Search NASA⌕ Search

SEARCH · Search NASA

Results for “Set theory”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
NASA NTRS1980

The primer vector in linear, relative-motion equations

Primer vector theory is used in analyzing a set of linear, relative-motion equations - the Clohessy-Wiltshire equations - to determine the criteria and necessary conditions for an optimal, N-impulse trajectory. Since the state vector for these equations is defined in terms of a linear system of ordinary differential equations, all fundamental relations defining the solution of the state and costate equations, and the necessary conditions for optimality, can be expressed in terms of elementary functions. The analysis develops the analytical criteria for improving a solution by (1) moving any dependent or independent variable in the initial and/or final orbit, and (2) adding intermediate impulses. If these criteria are violated, the theory establishes a sufficient number of analytical equations. The subsequent satisfaction of these equations will result in the optimal position vectors and times of an N-impulse trajectory. The solution is examined for the specific boundary conditions of (1) fixed-end conditions, two-impulse, and time-open transfer; (2) an orbit-to-orbit transfer; and (3) a generalized rendezvous problem. A sequence of rendezvous problems is solved to illustrate the analysis and the computational procedure.

Source record↗
NASA NTRS2003

Intelligent machines in the twenty-first century: foundations of inference and inquiry

The last century saw the application of Boolean algebra to the construction of computing machines, which work by applying logical transformations to information contained in their memory. The development of information theory and the generalization of Boolean algebra to Bayesian inference have enabled these computing machines, in the last quarter of the twentieth century, to be endowed with the ability to learn by making inferences from data. This revolution is just beginning as new computational techniques continue to make difficult problems more accessible. Recent advances in our understanding of the foundations of probability theory have revealed implications for areas other than logic. Of relevance to intelligent machines, we recently identified the algebra of questions as the free distributive algebra, which will now allow us to work with questions in a way analogous to that which Boolean algebra enables us to work with logical statements. In this paper, we examine the foundations of inference and inquiry. We begin with a history of inferential reasoning, highlighting key concepts that have led to the automation of inference in modern machine-learning systems. We then discuss the foundations of inference in more detail using a modern viewpoint that relies on the mathematics of partially ordered sets and the scaffolding of lattice theory. This new viewpoint allows us to develop the logic of inquiry and introduce a measure describing the relevance of a proposed question to an unresolved issue. Last, we will demonstrate the automation of inference, and discuss how this new logic of inquiry will enable intelligent machines to ask questions. Automation of both inference and inquiry promises to allow robots to perform science in the far reaches of our solar system and in other star systems by enabling them not only to make inferences from data, but also to decide which question to ask, which experiment to perform, or which measurement to take given what they have learned and what they are designed to understand.

Review↗
NASA NTRS2005

Distributed Adaptive Control: Beyond Single-Instant, Discrete Variables

In extensive form noncooperative game theory, at each instant t, each agent i sets its state x, independently of the other agents, by sampling an associated distribution, q(sub i)(x(sub i)). The coupling between the agents arises in the joint evolution of those distributions. Distributed control problems can be cast the same way. In those problems the system designer sets aspects of the joint evolution of the distributions to try to optimize the goal for the overall system. Now information theory tells us what the separate q(sub i) of the agents are most likely to be if the system were to have a particular expected value of the objective function G(x(sub 1),x(sub 2), ...). So one can view the job of the system designer as speeding an iterative process. Each step of that process starts with a specified value of E(G), and the convergence of the q(sub i) to the most likely set of distributions consistent with that value. After this the target value for E(sub q)(G) is lowered, and then the process repeats. Previous work has elaborated many schemes for implementing this process when the underlying variables x(sub i) all have a finite number of possible values and G does not extend to multiple instants in time. That work also is based on a fixed mapping from agents to control devices, so that the the statistical independence of the agents' moves means independence of the device states. This paper also extends that work to relax all of these restrictions. This extends the applicability of that work to include continuous spaces and Reinforcement Learning. This paper also elaborates how some of that earlier work can be viewed as a first-principles justification of evolution-based search algorithms.

Wolpert, David H.↗
DOE OSTI2022

Tracer-field cross-correlations with k -nearest neighbour distributions

ABSTRACT In astronomy and cosmology significant effort is devoted to characterizing and understanding spatial cross-correlations between points – e.g galaxy positions, high energy neutrino arrival directions, X-ray and AGN sources, and continuous fields – e.g. weak lensing meiand Cosmic Microwave Background maps. Recently, we introduced the k-nearest neighbour (kNN) formalism to better characterize the clustering of discrete (point) data sets. Here, we extend it to the point – field cross-correlations analysis. It combines kNN measurements of the point data set with measurements of the field smoothed at many scales. The resulting statistics are sensitive to all orders in the joint clustering of the points and the field. We demonstrate that this approach, unlike the 2-pt cross-correlation, can measure the statistical dependence of two data sets even when there are no linear (Gaussian) correlations between them. We further demonstrate that this framework is far more effective than the two point function in detecting cross-correlations when the continuous field is contaminated by high levels of noise. For a particularly high level of noise, the cross-correlation between haloes and the underlying matter field in a cosmological simulation, between 10 h−1 Mpc and 30 h−1 Mpc, is detected at >5σ significance using the technique presented here, when the two-point cross-correlation significance is ∼1σ. Finally, we show that kNN cross-correlations of haloes and the matter field can be well modelled on quasi-linear scales using the Hybrid Effective Field Theory (HEFT) framework, with the same set of bias parameters as are used for 2-pt cross-correlations. The substantial improvement in the statistical power of detecting cross-correlations using this method makes it a promising tool for various cosmological applications.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1981

PAN AIR: A computer program for predicting subsonic or supersonic linear potential flows about arbitrary configurations using a higher order panel method. Volume 1: Theory document (version 1.1)

Panel aerodynamics (PAN AIR) is a system of computer programs designed to analyze subsonic and supersonic inviscid flows about arbitrary configurations. A panel method is a program which solves a linear partial differential equation by approximating the configuration surface by a set of panels. An overview of the theory of potential flow in general and PAN AIR in particular is given along with detailed mathematical formulations. Fluid dynamics, the Navier-Stokes equation, and the theory of panel methods were also discussed.

Magnus, A. E.↗
DOE OSTI2022

Generalized symmetries of the graviton

We find the set of generalized symmetries associated with the free graviton theory in four dimensions. These are generated by gauge invariant topological operators that violate Haag duality in ring-like regions. As expected from general QFT grounds, we find a set of “electric” and a dual set of “magnetic” topological operators and compute their algebra. To do so, we describe the theory using phase space gauge-invariant electric and magnetic dual variables constructed out of the curvature tensor. Electric and magnetic fields satisfy a set of constraints equivalent to the ones of a stress tensor of a 3d CFT. The constraints give place to a group $\mathbb{R}^{20}$ of topological operators that are charged under space-time symmetries. Finally, we discuss similarities and differences between linearized gravity and tensor gauge theories that have been introduced recently in the context of fractonic systems in condensed matter physics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Robust, Accurate, and Efficient: Quantum Embedding Using the Huzinaga Level-Shift Projection Operator for Complex Systems

Using wave function (WF) in density functional theory (DFT) embedding methods provides a framework for performing localized, high-accuracy WF calculations on a system, while not incurring the full computational cost of the WF calculation on the full system. To effectively partition a system into localized WF and DFT subsystems, we utilize the Huzinaga level-shift projection operator within an absolutely localized basis. In this work, we study the ability of the absolutely localized Huzinaga level-shift projection operator method to study complex WF and DFT partitions, including partitions between multiple covalent bonds, a double bond, and transition-metal–ligand bonds. We find that our methodology can accurately describe all of these complex partitions. Additionally, we study the robustness of this method with respect to the WF method, specifically where the embedded systems were described using a multiconfigurational WF method. We found that the method is systematically improvable with respect to both the number of atoms in the WF region and the size of the basis set used, with energy errors less than 1 kcal/mol. Additionally, we calculated the adsorption energy of H2 to a model of an iron metal–organic framework (Fe-MOF-74) to within 1 kcal/mol compared to CASPT2 calculations performed on the full model while incurring only a small fraction of the full computational cost. In conclusion, this work demonstrates that the absolutely localized Huzinaga level-shift projection operator method is applicable to very complex systems with difficult electronic structures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1982

Quantitative tests of a steady state theory of solar wind electrons

A comparison is made of IMP 6, 7 and 8 electron data with the predictions of a solar wind electron steady state theory in which the control of transport by the macroscopic interplanetary electric and magnetic fields, as well as elastic Coulomb collisions with solar wind protons and thermal electrons, is assumed. While a ratio of forward to backward phase density for field-aligned extrathermal electrons of 6:1 is predicted, electron distribution measurements within the high speed solar wind show this ratio to be typically about an order of magnitude larger. A set of solar wind bulk speed anticorrelations predicted by the theory on the basis of a larger set of assumptions cannot be found in the IMP electron data set, so that improved agreement may require such modifications of the theory's assumptions as the inclusion of inelastic Coulomb and/or wave electron collisions.

Feldman, W. C.↗
NASA NTRS1991

Laser transit anemometer and Pitot probe comparative measurements in a sharp cone boundary layer at Mach 4

Laser transit anemometer (LTA) measurements of a 7 degree sharp cone boundary layer were conducted in the Air Force/AEDC Supersonic Tunnel A Mach 4 flow field. These measurements are compared with Pitot probe measurements and tricone theory provided by AEDC staff. Measurements were made both in laminar and turbulent boundary layers of the model. Comparison of LTA measurements with theory showed agreement to better than 1 percent for the laminar boundary layer cases. This level of agreement was obtained after small position corrections, 0.01 to 0.6 mm, were applied to the experimental data sets. Pitot probe data when compared with theory also showed small positioning errors. The Pitot data value was also limited due to probe interference with the flow near the model. The LTA turbulent boundary layer data indicated a power law dependence of 6.3 to 6.9. The LTA data was analyzed in the time (Tau) domain in which it was obtained and in the velocity domain. No significant differences were noted between Tau and velocity domain results except in one turbulent boundary layer case.

Hunter, W. W., Jr.↗
DOE OSTI2021

Infrared spectroscopy of RG–Co + (H 2 O) complexes (RG = Ar, Ne, He): The role of rare gas “tag” atoms

RG n –Co + (H 2 O) cation complexes (RG = Ar, Ne, He) are generated in a supersonic expansion by pulsed laser vaporization. Here, complexes are mass-selected using a time-of-flight spectrometer and studied with infrared laser photodissociation spectroscopy, measuring the respective mass channels corresponding to the elimination of the rare gas “tag” atom. Spectral patterns and theory indicate that the structures of the ions with a single rare gas atom have this bound to the cobalt cation opposite the water moiety in a near-C 2v arrangement. The O–H stretch vibrations of the complex are shifted compared to those of water because of the metal cation charge-transfer interaction; these frequencies also vary systematically with the rare gas atom attached. The efficiencies of photodissociation also vary with the rare gas atoms because of their widely different binding energies to the cobalt cation. The spectrum of the argon complex could only be measured when at least three argon atoms were attached. In the case of the helium complex, the low binding energy allows the spectra to be measured for the low-frequency H–O–H scissors bending mode and for the O–D stretches of the deuterated analog. The partially resolved rotational structure for the antisymmetric O–H and O–D stretches reveals the temperature of these complexes (6 K) and establishes the electronic ground state. The helium complex has the same 3 B 1 ground state as the tag-free complex studied previously by Metz and co-workers (2013), but the A rotational constant is contaminated by vibrational averaging from the bending motion of the helium.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Measurements of electroweak production of a photon in association with two jets in proton-proton collisions at $\sqrt{s}=13$ TeV

The first observation of electroweak production of a photon in association with two forward jets in proton-proton collisions is presented. The measurement uses data recorded by the CMS experiment at the LHC during 2016–2018 at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb −1 . The analysis is performed in a region enriched in photon production via vector boson fusion, with a requirement on the transverse momentum of the photon to exceed 200 GeV. The cross section is measured to be ${202}_{-32}^{+36}$ fb, at a significance with respect to the null hypothesis that exceeds five standard deviations. This is in agreement with the standard model prediction of ${177}_{-12}^{+13}$ fb. Differential cross sections are measured as a function of various observables. Limits are set on dimension-6 effective field theory operators that contribute to the WW γ interaction. The observed 95% confidence intervals for the corresponding Warsaw basis Wilson coefficients c W and c HWB are [−0.11, 0.16] and [−1.6, 1.5], respectively.

electroweak interaction↗
DOE OSTI2020

Determination of the strong coupling constant $\alpha_{S}(m_\mathrm{Z})$ from measurements of inclusive W$^\pm$ and Z boson production cross sections in proton-proton collisions at $ \sqrt{\mathrm{s}} $ = 7 and 8 TeV

Twelve measurements of inclusive cross sections of W$^{±}$ and Z boson production, performed in proton-proton collisions at centre-of-mass energies of 7 and 8 TeV, are compared with perturbative quantum chromodynamics calculations at next-to-next- to-leading order (NNLO) accuracy obtained with the CT14, HERAPDF2.0, MMHT14, and NNPDF3.0 parton distribution functions (PDFs). Data and theory agree well for all PDF sets, taking into account the experimental and theoretical uncertainties. A novel procedure is employed to extract the strong coupling constant at the Z pole mass from a detailed comparison of all the experimental fiducial cross sections to the corresponding NNLO theoretical predictions, yielding $ {\alpha}_{\mathrm{S}}\left({m}_{\mathrm{Z}}\right)={0.1163}_{-0.0031}^{+0.0024} $ (CT14), $ {0.1072}_{-0.0040}^{+0.0043} $ (HERAPDF2.0), 0.1186 ± 0.0025 (MMHT14), and 0.1147 ± 0.0023 (NNPDF3.0). Using the results obtained with the CT14 and MMHT14 PDFs, which yield the most robust and stable α$_{S}$(m$_{Z}$) extractions, a value $ {\alpha}_{\mathrm{S}}\left({m}_{\mathrm{Z}}\right)={0.1175}_{-0.0028}^{+0.0025} $ is determined.[graphic not available: see fulltext]

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Reproducibility of calculations on Li species with correlation-consistent basis sets

Here we have found that two different basis set series, both labeled cc-pVxZ, are widely available and widely used for calculation on Li compounds such that calculations that should be the same are different, causing a reproducibility problem. Here we study the magnitude of the disagreement of these nominally-the-same basis sets for wave function and density functional calculations of Li clusters. We find deviations among the basis sets of as large as 22 millihartrees. In most cases one obtains lower energies with the noncanonical choices. Therefore, it is important to specify which version of the basis set is used for calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Resilience of electric utilities during the COVID-19 pandemic in the framework of the CIGRE definition of Power System Resilience

Resilience is a vital concept in engineering, business, and natural sciences, and is a measure of the ability of an entity to withstand High Impact Low Probability (HILP) events. During the COVID-19 pandemic, which started in late 2019/early 2020, power system utilities around the globe have responded in effective and efficient ways to enhance the resilience of their organisations, both in terms of real-time operations and prudent management of its infrastructure, in order to continue their mandate in providing reliable supply to meet customer demands. Here, this paper presents the CIGRE definition for power system resilience, established by the C4.47 Working Group in 2018, and demonstrates the application of resilience-oriented thinking within the electrical sector. The response and recovery efforts are described, with respect to the key actionable measures integral to the power system resilience definition, taken before, during and after the COVID-19 pandemic. A practical conceptual framework is also presented for thinking about resilience in terms of three key components of resilience strategies: organisational, infrastructure and operational resilience. The paper also discusses the different strategies adopted in response to COVID-19, based on the C4.47 members’ experiences during the pandemic. Finally, a case study is presented, which proves the effectiveness of a set of response measures, using graph theory and the characteristics of the staff-asset interactions.

42 ENGINEERING↗
DOE OSTI2022

A unified finite strain gradient-enhanced micropolar continuum approach for modeling quasi-brittle failure of cohesive-frictional materials

Here, in this work, a novel framework for modeling quasi-brittle crack propagation and shear band dominated failure of cohesive-frictional materials like concrete, mortar, rock, tough ceramics, energetic materials, but also granular materials like sands or powders in terms of a unified continuum approach is proposed. It is based on a combination of the gradient-enhanced continuum with gradients of internal variables for representing quasi-brittle cracking, and the micropolar continuum, accounting for the deformation of the microstructure. For developing the gradient-enhanced micropolar framework, the set of balance equations and the kinematic relations are derived, and the constitutive relations are established in a general manner. The framework is formulated in a geometrically exact setting, based on the thermodynamically sound theory of hyperelasto-plasticity, and the numerical implementation by means of the finite element method is discussed. For assessing the approach, realizations of this new approach in terms of constitutive models for particular materials are developed. They are applied to numerical benchmark examples, investigating various loading conditions, and the obtained results are validated by means of a comparison with experiments from the literature.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Benchmark Data Set of Crystalline Organic Semiconductors

This work reports a Benchmark Data set of Crystalline Organic Semiconductors to test calculations of the structural and electronic properties of these materials in the solid state. The data set contains 67 crystals consisting of mostly rigid molecules with a single dominant conformer, covering the majority of known structural types. The experimental crystal structure is available for the entire data set, whereas zero-temperature unit cell volume can be reliably estimated for a subset of 28 crystals. Using this subset, we benchmark r 2 SCAN-D3 and PBE-D3 density functionals. Then, for the entire data set, we benchmark approximate density functional theory (DFT) methods, including GFN1-xTB and DFTB3(3ob-3-1), with various dispersion corrections against r 2 SCAN-D3. Our results show that r 2 SCAN-D3 geometries are accurate within a few percent, which is comparable to the statistical uncertainty of experimental data at a fixed temperature, but the unit cell volume is systematically underestimated by 2% on average. The several times faster PBE-D3 provides an unbiased estimate of the volume for all systems except for molecules with highly polar bonds, for which the volume is substantially overestimated in correlation with the underestimation of atomic charges. Considered approximate DFT methods are orders of magnitude faster and provide qualitatively correct but overcompressed crystal structures unless the dispersion corrections are fitted by unit cell volume.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Energy-Screened Many-Body Expansion for Protein–Ligand Interactions: Examining Convergence for Metalloenzymes Through Seven–Body Interactions

Fragment-based quantum chemistry is a powerful strategy for calculating protein−ligand interaction energies using quantum chemistry methods. Rigorous convergence often requires hundreds of atoms in the protein binding-site model, especially if that model is constructed using distance-based criteria to select amino acid residues, while three- and four-body calculations exhibit instability related to combinatorial proliferation in the number of subsystem calculations. Here, we report an energy-based screening protocol for the many-body expansion applied to protein−ligand interactions, implemented in the open-source FRAGME∩T code. Using a combination of aggressive screening based on semiempirical quantum chemistry, with an improved graph-theoretical algorithm to eliminate unimportant subsystems, we are able to perform n-body calculations up to n = 7 using density functional theory in triple-ζ basis sets. Distance cutoffs further reduce the cost without compromising accuracy. Rapid and stable convergence of the many-body expansion is obtained by n = 4, for a pair of metalloenzymes in which a divalent ion coordinates directly to the ligand. As compared to previous results that relied solely on distance cutoffs, oscillations in the n-body corrections are reduced or eliminated, although residual errors remain in one case. This work demonstrates that benchmark-quality protein−ligand interaction energies can be systematically converged using a method with excellent parallel efficiency and scalability.

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

Reaction Profiles and Kinetics for Radical–Radical Hydrogen Abstraction via Multireference Coupled Cluster Theory

Radical-radical abstractions in hydrocarbon oxidation chemistry are disproportionation reactions that are generally exothermic with little or no barrier yet are underappreciated and poorly studied. Such challenging multireference electronic structure problems are tackled here using the recently developed state-specific multireference coupled cluster methods Mk-MRCCSD and Mk-MRCCSD(T), as well as the companion perturbation theory Mk-MRPT2 and the established MRCISD, MRCISD+Q, and CASPT2 approaches. Reaction paths are investigated for five prototypes involving radical-radical hydrogen abstraction: H + BeH → H 2 + Be, H + NH 2 → H 2 + NH, CH 3 + C 2 H 5 → CH 4 + C 2 H 4 , H + C2H 5 → H 2 + C 2 H 4 , and H + HCO → H 2 + CO. Full configuration interaction (FCI) benchmark computations for the H + BeH, H + NH 2 , and H + HCO reactions prove that Mk-MRCCSD(T) provides superior accuracy for the interaction energies in the entrance channel, with mean absolute errors less than 0.3 kcal mol(-1) and percentage deviations less than 10% over the fragment separations of relevance to kinetics. To facilitate combustion studies, energetics for the CH 3 + C 2 H 5 , H + C 2 H 5 , and H + HCO reactions were computed at each level of theory with correlation-consistent basis sets (cc-pVXZ, X = T, Q 5) and extrapolated to the complete basis set (CBS) limit. These CBS energies were coupled with CASPT2 projected vibrational frequencies along a minimum energy path to obtain rate constants for these three reactions. The rigorous Mk-MRCCSD(T)/CBS results demonstrate unequivocally that these three reactions proceed with no barrier in the entrance channel, contrary to some earlier predictions. Mk-MRCCSD(T) also reveals that the economical CASPT2 method performs well for large interfragment separations but may deteriorate substantially at shorter distances.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗