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 1,333 records · Page 74
All sourcesNASA NTRSDOE OSTI
NASA NTRS2014

Fault Management Design Strategies

Development of dependable systems relies on the ability of the system to determine and respond to off-nominal system behavior. Specification and development of these fault management capabilities must be done in a structured and principled manner to improve our understanding of these systems, and to make significant gains in dependability (safety, reliability and availability). Prior work has described a fundamental taxonomy and theory of System Health Management (SHM), and of its operational subset, Fault Management (FM). This conceptual foundation provides a basis to develop framework to design and implement FM design strategies that protect mission objectives and account for system design limitations. Selection of an SHM strategy has implications for the functions required to perform the strategy, and it places constraints on the set of possible design solutions. The framework developed in this paper provides a rigorous and principled approach to classifying SHM strategies, as well as methods for determination and implementation of SHM strategies. An illustrative example is used to describe the application of the framework and the resulting benefits to system and FM design and dependability.

systems engineering↗
DOE OSTI2024

Symmetry-Based Structured Matrices for Efficient Approximately Equivariant Networks

There has been much recent interest in designing symmetry-aware neural networks (NNs) exhibiting relaxed equivariance. Such NNs aim to interpolate between being exactly equivariant and being fully flexible, affording consistent performance benefits. In a separate line of work, certain structured parameter matrices -- those with displacement structure, characterized by low displacement rank (LDR) -- have been used to design small-footprint NNs. Displacement structure enables fast function and gradient evaluation, but permits accurate approximations via compression primarily to classical convolutional neural networks (CNNs). In this work, we propose a general framework -- based on a novel construction of symmetry-based structured matrices -- to build approximately equivariant NNs with significantly reduced parameter counts. Our framework integrates the two aforementioned lines of work via the use of so-called Group Matrices (GMs), a forgotten precursor to the modern notion of regular representations of finite groups. GMs allow the design of structured matrices -- resembling LDR matrices -- which generalize the linear operations of a classical CNN from cyclic groups to general finite groups and their homogeneous spaces. We show that GMs can be employed to extend all the elementary operations of CNNs to general discrete groups. Further, the theory of structured matrices based on GMs provides a generalization of LDR theory focussed on matrices with cyclic structure, providing a tool for implementing approximate equivariance for discrete groups. We test GM-based architectures on a variety of tasks in the presence of relaxed symmetry. We report that our framework consistently performs competitively compared to approximately equivariant NNs, and other structured matrix-based compression frameworks, sometimes with a one or two orders of magnitude lower parameter count.

Samudre, Ashwin↗
DOE OSTI2024

Gravitational form factors of glueballs in Yang-Mills theory

This work presents preliminary results of the first determination of the energy-momentum tensor form factors of the scalar glueball, referred to as gravitational form factors (GFFs). The calculation has been carried out in lattice Yang-Mills theory at a single lattice spacing. Using variationally optimized operators, the matrix elements are extracted from ratios of three-point functions to two-point functions. The glueball GFFs and their kinematic dependence are compared to those of other hadrons from previous calculations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2016

Density functional theory investigation of the electronic structure and defect chemistry of Sr1-xKxFeO3

Solid oxide fuel cells (SOFCs) efficiently generate electricity, but high operating temperatures (T op > 800 °C) limit their utility. Reducing T op requires mixed ion–electron conducting (MIEC) cathode materials. Density functional theory is used here to investigate the role of potassium substitutions in the MIEC material Sr1-x K x FeO3 (SKFO). We predict that such substitutions are endothermic. SrFeO3 and SKFO have nearly identical metallic electronic structures. Oxygen vacancy formation energies decrease by ~0.2 eV when x K increases from 0 to 0.0625. SKFO is a promising SOFC MIEC cathode material; however, further experimental investigations must assess its long-term stability at the desired operating temperatures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1972

Respiratory protective device design using control system techniques

The feasibility of a control system analysis approach to provide a design base for respiratory protective devices is considered. A system design approach requires that all functions and components of the system be mathematically identified in a model of the RPD. The mathematical notations describe the operation of the components as closely as possible. The individual component mathematical descriptions are then combined to describe the complete RPD. Finally, analysis of the mathematical notation by control system theory is used to derive compensating component values that force the system to operate in a stable and predictable manner.

Burgess, W. A.↗
NASA NTRS1974

Power conversion in electrical networks

Aspects of dc to dc conversion were studied in terms of a class of switching voltage regulators from a stability viewpoint. Background concepts of nonlinear system theory were considered, including the problem of obtaining suitable realizations for a class of positive operators. It is shown that the state evolution equations for a power conversion network are in general of bilinear form, and that the theory of lie groups and lie algebras is useful in analyzing such systems. The feedback stabilization of a class of bilinear systems whose state space is a manifold is also discussed.

Wood, J. R.↗
NASA NTRS1984

Unsteady aerodynamics in time and frequency domains for finite time arbitrary motion of rotary wings in hover and forward flight

Several incompressible finite-time arbitrary-motion airfoil theories suitable for coupled flap-lag-torsional aeroelastic analysis of helicopter rotors in hover and forward flight are derived. These theories include generalized Greenberg's theory, generalized Loewy's theory, and a staggered cascade theory. The generalized Greenberg's and staggered cascade theories were derived directly in Laplace domain considering the finite length of the wake and using operational methods. The load expressions are presented in Laplace, frequency, and time domains. Approximate time domain loads for the various generalized theories, discussed in the paper, are obtained by developing finite state models using the Pade approximant of the appropriate lift deficiency functions. Three different methods for constructing Pade approximants of the lift deficiency functions were considered and the more flexible one was used. Pade approximants of Loewy's lift deficiency function, for various wake spacing and radial location parameters of a helicopter typical rotor blade section, are presented.

Dinyavari, M. A. H.↗
DOE OSTI2022

Improved Architectures and Training Algorithms for Deep Operator Networks

Operator learning techniques have recently emerged as a powerful tool for learning maps between infinite-dimensional Banach spaces. Trained under appropriate constraints, they can also be effective in learning the solution operator of partial differential equations (PDEs) in an entirely self-supervised manner. In this work we analyze the training dynamics of deep operator networks (DeepONets) through the lens of Neural Tangent Kernel theory, and reveal a bias that favors the approximation of functions with larger magnitudes. To correct this bias we propose to adaptively re-weight the importance of each training example, and demonstrate how this procedure can effectively balance the magnitude of back-propagated gradients during training via gradient descent. We also propose a novel network architecture that is more resilient to vanishing gradient pathologies. Taken together, our developments provide new insights into the training of DeepONets and consistently improve their predictive accuracy by a factor of 10-50x, demonstrated in the challenging setting of learning PDE solution operators in the absence of paired input-output observations.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1991

Task reports on developing techniques for scattering by 3D composite structures and to generate new solutions in diffraction theory using higher order boundary conditions

There are two tasks described in this report. First, an extension of a two dimensional formulation is presented for a three dimensional body of revolution. A Fourier series expansion of the vector electric and magnetic fields is employed to reduce the dimensionality of the system, and an exact boundary condition is employed to terminate the mesh. The mesh termination boundary is chosen such that it leads to convolutional boundary operators for low O(n) memory demand. Second, rigorous uniform geometrical theory of diffraction (UTD) diffraction coefficients are presented for a coated convex cylinder simulated with generalized impedance boundary conditions. Ray solutions are obtained which remain valid in the transition region and reduce uniformly those in the deep lit and shadow regions. A uniform asymptotic solution is also presented for observations in the close vicinity of the cylinder.

Volakis, John L.↗
DOE OSTI2018

Quantum Computation and Visualization of Hamiltonians Using Discrete Quantum Mechanics and IBM QISKit

Quantum computers have the potential to transform the ways in which we tackle some important problems. The efforts by companies like Google, IBM and Microsoft to construct quantum computers have been making headlines for years. Equally important is the challenge of translating problems into a state that can be fed to these machines. Because quantum computers are in essence controllable quantum systems, the problems that most naturally map to them are those of quantum mechanics. Quantum chemistry has seen particular success in the form of the variational quantum eigensolver (VQE) algorithm, which is used to determine the ground state energy of molecular systems. The goal of our work has been to use the matrix formulation of quantum mechanics to translate other systems so that they can be run through this same algorithm. We describe two ways of accomplishing this using a position basis approach and a Gaussian basis approach. We use this translation to compute finite temperature quantities such as the average energy as a function of temperature. We do this by constructing a 0+1- dimensional thermal field theory, constructing a thermal double of the system and using tensor products to construct operators in the system coupled to a heat bath. We also discuss how to include a chemical potential in the quantum computations. We then connect the 0+1 formalism to gauge theory by using an effective matrix model description used in nuclear theory. We study effective potentials for components of the gauge field and use the VQE algorithm to calculate the ground state energies. We also visualize the wave functions from the eigensolver and make comparisons to theoretical results obtained with continuous operators.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Efficiency at Maximum Power of Dissipative Thermoelectric Generators: A Finite-time Thermodynamic Analysis

In this paper we analyze the thermodynamic efficiency expected for a fully dissipative thermoelectric generator (TEG) operating under stationary conditions at a finite rate. Although a finite-time thermodynamic analysis of TEGs has been aimed at since long time, no complete theory is available yet. The state of the art of theory is reviewed, and a simple expression for the maximum achievable efficiency of TEGs operating under fully irreversible conditions is obtained. This also sets a reference efficiency for forthcoming studies of nonstationary operation of TEGs.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Theory of extreme correlations using canonical Fermions and path integrals

The t–J model is studied using a novel and rigorous mapping of the Gutzwiller projected electrons, in terms of canonical electrons. The mapping has considerable similarity to the Dyson–Maleev transformation relating spin operators to canonical Bosons. This representation gives rise to a non Hermitian quantum theory, characterized by minimal redundancies. A path integral representation of the canonical theory is given. Using it, the salient results of the extremely correlated Fermi liquid (ECFL) theory, including the previously found Schwinger equations of motion, are easily rederived. Further, a transparent physical interpretation of the previously introduced auxiliary Greens function and the ‘caparison factor’, is obtained. The low energy electron spectral function in this theory, with a strong intrinsic asymmetry, is summarized in terms of a few expansion coefficients. These include an important emergent energy scale Δ{sub 0} that shrinks to zero on approaching the insulating state, thereby making it difficult to access the underlying very low energy Fermi liquid behavior. The scaled low frequency ECFL spectral function, related simply to the Fano line shape, has a peculiar energy dependence unlike that of a Lorentzian. The resulting energy dispersion obtained by maximization is a hybrid of a massive and a massless Dirac spectrum E{sub Q}{sup ∗}∼γQ−√(Γ{sub 0}{sup 2}+Q{sup 2}), where the vanishing of Q, a momentum type variable, locates the kink minimum. Therefore the quasiparticle velocity interpolates between (γ∓1) over a width Γ{sub 0} on the two sides of Q=0, implying a kink there that strongly resembles a prominent low energy feature seen in angle resolved photoemission spectra (ARPES) of cuprate materials. We also propose novel ways of analyzing the ARPES data to isolate the predicted asymmetry between particle and hole excitations. -- Highlights: •Spectral function of the Extremely Correlated Fermi Liquid theory at low energy. •Electronic origin of low energy kinks in energy dispersion. •Non Hermitian representation of Gutzwiller projected electrons. •Analogy with Dyson–Maleev representation of spins. •Path integral formulation of extremely correlated electrons.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Conformal manifolds with boundaries or defects

We discuss conformal manifolds for conformal field theories with boundaries or defects. Using conformal perturbation theory we derive constraints on coefficients appearing in the boundary operator product expansion and three-point functions that need to be satisfied for the existence of marginal couplings. We present several explicit examples where we confirm that β-functions vanish using a position space regularization, differential regularization. Where possible, we confirm that our β-function results agree with the existing literature.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Fast Particle-Wave Interactions and Alfvén Eigenmodes in JET Tokamak Plasmas

This document serves as the closeout report of DOE Grant Award No. DE-FG02-99ER54563 with project period 1 April 2015 through 31 March 2020. The project comprised the international collaboration between MIT and EU scientists on the JET facility to improve our understanding of the physics of energetic particle-wave interactions by measuring the damping rates of stable Alfvén Eigenmodes (AEs) and unstable energetic particle driven modes. More specifically, this project involved the continued participation of MIT, the Culham Centre for Fusion Energy, the Swiss Plasma Center, and theorists from various European laboratories and from UC Irvine. Past contributions from the University of São Paulo are gratefully acknowledged. The Alfvén Eigenmode Active Diagnostic (AEAD) on JET discharges was successfully upgraded in this period and has extracted physically useful information, in primarily deuterium plasma discharges. It is expected that such experiments would be continued during the DT campaign in CY 2021 to assess the damping rates of similar modes in the presence of alpha particles, a product of fusing burning plasma. Only JET would carry out such experiments in the near term in the world. It is important to note that this collaboration was continued under DOE Grant Award No. DE-SC0014264 from 1 April 2020 through the present. In this grant period, the AEAD was upgraded with a set of individual amplifiers for each of a set of six antennas in two toroidally opposite locations. These new amplifiers allowed targeted selection of the antennas’ toroidal spectrum for AEs of interest with toroidal mode number | n | ≤ 20. The resonant detection and measurement of the damping rates of AEs was obtained from magnetic probes that could be compared with theory and simulations. This is a key topic of investigation for ITER and all other next-step fusion experiments, where such modes will interact with energetic particles produced by fusion reactions (alpha particles), Neutral Beam Injection (NBI) and Ion Cyclotron Resonance Heating (ICRH). The majority of the observations during this period were of Toroidal Alfvén Eigenmodes (TAEs) as these are most commonly observed on JET; a number of measurements were made during dedicated TAE experiments. However, a new set of lower frequency band filters were procured with the goal of studying Geodesic Acoustic Modes (GAMs), Beta (Acoustic) AEs (BAE/BAAEs), and Reverse Shear AEs (RSAEs), also predicted by theory. Commissioning and optimizations were successfully completed in this period, and the diagnostic has been in operation during the more recent JET campaigns. Initial results have been obtained in dedicated TAE experiments and successfully compared to drift-kinetic theory. A wide range of theoretical studies have been undertaken in support of the upcoming JET campaigns experiments. To supplement the ongoing use of ideal MHD codes, such as MISHKA during the studies of TAEs, gyrokinetic simulations of low frequency AEs were performed in collaboration with UC Irvine. The Gyrokinetic Toroidal Code (GTC) was used to determine the structure, frequencies and stability of AEs in JET plasmas. Thus, a solid scientific foundation has been laid for future DT campaigns in JET in the 2021 operation period when the damping rates of relevant modes in the presence of alpha particles could be assessed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Quantum Monte Carlo calculations of electromagnetic moments and transitions in A≤9 nuclei with meson-exchange currents derived from chiral effective field theory

Here, quantum Monte Carlo calculations of electromagnetic moments and transitions are reported for A ≤ 9 nuclei. The realistic Argonne v 18 two-nucleon and Illinois-7 three-nucleon potentials are used to generate the nuclear wave functions. Contributions of two-body meson-exchange current (MEC) operators are included for magnetic moments and M1 transitions. The MEC operators have been derived in both a standard nuclear physics approach and a chiral effective field theory formulation with pions and nucleons including up to one-loop corrections. The two-body MEC contributions provide significant corrections and lead to very good agreement with experiment. Their effect is particularly pronounced in the A=9, T=3/2 systems, in which they provide up to ~20% (~40%) of the total predicted value for the 9 Li( 9 C) magnetic moment.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Fermionic mean-field theory as a tool for studying spin Hamiltonians

The Jordan–Wigner transformation permits one to convert spin 1/2 operators into spinless fermion ones, or vice versa. In some cases, it transforms an interacting spin Hamiltonian into a noninteracting fermionic one, which is exactly solved at the mean-field level. Even when the resulting fermionic Hamiltonian is interacting, its mean-field solution can provide surprisingly accurate energies and correlation functions. Furthermore, Jordan–Wigner is, however, only one possible means of interconverting spin and fermionic degrees of freedom. Here, we apply several such techniques to the XXZ and J 1 –J 2 Heisenberg models, as well as to the pairing or reduced Bardeen–Cooper–Schrieffer Hamiltonian, with the aim of discovering which of these mappings is most useful in applying fermionic mean-field theory to the study of spin Hamiltonians.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗