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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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

The PASCAL-HDM Verification System

The PASCAL-HDM verification system is described. This system supports the mechanical generation of verification conditions from PASCAL programs and HDM-SPECIAL specifications using the Floyd-Hoare axiomatic method. Tools are provided to parse programs and specifications, check their static semantics, generate verification conditions from Hoare rules, and translate the verification conditions appropriately for proof using the Shostak Theorem Prover, are explained. The differences between standard PASCAL and the language handled by this system are explained. This consists mostly of restrictions to the standard language definition, the only extensions or modifications being the addition of specifications to the code and the change requiring the references to a function of no arguments to have empty parentheses.

Source record↗
DOE OSTI2021

Parton distributions and lattice-QCD calculations: Toward 3D structure

The strong force which binds hadrons is described by the theory of quantum chromodynamics (QCD). Determining the character and manifestations of QCD is one of the most important and challenging outstanding issues necessary for a comprehensive understanding of the structure of hadrons. Within the context of the QCD parton picture, the parton distribution functions (PDFs) have been remarkably successful in describing a wide variety of processes. However, these PDFs have generally been confined to the description of collinear partons within the hadron. New experiments and facilities provide the opportunity to additionally explore the transverse structure of hadrons which is described by generalized parton distributions (GPDs) and transverse-momentum-dependent parton distribution functions (TMD PDFs). In our previous report Lin et al. (2018), we compared and contrasted the two main approaches used to determine the collinear PDFs: the first based on perturbative QCD factorization theorems, and the second based on lattice-QCD calculations. In the present report, we provide an update of recent progress on the collinear PDFs, and also expand the scope to encompass the generalized PDFs (GPDs and TMD PDFs). We review the current state of the various calculations, and consider what new data might be available in the near future. We also examine how a shared effort can foster dialog between the PDF and lattice-QCD communities, and yield improvements for these generalized PDFs.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1980

On the existence, uniqueness, and asymptotic normality of a consistent solution of the likelihood equations for nonidentically distributed observations: Applications to missing data problems

A general theorem is given which establishes the existence and uniqueness of a consistent solution of the likelihood equations given a sequence of independent random vectors whose distributions are not identical but have the same parameter set. In addition, it is shown that the consistent solution is a MLE and that it is asymptotically normal and efficient. Two applications are discussed: one in which independent observations of a normal random vector have missing components, and the other in which the parameters in a mixture from an exponential family are estimated using independent homogeneous sample blocks of different sizes.

Peters, C.↗
DOE OSTI2023

Spin-squeezed Gottesman-Kitaev-Preskill codes for quantum error correction in atomic ensembles

Gottesman-Kitaev-Preskill (GKP) codes encode a qubit in displaced phase-space combs of a continuous-variable (CV) quantum system and are useful for correcting a variety of high-weight photonic errors. Here we propose atomic ensemble analogs of the single-mode CV GKP code by using the quantum central limit theorem to pull back the phase-space structure of a CV system to the compact phase space of a quantum spin system. We study the optimal recovery performance of these codes under error channels described by stochastic relaxation and isotropic ballistic dephasing processes using the diversity combining approach for calculating channel fidelity. Additionally, we find that the spin GKP codes outperform other spin system codes such as cat codes or binomial codes. Our spin GKP codes based on the two-axis countertwisting interaction and superpositions of SU(2) coherent states are direct spin analogs of the finite-energy CV GKP codes, whereas our codes based on one-axis twisting do not yet have well-studied CV analogs. A state preparation scheme for the spin GKP codes is proposed which uses the linear-combination-of-unitaries method, applicable to both the CV and spin GKP settings. Finally, we discuss a fault-tolerant approximate gate set for quantum computing with spin-GKP-encoded qubits, obtained by translating gates from the CV GKP setting using the quantum central limit theorem.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Thermal quasiparticle theory

The widely used thermal Hartree–Fock (HF) theory is generalized to include the effect of electron correlation while maintaining its quasi-independent-particle framework. An electron-correlated internal energy (or grand potential) is postulated in consultation with the second-order finite-temperature many-body perturbation theory (MBPT), which then dictates the corresponding thermal orbital (quasiparticle) energies in such a way that all fundamental thermodynamic relations are obeyed. The associated density matrix is of a one-electron type, whose diagonal elements take the form of the Fermi–Dirac distribution functions, when the grand potential is minimized. The formulas for the entropy and chemical potential are unchanged from those of Fermi–Dirac or thermal HF theory. The theory thus stipulates a finite-temperature extension of the second-order Dyson self-energy of one-particle many-body Green’s function theory and can be viewed as a second-order, diagonal, frequency-independent, thermal inverse Dyson equation. At low temperatures, the theory approaches finite-temperature MBPT of the same order, but it may outperform the latter at intermediate temperatures by including additional electron-correlation effects through orbital energies. Here, a physical meaning of these thermal orbital energies is proposed (encompassing that of thermal HF orbital energies, which has been elusive) as a finite-temperature version of Janak’s theorem.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS2003

A Survey of Logic Formalisms to Support Mishap Analysis

Mishap investigations provide important information about adverse events and near miss incidents. They are intended to help avoid any recurrence of previous failures. Over time, they can also yield statistical information about incident frequencies that helps to detect patterns of failure and can validate risk assessments. However, the increasing complexity of many safety critical systems is posing new challenges for mishap analysis. Similarly, the recognition that many failures have complex, systemic causes has helped to widen the scope of many mishap investigations. These two factors have combined to pose new challenges for the analysis of adverse events. A new generation of formal and semi-formal techniques have been proposed to help investigators address these problems. We introduce the term mishap logics to collectively describe these notations that might be applied to support the analysis of mishaps. The proponents of these notations have argued that they can be used to formally prove that certain events created the necessary and sufficient causes for a mishap to occur. These proofs can be used to reduce the bias that is often perceived to effect the interpretation of adverse events. Others have argued that one cannot use logic formalisms to prove causes in the same way that one might prove propositions or theorems. Such mechanisms cannot accurately capture the wealth of inductive, deductive and statistical forms of inference that investigators must use in their analysis of adverse events. This paper provides an overview of these mishap logics. It also identifies several additional classes of logic that might also be used to support mishap analysis.

Johnson, Chris↗
NASA NTRS1975

Almost periodic solutions to difference equations

The theory of Massera and Schaeffer relating the existence of unique almost periodic solutions of an inhomogeneous linear equation to an exponential dichotomy for the homogeneous equation was completely extended to discretizations by a strongly stable difference scheme. In addition it is shown that the almost periodic sequence solution will converge to the differential equation solution. The preceding theory was applied to a class of exponentially stable partial differential equations to which one can apply the Hille-Yoshida theorem. It is possible to prove the existence of unique almost periodic solutions of the inhomogeneous equation (which can be approximated by almost periodic sequences) which are the solutions to appropriate discretizations. Two methods of discretizations are discussed: the strongly stable scheme and the Lax-Wendroff scheme.

Bayliss, A.↗
DOE OSTI2025

Symmetry structure of a Riccati equation appearing in penetration mechanics

In the design of projectile penetration experiments a matter of considerable interest is scaling: that is, the potential relevance of small-scale experiments to their full-scale counterparts, in a manner analogous to that most often encountered in the context of fluid mechanics. From the theoretical standpoint, phenomena associated with scaling and scalability can be assessed using the well-established tools of dimensional analysis and the Buckingham-Pi Theorem. However, the familiar precepts of dimensional analysis are themselves a specific manifestation of the broader group invariance properties or symmetries of a mathematical model. Here, this work explores these notions – that is, dimensional analysis, the conditions for realizing complete similarity, and any additional symmetry structures – in the context of a Riccati differential equation appearing in the context of penetration mechanics. The aim of the investigation is twofold: 1) to complement existing empirical considerations with a concrete theoretical basis, and 2) to provide a deeper theoretical understanding of the projectile penetration model and its many implications.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1979

A fast technique for computing syndromes of BCH and RS codes

A combination of the Chinese Remainder Theorem and Winograd's algorithm is used to compute transforms of odd length over GF(2 to the m power). Such transforms are used to compute the syndromes needed for decoding CBH and RS codes. The present scheme requires substantially fewer multiplications and additions than the conventional method of computing the syndromes directly.

Reed, I. S.↗
NASA NTRS1980

On the application of a fast polynomial transform and the Chinese remainder theorem to compute a two-dimensional convolution

A fast algorithm is developed to compute two dimensional convolutions of an array of d sub 1 X d sub 2 complex number points, where d sub 2 = 2(M) and d sub 1 = 2(m-r+) for some 1 or = r or = m. This algorithm requires fewer multiplications and about the same number of additions as the conventional fast fourier transform method for computing the two dimensional convolution. It also has the advantage that the operation of transposing the matrix of data can be avoided.

Truong, T. K.↗
NASA NTRS2005

Coevolutionary Free Lunches

Recent work on the mathematical foundations of optimization has begun to uncover its rich structure. In particular, the "No Free Lunch" (NFL) theorems state that any two algorithms are equivalent when their performance is averaged across all possible problems. This highlights the need for exploiting problem-specific knowledge to achieve better than random performance. In this paper we present a general framework covering more search scenarios. In addition to the optimization scenarios addressed in the NFL results, this framework covers multi-armed bandit problems and evolution of multiple co-evolving players. As a particular instance of the latter, it covers "self-play" problems. In these problems the set of players work together to produce a champion, who then engages one or more antagonists in a subsequent multi-player game. In contrast to the traditional optimization case where the NFL results hold, we show that in self-play there are free lunches: in coevolution some algorithms have better performance than other algorithms, averaged across all possible problems. We consider the implications of these results to biology where there is no champion.

Wolpert, David H.↗
NASA NTRS1989

Optimized orbits for the constellation of Space Station polar platforms

The orbital configuration of the Eos polar-platform constellation is examined to determine if baseline orbital parameters are appropriately specified to meet the mission task of measuring global oceanic mesoscale variability. Using the Nyquist sampling theorem, spatial and temporal measurement requirements are first established for the constellation. Based upon these requirements, the optimum solution indicates that a total of five spacecraft equipped with nadir-pointing altimeters, or two multibeam-equipped platforms, would be required to meet the mesoscale mapping task. Additional analyses were performed on both one- and and two-platform configurations as well as the complete four-platform Eos constellation. The results of these calculations show that the preferred scenario would be to equip all four Eos polar platforms with multibeam altimeters.

Chase, Robert↗
NASA NTRS2003

Questions Revisited: A Close Examination of Calculus of Inference and Inquiry

In this paper I examine more closely the way in which probability theory, the calculus of inference, is derived from the Boolean lattice structure of logical assertions ordered by implication. I demonstrate how the duality between the logical conjunction and disjunction in Boolean algebra is lost when deriving the probability calculus. In addition, I look more closely at the other lattice identities to verify that they are satisfied by the probability calculus. Last, I look towards developing the calculus of inquiry demonstrating that there is a sum and product rule for the relevance measure as well as a Bayes theorem. Current difficulties in deriving the complete inquiry calculus will also be discussed.

Knuth, Kevin H.↗
NASA NTRS2005

Coevolutionary Free Lunches

Recent work on the foundations of optimization has begun to uncover its underlying rich structure. In particular, the "No Free Lunch" (NFL) theorems [WM97] state that any two algorithms are equivalent when their performance is averaged across all possible problems. This highlights the need for exploiting problem-specific knowledge to achieve better than random performance. In this paper we present a general framework covering most search scenarios. In addition to the optimization scenarios addressed in the NFL results, this framework covers multi-armed bandit problems and evolution of multiple co-evolving agents. As a particular instance of the latter, it covers "self-play" problems. In these problems the agents work together to produce a champion, who then engages one or more antagonists in a subsequent multi-player game In contrast to the traditional optimization case where the NFL results hold, we show that in self-play there are free lunches: in coevolution some algorithms have better performance than other algorithms, averaged across all possible problems. However in the typical coevolutionary scenarios encountered in biology, where there is no champion, NFL still holds.

Wolpert, David H.↗
DOE OSTI2025

Hierarchical Estimation For Planetary Protection

The software uses Bayes' theorem to describe the probability of an event based on prior knowledge of conditions that might be related to the event. The purpose of Bayesian analysis is to determine posterior probabilities based on prior probabilities where new information can be used in the decision-making process as additional data is gathered. The software will be used in Probabilistic Risk Assessments (PRAs) related to the Europa Clipper mission, which is one of NASA’s top priorities. Ultimately, the mission entails sending the Europa Clipper spacecraft to Jupiter’s Europa moon to orbit the planet and collect data for research and development. Europa is the smallest of the four Galilean moons orbiting Jupiter and is believed by researchers to be the most promising place to look for present-day environments suitable for life. Europa is thought to have an iron core, a rocky mantle, and a salt-water ocean covered by an ice-layered surface.

Gribok, Andrei [Idaho National Laboratory (INL), I↗
NASA NTRS1980

MCSCF wave functions for excited states of polar molecules - Application to BeO

A previously reported multi-configuration self-consistent field (MCSCF) algorithm based on the generalized Brillouin theorem is extended in order to treat the excited states of polar molecules. In particular, the algorithm takes into account the proper treatment of nonorthogonality in the space of single excitations and invokes, when necessary, a constrained optimization procedure to prevent the variational collapse of excited states. In addition, a configuration selection scheme (suitable for use in conjunction with extended configuration interaction methods) is proposed for the MCSCF procedure. The algorithm is used to study the low-lying singlet states of BeO, a system which has not previously been studied using an MCSCF procedure. MCSCF wave functions are obtained for three 1 Sigma + and two 1 Pi states. The 1 Sigma + results are juxtaposed with comparable results for MgO in order to assess the generality of the description presented here.

Bauschlicher, C. W., Jr.↗
DOE OSTI2021

New magnetic symmetries in (d + 2)-dimensional QED

Previous analyses of asymptotic symmetries in QED have shown that the subleading soft photon theorem implies a Ward identity corresponding to a charge generating divergent large gauge transformations on the asymptotic states at null infinity. In this work, we demonstrate that the subleading soft photon theorem is equivalent to a more general Ward identity. The charge corresponding to this Ward identity can be decomposed into an electric piece and a magnetic piece. The electric piece generates the Ward identity that was previously studied, but the magnetic piece is novel, and implies the existence of an additional asymptotic “magnetic” symmetry in QED.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Fiducial $q_T$ resummation of color-singlet processes at N$^3$LL+NNLO

We present a framework for $q_T$ resummation at N 3 LL+NNLO accuracy for arbitrary color-singlet processes based on a factorization theorem in SCET. Our implementation CuTe-MCFM is fully differential in the Born kinematics and matches to large-$q_T$ fixed-order predictions at relative order $α^2_s$. It provides an efficient way to estimate uncertainties from fixed-order truncation, resummation, and parton distribution functions. In addition to W ± , Z and H production, also the diboson processes $\gamma\gamma$, Z$\gamma$, ZH and W ± H are available, including decays. We discuss and exemplify the framework with several direct comparisons to experimental measurements as well as inclusive benchmark results. In particular, we present novel results for $\gamma\gamma$ and Z$\gamma\gamma$ at N 3 LL+NNLO and discuss in detail the power corrections induced by photon isolation requirements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗