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 91 records · Page 5

Exploring Diverse Data Sets and Developing New Theories and Ideas With Project Integration Architecture

The development of new ideas is the essence of scientific research. This is frequently done by developing models of physical processes and comparing model predictions with results from experiments. With models becoming ever more complex and data acquisition systems becoming more powerful, the researcher is burdened with wading through data ranging in volume up to a level of many terabytes and beyond. These data often come from multiple, heterogeneous sources and usually the methods for searching through it are at or near the manual level. In addition, current documentation methods are generally limited to researchers pen-and-paper style notebooks. Researchers may want to form constraint-based queries on a body of existing knowledge that is, itself, distributed over many different machines and environments and from the results of such queries then spawn additional queries, simulations, and data analyses in order to discover new insights into the problem being investigated. Currently, researchers are restricted to working within the boundaries of tools that are inefficient at probing current and legacy data to extend the knowledge of the problem at hand and reveal innovative and efficient solutions. A framework called the Project Integration Architecture is discussed that can address these desired functionalities.

Benyo, Theresa L.↗

Scale setting of SU⁡(𝑁) Yang–Mills theory, topology and large-𝑁 volume independence

We set the scale of SU⁡(𝑁) Yang-Mills theories for 𝑁 =3, 5, 8 and in the large-𝑁 limit via gradient flow, as a first step towards the computation of the large-𝑁 Λ-parameter using step scaling. We adopt twisted boundary conditions to achieve large-𝑁 volume reduction and the Parallel Tempering on Boundary Conditions algorithm to tame topological freezing. This setup allows accurate determinations of the gradient-flow scales down to lattice spacings as fine as ∼0.025 fm for all the explored values of 𝑁, a regime that has never been reached with ergodic algorithms. Moreover, we are able to precisely estimate the finite-size systematics related to topological freezing, and to show the suppression of finite-volume effects expected by virtue of large-𝑁 twisted volume reduction.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Functions of relaxed controls

Mathematical control theory problems involving solutions of certain partial differential equations, nonadditive set functions, or other functionals - approximation and existence theorems

FUNCTIONAL ANALYSIS↗

Pilot-Induced Oscillations and Human Dynamic Behavior

This is an in-depth survey and study of pilot-induced oscillations (PIO's) as interactions between human pilot and vehicle dynamics; it includes a broad and comprehensive theory of PIO's. A historical perspective provides examples of the diversity of PIO's in terms of control axes and oscillation frequencies. The constituents involved in PIO phenomena, including effective aircraft dynamics, human pilot dynamic behavior patterns, and triggering precursor events, are examined in detail as the structural elements interacting to produce severe pilot-induced oscillations. The great diversity of human pilot response patterns, excessive lags and/or inappropriate gain in effective aircraft dynamics, and transitions in either the human or effective aircraft dynamics are among the key sources implicated as factors in severe PIO's. The great variety of interactions which may result in severe PIO's is illustrated by examples drawn from famous PIO's. These are generalized under a pilot-behavior-theory-based set of categories proposed as a classification scheme pertinent to a theory of PIO's. Finally, a series of interim prescriptions to avoid PIO is provided.

McRuer, Duane T.↗

A non-linear dynamic lumped-parameter model of a rectangular plate.

A lumped-parameter model of a rectangular plate is developed by assuming fundamental mode solutions and using Hamilton's Principle and the Euler equations to set up the differential equation of motion for the system. The plate theory used may be described as the dynamic analogue of the von Karman large-deflection theory. Four sets of symmetrical boundary conditions are considered with the restriction of uniform pressure dynamic loads. The model takes the form of a mass on a cubic-hardening spring with each term defined by algebraic expressions of the plate parameters. The results for some specific problems are compared with two previous solutions. This method is less accurate but simpler to develop and apply.

Bayles, D. J.↗

Life analysis of helical gear sets using Lundberg-Palmgren theory

A mathematical model is developed for surface fatigue life of helical gears. The expected fatigue life of a pinion, gear, or gear set may be calculated from the model. An equation for the dynamic capacity of a gear set was also derived. Dynamic capacity is the transmitted tangential load which gives a 90 percent probability of survival of the gear set for one million pinion revolutions. The equations, when simplified by setting the helix angle to zero, reduce to the results which were previously developed for spur gears. A sample calculation is given which illustrates the use of the new fatigue life model.

Coy, J. J.↗

Constraint-Free Theories of Gravitation

Lovelock actions (more precisely, extended Gauss-Bonnet forms) when varied as Cartan forms on subspaces of higher dimensional flat Riemannian manifolds, generate well set, causal exterior differential systems. In particular, the Einstein- Hilbert action 4-form, varied on a 4 dimensional subspace of E(sub 10) yields a well set generalized theory of gravity having no constraints. Rcci-flat solutions are selected by initial conditions on a bounding 3-space.

Estabrook, Frank B.↗

Measurement of t -channel production of single top quarks and antiquarks in pp collisions at 13 TeV using the full ATLAS Run 2 data sample

The production of single top quarks and top antiquarks via the t-channel exchange of a virtual W boson is measured in proton-proton collisions at a centre-of-mass energy of 13 TeV at the LHC using 140 fb -1 of ATLAS data. The total cross-sections are determined to be σ(tq) = 137$^{+8}_{-8}$ pb and σ($\bar{t}q$) = 84$^{+6}_{-5}$ pb for top-quark and top-antiquark production, respectively. The combined cross-section is found to be σ(tq + $\bar{t}q$) = 221$^{+13}_{-13}$ pb and the cross-section ratio is R t = σ(tq) / σ($\bar{t}q$) = 1.636$^{+0.036}_{-0.034}$. The predictions at next-to-next-to-leading-order in quantum chromodynamics are in good agreement with these measurements. The predicted value of R t using different sets of parton distribution functions is compared with the measured value, demonstrating the potential to further constrain the functions when using this result in global fits. The measured cross-sections are interpreted in an effective field theory approach, setting limits at the 95% confidence level on the strength of a four-quark operator and an operator coupling the third quark generation to the Higgs boson doublet: -0.37 < C$^{3,1}_{Qq}$ /Λ 2 < 0.06 and -0.87 < C$^{3}_{ΦQ}$ / Λ 2 < 1.42. The constraint |V tb | > 0.95 at the 95% confdence level is derived from the measured value of σ(tq + $\bar{t}q$), assuming that the Wtb interaction is a left-handed weak coupling and that |V tb | $\gg$ |V td |, |V ts |. In a more general approach, pairs of CKM matrix elements involving top quarks are simultaneously constrained, leading to confdence contours in the corresponding two-dimensional parameter spaces.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

The evolution of volcanism, tectonics, and volatiles on Mars - An overview of recent progress

Significant results of the 'Mars: Evolution of Volcanism, Tectonics, and Volatiles' (MEVTV) project are presented. The data for the project are based on geological mapping from the Viking images, petrologic and chemical analyses of SNC meteorites, and both mapping and temporal grouping of major fault systems. The origin of the planet's crustal dichotomy is examined in detail, the kinematics and formation of wrinkle ridges are discussed, and some new theories are set forth. Because the SNC meteorites vary petrologically and isotopically, the sources of the parental Martian magma are heterogeneous. Transcurrent faulting coupled with the extensional strains that form Valles Marineris suggest early horizontal movement of lithospheric blocks. A theory which connects the formation of the crustal dichotomy to the Tharsis region associates the horizontal motions with plate tectonics that generated a new lithosphere.

Zimbelman, James R.↗

Final Results of the M AJORANA D EMONSTRATOR ’s Search for Double-Beta Decay of 76 Ge to Excited States of 76 Se

76 Ge can 𝛽⁢𝛽 decay into three possible excited states of 76 Se , with the emission of two or, if the neutrino is Majorana, zero neutrinos. None of these six transitions have yet been observed. The M AJORANA D EMONSTRATOR was designed to study 𝛽⁢𝛽 decay of 76 Ge using a low background array of high purity germanium detectors. With 98.2 kg-y of isotopic exposure, the demonstrator sets the strongest half-life limits to date for all six transition modes. For 2⁢𝜈⁢𝛽⁢𝛽 to the 0$^+_1$ state of 76 Se , this search has begun to probe for the first time half-life values predicted using modern many-body nuclear theory techniques, setting a limit of 𝑇 1/2 > 1.5 × 10 24 y (90% CL).

Majorana neutrinos↗

Accurate Heats of Formation for SiF(n) and SiF(n+), for N=1-4

Accurate heats of formation are computed for SiFn and SiFn+, for n=1-4. The vibrational frequencies are determined at the B3LYP level of theory. The energetics are determined at the CCSD(T) level of theory. Basis set limit values are obtained by extrapolation. In those cases where the CCSD(T) calculations become prohibitively large, the basis set extrapolation is performed at the MP2 level. The temperature dependence of the heat of formation, heat capacity, and entropy are computed for the temperature range 300 to 4000 K and fit to a polynomial. The CCSD(T) bond energies are compared with those obtained at the B3LYP, MP2, G2, and G2MP2 levels of theory.

Bauschlicher, Charles W., Jr.↗

Low-frequency oscillations in radiative-convective systems

Although eastward propagation has long been considered one of the essential features of the Madden-Julian waves, recent observations have revealed a stationary or quasi-stationary component in the oscillations, particularly in measures of the diabatic heating rate. Wave-CISK theories of the low-frequency oscillations have struggled to explain the observed period and vertical structure of the waves. On the other hand, theoretical and numerical studies have shown that low-frequency waves strongly resembling the observed oscillations can be excited by specified low-frequency oscillations of the convective heating. A problem with the latter set of theories is that the cause of the oscillatory heating has not been satisfactorily explained. It is proposed here that the observed low-frequency wave motions are the response to forcing by an essentially stationary, self-excited oscillating heat source that is produced by nonlinear interactions among radiation, cumulus convection, and the surface fluxes of sensible heat and moisture. Feedback of the large-scale motions on the latent heating is not required. Results from two very different one-dimensional models are presented to support this hypothesis. The physical processes included in the models are essentially the same, that is, radiation, cumulus convection, and the surface fluxes of sensible heat and moisture; the first model is highly simplified, however, while the second includes relatively sophisticated parameterizations of all the relevant physical processes. Results from both models show low-frequency oscillations of the latent heating, temperature, and moisture. Experiments show that the oscillations are favored by a warm sea surface and weak surface wind speeds, consistent with the observed conditions over the Indian Ocean and the tropical western Pacific Ocean.

Hu, QI↗

A Practical On-line Framework for a Modified Energy Detector by Whitening Ambient PMU Data

A key application of Phasor Measurement Units (PMUs) is power system oscillation detection. An energy detector is a straightforward detection method, but setting thresholds requires extensive and time consuming baselining of data. This paper proposes a novel on-line method of whitening PMU measurements supporting a framework for detecting forced oscillations without requiring extensive baselining. An example of 24 hours of actual PMU data illustrates how a forced oscillation is very visible in the energy signal of the whitened data, while being hard to detect in the colored ambient noise. With this framework, the statistical theory for setting thresholds without baselining is much more straightforward and is the focus of future work.

Xu, Zikai↗