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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1999

Unsteady Aerodynamics - Subsonic Compressible Inviscid Case

This paper presents a new analytical treatment of Unsteady Aerodynamics - the linear theory covering the subsonic compressible (inviscid) case - drawing on some recent work in Operator Theory and Functional Analysis. The specific new results are: (a) An existence and uniqueness proof for the Laplace transform version of the Possio integral equation as well as a new closed form solution approximation thereof. (b) A new representation for the time-domain solution of the subsonic compressible aerodynamic equations emphasizing in particular the role of the initial conditions.

Balakrishnan, A. V.↗
NASA NTRS1973

Interior radiances in optically deep absorbing media. I - Exact solutions for one-dimensional model.

An exact analytic solution to the one-dimensional scattering problem with arbitrary single scattering albedo and arbitrary surface albedo is presented. Expressions are given for the emergent flux from a homogeneous layer, the internal flux within the layer, and the radiative heating. A comparison of these results with the values calculated from the matrix operator theory indicates an exceedingly high accuracy. A detailed study is made of the error in the matrix operator results and its dependence on the accuracy of the starting value.

Kattawar, G. W.↗
DOE OSTI2026

Compositional Reasoning for Hierarchical State Machines

Harel statecharts and its derivatives are popular graphical languages for specifying discrete control systems via hierarchical state machines. Separately, there has been a long line of work on specifying concurrent systems with process calculi which come equipped with an algebraic theory, the ability reason compositionally about various temporal properties, and strong type systems. While these two approaches to modeling systems are tantalizingly similar, the integrated reasoning principles that exist for process calculi have not been demonstrated in hierarchical state machines. A key issue is that operational theories for process calculi do not behave like control systems, and thus, there is virtually no tool support for modeling control systems with such languages. For a control system designer, bringing the integrated, more scalable reasoning from the process calculi to state-machine languages would enable the specification of more complex systems and a more modular systems development process. Our insight is that we can recover many important results from the process calculi in hierarchical state machines with local scope. We employ a structural operational semantics, which is ubiquitous in process and 𝜆-calculi but uncommon in hierarchical statemachine formalizations, to enable inductive reasoning about behavior. Taking inspiration from the structure of process calculi metatheories, we define a calculus of refinement and equivalence that we prove sound with respect to local notion of (bi)simulation. Furthermore, we prove that the calculus preserves the behavioral properties of reactivity, observational determinism, traces, and linear temporal properties. Our results are mechanized in the Rocq proof assistant.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1975

Generalized photoclinometry for Mariner 9

A theory is developed for the photoclinometric determination of topography when the photometric function of a planetary surface is not restricted beyond the expectation that it is a function of phase angle, angle of incidence, and angle of emergence. Several versions of such an operational theory are presented together with several approaches to the numerical analysis. Reasons for the differences in numerical techniques are discussed. A preliminary result is considered which has been produced for an early Mariner 9 frame wherein the dust-laden atmosphere seems to exhibit standing-wave patterns. It is shown that if the assumption of homologous departures from plane-parallel atmospheric configuration is valid, the photoclinometry implies that laminar flow lines in the optically observable dust layer undergo a near-sinusoidal rise and fall of about 40 to 50 meters.

Wildey, R. L.↗
DOE OSTI2022

Learning Distributed Geometric Koopman Operator for Sparse Networked Dynamical Systems

Koopman operator theory provides an alternative to study nonlinear networked dynamical systems by mapping the state space to an abstract higher dimensional space where the system evolution is linear. Recent works show the application of graph neural networks (GNNs) to learn state to object-centric embeddings and achieve centralized block-wise computation of Koopman operator (KO) under additional assumptions on the underlying agents properties and constraints on the KO structure. However, the computational complexity of learning the Koopman increases exponentially for networked systems where the number of possible system states grows in a combinatorial fashion with the number of nodes. The learning challenge is further amplified for sparse networks by two factors: 1) sample sparsity for learning the Koopman operator in the non-linear space, and 2) the divergence in the dynamics of individual nodes or from one subgraph to another. Our work aims to address these challenge by formulating the representation learning of networked dynamical systems into a multi-agent paradigm and learning the Koopman operator in a distributive manner. The computational as well as performance advantages of distributed Koopman is predominant for sparse networks whereas for fully connected networks, it is shown to coincide with the centralized one. The empirical study on rope system, network of oscillators and a synthetic power system show comparable and superior performance along with computational benefits with the state-of-the-art methods.

Mukherjee, Sayak↗
DOE OSTI2023

Magneto-optical measurement of magnetic field and electrical current on a short pulse high energy pulsed power accelerator

We describe a direct magneto-optical approach to measuring the magnetic field driven by a narrow pulse width (<10 ns), 20 kA electrical current flow in the transmission line of a high energy pulsed power accelerator. The magnetic field and electrical current are among the most important operating parameters in a pulsed power accelerator and are critical to understanding the properties of the radiation output. However, accurately measuring these fields and electrical currents using conventional pulsed power diagnostics is difficult due to the strength of ionizing radiation and electromagnetic interference. Our approach uses a fiber coupled laser beam with a rare earth element sensing crystal sensor that is highly resistant to electromagnetic interference and does not require external calibration. Here, we focus on device theory, operating parameters, results from an experiment on a high energy pulsed power accelerator, and comparison to a conventional electrical current shunt sensor.

42 ENGINEERING↗
DOE OSTI2024

Predicting Critical Transitions in Multiscale Data

Predicting the dynamics of complex nonlinear systems remains a challenging problem both in dynamical systems theory as well as real world science and engineering applications. Data-driven methods utilizing the latest advances in machine learning (ML) provide a promising new paradigm for this task. Our work centered on Reservoir Computing (RC), which has shown itself to be capable of skillfully predicting chaotic dynamics in multiscale systems. In the first part of the work, the focus is on how to improve predictions of critical transitions in a class of slow-fast metastable systems in which the equations are known. An additional goal was to determine whether a relationship exists between RC and Koopman operator theory, to improve the efficiency and broaden the applicability of the approach. In the second part of this work, a variation on the RC model known as Reconstructive Reservoir Computing (RRC) is applied to real-world data to identify anomalies.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Absolute magneto-optical measurement of magnetic field on a long pulse high electrical current driven solenoid

We describe a direct absolute magneto-optical approach to measuring the magnetic field driven by long pulse width (>5 ms) and high electrical current (∼kA) in a solenoidal coil. The magnetic field and electrical current are among the most important operating parameters in lightning research and electrical power distribution and are essential to understanding the properties of the radiation output in pulsed energy accelerators as well as other research platforms. However, accurately measuring these magnetic fields and electrical currents using conventional electrical diagnostics is difficult due to the strength of ionizing radiation and electromagnetic interference. Our approach uses a fiber coupled laser beam with a rare earth element material sensing crystal that is highly resistant to electromagnetic interference, allows for absolute measurement, and does not require an external calibration. Here, we focus on device theory, operating parameters, magneto-optical results from an experiment on a high current solenoid, and comparison with a calculation of the magnetic field and reference electrical current flowing downstream of the solenoid.

Owens, Israel [Sandia National Laboratories (SNL-N↗
DOE OSTI2022

Deep transfer operator learning for partial differential equations under conditional shift

Transfer learning enables the transfer of knowledge gained while learning to perform one task (source) to a related but different task (target), hence addressing the expense of data acquisition and labelling, potential computational power limitations and dataset distribution mismatches. Here, we propose a new transfer learning framework for task-specific learning (functional regression in partial differential equations) under conditional shift based on the deep operator network (DeepONet). Task-specific operator learning is accomplished by fine-tuning task-specific layers of the target DeepONet using a hybrid loss function that allows for the matching of individual target samples while also preserving the global properties of the conditional distribution of the target data. Inspired by conditional embedding operator theory, we minimize the statistical distance between labelled target data and the surrogate prediction on unlabelled target data by embedding conditional distributions onto a reproducing kernel Hilbert space. We demonstrate the advantages of our approach for various transfer learning scenarios involving nonlinear partial differential equations under diverse conditions due to shifts in the geometric domain and model dynamics. Our transfer learning framework enables fast and efficient learning of heterogeneous tasks despite considerable differences between the source and target domains.

42 ENGINEERING↗
DOE OSTI2024

Renormalization of beta decay at three loops and beyond

The anomalous dimension for heavy-heavy-light effective theory operators describing nuclear beta decay is computed through three-loop order in the static limit. The result at order Z 2 α 3 corrects a previous result in the literature. An all-orders symmetry is shown to relate the anomalous dimensions at leading and subleading powers of Z at a given order of α . The first unknown coefficient for the anomalous dimension now appears at O ( Z 2 α 4 ) . Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

e + e – → ZH process in the SMEFT beyond leading order

We systematically study potential effects of Beyond the Standard Model physics in the e + e – → ZH process. To this end, we include all relevant dimension-6 Standard Model Effective Field Theory operators and work to next-to-leading order (NLO) accuracy in the electroweak coupling. We consider both polarized and unpolarized electron and positron beams and present results for $\sqrt {s}$ = 240, 365 and 500 GeV, emphasizing contributions where the NLO predictions differ significantly from the leading order results. At NLO, a sensitivity arises to operators that do not contribute at tree level, such as the Higgs tri-linear coupling, CP-violating operators, and dimension-6 operators involving the top quark, among many others. We compare the prospects of future e + e – colliders to explore these new physics effects with existing measurements from the LHC, electron EDMs (for CP violating operators), and Z pole measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Vector boson scattering and anomalous quartic couplings in final states with ℓνqq or ℓℓqq plus jets using proton-proton collisions at $\sqrt{s}=13$ TeV

A measurement is presented of the electroweak vector boson scattering production of ZV (V = W, Z) boson pairs associated with two jets in proton-proton collisions at a center-of-mass energy of 13 TeV. The data, corresponding to an integrated luminosity of 138 fb −1 , were collected at the CERN LHC with the CMS detector during the 2016–2018 data-taking period. The analysis targets final states with a pair of isolated electrons or muons from Z boson decays and three or four jets, depending on the momentum of the vector boson that decays into quarks. Signal strength is measured for events characterized by a large invariant mass of two forward jets with a wide pseudorapidity gap between them. The electroweak production of ZV in association with two jets is measured with an observed (expected) significance of 1.3 (1.8) standard deviations. A combination of the analyses of ZV channel and the previously published WV channel in the lepton plus jets final state places constraints on effective field theory parameters that describe anomalous electroweak production of WW, WZ, and ZZ boson pairs in association with two jets. Several world best limits are set on anomalous quartic gauge couplings in terms of dimension-8 standard model effective field theory operators.

Hadron-Hadron Scattering↗
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 OSTI2024

Interpretations of the ATLAS measurements of Higgs boson production and decay rates and differential cross-sections in pp collisions at $\sqrt{s}$ = 13 TeV

Measurements of the Higgs boson production times decay rates and differential cross-sections have recently been performed by the ATLAS experiment in several decay channels using up to 139 fb -1 of proton-proton collision data at $\sqrt{s}$ = 13 TeV recorded at the Large Hadron Collider. This paper presents multiple interpretations of these Higgs boson measurements. Measurements of production-mode cross-sections, simplified template cross-sections and fiducial differential cross-sections in different decay channels are reparameterised in terms of the impact of Standard Model effective field theory operators, and constraints are reported on the corresponding Wilson coefficients. Production and decay rate measurements are interpreted in UV-complete extensions of the Standard Model, namely the two-Higgs-doublet model (2HDM) near the alignment limit and the Minimal Supersymmetric Standard Model (MSSM) for various MSSM benchmark scenarios. The constraints on the 2HDM parameters (cos(β - α), tanβ) and the MSSM parameters (m A , tanβ) are complementary to those obtained from direct searches for additional Higgs bosons.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Measurement of the electroweak production of W$\gamma$ in association with two jets in proton-proton collisions at $\sqrt{s}$ = 13 TeV

A measurement is presented for the electroweak production of a W boson, a photon ($\gamma$), and two jets (j) in proton-proton collisions. The leptonic decay of the W boson is selected by requiring one identified electron or muon and large missing transverse momentum. The two jets are required to have large invariant dijet mass and large separation in pseudorapidity. The measurement is performed with the data collected by the CMS detector at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb –1 . The cross section for the electroweak W$\gamma$jj production is 23.5$^{+4.9}_{–4.7}$ fb , whereas the total cross section for W$\gamma$jj production is 113 ± 13 fb . Differential cross sections are also measured with the distributions unfolded to the particle level. All results are in agreement with the standard model expectations. Constraints are placed on anomalous quartic gauge couplings (aQGCs) in terms of dimension-8 effective field theory operators. These are the most stringent limits to date on the aQGCs parameters $f$ M,2–5 /Λ 4 and $f$ T,6–7 /Λ 4 .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Search for the Z Boson Decay to τ τ μ μ in Proton-Proton Collisions at s = 13 TeV

The first search for the Z boson decay to τ τ μ μ at the CERN LHC is presented, based on data collected by the CMS experiment at the LHC in proton-proton collisions at a center-of-mass energy of 13 TeV and corresponding to an integrated luminosity of 138 fb − 1 . The data are compatible with the predicted background. For the first time, an upper limit at the 95% confidence level of 6.9 times the standard model expectation is placed on the ratio of the Z → τ τ μ μ to Z → 4 μ branching fractions. Limits are also placed on the six flavor-conserving four-lepton effective-field-theory operators involving two muons and two tau leptons, for the first time testing all such operators. © 2024 CERN, for the CMS Collaboration 2024 CERN

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗