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DOE OSTI2022

Landau discriminants

Scattering amplitudes in quantum field theories have intricate analytic properties as functions of the energies and momenta of the scattered particles. In perturbation theory, their singularities are governed by a set of nonlinear polynomial equations, known as Landau equations, for each individual Feynman diagram. The singularity locus of the associated Feynman integral is made precise with the notion of the Landau discriminant, which characterizes when the Landau equations admit a solution. In order to compute this discriminant, we present approaches from classical elimination theory, as well as a numerical algorithm based on homotopy continuation. These methods allow us to compute Landau discriminants of various Feynman diagrams up to 3 loops, which were previously out of reach. For instance, the Landau discriminant of the envelope diagram is a reducible surface of degree 45 in the three-dimensional space of kinematic invariants. We investigate geometric properties of the Landau discriminant, such as irreducibility, dimension and degree. In particular, we find simple examples in which the Landau discriminant has codimension greater than one. Furthermore, we describe a numerical procedure for determining which parts of the Landau discriminant lie in the physical regions. In order to study degenerate limits of Landau equations and bounds on the degree of the Landau discriminant, we introduce Landau polytopes and study their facet structure. Finally, we provide an efficient numerical algorithm for the computation of the number of master integrals based on the connection to algebraic statistics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Transient anisotropic kernel for probabilistic learning on manifolds

PLoM (Probabilistic Learning on Manifolds) is a method introduced in 2016 for handling small training datasets by projecting an Itô equation from a stochastic dissipative Hamiltonian dynamical system, acting as the MCMC generator, for which the KDE-estimated probability measure with the training dataset is the invariant measure. PLoM performs a projection on a reduced-order vector basis related to the training dataset, using the diffusion maps (DMAPS) basis constructed with a time-independent isotropic kernel. In this paper, we propose a new ISDE projection vector basis built from a transient anisotropic kernel, providing an alternative to the DMAPS basis to improve statistical surrogates for stochastic manifolds with heterogeneous data. The construction ensures that for times near the initial time, the DMAPS basis coincides with the transient basis. For larger times, the differences between the two bases are characterized by the angle of their spanned vector subspaces. The optimal instant yielding the optimal transient basis is determined using an estimation of mutual information from Information Theory, which is normalized by the entropy estimation to account for the effects of the number of realizations used in the estimations. Consequently, this new vector basis better represents statistical dependencies in the learned probability measure for any dimension. Three applications with varying levels of statistical complexity and data heterogeneity validate the proposed theory, showing that the transient anisotropic kernel improves the learned probability measure.

Diffusion maps↗

DOE OSTI2020

Determining topological order from infinite projected entangled pair states

In this work, we present a method of extracting information about the topological order from the ground state of a strongly correlated two-dimensional system computed with the infinite projected entangled pair state (iPEPS). For topologically ordered systems, the iPEPS wrapped on a torus becomes a superposition of degenerate, locally indistinguishable ground states. Projectors in the form of infinite matrix product operators onto states with well-defined anyon flux are used to compute topological S and T matrices (encoding mutual and self-statistics of emergent anyons). The algorithm is shown to be robust against a perturbation driving string-net toric code across a phase transition to a ferromagnetic phase. Our approach provides accurate results near quantum phase transition, where the correlation length is prohibitively large for other numerical methods. Moreover, we used numerically optimized iPEPS describing the ground state of the Kitaev honeycomb model in the toric code phase and obtained topological data in excellent agreement with theoretical prediction.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Large scale structure reconstruction with short-wavelength modes

Large scale density modes are difficult to measure because they are sensitive to systematic observational errors in galaxy surveys, but we can study them indirectly by observing their impact on small scale perturbations. Cosmological perturbation theory predicts that second-order density inhomogeneities are a convolution of a short- and a long-wavelength mode. This arises physically because small scale structures grow at different rates depending on the large scale environment in which they reside. This induces an off-diagonal term in the two-point statistics in Fourier space that we use as the basis for a quadratic estimator for the large scale field. Here, we demonstrate that this quadratic estimator works well on an N-body simulation of size (2.5 h -1 Gpc) 3 . In particular, the quadratic estimator successfully reconstructs the long-wavelength modes using only small-scale information. This opens up novel opportunities to study structure on the largest observable scales.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Direct statistical simulation of the Lorenz96 system in model reduction approaches

Direct statistical simulation (DSS) of nonlinear dynamical systems bypasses the traditional route of accumulating statistics by lengthy direct numerical simulations by solving the equations that govern the statistics themselves. DSS suffers, however, from the curse of dimensionality as the statistics (such as correlations) generally have higher dimensions than the underlying dynamical variables. Here we investigate two approaches to reduce the dimensionality of DSS, illustrating each method with numerical experiments with the Lorenz96 dynamical system. The forms of DSS chosen here involve approximate closures at second and third order in the equal-time cumulants. We demonstrate significant reduction in computational effort that can be achieved without sacrificing the accuracy of DSS. The methods developed here can be applied to turbulent fluid and magnetohydrodynamical systems. Published by the American Physical Society 2025

Li, Kuan↗

DOE OSTI2022

$$\alpha $$-event characterization and rejection in point-contact HPGe detectors

Abstract P-type point contact (PPC) HPGe detectors are a leading technology for rare event searches due to their excellent energy resolution, low thresholds, and multi-site event rejection capabilities. We have characterized a PPC detector’s response to $$\alpha $$ α particles incident on the sensitive passivated and p $$^+$$ + surfaces, a previously poorly-understood source of background. The detector studied is identical to those in the Majorana Demonstrator experiment, a search for neutrinoless double-beta decay ( $$0\nu \beta \beta $$ 0 ν β β ) in $$^{76}$$ 76 Ge. $$\alpha $$ α decays on most of the passivated surface exhibit significant energy loss due to charge trapping, with waveforms exhibiting a delayed charge recovery (DCR) signature caused by the slow collection of a fraction of the trapped charge. The DCR is found to be complementary to existing methods of $$\alpha $$ α identification, reliably identifying $$\alpha $$ α background events on the passivated surface of the detector. We demonstrate effective rejection of all surface $$\alpha $$ α events (to within statistical uncertainty) with a loss of only 0.2% of bulk events by combining the DCR discriminator with previously-used methods. The DCR discriminator has been used to reduce the background rate in the $$0\nu \beta \beta $$ 0 ν β β region of interest window by an order of magnitude in the Majorana Demonstrator and will be used in the upcoming LEGEND-200 experiment.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Using the Carbon Capture Simulation Initiative (CCSI) Tool to Design the Experiments in the Parametric Campaign of a Novel Compact Absorber for Carbon Capture

Gas absorption towers with structured packing and solvent have been used for Carbon Dioxide (CO 2 ) Capture for about many decades. To overcome process limitations and practical disadvantages for CO 2 capture from the stationary emitter (e.g. NG and coal power plant), many new designs have been proposed and explored at the various scales in the last decade with aim of either low energy penalty or low capital cost. To reduce the size of the absorption tower and hence the total cost of CO 2 capture, the University of Kentucky Center for Applied Energy Research Center (UK CAER) has designed and built a novel CO 2 capture absorption tower or Compact Absorber, integrated into an existing large-bench scale CO 2 capture unit. The Compact Absorber has three sections. The top of the column is a fogging section where the solvent is sprayed through a nozzle producing droplets flowing downward in a co-current fashion with the flue gas. The center of the column is a frothing section where the solvent and flue gas flow through regenerative frothing screens designed by Industrial Climate Solutions, Inc. The bottom of the column is a typical structured packing section were the flue gas and solvent flow in a counter-current fashion. The parametric campaign will be conducted in order to optimize the operating parameters for CO 2 capture including liquid/gas ratio, lean loading, and temperature, liquid residence time. A simulated flue gas with 14% CO 2 will be used along with a UK CAER developed proprietary solvent. The 100-hour parametric campaign is designed using a statistical approach of the Sequential Design of Experiments (sDOE). sDOE is one of the CCSI tools that provides an adaptive statistical approach for designing future experiments based on the results of previous experiments. Application of a typical DOE provides the user with the minimum number of experiments required to get the same data, but sDOE allows the user to make an informed choice of experiments based on the results of previous experiments. The complete absorption column has been constructed and has been partially commissioned. Initial data has been collected by operating using the fogging section and the frothing section. The fogging section produces solvent droplets of about 100 μm sauter mean diameter and as small as 25 μm using a hydraulic nozzle by BETE. The frothing section produces bubbles of about 5mm with high mixing of solvent promoting the higher mass transfer from gas to liquid. The absorber reaches the capture efficiency of about 50% with only two sections in operation. Based on the current results, it can be deduced that increasing the solvent feed temperature and including the packed section for absorption the capture efficiency will increase further. Initial data will be collected using all three sections of the absorber and will be used for sDOE. Non-Uniform Space Filling model of sDOE will be used to prioritize the input conditions resulting into maximum capture efficiency. sDOE is performed using the platform called Framework Optimization, Quantification of Uncertainty, and Surrogates (FOQUS). The method and results demonstrating the progress of the parametric campaign from the initial set of experiments to the final stage of obtaining optimized parameters using sDOE tool will be presented in detail.

20 FOSSIL-FUELED POWER PLANTS↗

DOE OSTI2022

Development of an Open-source Alloy Selection and Lifetime Assessment Tool for Structural Components in CSP

Lack of sufficient data on high temperature mechanical and corrosion behavior of structural materials is a huge barrier in the technological maturity of current and future Concentrating Solar Power (CSP) technologies. Rapid development and selection of materials cannot be achieved by expensive and time-consuming acquisition of experimental data. The goal of the proposed work is development of an open-source alloy selection and lifetime prediction tool that will integrate validated physics-based models to describe influence of temperature, alloy composition, environment and component geometry (thickness) on mechanical and corrosion behavior of Ni and Fe-based alloys employed in molten salts/sCO 2 heat exchangers. This one-year project leveraged the extensive dataset on the creep\corrosion behavior of candidate materials generated at ORNL through past projects and input from current collaborations with industrial partners. Based on previous experience and the feedback provided by industry (Brayton Energy and Echogen), three candidate materials of interest, Ni-based alloys 740H, 282 and 625 and application-specific operating conditions (max. temperature of 730 °C and stress of 150 MPa) were identified for the heat exchanger. An extensive corrosion and creep dataset was assimilated for the relevant operating conditions and was supported by detailed characterization of about 100 metallographic cross-sections. The corrosion dataset consisted of scanning electron microscopy images (secondary electron and backscatter electron), measured concentration profiles of alloying elements using energy dispersive X-ray spectroscopy (EDS), widths of denuded zones (dissolution of strengthening phases) and depths of attack in molten KCl-MgCl 2 mixtures using image analyses. The creep dataset comprised of creep rupture data and creep strain curves (for 740H and 282). Coupled thermodynamic-kinetic microstructure-based models were employed to predict the stress-corrosion induced compositional and phase evolutions in the alloy during operation under the identified operating conditions. Reduced order models were developed from advanced physics-based models and were integrated in a user-friendly alloy selection tool. The corrosion model was able to predict the time to a critical Cr concentration at the oxide/alloy interface (chemical lifetime) within ±10% (1 standard deviation) of typical statistical variation in corrosion tests and EDS measurement errors (±0.5 wt%). The initial scope of the project was limited to predict creep rupture times (Larson-Miller parameter). Based on the input provided by industry, the mechanical lifetime of the heat exchanger is governed by accumulated creep strains (2%) rather than creep rupture. To be able to predict the times to specific creep strains, a more extensive creep model development was undertaken largely beyond the initial scope of the project. The continuum damage mechanics creep model was able to predict times to 2% creep strain, t 2% with an accuracy of ±500h. Ultimately, a screening protocol for SiC was generated to demonstrate the pathway for integration of one of the currently immature materials from a commercial adoption standpoint in the current material evaluation tool. The modeling tool developed here is accessible to the science community and stakeholders and lays the foundation for methods that will enable a rapid evaluation of optimum materials for CSP applications and reliable prediction of material degradation thereby considerably reducing operational costs, improving reliability and increasing overhaul intervals. However, the complete potential of such a tool to include a wider range of materials and test conditions can only be realized with a more concentrated combined experimental-characterization-computation effort.

14 SOLAR ENERGY↗

DOE OSTI2022

Limits on X-Ray Polarization at the Core of Centaurus A as Observed with the Imaging X-Ray Polarimetry Explorer

We present measurements of the polarization of X-rays in the 2–8 keV band from the nucleus of the radio galaxy Centaurus A (Cen A), using a 100 ks observation from the Imaging X-ray Polarimetry Explorer (IXPE). Nearly simultaneous observations of Cen A were also taken with the Swift, NuSTAR, and INTEGRAL observatories. No statistically significant degree of polarization is detected with IXPE. These observations have a minimum detectable polarization at 99% confidence (MDP 99 ) of 6.5% using a weighted, spectral model-independent calculation in the 2–8 keV band. The polarization angle ψ is consequently unconstrained. Spectral fitting across three orders of magnitude in X-ray energy (0.3–400 keV) demonstrates that the SED of Cen A is well described by a simple power law with moderate intrinsic absorption (N H ~ 10 23 cm -2 ) and a Fe Kα emission line, although a second unabsorbed power law is required to account for the observed spectrum at energies below 2 keV. This spectrum suggests that the reprocessing material responsible for this emission line is optically thin and distant from the central black hole. Our upper limits on the X-ray polarization are consistent with the predictions of Compton scattering, although the specific seed photon population responsible for the production of the X-rays cannot be identified. The low polarization degree, variability in the core emission, and the relative lack of variability in the Fe Kα emission line support a picture where electrons are accelerated in a region of highly disordered magnetic fields surrounding the innermost jet.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

Enhanced climate reproducibility testing with false discovery rate correction

Simulating the Earth's climate is an important and complex problem, thus climate models are similarly complex, comprised of millions of lines of code. In order to appropriately utilize the latest computational and software infrastructure advancements in Earth system models running on modern hybrid computing architectures to improve their performance, precision, accuracy, or all three; it is important to ensure that model simulations are repeatable and robust. This introduces the need for establishing statistical or non-bit-for-bit reproducibility, since bit-for-bit reproducibility may not always be achievable. Here, we propose a short-simulation ensemble-based test for an atmosphere model to evaluate the null hypothesis that modified model results are statistically equivalent to that of the original model. We implement this test in version 2 of the US Department of Energy's Energy Exascale Earth System Model (E3SM). The test evaluates a standard set of output variables across the two simulation ensembles and uses a false discovery rate correction to account for multiple testing. The false positive rates of the test are examined using re-sampling techniques on large simulation ensembles and are found to be lower than the currently implemented bootstrapping-based testing approach in E3SM. We also evaluate the statistical power of the test using perturbed simulation ensemble suites, each with a progressively larger magnitude of change to a tuning parameter. The new test is generally found to exhibit more statistical power than the current approach, being able to detect smaller changes in parameter values with higher confidence.

Kelleher, Michael E. [Oak Ridge National Laborator↗

NASA NTRS1984

Correlation between proton anisotropy and magnetic field direction in the distant geotail

A statistical analysis has been conducted of the anisotropy of suprathermal protons and the polarity of the magnetic field during April 10-16, 1983. At this time, ISEE-3 was at lunar distances in the geomagnetic tail of the earth, and well within the nominal magnetopause. The first-order anisotropy is presently correlated with the latitude angle and the z-component of the magnetic field. The anisotropy direction's frequency distribution is strongly peaked in the earthward and tailward direction, indicating fast earthward and tailward flows. For large anisotropies, and within 5 earth radii of the nominal neutral sheet position, a strong correlation is found between the earthward-streaming suprathermal protons and the northward polarity of the magnetic field; large tailward anisotropies are generally correlated with southward magnetic field polarity. This correlation is most simply interpreted in terms of a neutral line or reconnection model.

Klecker, B.↗

NASA NTRS1986

Simulation and analysis of natural rain in a wind tunnel via digital image processing techniques

It is desired to simulate natural rain in a wind tunnel in order to investigate its influence on the aerodynamic characteristics of aircraft. Rain simulation nozzles have been developed and tested at JPL. Pulsed laser sheet illumination is used to photograph the droplets in the moving airstream. Digital image processing techniques are applied to these photographs for calculation of rain statistics to evaluate the performance of the nozzles. It is found that fixed hypodermic type nozzles inject too much water to simulate natural rain conditions. A modification uses two aerodynamic spinners to flex a tube in a pseudo-random fashion to distribute the water over a larger area.

Aaron, K. M.↗

NASA NTRS1996

Detectability of the Reflection Signal from Inner Planets

Mayor and Queloz (1996) and Marcy and Butler (1996) have found massive planets with orbital periods Tp=approx.4 days around two solar-like stars (51 Pegasi and v Andromeda). These planets are most likely similar in size and composition to the gas giants in our solar system (Burrows et al 1996). Based on this expectation and assuming the same albedo as Jupiter, we examined the feasibility of searching for similar planets with a dedicated space-based 1-m telescope. The Kepler mission will survey approximately 70,000 main-sequence dwarf stars from 9 to 14 mag continuously for four years to detect transiting Earthlike planets. Based on the detection statistics of Marcy and Butler, we expect to detect 1400 inner-orbit giant planets. Such planets in a much wider range of orbital inclinations (i) will produce nearly sinusoidal modulations of the star light flux due to the varying planetary phases. The relative signal amplitudes are of order 2x10(exp -5) and decrease as Tp(exp 4/3) for i >> 0deg. We estimated the expected signal to noise ratio (SNR) using the solar irradiance measurements from the ACRIM 1 experiment along with expected shot and detector noises. The figure shows SNR as a function of Tp for a 12 mag star, and indicates the planet radius required for detection. The survey will be sensitive to planets with periods from 12 hr to approx.8 days at the 6 sigma level.

Borucki, W. J.↗

NASA NTRS2001

Development of a Novel Method for Determination of Residual Stresses in a Friction Stir Weld

Material constitutive properties, which describe the mechanical behavior of a material under loading, are vital to the design and implementation of engineering materials. For homogeneous materials, the standard process for determining these properties is the tensile test, which is used to measure the material stress-strain response. However, a majority of the applications for engineering materials involve the use of heterogeneous materials and structures (i.e. alloys, welded components) that exhibit heterogeneity on a global or local level. Regardless of the scale of heterogeneity, the overall response of the material or structure is dependent on the response of each of the constituents. Therefore, in order to produce materials and structures that perform in the best possible manner, the properties of the constituents that make up the heterogeneous material must be thoroughly examined. When materials exhibit heterogeneity on a local level, such as in alloys or particle/matrix composites, they are often treated as statistically homogenous and the resulting 'effective' properties may be determined through homogenization techniques. In the case of globally heterogeneous materials, such as weldments, the standard tensile test provides the global response but no information on what is Occurring locally within the different constituents. This information is necessary to improve the material processing as well as the end product.

Reynolds, Anthony P.↗

NASA NTRS2008

Sensor Selection and Data Validation for Reliable Integrated System Health Management

For new access to space systems with challenging mission requirements, effective implementation of integrated system health management (ISHM) must be available early in the program to support the design of systems that are safe, reliable, highly autonomous. Early ISHM availability is also needed to promote design for affordable operations; increased knowledge of functional health provided by ISHM supports construction of more efficient operations infrastructure. Lack of early ISHM inclusion in the system design process could result in retrofitting health management systems to augment and expand operational and safety requirements; thereby increasing program cost and risk due to increased instrumentation and computational complexity. Having the right sensors generating the required data to perform condition assessment, such as fault detection and isolation, with a high degree of confidence is critical to reliable operation of ISHM. Also, the data being generated by the sensors needs to be qualified to ensure that the assessments made by the ISHM is not based on faulty data. NASA Glenn Research Center has been developing technologies for sensor selection and data validation as part of the FDDR (Fault Detection, Diagnosis, and Response) element of the Upper Stage project of the Ares 1 launch vehicle development. This presentation will provide an overview of the GRC approach to sensor selection and data quality validation and will present recent results from applications that are representative of the complexity of propulsion systems for access to space vehicles. A brief overview of the sensor selection and data quality validation approaches is provided below. The NASA GRC developed Systematic Sensor Selection Strategy (S4) is a model-based procedure for systematically and quantitatively selecting an optimal sensor suite to provide overall health assessment of a host system. S4 can be logically partitioned into three major subdivisions: the knowledge base, the down-select iteration, and the final selection analysis. The knowledge base required for productive use of S4 consists of system design information and heritage experience together with a focus on components with health implications. The sensor suite down-selection is an iterative process for identifying a group of sensors that provide good fault detection and isolation for targeted fault scenarios. In the final selection analysis, a statistical evaluation algorithm provides the final robustness test for each down-selected sensor suite. NASA GRC has developed an approach to sensor data qualification that applies empirical relationships, threshold detection techniques, and Bayesian belief theory to a network of sensors related by physics (i.e., analytical redundancy) in order to identify the failure of a given sensor within the network. This data quality validation approach extends the state-of-the-art, from red-lines and reasonableness checks that flag a sensor after it fails, to include analytical redundancy-based methods that can identify a sensor in the process of failing. The focus of this effort is on understanding the proper application of analytical redundancy-based data qualification methods for onboard use in monitoring Upper Stage sensors.

Garg, Sanjay↗

NASA NTRS2011

Space Suit Joint Torque Testing

In 2009 and early 2010, a test was performed to quantify the torque required to manipulate joints in several existing operational and prototype space suits in an effort to develop joint torque requirements appropriate for a new Constellation Program space suit system. The same test method was levied on the Constellation space suit contractors to verify that their suit design meets the requirements. However, because the original test was set up and conducted by a single test operator there was some question as to whether this method was repeatable enough to be considered a standard verification method for Constellation or other future space suits. In order to validate the method itself, a representative subset of the previous test was repeated, using the same information that would be available to space suit contractors, but set up and conducted by someone not familiar with the previous test. The resultant data was compared using graphical and statistical analysis and a variance in torque values for some of the tested joints was apparent. Potential variables that could have affected the data were identified and re-testing was conducted in an attempt to eliminate these variables. The results of the retest will be used to determine if further testing and modification is necessary before the method can be validated.

Valish, Dana J.↗

NASA NTRS2011

Modeling the Quiet Time Outflow Solution in the Polar Cap

We use the Polar Wind Outflow Model (PWOM) to study the geomagnetically quiet conditions in the polar cap during solar maximum, The PWOM solves the gyrotropic transport equations for O(+), H(+), and He(+) along several magnetic field lines in the polar region in order to reconstruct the full 3D solution. We directly compare our simulation results to the data based empirical model of Kitamura et al. [2011] of electron density, which is based on 63 months of Akebono satellite observations. The modeled ion and electron temperatures are also compared with a statistical compilation of quiet time data obtained by the EISCAT Svalbard Radar (ESR) and Intercosmos Satellites (Kitamura et al. [2011]). The data and model agree reasonably well. This study shows that photoelectrons play an important role in explaining the differences between sunlit and dark results, ion composition, as well as ion and electron temperatures of the quiet time polar wind solution. Moreover, these results provide validation of the PWOM's ability to model the quiet time ((background" solution.

Glocer, Alex↗

NASA NTRS2012

Space Suit Joint Torque Measurement Method Validation

In 2009 and early 2010, a test method was developed and performed to quantify the torque required to manipulate joints in several existing operational and prototype space suits. This was done in an effort to develop joint torque requirements appropriate for a new Constellation Program space suit system. The same test method was levied on the Constellation space suit contractors to verify that their suit design met the requirements. However, because the original test was set up and conducted by a single test operator there was some question as to whether this method was repeatable enough to be considered a standard verification method for Constellation or other future development programs. In order to validate the method itself, a representative subset of the previous test was repeated, using the same information that would be available to space suit contractors, but set up and conducted by someone not familiar with the previous test. The resultant data was compared using graphical and statistical analysis; the results indicated a significant variance in values reported for a subset of the re-tested joints. Potential variables that could have affected the data were identified and a third round of testing was conducted in an attempt to eliminate and/or quantify the effects of these variables. The results of the third test effort will be used to determine whether or not the proposed joint torque methodology can be applied to future space suit development contracts.

Valish, Dana↗