Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Operator 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 1,279 records · Page 71

Huzinaga projection embedding for efficient and accurate energies of systems with localized spin-densities

We demonstrate the accuracy and efficiency of the restricted open-shell and unrestricted formulation of the absolutely localized Huzinaga projection operator embedding method. Restricted open-shell and unrestricted Huzinaga projection embedding in the full system basis is formally exact to restricted open-shell and unrestricted Kohn–Sham density functional theory, respectively. By utilizing the absolutely localized basis, we significantly improve the efficiency of the method while maintaining high accuracy. Furthermore, the absolutely localized basis allows for high accuracy open-shell wave function methods to be embedded into a closed-shell density functional theory environment. The open-shell embedding method is shown to calculate electronic energies of a variety of systems to within 1 kcal/mol accuracy of the full system wave function result. For certain highly localized reactions, such as spin transition energies on transition metals, we find that very few atoms are necessary to include in the wave function region in order to achieve the desired accuracy. This extension further broadens the applicability of our absolutely localized Huzinaga level-shift projection operator method to include open-shell species. Here, we apply our method to several representative examples, such as spin splitting energies, catalysis on transition metals, and radical reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Analytical parametric investigation of low pressure ratio fan noise

The results of an analytical study are reported which shows the effect of various physical and operating parameters on noise produced by low pressure ratio propulsive fans operating at subsonic top speeds. Acoustical duct lining effects are included in the study. The concepts used to develop the noise theory used in the study, as well as the correlation between the theory and model test results are also presented. It is shown that good correlation has been established between theory and experiment. Using the theory, it is shown that good aerodynamic design, maximum acceptable fan solidity, low tip speed operation and use of few blades and vanes leads to the lowest noise levels. Typical results of the study indicate that a fan operating at 1.2 fan pressure ratio and 700 ft/second tip speed with 12 blades and 7 vanes and including modest acoustic treatment on the duct wall would produce levels allowing a 100,000 lb. STOL aircraft to meet a noise level objective of 95 PNdB at 500 ft at takeoff.

Metzger, F. B.↗

Theory of Trotter Error with Commutator Scaling

The Lie-Trotter formula, together with its higher-order generalizations, provides a simple approach to decomposing the exponential of a sum of operators. Despite significant effort, the error scaling of such product formulas remains poorly understood. We develop a theory of Trotter error that overcomes the limitations of truncating the Baker-Campbell-Hausdorff expansion. Our analysis directly exploits the commutativity of operator summands, producing tighter error bounds for both real- and imaginary-time evolutions. Whereas previous work achieves similar goals for systems with geometric locality or Lie-algebraic structure, our approach holds in general. We give a host of improved algorithms for digital quantum simulation and quantum Monte Carlo methods, nearly matching or even outperforming the best previous results. Our applications include: (i) a simulation of second-quantized plane-wave electronic structure, nearly matching the interaction-picture algorithm of Low and Wiebe; (ii) a simulation of $k$-local Hamiltonians almost with induced one-norm scaling, faster than the qubitization algorithm of Low and Chuang; (iii) a simulation of rapidly decaying power-law interactions, outperforming the Lieb-Robinson-based approach of Tran et al.; (iv) a hybrid simulation of clustered Hamiltonians, dramatically improving the result of Peng, Harrow, Ozols, and Wu; and (v) quantum Monte Carlo simulations of the transverse field Ising model and quantum ferromagnets, tightening previous analyses of Bravyi and Gosset. We obtain further speedups using the fact that product formulas can preserve the locality of the simulated system. Specifically, we show that local observables can be simulated with complexity independent of the system size for power-law interacting systems, which implies a Lieb-Robinson bound nearly matching a recent result of Tran et al. Our analysis reproduces known tight bounds for first- and second-order formulas. We further investigate the tightness of our bounds for higher-order formulas. For quantum simulation of a one-dimensional Heisenberg model with an even-odd ordering of terms, our result overestimates the complexity by only a factor of $5$. Our bound is also close to tight for power-law interactions and other orderings of terms. This suggests that our theory can accurately characterize Trotter error in terms of both the asymptotic scaling and the constant prefactor.

quantum computing, numerical analysis↗

On systems of maximal quantum chaos

A remarkable feature of chaos in many-body quantum systems is the existence of a bound on the quantum Lyapunov exponent. An important question is to understand what is special about maximally chaotic systems which saturate this bound. Here we provide further evidence for the ‘hydrodynamic’ origin of chaos in such systems, and discuss hallmarks of maximally chaotic systems. We first provide evidence that a hydrodynamic effective field theory of chaos we previously proposed should be understood as a theory of maximally chaotic systems. We then emphasize and make explicit a signature of maximal chaos which was only implicit in prior literature, namely the suppression of exponential growth in commutator squares of generic few-body operators. We provide a general argument for this suppression within our chaos effective field theory, and illustrate it using SYK models and holographic systems. We speculate that this suppression indicates that the nature of operator scrambling in maximally chaotic systems is fundamentally different to scrambling in non-maximally chaotic systems. We also discuss a simplest scenario for the existence of a maximally chaotic regime at sufficiently large distances even for non-maximally chaotic systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Investigation, development and application of optimal output feedback theory. Volume 2: Development of an optimal, limited state feedback outer-loop digital flight control system for 3-D terminal area operation

This report contains the development of a digital outer-loop three dimensional radio navigation (3-D RNAV) flight control system for a small commercial jet transport. The outer-loop control system is designed using optimal stochastic limited state feedback techniques. Options investigated using the optimal limited state feedback approach include integrated versus hierarchical control loop designs, 20 samples per second versus 5 samples per second outer-loop operation and alternative Type 1 integration command errors. Command generator tracking techniques used in the digital control design enable the jet transport to automatically track arbitrary curved flight paths generated by waypoints. The performance of the design is demonstrated using detailed nonlinear aircraft simulations in the terminal area, frequency domain multi-input sigma plots, frequency domain single-input Bode plots and closed-loop poles. The response of the system to a severe wind shear during a landing approach is also presented.

Broussard, J. R.↗

Holographic operator mapping in dS / CFT and cluster decomposition

The bulk-to-boundary mapping for massive scalar fields is constructed, providing a de Sitter analog of the Lehmann-Symanzik-Zimmermann reduction formula. The set of boundary correlators thus obtained defines a potentially new class of conformal field theories based on principal series representations of the global conformal group. Conversely, we show that bulk field operators in de Sitter may be reconstructed from boundary operators. While consistent at the level of the free field theory, the boundary conformal field theory does not satisfy cluster decomposition. Furthermore, the resulting conformal field theory does not satisfy the basic axioms of Euclidean quantum field theory due to Osterwalder and Schrader, so it is likely not well defined once interactions are included.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Bootstrapping a stress-tensor form factor through eight loops

We bootstrap the three-point form factor of the chiral stress-tensor multiplet in planar $\mathcal{N}$ = 4 supersymmetric Yang-Mills theory at six, seven, and eight loops, using boundary data from the form factor operator product expansion. This may represent the highest perturbative order to which multi-variate quantities in a unitary four-dimensional quantum field theory have been computed. In computing this form factor, we observe and employ new restrictions on pairs and triples of adjacent letters in the symbol. We provide details about the function space required to describe the form factor through eight loops. Plotting the results on various lines provides striking numerical evidence for a finite radius of convergence of perturbation theory. By the principle of maximal transcendentality, our results are expected to give the highest weight part of the gg → Hg and H → ggg amplitudes in the heavy-top limit of QCD through eight loops. These results were also recently used to discover a new antipodal duality between this form factor and a six-point amplitude in the same theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Zero modes in the light-front coupled-cluster method

The light-front coupled-cluster (LFCC) method is a technique for solving Hamiltonian eigenvalue problems in light-front-quantized field theories. Its primary purpose is to provide a systematic sequence of solvable approximations to the original eigenvalue problem without the truncation of Fock space. Here we discuss the incorporation of zero modes, modes of zero longitudinal momentum, into the formalism of the method. Without zero modes, the light-front vacuum is trivial, and the vacuum expectation value of the field is always zero. The LFCC method with zero modes provides for vacuum structure, in the form of a generalized coherent state of zero modes, as is illustrated here in two-dimensional model field theories. -- Highlights: •Extends the light-front coupled-cluster method to include zero modes. •Illustrates with an analysis of vacuum structure for phi-3, phi-4, and Wick–Cutkosky model field theories. •Demonstrates the applicability of the LFCC method to theories with spontaneous symmetry breaking.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Construction of the noncommutative complex ball

We describe the construction of the noncommutative complex ball whose commutative analog is the Hermitian symmetric space D = SU(m, 1)/U(m), with the method of coherent state quantization. In the commutative limit, we obtain the standard manifold. We also consider a quantum field theory model on the noncommutative manifold.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Theory-guided Design of Refractory MPEAs for High-Temperature, Harsh-Service Conditions

Focusing on novel materials for harsh-service environments (oxidation, corrosion, and load), durability, higher operational temperature, and direct impact on power-generation technology, the goal was, using a quantitative theory-guided design approach integrated with high-throughput synthesis and characterization for validation, to accelerate by 50% the development of high temperature, refractory-based multi-principal element alloys (MPEAs) materials platforms (with co-designed oxidation-resistant, self-healing coatings) that demonstrate phase-stable operation with desired properties at 10-20% higher temperatures in oxidizing environments over state-ofthe- art systems (like Ni-stainless steels, i.e., Haynes 282 – used in critical gas turbine applications, and refractory TZM, i.e., molybdenum-rich Mo99.4-Ti0.5-Zr0.08-C0.02 in wt%). Notably, refractory MPEAs may achieve higher operational temperatures with superior creep strength and offer 50-100% larger thermal conductivity (140-170 W/m-K) than Ni-based systems, potentially eliminating active cooling, reducing system weight, complexity, and cost. Achieving this goal addresses DOE material challenges in energy generation and efficiency (higher-temperature operation), reduced lifecycle energy (waste-heat recovery), and accelerating materials development in support of AMO’s Strategic Plan and QTR goals. DOE’s Advanced Manufacturing Office (AMO) goal of reducing industrial energy intensity and GHG emissions is addressed by development of coated refractory MPEAs exhibiting 20%+ higher operational temperature (direct increase of Carnot efficiency), higher melting temperatures (better phase stability), superior creep strength (better lifetime with creep rate lower by factor of 10), larger (50-100%) thermal conductivity (improved cooling without active cooling), reduced complexity (single-phase alloys), self-healing coating (reliable oxidation-resistance) and cost.

36 MATERIALS SCIENCE↗

Advanced Power Systems Measurements: A Literature Review

In 2020, a literature survey was performed as part of a project aimed at producing guidance for the Department of Energy in the form of a Roadmap. The topic of the Roadmap was measurement. That was viewed as being generally underrepresented in consideration of sensing and measurement or instrumentation and measurement. Sensing is just the beginning of a process, and the instrument is just the container for the process. Measurement, the experimental process, has acquired a considerable body of theory over the last few decades, theory that is not widely taught and disseminated. The results of the survey can be said broadly to reflect that lack of appreciation. Specifically, the review found that there is support for the development of a more “capable” PMU. New algorithms and new documentary standards will be needed. Some of the findings are: (1) Point-on-wave technology adds new capability to the existing suite of measurements, and could allow for improved operation and protection (2) Power quality analysis has historically been concerned with assessment of how non-sinusoidal the delivered voltage shows promise in signature recognition, a departure from the modeling that has historically characterized power system measurements. (3) The PMU is assed as being a remarkable measurement system, but its performance is held back by the lack of understanding of the measurement theory underpinning its operation. (4) The PMU is being considered for application in the distribution system. There is a danger that it will be seen only in the light of the successful PMU implementation in transmission, and the two have different requirements. These various expansions of measurements will no doubt benefit from a better appreciation of the theoretical aspects of measurement. In this, and other, regards, our survey of the literature has identified gaps as well as possibilities.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Twisted vertex algebras, bicharacter construction and boson-fermion correspondences

The boson-fermion correspondences are an important phenomena on the intersection of several areas in mathematical physics: representation theory, vertex algebras and conformal field theory, integrable systems, number theory, cohomology. Two such correspondences are well known: the types A and B (and their super extensions). As a main result of this paper we present a new boson-fermion correspondence of type D-A. Further, we define a new concept of twisted vertex algebra of order N, which generalizes super vertex algebra. We develop the bicharacter construction which we use for constructing classes of examples of twisted vertex algebras, as well as for deriving formulas for the operator product expansions, analytic continuations, and normal ordered products. By using the underlying Hopf algebra structure we prove general bicharacter formulas for the vacuum expectation values for two important groups of examples. We show that the correspondences of types B, C, and D-A are isomorphisms of twisted vertex algebras.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Seventh Annual Conference on Manual Control

The Seventh Annual NASA/AF/University Conference on Manual Control was held at the University of Southern California from June 2-4, 1971. Some eighty specialists, including colleagues from Canada, Netherlands and West Germany, attended the Conference, which was organized by the authors of this Summary. Generally at this conference there was less emphasis on theory and more on applications than at some previous meetings. In addition to the well-established areas of human operator modeling and display systems, this conference devoted considerable time to the extensions of manual control theory to such diverse areas as automobile driving, air traffic control and industrial management. This interest in meaningful applications of the existing theoretical knowledge in man-machine systems is encouraging and timely.

Source record↗

Electronic Transition Dipole Moments in Relativistic Coupled-Cluster Theory: the Finite-Field Method

The determination of the matrix elements of single-electron operators for the transitions between electronic states (primarily, the dipole moments of electron transitions) is one of the critical problems in simulating the atomic and molecular spectra. In this study, the efficiency of a simple version of the finite-field method for calculating these values within the Fock-space coupled-cluster theory has been investigated.

74 ATOMIC AND MOLECULAR PHYSICS↗

Line operators, vortex statistics, and Higgs versus confinement dynamics

We study a 2+1D lattice gauge theory with fundamental representation scalar fields which has both Higgs and confining regimes with a spontaneously-broken U(1) 0-form symmetry. We show that the Higgs and confining regimes may be distinguished by a natural gauge invariant observable: the phase Ω of a correlation function of a vortex line operator linking with an electric Wilson line. We employ dualities and strong coupling expansions to analytically explore parameter regimes which were inaccessible in previous continuum calculations, and discuss possible implications for the phase diagram.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Berry Phase Effects in Dipole Density and the Mott Relation

Here, we provide a unified semiclassical theory for thermoelectric responses of any observable represented by an operator $\hat{θ}$ that is well defined in periodic crystals. The Einstein and Mott relations are established generally in the presence of Berry phase effects for various physical realizations of $\hat{θ}$ in electronic systems, including the familiar case of the electric current as well as the currently controversial cases of the spin polarization and spin current. The magnetization current, which has been proven indispensable in the thermoelectric response of electric current, is generalized to the cases of various $\hat{θ}$. In our theory the dipole density of a physical quantity emerges and plays a vital role, which contains not only the statistical sum of the dipole moment of $\hat{θ}$ but also a Berry phase correction.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

The trispectrum in the effective theory of inflation with Galilean symmetry

We calculate the trispectrum of curvature perturbations for a model of inflation endowed with Galilean symmetry at the level of the fluctuations around an FRW background. Such a model has been shown to posses desirable properties such as non-renormalization of the leading operators. The cubic curvature fluctuations of this model produce quite distinct signatures at the level of the bispectrum. Our analysis shows how this holds true at higher order in perturbations. We provide a detailed study of the trispectrum shape-functions in different configurations and a comparison with existent literature. Most notably, predictions markedly differ from their P(X,φ) counterpart in the so called equilateral trispectrum configuration.

79 ASTRONOMY AND ASTROPHYSICS↗

Experimental Study of the 3 He and Neutron Spin Structure at Low Q 2 and The Upgrade of the JLab Polarized 3 He Target

In the scattering process off a nuclear or nucleon target, the Gerasimov-Drell-Hearn (GDH) sum rule for real photons (Q 2 =0 where Q 2 &equiv; -q 2 with q the photon's 4-momentum) relates static properties of the target particle's ground state to dynamic properties of all its excited states. On the other side of the Q 2 spectrum, the Bjorken sum rule holds in the Bjorken limit Q 2 &rarr; &infin;. Bjorken sum rule relates the final structure functions of the proton and neutron to the nucleon axial coupling constant in weak decay. These two sum rules belong to domains where calculations are achievable but use different degrees of freedom: hadronic degrees of freedom at low Q 2 versus partonic degrees of freedom at intermediate Q 2 . Meanwhile, different methods have been used to connect the two sum rules at finite Q 2 values: Chiral Perturbation Theory is used to expand the GDH sum rule while Operator Product Expansion is used to expand the Bjorken sum rule. In recent decades, improvements in polarized beam and polarized target techniques have made it possible to test theoretical predictions in the intermediate Q 2 region. During the Jefferson Lab (JLab) Hall A E97110 experiment, a precise measurement of polarized cross sections was performed at 0.02 < Q 2 < 0.3 GeV 2 using a polarized 3 He target as an effective polarized neutron target. The measured data allowed us to test predictions of Chiral Perturbation Theory at very low Q 2 . Furthermore, an extrapolation to the real photon point Q 2 =0 tests the GDH sum rule on the neutron. In order to reach the small angles necessary for the low Q 2 range, a new septum magnet was installed in Hall A for this experiment. Unfortunately, the magnet was mis-wired during initial running. There were therefore two periods for this experiment: the first period had the defective magnet due to mis-wiring; while in the second period, the magnet had been fixed and was working properly. The cross sections and the asymmetries for the first period must be extracted using a difficult and unusual method employing focal plane variables in the spectrometer. In the work described in this thesis, the target-plane and focal-plane method will be established first and confirmed by elastic scattering cross section measurements from carbon foil and 3 He targets. Cross sections and asymmetries of inelastic scattering were then extracted using the same method, which constitute the main physics results of this thesis. Preliminary results on ITT , the integral of the polarized cross section, were also extracted and are presented in this thesis. In addition to the data analysis of E97110, this thesis includes instrumentation work performed on the polarized 3 He target at JLab. For the 12 GeV program of JLab, the polarized 3 He target is being upgraded to satisfy new experimental requirements. The new target is a convection-based cell with two transfer tubes rather than a single transfer tube as in the former 6 GeV design. The first stage of the target upgrade aims to produce a 40 cm long, 10 amg target that can withstand 30 &mu;A of electron beam current with an in-beam polarization of 55%, doubling the figure-of-merit from the 6 GeV time. Several studies were conducted at the Test Lab of JLab on the new convection cell. Work and improvement done on the Pulse Nuclear Magnetic Resonance (NMR) polarimetry and its test results will be presented. As this thesis is written, the target is being installed in Hall C of JLab in preparation for a 6-month long running from November 2019 to May 2020.

Ton, Nguyen↗