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 793 records · Page 44
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Geometric entropies and their Hamiltonian flows

In holographic theories, the Hubeny-Rangamani-Takayanagi (HRT) area operator plays a key role in our understanding of the emergence of semiclassical Einstein-Hilbert gravity. When higher derivative corrections are included, the role of the area is instead played by a more general functional known as the geometric entropy. It is thus of interest to understand the flow generated by the geometric entropy on the classical phase space. In particular, the fact that the associated flow in Einstein-Hilbert or Jackiw-Teitelboim (JT) gravity induces a relative boost between the left and right entanglement wedges is deeply related to the fact that gravitational dressing promotes the von Neumann algebra of local fields in each wedge to type II. This relative boost is known as a boundary-condition-preserving (BCP) kink-transformation. In a general theory of gravity (with arbitrary higher-derivative terms), it is straightforward to show that the flow continues to take the above geometric form when acting on a spacetime where the HRT surface is the bifurcation surface of a Killing horizon. However, the form of the flow on other spacetimes is less clear. In this paper, we use the manifestly-covariant Peierls bracket to explore such flows in two-dimensional theories of JT gravity coupled to matter fields with higher derivative interactions. The results no longer take a purely geometric form and, instead, demonstrate new features that should be expected of such flows in general higher derivative theories. We also show how to obtain the above flows using Poisson brackets.

AdS-CFT correspondence↗
DOE OSTI2024

Universal bounds on CFT Distance Conjecture

For any unitary conformal field theory in two dimensions with the central charge c, we prove that, if there is a nontrivial primary operator whose conformal dimension ∆ vanishes in some limit on the conformal manifold, the Zamolodchikov distance t to the limit is infinite, the approach to this limit is exponential ∆ = exp(−αt + O(1)), and the decay rate obeys the universal bounds c−1/2 ≤ α ≤ 1. In the limit, we also find that an infinite tower of primary operators emerges without a gap above the vacuum and that the conformal field theory becomes locally a tensor product of a sigma-model in the large radius limit and a compact theory. As a corollary, we establish a part of the Distance Conjecture about gravitational theories in three-dimensional anti-de Sitter space. In particular, our bounds on α indicate that the emergence of exponentially light states is inevitable as the moduli field corresponding to t rolls beyond the Planck scale along the steepest path and that this phenomenon can begin already at the curvature scale of the bulk geometry. We also comment on implications of our bounds for gravity in asymptotically flat spacetime by taking the flat space limit and compare with the Sharpened Distance Conjecture.

AdS-CFT Correspondence↗
NASA NTRS2003

Investigation Leads to Improved Understanding of Space Shuttle RSRM Internal Insulation Joints

The Space Shuttle Reusable Solid Rocket Motor (RSRM) uses an internal insulation J-joint design for the mated insulation interface between two assembled RSRM segments. In this assembled (mated) segment configuration, this J-joint design serves as a thermal barrier to prevent hot gases from affecting the case field joint metal surfaces and O-rings. A pressure sensitive adhesive (PSA) provides some adhesion between the two mated insulation surfaces. In 1995, after extensive testing, a new ODC-free PSA (free of ozone depleting chemicals) was selected for flight on RSRM-55 (STS-78). Post-flight inspection revealed that the J-joint, equipped with the new ODC-free PSA, did not perform well. Hot gas seeped inside the J-joint interface. Although not a flight safety threat, the J-joint hot gas intrusion on RSRM-55 was a mystery to the investigators since the PSA had previously worked well on a full-scale static test. A team was assembled to study the J-joint and PSA further. All J-joint design parameters, measured data, and historical performance data were re-reviewed and evaluated by subscale testing and analysis. Although both the ODC-free and old PSA were weakened by humidity, the ODC-free PSA strength was lower to start with. Another RSRM full-scale static test was conducted in 1998 and intentionally duplicated the gas intrusion. This test, along with many concurring tests, showed that if a J-joint was 1) mated with the new ODC-free PSA, 2) exposed to a history of high humidity (Kennedy Space Center levels), and 3) also a joint which experienced significant but normal joint motion (J-joint deformation resulting from motor pressurization dynamics) then that J-joint would open (allow gas intrusion) during motor operation. When all of the data from the analyses, subscale tests, and full-scale tests were considered together, a theory emerged. Most of the joint motion on the RSRM occurs early in motor operation at which point the J-joints are pulled into tension. If the new PSA has been weakened due to humidity, then the J-joint will partially pull apart (inboard side), and the J-joint surfaces will be charred by exposure to hot gases. After early operation, a J-joint that has been pulled apart will come back together as the J-joint deformation decreases. This J-joint heating event is relatively short and occurs only during the first part of motor operation. Internal instrumentation was developed for another full-scale static test in February 2000. The static test instrumentation did indeed prove this theory to be correct. Post-test inspection revealed very similar charring characteristics as observed on RSRM-55. This experience of the development of a new PSA, its testing, the RSRM-55 flight, followed by the J-joint investigation led to good 'lessons learned' and to an additional fundamental understanding of the RSRM J-joint function.

McWhorter, Bruce B.↗
DOE OSTI2023

Two-point correlator of twist-2 light-ray operators in N=4 SYM in BFKL approximation

We generalize local operators of the leading twist-2 of N = 4 SYM theory to the case of complex Lorentz spin j using principal series representation of sl(2,R). We give the direct computation of correlation function of two such non-local operators in the BFKL regime when j → 1. The correlator appears to have the expected conformal coordinate dependence governed by the anomalous dimension of twist-2 operator in NLO BFKL approximation predicted by Kotikov and Lipatov.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Backgrounds in gravitational effective field theory

Effective field theories describing gravity coupled to matter are investigated, allowing for operators of arbitrary mass dimension. Terms violating local Lorentz and diffeomorphism invariance while preserving internal gauge symmetries are included. The theoretical framework for violations of local Lorentz and diffeomorphism invariance and associated conceptual issues are discussed, including transformations in curved and approximately flat spacetimes, the treatment of various types of backgrounds, the implications of symmetry breaking, and the no-go constraints for explicit violation in Riemann geometry. Furthermore, techniques are presented for the construction of effective operators, and the possible terms in the gravity, gauge, fermion, and scalar sectors are classified and enumerated. Explicit expressions are obtained for terms containing operators of mass dimension six or less in the effective action for General Relativity coupled to the Standard Model of particle physics. Special cases considered include Einstein-Maxwell effective field theories and the limit with only scalar coupling constants.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Semiclassical theory and the Koopman-van Hove equation *

Abstract The phase space Koopman-van Hove (KvH) equation can be derived from the asymptotic semiclassical analysis of partial differential equations. Semiclassical theory yields the Hamilton–Jacobi equation for the complex phase factor and the transport equation for the amplitude. These two equations can be combined to form a nonlinear semiclassical version of the KvH equation in configuration space. There is a natural injection of configuration space solutions into phase space and a natural projection of phase space solutions onto configuration space. Hence, every solution of the configuration space KvH equation satisfies both the semiclassical phase space KvH equation and the Hamilton–Jacobi constraint. For configuration space solutions, this constraint resolves the paradox that there are two different conserved densities in phase space. For integrable systems, the KvH spectrum is the Cartesian product of a classical and a semiclassical spectrum. If the classical spectrum is eliminated, then, with the correct choice of Jeffreys–Wentzel–Kramers–Brillouin (JWKB) matching conditions, the semiclassical spectrum satisfies the Einstein–Brillouin–Keller quantization conditions which include the correction due to the Maslov index. However, semiclassical analysis uses different choices for boundary conditions, continuity requirements, and the domain of definition. For example, use of the complex JWKB method allows for the treatment of tunneling through the complexification of phase space. Finally, although KvH wavefunctions include the possibility of interference effects, interference is not observable when all observables are approximated as local operators on phase space. Observing interference effects requires consideration of nonlocal operations, e.g. through higher orders in the asymptotic theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1995

Finite-element time evolution operator for the anharmonic oscillator

The finite-element approach to lattice field theory is both highly accurate (relative errors approximately 1/N(exp 2), where N is the number of lattice points) and exactly unitary (in the sense that canonical commutation relations are exactly preserved at the lattice sites). In this talk I construct matrix elements for dynamical variables and for the time evolution operator for the anharmonic oscillator, for which the continuum Hamiltonian is H = p(exp 2)/2 + lambda q(exp 4)/4. Construction of such matrix elements does not require solving the implicit equations of motion. Low order approximations turn out to be extremely accurate. For example, the matrix element of the time evolution operator in the harmonic oscillator ground state gives a results for the anharmonic oscillator ground state energy accurate to better than 1 percent, while a two-state approximation reduces the error to less than 0.1 percent.

Milton, Kimball A.↗
DOE OSTI2024

Definition of fragmentation functions and the violation of sum rules

We point out a problem with the formulation and derivations of sum rules for quark fragmentation functions that impacts their validity in QCD, but which potentially points toward an improved understanding of final states in inclusive hard processes. Fragmentation functions give the distribution of final-state hadrons arising from a parton exiting a hard scattering, and the sum rules for momentum, electric charge, etc. express conservation of these quantities. The problem arises from a mismatch between the quark quantum numbers of the initial quark and the fact that all observed final-state hadrons are confined bound states with color zero. We point that, in a confining theory like QCD, the Wilson line in the operator definition of a fragmentation function entails that the final state in a fragmentation function includes a bound state in the external field generated by the Wilson line. We justify this with the aid of general features of string hadronization. The anomalous bound states are restricted to fractional momentum z = 0 . They tend to invalidate sum rules like the one for charge conservation when applied to the fragmentation functions inferred from experimental data but not the momentum sum rule. We propose to exploit our ideas in future studies as a way to relate the fragmentation functions extracted from inclusive cross sections to more detailed nonperturbative descriptions of final state hadronization. We also describe scenarios wherein the traditional sum rules might remain approximately valid with a reasonably high degree of accuracy. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Taming the fixed-node error in diffusion Monte Carlo via range separation

By combining density-functional theory (DFT) and wave function theory via the range separation (RS) of the interelectronic Coulomb operator, we obtain accurate fixed-node diffusion Monte Carlo (FN-DMC) energies with compact multi-determinant trial wave functions. In particular, we combine here short-range exchange-correlation functionals with a flavor of selected configuration interaction known as configuration interaction using a perturbative selection made iteratively (CIPSI), a scheme that we label RS-DFT-CIPSI. One of the take-home messages of the present study is that RS-DFT-CIPSI trial wave functions yield lower fixed-node energies with more compact multi-determinant expansions than CIPSI, especially for small basis sets. Indeed, as the CIPSI component of RS-DFT-CIPSI is relieved from describing the short-range part of the correlation hole around the electron-electron coalescence points, the number of determinants in the trial wave function required to reach a given accuracy is significantly reduced as compared to a conventional CIPSI calculation. Importantly, by performing various numerical experiments, we evidence that the RS-DFT scheme essentially plays the role of a simple Jastrow factor by mimicking short-range correlation effects, hence avoiding the burden of performing a stochastic optimization. Considering the 55 atomization energies of the Gaussian-1 benchmark set of molecules, we show that using a fixed value of mu = 0.5 bohr(-1) provides effective error cancellations as well as compact trial wave functions, making the present method a good candidate for the accurate description of large chemical systems.

Scemama, Anthony↗
DOE OSTI2020

AdS/CFT unitarity at higher loops: high-energy string scattering

What is the space of weakly-coupled, gravitational theories which contain massive, higher-spin particles? This class of theories is highly constrained and it is conjectured their ultraviolet completion must be string theory. We provide more evidence for this conjecture by studying the Regge limit in large N, 4d CFTs with single-trace operators of unbounded spin. We show that in the Regge limit, these theories have bulk scattering amplitudes which are consistent with the string theory prediction to all orders in 1/N for large, but finite, coupling. In the language of Regge theory, we show Pomeron exchange naturally exponentiates in the 1/N expansion. To do this, we solve the bootstrap equations at tree-level and then use the Lorentzian inversion formula to find the one-loop correlator in the Regge limit. This is a unitarity method for AdS/CFT which can be repeated iteratively to make all orders statements. We also explain under what conditions the tree-level result exponentiates in the 1/N expansion at arbitrary coupling. Finally, we comment on further inelastic effects and show they give subleading contributions at large coupling. As a consistency check, we recover results from bulk Einstein gravity in the limit where all higher-spin particles decouple.

1/N Expansion↗
DOE OSTI2023

OPERATOR 4.0 FOR HYBRID MANUFACTURING

Hybrid manufacturing, a combination of additive and subtractive manufacturing capabilities in one system, has recently become a more viable production option across several industries. Although current hybrid manufacturing research covers a broad range of topics, there is a lack of focus on how this new technology impacts both the designer and the operator of hybrid systems. This paper identifies areas of literature across design theory and Industry/Operator 4.0 research efforts and presents a path for applying this research to hybrid manufacturing users. The unique relationship between operator and designer is highlighted as they learn new strategies and develop new intuitive judgements over time to become the first experienced/expert users of hybrid manufacturing. The potential impact of excessive cognitive workload due to the novel combination of processes is discussed. This paper begins a critical discussion about proper knowledge transfer to other hybrid designers and operators, as well as towards efforts of monitoring, inspecting, and automating hybrid manufacturing processes.

Fillingim, Blane↗
NASA NTRS1984

Target detection using microwave irradiances from natural sources: A passive, local and global surveillance system

Detection of metal objects on or near the Earth's surface was investigated using existing, passive, microwave sensors operating from Earth orbit. The range equations are derived from basic microwave principles and theories and the expressions are given explicitly to estimate the signal to noise ratio for detecting metal targets operating as bistatic scatterers. Actual measurements are made on a range of metal objects observed from orbit using existing passive microwave receiving systems. The details of the measurements and the results are tabulated and discussed. The advantages of a passive microwave sensor as it is applied to surveillance of metal objects as viewed from aerial platforms or from orbit, are examined.

Stacey, J. M.↗
NASA NTRS1992

Experimental validation of clock synchronization algorithms

The objective of this work is to validate mathematically derived clock synchronization theories and their associated algorithms through experiment. Two theories are considered, the Interactive Convergence Clock Synchronization Algorithm and the Midpoint Algorithm. Special clock circuitry was designed and built so that several operating conditions and failure modes (including malicious failures) could be tested. Both theories are shown to predict conservative upper bounds (i.e., measured values of clock skew were always less than the theory prediction). Insight gained during experimentation led to alternative derivations of the theories. These new theories accurately predict the behavior of the clock system. It is found that a 100 percent penalty is paid to tolerate worst-case failures. It is also shown that under optimal conditions (with minimum error and no failures) the clock skew can be as much as three clock ticks. Clock skew grows to six clock ticks when failures are present. Finally, it is concluded that one cannot rely solely on test procedures or theoretical analysis to predict worst-case conditions.

Palumbo, Daniel L.↗
NASA NTRS2002

Simulating Activities: Relating Motives, Deliberation and Attentive Coordination

Activities are located behaviors, taking time, conceived as socially meaningful, and usually involving interaction with tools and the environment. In modeling human cognition as a form of problem solving (goal-directed search and operator sequencing), cognitive science researchers have not adequately studied "off-task" activities (e.g., waiting), non-intellectual motives (e.g., hunger), sustaining a goal state (e.g., playful interaction), and coupled perceptual-motor dynamics (e.g., following someone). These aspects of human behavior have been considered in bits and pieces in past research, identified as scripts, human factors, behavior settings, ensemble, flow experience, and situated action. More broadly, activity theory provides a comprehensive framework relating motives, goals, and operations. This paper ties these ideas together, using examples from work life in a Canadian High Arctic research station. The emphasis is on simulating human behavior as it naturally occurs, such that "working" is understood as an aspect of living. The result is a synthesis of previously unrelated analytic perspectives and a broader appreciation of the nature of human cognition. Simulating activities in this comprehensive way is useful for understanding work practice, promoting learning, and designing better tools, including human-robot systems.

Clancey, William J.↗
DOE OSTI2022

Duality and form factors in the thermally deformed two-dimensional tricritical Ising model

The thermal deformation of the critical point action of the 2D tricritical Ising model gives rise to an exact scattering theory with seven massive excitations based on the exceptional E_7 E 7 Lie algebra. The high and low temperature phases of this model are related by duality. This duality guarantees that the leading and sub-leading magnetisation operators, \sigma(x) σ ( x ) and \sigma'(x) σ ′ ( x ) , in either phase are accompanied by associated disorder operators, \mu(x) μ ( x ) and \mu'(x) μ ′ ( x ) . Working specifically in the high temperature phase, we write down the sets of bootstrap equations for these four operators. For \sigma(x) σ ( x ) and \sigma'(x) σ ′ ( x ) , the equations are identical in form and are parameterised by the values of the one-particle form factors of the two lightest \mathbb{Z}_2 ℤ 2 odd particles. Similarly, the equations for \mu(x) μ ( x ) and \mu'(x) μ ′ ( x ) have identical form and are parameterised by two elementary form factors. Using the clustering property, we show that these four sets of solutions are eventually not independent; instead, the parameters of the solutions for \sigma(x)/\sigma'(x) σ ( x ) / σ ′ ( x ) are fixed in terms of those for \mu(x)/\mu'(x) μ ( x ) / μ ′ ( x ) . We use the truncated conformal space approach to confirm numerically the derived expressions of the matrix elements as well as the validity of the \Delta Δ -sum rule as applied to the off-critical correlators. We employ the derived form factors of the order and disorder operators to compute the exact dynamical structure factors of the theory, a set of quantities with a rich spectroscopy which may be directly tested in future inelastic neutron or Raman scattering experiments.

Cortes Cubero, Axel↗
DOE OSTI2025

Benchmarking and Fidelity Response Theory of High-Fidelity Rydberg Entangling Gates

The fidelity of entangling operations is a key figure of merit in quantum information processing, especially in the context of quantum error correction. High-fidelity entangling gates in neutral atoms have seen remarkable advancement recently. A full understanding of error sources and their respective contributions to gate infidelity will enable the prediction of fundamental limits on quantum gates in neutral atom platforms with realistic experimental constraints. In this work, we implement the time-optimal Rydberg controlled-Z (CZ) gate, design a circuit to benchmark its fidelity, and achieve a fidelity, averaged over symmetric input states, of 0.9971 ( 5 ) , downward corrected for leakage error, which together with our recent work [Nature 634, 321–327 (2024)] forms a new state of the art for neutral atoms. The remaining infidelity is explained by an error model, consistent with our experimental results over a range of gate speeds, with varying contributions from different error sources. Further, we develop a fidelity response theory to efficiently predict infidelity from laser noise with nontrivial power spectral densities and derive scaling laws of infidelity with gate speed. Besides its capability of predicting gate fidelity, we also utilize the fidelity response theory to compare and optimize gate protocols, to learn laser frequency noise, and to study the noise response for quantum simulation tasks. Finally, we predict that a CZ gate fidelity of ≳ 0.999 is feasible with realistic experimental upgrades. Published by the American Physical Society 2025

Tsai, Richard Bing-Shiun (ORCID:0000000286758677)↗
NASA NTRS1988

An adaptive human response mechanism controlling the V/STOL aircraft. Appendix 3: The adaptive control model of a pilot in V/STOL aircraft control loops

Importance of the role of human operator in control systems has led to the particular area of manual control theory. Human describing functions were developed to model human behavior for manual control studies to take advantage of the successful and safe human operations. A single variable approach is presented that can be extended for multi-variable tasks where a low order human response model is used together with its rules, to adapt the model on-line, being capable of responding to the changes in the controlled element dynamics. Basic control theory concepts are used to combine the model, constrained with the physical observations, particularly, for the case of aircraft control. Pilot experience is represented as the initial model parameters. An adaptive root-locus method is presented as the adaptation law of the model where the closed loop bandwidth of the system is to be preserved in a stable manner with the adjustments of the pilot handling qualities which relate the latter to the closed loop bandwidth and damping of the closed loop pilot aircraft combination. A Kalman filter parameter estimator is presented as the controlled element identifier of the adaptive model where any discrepancies of the open loop dynamics from the presented one, are sensed to be compensated.

Kucuk, Senol↗
DOE OSTI2022

Measurement of the polarisation of single top quarks and antiquarks produced in the $t$-channel at $ \sqrt{s} $ = 13 TeV and bounds on the $tWb$ dipole operator from the ATLAS experiment

A simultaneous measurement of the three components of the top-quark and top-antiquark polarisation vectors in t-channel single-top-quark production is presented. This analysis is based on data from proton–proton collisions at a centre-of-mass energy of 13 TeV corresponding to an integrated luminosity of 139 fb –1 , collected with the ATLAS detector at the LHC. Selected events contain exactly one isolated electron or muon, large missing transverse momentum and exactly two jets, one being b-tagged. Stringent selection requirements are applied to discriminate t-channel single-top-quark events from the background contributions. The top-quark and top-antiquark polarisation vectors are measured from the distributions of the direction cosines of the charged-lepton momentum in the top-quark rest frame. The three components of the polarisation vector for the selected top-quark event sample are P x' = 0.01 ± 0.18, P y' = –0.029 ± 0.027, P z' = 0.91 ± 0.10 and for the top-antiquark event sample they are P x' = –0.02 ± 0.20, P y' = –0.007 ± 0.051, P z' = 0.79 ± 0.16. Normalised differential cross-sections corrected to a fiducial region at the stable-particle level are presented as a function of the charged-lepton angles for top-quark and top-antiquark events inclusively and separately. These measurements are in agreement with Standard Model predictions. The angular differential cross-sections are used to derive bounds on the complex Wilson coefficient of the dimension-six O tW operator in the framework of an effective field theory. The obtained bounds are C tW ϵ [–0.9, 1.4] and C itW ϵ [–0.8, 0.2], both at 95% confidence level.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗