelectric materials rely on low thermal conductivity to enhance their efficiency but suffer from inherently limited power factors. Innovative pathways to optimize electronic transport are thus crucial. Here, we achieve ultrahigh power factors in Ni 3 Ge-based systems through an unconventional thermoelectric materials design principle. When overlapping flat and dispersive bands are engineered to the Fermi level, charge carriers can undergo intense interband scattering, yielding an energy filtering effect similar to what has long been predicted in certain nanostructured materials. Via a multistep DFT-based screening method developed here, we find a family of L1 2 -ordered binary compounds with ultrahigh power factors up to 11 mW m −1 K −2 near room temperature, which are driven by an intrinsic phonon-mediated energy filtering mechanism. Our comprehensive experimental and theoretical study of these intriguing materials paves the way for understanding and designing high-performance scattering-tuned metallic thermoelectrics.

Science & Technology - Other Topics↗
DOE OSTI2023

(U) A General-Purpose Code for Correlated Sampling Using Batch Statistics with MCNP6 for Fixed-Source Problems

Correlated sampling can be used to reduce the uncertainty of a difference of tallies by taking advantage of the negative covariance term in the sandwich formula. Booth first showed how correlated sampling can be applied with batch statistics using MCNP’s tally fluctuation chart (TFC) to reduce the uncertainty of a difference of tallies in fixed-source problems. Booth presented a problem in which a 1273% uncertainty in a difference was reduced to 8% by accounting for correlations. Researchers He and Su recently studied correlated sampling using the TFC in MCNP version 5. They determined that the code did not print enough digits in the TFC tally means for accurate batch statistics in some cases. After modifying the source code, they concluded that “correlated sampling can yield a standard deviation of about one magnitude smaller than that predicted by the direct, un-correlated simulation when the changes in system response are small (say about 1%), which is equivalent to saving in CPU time by a factor of 100. Such saving [sic] becomes less significant as the change in system response becomes larger.” He and Su provided the formulas needed to apply batch statistics to compute the correlated uncertainty of a difference of tallies. In this report, we follow up on their work by providing the formulas needed to apply batch statistics to compute the correlated uncertainty of a ratio of tallies and of a difference of two tallies divided by a third tally. We extend these formulas to differences and ratios of ratios. These formulas are applied to reduce the uncertainty associated with calculating a relative sensitivity. He and Su did not investigate the accuracy of their correlated sampling uncertainty estimates. We use their test problems and evaluate the accuracy of the uncertainty estimates by comparing with results obtained from random sampling, and, in simple cases, with theoretical values of the “exact” uncertainties. We find that the uncertainties obtained from batch statistics are accurate as long as at least 100 batches are used. We present a new computer code, COSUBS (COrrelated Sampling Using Batch Statistics), that reads MCNP6 TFCs and applies correlated sampling using batch statistics for the tally combinations that the user specifies. COSUBS is a very general tool that compares all TFCs for a base case and one or two perturbed cases. It computes uncertainties for ratios if given only a base case. This report is organized as follows. The equations to apply batch statistics to the difference of random tallies are reviewed in Sec. II. Section III presents the equations for applying batch statistics to a ratio of random tallies; this is useful for computing relative sensitivities using a one-sided finite difference and the relative sensitivity using the differential operator method. Section IV presents the equations for applying batch statistics to a difference of two random tallies divided by a third; this is useful for computing a relative sensitivities using a central difference. Section V presents the equations for applying batch statistics to a difference of two ratios with four random tallies. Section VI presents the equations for applying batch statistics to a one-sided finite difference estimate of the relative sensitivity of a ratio (this uses four random tallies). Section VII presents the equations for applying batch statistics to a central difference estimate of the relative sensitivity of a ratio (this uses six random tallies). Section VIII presents the equations for applying batch statistics to a sum of random tallies. Section IX discusses how to apply batch statistics using MCNP6. Section X presents COSUBS, describing its command-line options and logic. Sections XI through XVI present numerical results for various test problems. Section XVII is a summary and conclusions. Appendix A derives the theoretical Monte Carlo tally variance given certain assumptions; these variances are used to verify the batch statistics for some of the problems. Appendix B lists the MCNP6 input for the unperturbed example problem. Appendix C presents modifications made to MCNP6.3 to support this work.

97 MATHEMATICS AND COMPUTING↗