Nonlinear systems identification in presence of nonuniqueness
Nonlinear systems for matching input-output of mathematical model to physical system
Aubrun, J.-N.↗
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Results for “Mathematical Physics”
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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Wave propagation in a random medium
A simple technique is used to derive statistical characterizations of the perturbations imposed upon a wave (plane, spherical or beamed) propagating through a random medium. The method is essentially physical rather than mathematical, and is probably equivalent to the Rytov method. The limitations of the method are discussed in some detail; in general they are restrictive only for optical paths longer than a few hundred meters, and for paths at the lower microwave frequencies. Situations treated include arbitrary path geometries, finite transmitting and receiving apertures, and anisotropic media. Results include, in addition to the usual statistical quantities, time-lagged functions, mixed functions involving amplitude and phase fluctuations, angle-of-arrival covariances, frequency covariances, and other higher-order quantities.
Lee, R. W.↗
Modulation of ring-laser mode coupling.
This paper develops an analytical, algebraic formalism that predicts effects induced in ring lasers by phase modulation, corresponding both to mode-decoupling mechanisms deliberately incorporated in the ring laser and to naturally occurring periodic or random angular or linear accelerations. The analysis is based on an approach that seems potentially convenient in the analysis of other systems that are physically stable but mathematically nonlinear.
Whitney, C.↗
Structure of massive main-sequence stars.
Core hydrogen-burning models are discussed together with the associated physical instabilities. A mathematical relation for dynamical instability is presented. Conditions leading to convective instability are analyzed, giving attention to the nature of the convectively unstable, chemically inhomogeneous, zone that is left behind by the retreating convective core. Questions of pulsational instability are also investigated.
Stothers, R.↗
A new formulation for anisotropic radiative transfer problems. I - Solution with a variational technique
The equations of radiative transfer in anisotropically scattering media are reformulated as linear operator equations in a single independent variable. The resulting equations are suitable for solution by a variety of standard mathematical techniques. The operators appearing in the resulting equations are in general nonsymmetric; however, it is shown that every bounded linear operator equation can be embedded in a symmetric linear operator equation and a variational solution can be obtained in a straightforward way. For purposes of demonstration, a Rayleigh-Ritz variational method is applied to three problems involving simple phase functions. It is to be noted that the variational technique demonstrated is of general applicability and permits simple solutions for a wide range of otherwise difficult mathematical problems in physics.
Cheyney, H., III↗
Theoretical interpretation of Traveling Interplanetary Phenomena and their solar origins
A review is made of recent theoretical studies on Traveling Interplanetary Phenomena (TIP) and their possible solar origins in the context of mathematical methods and physical processes. Flare-generated interplanetary shocks are used as examples to illustrate the following set of contrasting approaches to the phenomena: analytical vs numerical, hydrodynamic vs magnetohydrodynamic, dissipative vs non-dissipative, continuum/macroscopic vs kinetic/microscopic. It is suggested in conclusion that future research should emphasize continuum/macroscopic physical processes together with the kinetic approach to deepen understanding of microscopic interactions.
Wu, S. T.↗
Effects of friction dampers on aerodynamically unstable rotor stages
Attention is given to the physical concepts and mathematical techniques useful in the analysis of the stabilizing effect of friction on aerodynamically unstable rotor stages. Results are presented for three-, four-, and five-bladed disks. In the present multidegree-of-freedom model of an aerodynamically unstable rotor stage, a harmonic steady state solution due to the friction dampers may be either a stability limit, a stable cycle limit, or neither. A criterion is established in the form of an energy function which determines whether the solution is a stability limit. In the event that the initial displacement and velocity exeed those associated with the steady state solution corresponding to a stability limit, the reponse becomes unbounded.
Griffin, J. H.↗
Vectorized Monte Carlo methods for reactor lattice analysis
Some of the new computational methods and equivalent mathematical representations of physics models used in the MCV code, a vectorized continuous-enery Monte Carlo code for use on the CYBER-205 computer are discussed. While the principal application of MCV is the neutronics analysis of repeating reactor lattices, the new methods used in MCV should be generally useful for vectorizing Monte Carlo for other applications. For background, a brief overview of the vector processing features of the CYBER-205 is included, followed by a discussion of the fundamentals of Monte Carlo vectorization. The physics models used in the MCV vectorized Monte Carlo code are then summarized. The new methods used in scattering analysis are presented along with details of several key, highly specialized computational routines. Finally, speedups relative to CDC-7600 scalar Monte Carlo are discussed.
Brown, F. B.↗
Recent advances in methods for numerical solution of O.D.E. initial value problems
In the mathematical modeling of physical systems, it is often necessary to solve an initial value problem (IVP), consisting of a system of ordinary differential equations (ODE). A typical program produces approximate solutions at certain mesh points. Almost all existing codes try to control the local truncation error, while the user is really interested in controlling the true or global error. The present investigation provides a review of recent advances regarding the solution of the IVP, giving particular attention to stiff systems. Stiff phenomena are customarily defined in terms of the eigenvalues of the Jacobian. There are, however, some difficulties connected with this approach. It is pointed out that an estimate of the Lipschitz constant proves to be a very practical way to determine the stiffness of a problem.
Bui, T. D.↗
Structural Error and Identifiability in Mathematical Models
Errors and previously implicit assumptions treated explicitly. Paper discusses errors in mathematical models of physical systems and problem of identifying model from system input and output. Problem approached by explicitly taking account of erroneous choices of model structure. Paper concerned specifically with linear or weakly nonlinear models.
Hadaegh, F. Y.↗
Identifiability Of Systems With Modeling Errors
Advances in theory of modeling errors reported. Recent paper on errors in mathematical models of deterministic linear or weakly nonlinear systems. Extends theoretical work described in NPO-16661 and NPO-16785. Presents concrete way of accounting for difference in structure between mathematical model and physical process or system that it represents.
Hadaegh, Yadolah "fred"↗
Software For Design Of Life-Support Systems
Design Assistant Workstation (DAWN) computer program is prototype of expert software system for analysis and design of regenerative, physical/chemical life-support systems that revitalize air, reclaim water, produce food, and treat waste. Incorporates both conventional software for quantitative mathematical modeling of physical, chemical, and biological processes and expert system offering user stored knowledge about materials and processes. Constructs task tree as it leads user through simulated process, offers alternatives, and indicates where alternative not feasible. Also enables user to jump from one design level to another.
Rudokas, Mary R.↗
A system approach to aircraft optimization
Mutual couplings among the mathematical models of physical phenomena and parts of a system such as an aircraft complicate the design process because each contemplated design change may have a far reaching consequence throughout the system. Techniques are outlined for computing these influences as system design derivatives useful for both judgemental and formal optimization purposes. The techniques facilitate decomposition of the design process into smaller, more manageable tasks and they form a methodology that can easily fit into existing engineering organizations and incorporate their design tools.
Sobieszczanski-Sobieski, Jaroslaw↗
Lightning-Sensor Data Help In Understanding Thunderstorms
NASA technical memorandum discusses research on use of data from network of ground-based magnetic direction-finding ground-strike lightning sensors to diagnose and predict occurrence and evolution of thunderstorms. Purposes of study to explore applicability and limitations of extrapolation techniques used to generate forecasts from data; to examine physically-based, nonlinear mathematical models for applicability to lightning-forecast problem; and to determine valid extrapolation ranges of such models for various weather scenarios.
Goodman, Steven J.↗
Inverse problems in the design, modeling and testing of engineering systems
Formulations, classification, areas of application, and approaches to solving different inverse problems are considered for the design of structures, modeling, and experimental data processing. Problems in the practical implementation of theoretical-experimental methods based on solving inverse problems are analyzed in order to identify mathematical models of physical processes, aid in input data preparation for design parameter optimization, help in design parameter optimization itself, and to model experiments, large-scale tests, and real tests of engineering systems.
Alifanov, Oleg M.↗
SEL Ada reuse analysis and representations
Overall, it was revealed that the pattern of Ada reuse has evolved from initial reuse of utility components into reuse of generalized application architectures. Utility components were both domain-independent utilities, such as queues and stacks, and domain-specific utilities, such as those that implement spacecraft orbit and attitude mathematical functions and physics or astronomical models. The level of reuse was significantly increased with the development of a generalized telemetry simulator architecture. The use of Ada generics significantly increased the level of verbatum reuse, which is due to the ability, using Ada generics, to parameterize the aspects of design that are configurable during reuse. A key factor in implementing generalized architectures was the ability to use generic subprogram parameters to tailor parts of the algorithm embedded within the architecture. The use of object oriented design (in which objects model real world entities) significantly improved the modularity for reuse. Encapsulating into packages the data and operations associated with common real world entities creates natural building blocks for reuse.
Kester, Rush↗
A system approach to aircraft optimization
Mutual couplings among the mathematical models of physical phenomenon and parts of a system such as an aircraft complicate the design process because each contemplated design change may have far reaching consequences throughout the system. This paper outlines techniques for computing these influences as system design derivatives useful in both judgmental and formal optimization purposes. The techniques facilitate decomposition of the design process into smaller, more manageable tasks and they form a methodology that can easily fit into existing engineering optimizations and incorporate their design tools.
Sobieszczanski-Sobieski, Jaroslaw↗
Multidisciplinary design and optimization
Mutual couplings among the mathematical models of physical phenomena and parts of a system such as an aircraft complicate the design process because each contemplated design change may have a far reaching consequence throughout the system. This paper outlines techniques for computing these influences as system design derivatives useful to both judgmental and formal optimization purposes. The techniques facilitate decomposition of the design process into smaller, more manageable tasks and they form a methodology that can easily fit into existing engineering optimizations and incorporate their design tools.
Sobieszczanski-Sobieski, Jaroslaw↗