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Results for “linear 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.

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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

A linear accelerator for simulated micrometeors.

Review of the theory, design parameters, and construction details of a linear accelerator designed to impart meteoric velocities to charged microparticles in the 1- to 10-micron diameter range. The described linac is of the Sloan Lawrence type and, in a significant departure from conventional accelerator practice, is adapted to single particle operation by employing a square wave driving voltage with the frequency automatically adjusted from 12.5 to 125 kHz according to the variable velocity of each injected particle. Any output velocity up to about 30 km/sec can easily be selected, with a repetition rate of approximately two particles per minute.

Slattery, J. C.↗
NASA NTRS1988

Properties of aircraft tire materials

A summary is presented of measured elastomeric composite response suitable for linear structural and thermoelastic analysis in aircraft tires. Both real and loss properties are presented for a variety of operating conditions including the effects of temperature and frequency. Suitable micro-mechanics models are used for predictions of these properties for other material combinations and the applicability of laminate theory is discussed relative to measured values.

Dodge, Richard N.↗
DOE OSTI2022

Solving nuclear structure problems with the adaptive variational quantum algorithm

Here we use the Lipkin-Meshkov-Glick (LMG) model and the valence-space nuclear shell model to examine the likely performance of variational quantum eigensolvers in nuclear-structure theory. The LMG model exhibits both a phase transition and spontaneous symmetry breaking at the mean-field level in one of the phases, features that characterize collective dynamics in medium-mass and heavy nuclei. We show that with appropriate modifications, the ADAPT-VQE algorithm, a particularly flexible and accurate variational approach, is not troubled by these complications. We treat up to 12 particles and show that the number of quantum operations needed to approach the ground-state energy scales linearly with the number of qubits. We find similar scaling when the algorithm is applied to the nuclear shell model with realistic interactions in the sd and pf shells. Although most of these simulations contain no noise, we use a noise model from real IBM hardware to show that for the LMG model with four particles, weak noise has no effect on the efficiency of the algorithm.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS2015

The Prediction of Scattered Broadband Shock-Associated Noise

A mathematical model is developed for the prediction of scattered broadband shock-associated noise. Model arguments are dependent on the vector Green's function of the linearized Euler equations, steady Reynolds-averaged Navier-Stokes solutions, and the two-point cross-correlation of the equivalent source. The equivalent source is dependent on steady Reynolds-averaged Navier-Stokes solutions of the jet flow, that capture the nozzle geometry and airframe surface. Contours of the time-averaged streamwise velocity component and turbulent kinetic energy are examined with varying airframe position relative to the nozzle exit. Propagation effects are incorporated by approximating the vector Green's function of the linearized Euler equations. This approximation involves the use of ray theory and an assumption that broadband shock-associated noise is relatively unaffected by the refraction of the jet shear layer. A non-dimensional parameter is proposed that quantifies the changes of the broadband shock-associated noise source with varying jet operating condition and airframe position. Scattered broadband shock-associated noise possesses a second set of broadband lobes that are due to the effect of scattering. Presented predictions demonstrate relatively good agreement compared to a wide variety of measurements.

Miller, Steven A. E.↗
NASA NTRS2018

Ion Injection Triggered EMIC Waves in the Earth's Magnetosphere

We present Van Allen Probe observations of electromagnetic ion cyclotron (EMIC) waves triggered solely due to individual substorm-injected ions in the absence of storms or compressions of the magnetosphere during 9 August 2015. The time at which the injected ions are observed directly corresponds to the onset of EMIC waves at the location of Van Allen Probe A (L = 5.5 and 18:06 magnetic local time). The injection was also seen at geosynchronous orbit by the Geostationary Operational Environmental Satellite and Los Alamos National Laboratory spacecraft, and the westward(eastward) drift of ions(electrons) was monitored by Los Alamos National Laboratory spacecraft at different local times. The azimuthal location of the injection was determined by tracing the injection signatures backward intime to their origin assuming a dipolar magnetic field of Earth. The center of this injection location wasdetermined to be close to 20:00 magnetic local time. Geostationary Operational Environmental Satelliteand ground magnetometer responses confirm substorm onset at approximately the same local time.The observed EMIC wave onsets at Van Allen Probe were also associated with a magnetic field decrease.The arrival of anisotropic ions along with the decrease in the magnetic field favors the growth of the EMICwave instability based on linear theory analysis.

Van Allen Probes↗
NASA NTRS1975

Optimum testing of multiple hypotheses in quantum detection theory

The problem of specifying the optimum quantum detector in multiple hypotheses testing is considered for application to optical communications. The quantum digital detection problem is formulated as a linear programming problem on an infinite-dimensional space. A necessary and sufficient condition is derived by the application of a general duality theorem specifying the optimum detector in terms of a set of linear operator equations and inequalities. Existence of the optimum quantum detector is also established. The optimality of commuting detection operators is discussed in some examples. The structure and performance of the optimal receiver are derived for the quantum detection of narrow-band coherent orthogonal and simplex signals. It is shown that modal photon counting is asymptotically optimum in the limit of a large signaling alphabet and that the capacity goes to infinity in the absence of a bandwidth limitation.

Yuen, H. P.↗
NASA NTRS1989

Prediction and measurement of low-frequency harmonic noise of a hovering model helicopter rotor

Far-field acoustic data for a model helicopter rotor have been gathered in a large open-jet, acoustically treated wind tunnel with the rotor operating in hover and out of ground-effect. The four-bladed Boeing 360 model rotor with advanced airfoils, planform, and tip shape was run over a range of conditions typical of today's modern helicopter main rotor. Near in-plane acoustic measurements were compared with two independent implementations of classical linear theory. Measured steady thrust and torque were used together with a free-wake analysis (to predict the thrust and drag distributions along the rotor radius) as input to this first-principles theoretical approach. Good agreement between theory and experiment was shown for both amplitude and phase for measurements made in those positions that minimized distortion of the radiated acoustic signature at low-frequencies.

Aggarawal, H. R.↗
NASA NTRS1996

USAF Flight Test Investigation of Focused Sonic Booms: Project Have Bears

Supersonic operations from military aircraft generate sonic booms that can affect people, animals and structures. A substantial experimental data base exists on sonic booms for aircraft in steady flight and confidence in the predictive techniques has been established. All the focus sonic boom data that are in existence today were collected during the 60's and 70's as part of the information base to the US Supersonic Transport program and the French Jericho studies for the Concorde. These experiments formed the data base to develop sonic boom propagation and prediction theories for focusing. There is a renewed interest in high-speed transports for civilian application. Moreover, today's fighter aircraft have better performance capabilities, and supersonic flights ars more common during air combat maneuvers. Most of the existing data on focus booms are related to high-speed civil operations such as transitional linear accelerations and mild turns. However, military aircraft operating in training areas perform more drastic maneuvers such as dives and high-g turns. An update and confirmation of USAF prediction capabilities is required to demonstrate the ability to predict and control sonic boom impacts, especially those produced by air combat maneuvers.

Downing, Micah↗
NASA NTRS1987

Nonlinear flight test trajectory controllers for aircraft

Flight test trajectory control systems are designed to enable the pilot to follow complex trajectories for evaluating an aircraft within its known flight envelope and to explore the boundaries of its capabilities. Previous design approaches were baed on linearized aircraft models necessitating a large amount of data storage along with gain schedules. In this paper, the synthesis of nonlinear flight test trajectory controllers for a fixed-wing aircraft is described. This approach uses singular perturbation theory and the recently developed theory of prelinearizing transformations. These controllers do not require gain scheduling for satisfactory operation, can be used in arbitrarily nonlinear maneuvers, and are mechanized with a direct, noniterative analytic solution.

Menon, P. K. A.↗
DOE OSTI2025

Dynamic Modeling, Trajectory Optimization, and Linear Control of Cable-Driven Parallel Robots for Automated Panelized Building Retrofits

The construction industry faces a growing need for automation to reduce costs, improve accuracy and productivity, and address labor shortages. One area that stands to benefit significantly from automation is panelized prefabricated building envelope retrofits, which can improve a building’s energy efficiency in heating and cooling interior spaces. In this paper, we propose using cable-driven parallel robots (CDPRs), which can effectively lift and handle large objects, to install these panels. However, implementing CDPRs presents significant challenges because of their nonlinear dynamics, complex trajectory planning, and precise control requirements. To tackle these challenges, this work focuses on a new application of established control and trajectory optimization theories in a CDPR simulation of a building envelope retrofit under real-world conditions. We first model the dynamics of CDPRs, highlighting the critical role of damping in system behavior. Building on this dynamic model, we formulate a trajectory optimization problem to generate feasible and efficient motion plans for the robot under operational and environmental constraints. Given the high precision required in the construction industry, accurately tracking the optimized trajectory is essential. However, challenges such as partial observability and external vibrations complicate this task. To address these issues, a Linear Quadratic Gaussian control framework is applied, enabling the robot to track the optimized trajectories with precision. Simulation results show that the proposed controller enables precise end effector positioning with errors under 4 mm, even in the presence of external wind disturbances. Through comprehensive simulations, our approach allows for an in-depth exploration of the system’s nonlinear dynamics, trajectory optimization, and control strategies under controlled yet highly realistic conditions. The results demonstrate the feasibility of CDPRs for automating panel installation and provide insights into their practical deployment.

CDPR↗
NASA NTRS2012

Adaptive Control of Linear Modal Systems Using Residual Mode Filters and a Simple Disturbance Estimator

Flexible structures containing a large number of modes can benefit from adaptive control techniques which are well suited to applications that have unknown modeling parameters and poorly known operating conditions. In this paper, we focus on a direct adaptive control approach that has been extended to handle adaptive rejection of persistent disturbances. We extend our adaptive control theory to accommodate troublesome modal subsystems of a plant that might inhibit the adaptive controller. In some cases the plant does not satisfy the requirements of Almost Strict Positive Realness. Instead, there maybe be a modal subsystem that inhibits this property. This section will present new results for our adaptive control theory. We will modify the adaptive controller with a Residual Mode Filter (RMF) to compensate for the troublesome modal subsystem, or the Q modes. Here we present the theory for adaptive controllers modified by RMFs, with attention to the issue of disturbances propagating through the Q modes. We apply the theoretical results to a flexible structure example to illustrate the behavior with and without the residual mode filter.

Balas, Mark↗
NASA NTRS1989

Optimum design of structures subject to general periodic loads

A simplified version of Icerman's problem regarding the design of structures subject to a single harmonic load is discussed. The nature of the restrictive conditions that must be placed on the design space in order to ensure an analytic optimum are discussed in detail. Icerman's problem is then extended to include multiple forcing functions with different driving frequencies. And the conditions that now must be placed upon the design space to ensure an analytic optimum are again discussed. An important finding is that all solutions to the optimality condition (analytic stationary design) are local optima, but the global optimum may well be non-analytic. The more general problem of distributing the fixed mass of a linear elastic structure subject to general periodic loads in order to minimize some measure of the steady state deflection is also considered. This response is explicitly expressed in terms of Green's functional and the abstract operators defining the structure. The optimality criterion is derived by differentiating the response with respect to the design parameters. The theory is applicable to finite element as well as distributed parameter models.

Reiss, Robert↗
NASA NTRS1990

Learning-based position control of a closed-kinematic chain robot end-effector

A trajectory control scheme whose design is based on learning theory, for a six-degree-of-freedom (DOF) robot end-effector built to study robotic assembly of NASA hardwares in space is presented. The control scheme consists of two control systems: the feedback control system and the learning control system. The feedback control system is designed using the concept of linearization about a selected operating point, and the method of pole placement so that the closed-loop linearized system is stabilized. The learning control scheme consisting of PD-type learning controllers, provides additional inputs to improve the end-effector performance after each trial. Experimental studies performed on a 2 DOF end-effector built at CUA, for three tracking cases show that actual trajectories approach desired trajectories as the number of trials increases. The tracking errors are substantially reduced after only five trials.

Nguyen, Charles C.↗
NASA NTRS1989

Convergence of infinite dimensional sampled LQR problems - Theory and numerical results

A theory is developed for the convergence of the closed-loop solution to infinite-dimensional discrete-time linear-quadratic regulator (LQR) problems on the infinite time interval to the solution of a corresponding continuous-time LQR problem as the length of the sampling interval tends toward zero. Convergence of solutions to the operator algebraic Riccati equation and corresponding optimal feedback control gains is guaranteed under appropriate uniform stabilizability and detectability conditions and consistent sampling. Also presented are numerical results involving the optimal LQ control of a heat or diffusion equation, a hereditary or delay differential equation, and a hybrid system of ordinary and partial differential equations describing the transverse vibration of a cantilevered Voigt-Kelvin viscoelastic beam with tip mass.

Rosen, I. G.↗
NASA NTRS1991

Operator-assisted planning and execution of proximity operations subject to operational constraints

Future multi-vehicle operations will involve multiple scenarios that will require a planning tool for the rapid, interactive creation of fuel-efficient trajectories. The planning process must deal with higher-order, non-linear processes involving dynamics that are often counter-intuitive. The optimization of resulting trajectories can be difficult to envision. An interaction proximity operations planning system is being developed to provide the operator with easily interpreted visual feedback of trajectories and constraints. This system is hosted on an IRIS 4D graphics platform and utilizes the Clohessy-Wiltshire equations. An inverse dynamics algorithm is used to remove non-linearities while the trajectory maneuvers are decoupled and separated in a geometric spreadsheet. The operator has direct control of the position and time of trajectory waypoints to achieve the desired end conditions. Graphics provide the operator with visualization of satisfying operational constraints such as structural clearance, plume impingement, approach velocity limits, and arrival or departure corridors. Primer vector theory is combined with graphical presentation to improve operator understanding of suggested automated system solutions and to allow the operator to review, edit, or provide corrective action to the trajectory plan.

Grunwald, Arthur J.↗
DOE OSTI2025

A Solution to the Hierarchy Problem with Non-Linear Quantum Mechanics

We argue that the hierarchy problem of the standard model of particle physics can be solved by adding a state-dependent term to the Higgs sector. We present an example of a scalar field with a Higgs-like potential with an additional term proportional to the expectation value of the squared Higgs field operator. We show that the mass can be parametrically lighter than the theory's energy-momentum cutoff without fine tuning. We find the Higgs mass can be technically natural, even with a Planck-scale cutoff. The simplest version of the theory may not be distinguishable from the standard model at colliders, but other versions might. In addition, some aspects of cosmological evolution can be different in this model, in some cases radically.

Kaplan, David E. [Johns Hopkins U.; Tokyo U., IPMU↗
NASA NTRS1972

General theory of spherically symmetric boundary-value problems of the linear transport theory.

A general theory of spherically symmetric boundary-value problems of the one-speed neutron transport theory is presented. The formulation is also applicable to the 'gray' problems of radiative transfer. The Green's function for the purely absorbing medium is utilized in obtaining the normal mode expansion of the angular densities for both interior and exterior problems. As the integral equations for unknown coefficients are regular, a general class of reduction operators is introduced to reduce such regular integral equations to singular ones with a Cauchy-type kernel. Such operators then permit one to solve the singular integral equations by the standard techniques due to Muskhelishvili. We discuss several spherically symmetric problems. However, the treatment is kept sufficiently general to deal with problems lacking azimuthal symmetry. In particular the procedure seems to work for regions whose boundary coincides with one of the coordinate surfaces for which the Helmholtz equation is separable.

Kanal, M.↗
DOE OSTI2026

JIMWLK on a quantum computer

We propose a method for solving the Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner (JIMWLK) evolution equation on quantum computers. Our approach exploits the reformulation of the JIMWLK equation as a Lindblad master equation governing the rapidity evolution of the hadronic density matrix, as established in prior work. To render the problem tractable for quantum simulation, we introduce several approximations: the two-dimensional transverse plane is reduced to a one-dimensional radial lattice by assuming azimuthal symmetry of the jump operators; the gauge group is restricted to SU(2); and the infinite Wilson lines of the JIMWLK equation are replaced by finite Wilson links along the light-cone direction. The resulting bosonic Hilbert space is truncated using the electric field basis familiar from Hamiltonian lattice gauge theory, with states restricted to angular momenta 𝑗 ≤ 𝑗 max . We derive the matrix elements of the JIMWLK Lindblad jump operators in this basis. As a benchmark, we demonstrate rapid convergence of the fundamental dipole expectation value with 𝑗 max for both pure and mixed Gaussian initial density matrices. For the simplest truncation, 𝑗 max =1/2, we implement the Lindblad evolution using a quantum simulation algorithm verified with the Qiskit statevector simulator by decomposing the non-unitary evolution operator into a linear combination of unitaries. This work establishes a concrete pathway toward quantum simulation of high-energy quantum chromodynamics evolution equations, with direct relevance to the physics program of the Electron-Ion Collider.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗