Search NASA⌕ Search

SEARCH · Search NASA

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 253 records · Page 14

On the oscillation of the laterally heterogeneous earth, 1

The perturbative effects, as cause by lateral inhomogeneities in the earth structure and by Coriolis force, contaminate the originally toroidal and spheroidal earth's oscillations, making them of mixed type. For this reason, in order to make the computation of the perturbations more uniform and homogeneous, it was suggested that the earth's free oscillations be expanded into a series in terms of generalized harmonics familiar from the theory of angular momentum in quantum mechanics. Making use of Gibbsian symbolism and of some operators from the theory of angular momentum, explicit expressions were deduced for the perturbative terms in the differential equation of the earth's free oscillations. Decomposition of the strain tensor in terms of canonical vectors was also obtained.

Musen, P.↗

Newton's method: A link between continuous and discrete solutions of nonlinear problems

Newton's method for nonlinear mechanics problems replaces the governing nonlinear equations by an iterative sequence of linear equations. When the linear equations are linear differential equations, the equations are usually solved by numerical methods. The iterative sequence in Newton's method can exhibit poor convergence properties when the nonlinear problem has multiple solutions for a fixed set of parameters, unless the iterative sequences are aimed at solving for each solution separately. The theory of the linear differential operators is often a better guide for solution strategies in applying Newton's method than the theory of linear algebra associated with the numerical analogs of the differential operators. In fact, the theory for the differential operators can suggest the choice of numerical linear operators. In this paper the method of variation of parameters from the theory of linear ordinary differential equations is examined in detail in the context of Newton's method to demonstrate how it might be used as a guide for numerical solutions.

Thurston, G. A.↗

Celestial soft currents at one-loop and their OPEs

Conformally soft operators and their associated soft theorems on the celestial sphere encode the low energy behaviour of bulk scattering amplitudes. They lead to an infinite dimensional symmetry algebra of the celestial CFT at tree-level. In this paper, focusing our attention to Yang-Mills theory, we introduce new operators in the boundary celestial CFT in order to extend the definition of conformally soft currents to include one-loop effects. We then compute their OPEs with other operators in the theory. We also examine new subtleties that arise in defining OPEs of two conformally soft operators. We elucidate the connection between the new operators and loop corrected soft theorems in the bulk. Finally, we conclude by demonstrating how these operators fit into the framework of a logarithmic CFT.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Solid state photomultiplier for astronomy, phase 2

Epitaxial layers with varying donor concentration profiles were grown on silicon substrate wafers using chemical vapor deposition (CVD) techniques, and solid state photomultiplier (SSPM) devices were fabricated from the wafers. Representative detectors were tested in a low background photon flux, low temperature environment to determine the device characteristics for comparison to NASA goals for astronomical applications. The SSPM temperatures varied between 6 and 11 K with background fluxes in the range from less than 5 x 10 to the 6th power to 10 to the 13th power photons/square cm per second at wavelengths of 3.2 and 20 cm. Measured parameters included quantum efficiency, dark count rate and bias current. Temperature for optimal performance is 10 K, the highest ever obtained for SSPMs. The devices exhibit a combination of the lowest dark current and highest quantum efficiency yet achieved. Experimental data were reduced, analyzed and used to generate recommendations for future studies. The background and present status of the microscopic theory of SSPM operation were reviewed and summarized. Present emphasis is on modeling of the avalanche process which is the basis for SSPM operation. Approaches to the solution of the Boltzmann transport equation are described and the treatment of electron scattering mechanisms is presented. The microscopic single-electron transport theory is ready to be implemented for large-scale computations.

Besser, P. J.↗

Performance Measures for Aircraft Landings as a Function of Aircraft Dynamics

A theory of performance measurement for operator controlled systems is presented. The theory permits synthesis of a system performance measure which scores performance on successive data samples based on the impact of the sampled performance on the overall summary of performance. The development of measures for aircraft carrier landings for the glide path and angle of attack control channels is documented. While developing the performance measures, the measures used previously were evaluated and were found to lack the necessary discrimination capability. The previously used measure, the RMS of deviations from the glide path, can, for instance, provide identical scores for both satisfactory and unsatisfactory flight paths. Two types of performance measures developed for aircraft landings are described. Also, an argument is given for the need to test performance measures prior to their use. A suggested test of the measures is offered.

Connelly, E. M.↗

Low Frequency High Amplitude Temperature Oscillations in Loop Heat Pipe Operation

This paper presents a theory that explains low frequency, high amplitude temperature oscillations in loop heat pipe (LHP) operation. Oscillations of the CC temperature with amplitudes on the order of tens of degrees Kelvin and periods on the order of hours have been observed in some LHPs during ambient testing. There are presently no satisfactory explanations for such a phenomenon in the literature. It is well-known that the operating temperature of an LHP with a single evaporator is governed by the compensation chamber (CC) temperature, which in turn is a function of the evaporator heat load, sink temperature, and ambient temperature. As the operating condition changes, the CC temperature will change during the transient but eventually reach a new steady temperature. Under certain conditions, however, the LHP never really reaches a true steady state, but instead displays an oscillatory behavior. The proposed new theory describes why low frequency, high amplitude oscillations may occur when the LHP has a low evaporator power, a low heat sink temperature (below ambient temperature), and a large thermal mass attached to the evaporator. When this condition prevails, there are some complex interactions between the CC, condenser, thermal mass and ambient. The temperature oscillation is a result of the large movement of the vapor front inside the condenser, which is caused by a change in the net evaporator power modulated by the large thermal mass through its interaction with the sink and CC. The theory agrees very well with previously published test data. Effects of various parameters on the amplitude and frequency of the temperature oscillation are also discussed.

Ku, Jentung↗

Physical Meaning of the Optimum Measurement Process in Quantum Detection Theory

The optimum measurement processes are represented as the optimum detection operators in the quantum detection theory. The error probability by the optimum detection operators goes beyond the standard quantum limit automatically. However the optimum detection operators are given by pure mathematical descriptions. In order to realize a communication system overcoming the standard quantum limit, we try to give the physical meaning of the optimum detection operators.

Osaki, Masao↗

A theory of human error

Human errors tend to be treated in terms of clinical and anecdotal descriptions, from which remedial measures are difficult to derive. Correction of the sources of human error requires an attempt to reconstruct underlying and contributing causes of error from the circumstantial causes cited in official investigative reports. A comprehensive analytical theory of the cause-effect relationships governing propagation of human error is indispensable to a reconstruction of the underlying and contributing causes. A validated analytical theory of the input-output behavior of human operators involving manual control, communication, supervisory, and monitoring tasks which are relevant to aviation, maritime, automotive, and process control operations is highlighted. This theory of behavior, both appropriate and inappropriate, provides an insightful basis for investigating, classifying, and quantifying the needed cause-effect relationships governing propagation of human error.

Mcruer, D. T.↗

A theory of human error

Human error, a significant contributing factor in a very high proportion of civil transport, general aviation, and rotorcraft accidents is investigated. Correction of the sources of human error requires that one attempt to reconstruct underlying and contributing causes of error from the circumstantial causes cited in official investigative reports. A validated analytical theory of the input-output behavior of human operators involving manual control, communication, supervisory, and monitoring tasks which are relevant to aviation operations is presented. This theory of behavior, both appropriate and inappropriate, provides an insightful basis for investigating, classifying, and quantifying the needed cause-effect relationships governing propagation of human error.

Mcruer, D. T.↗

An optimal output feedback gain variation scheme for the control of plants exhibiting gross parameter changes

A concept for optimally designing output feedback controllers for plants whose dynamics exhibit gross changes over their operating regimes was developed. This was to formulate the design problem in such a way that the implemented feedback gains vary as the output of a dynamical system whose independent variable is a scalar parameterization of the plant operating point. The results of this effort include derivation of necessary conditions for optimality for the general problem formulation, and for several simplified cases. The question of existence of a solution to the design problem was also examined, and it was shown that the class of gain variation schemes developed are capable of achieving gain variation histories which are arbitrarily close to the unconstrained gain solution for each point in the plant operating range. The theory was implemented in a feedback design algorithm, which was exercised in a numerical example. The results are applicable to the design of practical high-performance feedback controllers for plants whose dynamics vary significanly during operation. Many aerospace systems fall into this category.

Moerder, Daniel D.↗

Summary

Summary of papers presented at NASA-university program conference on dynamic and other models, control devices, operator performance, and information theory related to manual control

OPERATOR PERFORMANCE↗

A Simplified Theory of Coupled Oscillator Array Phase Control

Linear and planar arrays of coupled oscillators have been proposed as means of achieving high power rf sources through coherent spatial power combining. In such - applications, a uniform phase distribution over the aperture is desired. However, it has been shown that by detuning some of the oscillators away from the oscillation frequency of the ensemble of oscillators, one may achieve other useful aperture phase distributions. Notable among these are linear phase distributions resulting in steering of the output rf beam away from the broadside direction. The theory describing the operation of such arrays of coupled oscillators is quite complicated since the phenomena involved are inherently nonlinear. This has made it difficult to develop an intuitive understanding of the impact of oscillator tuning on phase control and has thus impeded practical application. In this work a simpl!fied theory is developed which facilitates intuitive understanding by establishing an analog of the phase control problem in terms of electrostatics.

Pogorzelski, R. J.↗

ATLAS, an integrated structural analysis and design system. Volume 6: Design module theory

The automated design theory underlying the operation of the ATLAS Design Module is decribed. The methods, applications and limitations associated with the fully stressed design, the thermal fully stressed design and a regional optimization algorithm are presented. A discussion of the convergence characteristics of the fully stressed design is also included. Derivations and concepts specific to the ATLAS design theory are shown, while conventional terminology and established methods are identified by references.

Backman, B. F.↗

Ndarts

Ndarts software provides algorithms for computing quantities associated with the dynamics of articulated, rigid-link, multibody systems. It is designed as a general-purpose dynamics library that can be used for the modeling of robotic platforms, space vehicles, molecular dynamics, and other such applications. The architecture and algorithms in Ndarts are based on the Spatial Operator Algebra (SOA) theory for computational multibody and robot dynamics developed at JPL. It uses minimal, internal coordinate models. The algorithms are low-order, recursive scatter/ gather algorithms. In comparison with the earlier Darts++ software, this version has a more general and cleaner design needed to support a larger class of computational dynamics needs. It includes a frames infrastructure, allows algorithms to operate on subgraphs of the system, and implements lazy and deferred computation for better efficiency. Dynamics modeling modules such as Ndarts are core building blocks of control and simulation software for space, robotic, mechanism, bio-molecular, and material systems modeling.

Jain, Abhinandan↗