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 1,639 records · Page 91
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Broadband integrated polarization splitter and rotator using subwavelength grating claddings

We present a broadband integrated photonic polarization splitter and rotator (PSR) using adiabatically tapered coupled waveguides with subwavelength grating (SWG) claddings. The PSR adiabatically rotates and splits the fundamental transverse-magnetic (TM 0 ) input to the fundamental transverse-electric (TE 0 ) mode in the coupler waveguide, while passing the TE 0 input through the same waveguide. The SWGs work as an anisotropic metamaterial and facilitate modal conversions, making the PSR efficient and broadband. We rigorously present our design approaches in each section and show the SWG effect by comparing with and without the SWG claddings. The coupling coefficients in each segment explicitly show a stronger coupling effect when the SWGs are included, confirmed by the coupled-mode theory simulations. The full numerical simulation shows that the SWG-PSR operates at 1500–1750 nm (≈250 nm) wavelengths with an extinction ratio larger than 20 dB, confirmed by the experiment for the 1490–1590 nm range. The insertion losses are below 1.3 dB. Since our PSR is designed based on adiabatical mode evolution, the proposed PSR is expected to be tolerant to fabrication variations and should be broadly applicable to polarization management in photonic integrated circuits.

47 OTHER INSTRUMENTATION↗
DOE OSTI2016

Performance Improvements for Coarse Mesh Finite Difference Acceleration L3:RTM.PRT.P13.02

The development of VERA-CS in recent years has focused on developing the capability to simulate multiple cycles of operating commercial nuclear power plants. Now that these capabilities have advanced to the point where it is being deployed to users, the focus is on improving the computational performance of various components in VERA-CS. In this work, the focus is on the Coarse Mesh Finite Difference (CMFD) solution in MPACT. CMFD serves multiple purposes in the 2D/1D solution methodology. First, it is a natural mechanism to tie together the radial MOC transport and the axial SP3 solution. Because the CMFD system solves the multigroup three-dimensional core in one system, it pulls together the global response of the system. In addition, the CMFD solution provides a framework to accelerate the convergence of the eigenvalue problem.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2021

A Convex Data-Driven Approach for Nonlinear Control Synthesis

We consider a class of nonlinear control synthesis problems where the underlying mathematical models are not explicitly known. We propose a data-driven approach to stabilize the systems when only sample trajectories of the dynamics are accessible. Our method is built on the density-function-based stability certificate that is the dual to the Lyapunov function for dynamic systems. Unlike Lyapunov-based methods, density functions lead to a convex formulation for a joint search of the control strategy and the stability certificate. This type of convex problem can be solved efficiently using the machinery of the sum of squares (SOS). For the data-driven part, we exploit the fact that the duality results in the stability theory can be understood through the lens of Perron–Frobenius and Koopman operators. This allows us to use data-driven methods to approximate these operators and combine them with the SOS techniques to establish a convex formulation of control synthesis. The efficacy of the proposed approach is demonstrated through several examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Neural Scaling Laws of Deep ReLU and Deep Operator Network: A Theoretical Study

Neural scaling laws play a pivotal role in the performance of deep neural networks and have been observed in a wide range of tasks. However, a complete theoretical framework for understanding these scaling laws remains underdeveloped. In this paper, we explore the neural scaling laws for deep operator networks, which involve learning mappings between function spaces, with a focus on the Chen and Chen style architecture. These approaches, which include the popular Deep Operator Network (DeepONet), approximate the output functions using a linear combination of learnable basis functions and coefficients that depend on the input functions. We establish a theoretical framework to quantify the neural scaling laws by analyzing its approximation and generalization errors. We articulate the relationship between the approximation and generalization errors of deep operator networks and key factors such as network model size and training data size. Moreover, we address cases where input functions exhibit low-dimensional structures, allowing us to derive tighter error bounds. These results also hold for deep ReLU networks and other similar structures. Our results offer a partial explanation of the neural scaling laws in operator learning and provide a theoretical foundation for their applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Polymer Modeling Library

SAND2022-12598 O The Polymer Modeling Library is a software package for modeling polymer chains, networks, and materials by applying existing theories and methods. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Buche, Michael [Sandia National Lab. (SNL-CA), Liv↗
NASA NTRS1962

Empire. a study of early manned interplanetary missions final report, may 26 - nov. 25, 1962

This report summarizes the investigations and results of the EMPIRE Study Program undertaken by Aeronutronic Division of Ford Motor Company for the Future Projects Office, Marshall Space Flight Center, under Contract NAS8-5025. The dual planet flyby missions of the Crocco and Symmetric trajectory classes are discussed. The Crocco mission with an August 1971 launch window requires an interplanetary injection velocity increment of i0.i km/sec, has a return velocity of 13.5 km/sec, and takes approximately 400 days. The Symmetric mission with a July 1970 launch window has an injection velocity increment of 5.3 km/sec, a return velocity of 15.8 km/sec, and takes approximately 630 days. Additional results of the trajectory studies and abort trajectories are reported. The guidance and navigation subsystem, midcourse corrections, and planetary approach corrections are discussed. A detailed analysis of the reentry phase of EMPIRE includes consideration of an Apollo-type, a Drag Brake, and a lifting-type reentry vehicle to return the six-man crew at mission completion or in an aborted condition. The High L/D reentry vehicle is used in the missions considered. The various technological areas required for design criteria are developed and several spacecraft designs are considered. The all chemical propulsion Crocco system is discarded due to weight, complexity, and cost. The nuclear injected Crocco is treated in a similar manner. The lower energy injection for the Symmetric Mission leads to the feasibility of a nuclear injected vehicle with an Earth orbit weight of about 180,000 kilograms (400,000 pounds) before interplanetary transit. In addition, two chemical symmetric vehicles are treated. Conservative radiation exposures are derived, for the 630 day mission, of less than 200 REM and a polyethelene radiation shelter is designed. Scientific aspects of the missions are discussed. Mission Success Probabilities are presented for the various missions considered and for Saturn C-5, Nova, and Super-Nova Earth launch vehicles in light of possible development. The need for acceleration of nuclear rocket engine developments and auxiliary power developments is indicated. Definition of a larger nuclear engine of the order of 200,000 pounds thrust and about 800 seconds burning time or 50,000 pound thrust and 3600 seconds burning time is indicated for the Symmetric Mission in 1970 (energy requirements are higher in 1972 and for later launch due to the less favorable position of Mars)_ Immediate development of this advanced nuclear propulsion capability is recommended. A Development Plan and Funding Schedule is given for the 1970 launch window pinpointing the critical development areas and indicating a total program cost of $12.6 billion independent of other programmed R&D costs. In conclusion, technological feasibility for an early manned dual planet Mars-Venus flyby is believed to be demonstrated in this study. Several areas of accelerated development and experimental confirmation of theory are pinpointed. The necessary funding and development of Nova or orbital operations capability with Saturn C-5's is required. The 1970 launch window appears to offer the least expensive Symmetric Mission for several years into the 1980's.

F. P. Dixon↗
NASA NTRS1972

Two phase pumping of cryogenic propellants

Two-phase cryogenic propellant pumping techniques developed during the past 5 years are discussed. During this period the theory of two-phase pumping of hydrogen was developed into an operational technique that can result in significant benefits to space vehicle propulsion systems. Using two-phase pumping techniques, zero LH2 tank net positive suction head (NPSH) was demonstrated on turbopump and rocket engine firings, and limited experimental results show that two-phase pumping of liquid oxygen is feasible. Design techniques were developed for improving the two-phase pumping capability of inducers.

H P Stinson↗
NASA NTRS1971

Heat pipe technology: A bibliography with abstracts

The annual supplement on heat pipe technology for 1971 is presented. The document contains 101 references with abstracts and 47 patents. The subjects discussed are: (1) heat pipe applications, (2) heat pipe theory, (3) design, development, and fabrication of heat pipes, (4) testing and operation, (5) subject and author index, and (6) heat pipe related patents.

Source record↗
NASA NTRS1976

Stimulation of a turbofan engine for evaluation of multivariable optimal control concepts

The development of control systems for jet engines requires a real-time computer simulation. The simulation provides an effective tool for evaluating control concepts and problem areas prior to actual engine testing. The development and use of a real-time simulation of the Pratt and Whitney F100-PW100 turbofan engine is described. The simulation was used in a multi-variable optimal controls research program using linear quadratic regulator theory. The simulation is used to generate linear engine models at selected operating points and evaluate the control algorithm. To reduce the complexity of the design, it is desirable to reduce the order of the linear model. A technique to reduce the order of the model; is discussed. Selected results between high and low order models are compared. The LQR control algorithms can be programmed on digital computer. This computer will control the engine simulation over the desired flight envelope.

Seldner, K.↗
NASA NTRS1976

Simulation of a turbofan engine for evaluation of multivariable optimal control concepts

This paper describes the development and use of a real-time simulation of the F100-PW-100 turbofan engine. The simulation is being used in a multi-variable optimal controls research program using linear quadratic regulatory theory. The simulation is used to generate linear engine models at selected operating points and evaluate the control algorithm. The paper discusses a technique to reduce the order of the model and compares selected results between high and low order models.

Seldner, K.↗
NASA NTRS1987

Approximation of discrete-time LQG compensators for distributed systems with boundary input and unbounded measurement

The approximation of optimal discrete-time linear quadratic Gaussian (LQG) compensators for distributed parameter control systems with boundary input and unbounded measurement is considered. The approach applies to a wide range of problems that can be formulated in a state space on which both the discrete-time input and output operators are continuous. Approximating compensators are obtained via application of the LQG theory and associated approximation results for infinite dimensional discrete-time control systems with bounded input and output. Numerical results for spline and modal based approximation schemes used to compute optimal compensators for a one dimensional heat equation with either Neumann or Dirichlet boundary control and pointwise measurement of temperature are presented and discussed.

Gibson, J. S.↗
NASA NTRS1987

Near fields in the vicinity of pulsed electron beams in space

Most measurements of the radio frequency emissions from artificial electron beams in space have been made in close proximity to the beam. This paper presents theory and results for the near-field radiation associated with the operation of a pulsed electron beam, taking into account the effects of the ionospheric plasma. The beam is modeled as an infinite train of square-wave pulses and the radiation is obtained by adding coherently the radiation from each individual electron in the idealized helical trajectory assumed by the beam as it traverses the magnetized plasma. The mathematical solution is obtained by taking the Fourier transform in space and time of Maxwell's equations and the driving modulated beam current, and then taking the inverse transform of the resulting electric field. Typical electric field strengths are presented for a range of modulation frequencies extending from below the ion cyclotron to the electron cyclotron frequency.

Harker, K. J.↗
NASA NTRS1988

Approximation of discrete-time LQG compensators for distributed systems with boundary input and unbounded measurement

The approximation of optimal discrete-time linear quadratic Gaussian (LQG) compensators for distributed parameter control systems with boundary input and unbounded measurement is considered. The approach applies to a wide range of problems that can be formulated in a state space on which both the discrete-time input and output operators are continuous. Approximating compensators are obtained via application of the LQG theory and associated approximation results for infinite dimensional discrete-time control systems with bounded input and output. Numerical results for spline and modal based approximation schemes used to compute optimal compensators for a one-dimensional heat equation with either Neumann or Dirichlet boundary control and pointwise measurement of temperature are presented and discussed.

Gibson, J. S.↗
NASA NTRS1999

Flame-Vortex Interactions in Microgravity to Improve Models of Turbulent Combustion

A unique flame-vortex interaction experiment is being operated in microgravity in order to obtain fundamental data to assess the Theory of Flame Stretch which will be used to improve models of turbulent combustion. The experiment provides visual images of the physical process by which an individual eddy in a turbulent flow increases the flame surface area, changes the local flame propagation speed, and can extinguish the reaction. The high quality microgravity images provide benchmark data that are free from buoyancy effects. Results are used to assess Direct Numerical Simulations of Dr. K. Kailasanath at NRL, which were run for the same conditions.

Driscoll, James F.↗