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NASA NTRS1982

Theory of design using nonlinear transformations

This paper is presenting an overview of the theory of transformations from nonlinear systems to linear systems. Topics covered include (1) necessary and sufficient conditions for transformations to exist, (2) a method of constructing transformations (3) robustness in design (based on transformations theory) and Liapunov functions, (4) estimation theory, and (5) the relationship between transformation theory and 'nonlinear zeros'. Application of these results to automatic flight control is presented in another paper at this session.

Su, R.↗

NASA NTRS1983

Theory of hydromagnetic waves in the magnetosphere

A survey of theoretical and experimental research on the origin and characteristics of low-frequency hydromagnetic (HM) waves in the magnetosphere is presented, with a focus on advances in theory made in the last ten years. Basic wave theory and a collisionless plasma theory are applied to the magnetosphere as a HM system. Continuous energy sources are considered, such as the Kelvin-Helmholtz instability, the ring-current plasma, and drift instabilities. Other topics discussed include the theory of inhomogeneous HM waves, signal behavior in atmosphere and ionosphere, Alfven waves and ionosphere-magnetosphere coupling, Pi2 signals, damping, pulsating aurora, heavy-ion scattering, and standing waves in high-speed flows (like the wake phenomena caused on Jupiter by the passing of Io, observed by Voyager 1).

Southwood, D. J.↗

NASA NTRS1983

Estimation of parameters involved in high angle-of-attack aerodynamic theory using spin flight test data

The difficulty in applying parameter estimation techniques to spinning airplanes is due in part to the unwieldy number of possible combinations of terms in the equations of motion, when the model structure is unknown. The combination of high angle of attack and high rotation rate results in aerodynamic functions which are quite complex. For wing dominated configurations it is advantageous to use aerodynamic theory to generate the model structure. In this way, the number of unknown parameters is reduced and the model accuracy may be increased. Under conditions for which the theory is inadequate, however, model accuracy may be reduced. Strip theory, for example, is incapable of predicting autorotative rolling moments indicated by wind tunnel tests at angles of attack exceeding 40 degrees. An improved aerodynamic theory would be necessary to successfully apply the technique advanced for such regions.

Taylor, L. W., Jr.↗

NASA NTRS1984

Wave-particle transport from density drift instabilities - A comparison of local and nonlocal theories

Second-order Vlasov theory is used to compute the dissipation rates of plasma irregularities with a variety of shapes. A derivation of the nonlocal dispersion equation using linearized Vlasov theory is presented. Expressions for the normalized amplitudes of the first-order plasma density and electrostatic potential fluctuations are derived. Expressions are given for the saturation amplitudes of the electrostatic eigenmodes. The wave-particle transport and irregularity dissipation rate are computed by using formulas whose derivation is presented. Computational results for specific density variations are shown, and conclusions on the validity of the local theory as opposed to the nonlocal theory are given.

Bernhardt, P. A.↗

NASA NTRS1985

Statistical theories of Langmuir turbulence. II - Subsonic to sonic transition

The subsonic limit of the quadratic direct interaction approximation (DIA) applied to the Zakharov equations is compared with the cubic DIA applied to the nonlinear Schroedinger equation, which is the subsonic limit of the Zakharov equations. Comparisons with Monte Carlo simulations of a truncated system show that the first theory more accurately describes the regime of stationary turbulence, while the second theory more accurately describes the subsonic evolution of the modulational instability. The weak turbulence limits of the two theories describe the sonic and subsonic regimes, respectively. The addition of vertex corrections to the DIA leads to a hybrid weak turbulence theory that smoothly interpolates between the sonic and subsonic regimes.

Dubois, D. F.↗

NASA NTRS1985

Nonlinear spiral density waves - An inviscid theory

It is pointed out that the theory of spiral density waves, invented to explain the spiral structure of disk galaxies, has also been found useful for the study of planetary rings. The linear theory is by now well developed, while the nonlinear theory is less complete. Analytical calculations which include self-gravitation have, so far, obtained results only in the slightly nonlinear regime, or have concentrated on partial effects which are not of primary importance to the physical problem at hand. In the present paper, it is attempted to remedy these shortcomings. The simplest asymptotic ordering which can still yield useful results is adopted. Attention is given to the reduction to a nonlinear integral equation in a single variable, the use of the Wentzel-Kramers-Brillouin-Jeffreys theory, and the replacement of an equation by another which is easier to handle numerically.

Shu, F. H.↗

NASA NTRS1985

The determination of physical and dynamical parameters of Pluto/Charon and binary asteroids by least-square formation of a matched filter for a time series of images. I - The operational theory

A theory is derived for the determination of the masses, radii, and orbital elements of the Pluto/Charon, or similar, system based on the prediction of an image distribution over space and time and its comparison with observation. The comparison may be ultimately through the theory of least squares or the application of a matched filter to the observations as a three-dimensional signal stream at an initial or intermediate state. The theory is an approximation correct to fifth order in the diameters of celestial bodies. The theory of astronomical seeing that is used is based on Kolmogorov turbulence in the long-exposure limit. The images must be photometric. Linear tracking errors that can be removed are preferable to either automatic or manual guiding, in the collection of candidate observations.

Wildey, R. L.↗

NASA NTRS1986

Ostwald ripening theory

The Ostwald-ripening theory is deduced and discussed starting from the fundamental principles such as Ising model concept, Mayer cluster expansion, Langer condensation point theory, Ginzburg-Landau free energy, Stillinger cutoff-pair potential, LSW-theory and MLSW-theory. Mathematical intricacies are reduced to an understanding version. Comparison of selected works, from 1949 to 1984, on solution of diffusion equation with and without sink/sources term(s) is presented. Kahlweit's 1980 work and Marqusee-Ross' 1954 work are more emphasized. Odijk and Lekkerkerker's 1985 work on rodlike macromolecules is introduced in order to simulate interested investigators.

Baird, J. K.↗

NASA NTRS1986

Electromagnetic scattering theory

Electromagnetic scattering theory is discussed with emphasis on the general stochastic variational principle (SVP) and its applications. The stochastic version of the Schwinger-type variational principle is presented, and explicit expressions for its integrals are considered. Results are summarized for scalar wave scattering from a classic rough-surface model and for vector wave scattering from a random dielectric-body model. Also considered are the selection of trial functions and the variational improvement of the Kirchhoff short-wave approximation appropriate to large size-parameters. Other applications of vector field theory discussed include a general vision theory and the analysis of hydromagnetism induced by ocean motion across the geomagnetic field. Levitational force-torque in the magnetic suspension of the disturbance compensation system (DISCOS), now deployed in NOVA satellites, is also analyzed using the developed theory.

Bird, J. F.↗

NASA NTRS1986

A test of Lee's quasi-linear theory of ion acceleration by interplanetary traveling shocks

Lee's (1983) quasi-linear theory of ion acceleration is tested using ISEE-3 measurements of the November 12, 1978 quasi-parallel interplanetary shock. His theory accounts with varying degrees of precision for the energetic proton spatial profiles; the dependence of the spectral index of the power law proton velocity distribution upon the shock compression ratio; the power law dependence of the upstream proton scalelength upon energy; the absolute magnitude of the upstream proton scale length; the behavior of the energetic proton anisotropy upstream and downstream of the shock; the behavior of the alpha-particle proton ratio upstream; the equality of the spatial scale lengths at the shock of the upstream waves and of the protons that resonate with them; and the dependence of the integrated wave energy density upon the proton energy density at the shock. However, the trace magnetic field frequency spectra disagree with his theory in two ways. The part of the spectrum that can resonate with the observed protons via first-order cyclotron resonance is flat, whereas Lee's theory predicts an f exp - 7/4 frequency dependence for the November 12 shock. Higher frequency waves, which could not resonate with the observed upstream protons, increased in amplitude as the shock approached, suggesting that they too were generated by the shock.

Kennel, C. F.↗

NASA NTRS1987

Application of stability theory to laminar flow control - Progress and requirements

Paper briefly summarizes the current status of linear stability theory as applied to laminar flow control for aerodynamics. Results indicate that the conventional 'N factor' method of correlating stability theory and transition has a broad application range, including low- and high-speeds, two- and three-dimensional mean flow and TS, Gortler and crossflow disturbance modes. Linear theory is particularly applicable to the laminar flow control problem as, for system efficiency, control must be exercised and disturbances maintained in the linear regime. Current areas of concern for LFC, which require further stability theory research, include TS-crossflow interaction, combined disturbance fields (roughness, waviness, noise) and suction-induced disturbances. Some results on wave-interactions are presented.

Bushnell, D. M.↗

NASA NTRS1988

Biaxial experiments supporting the development of constitutive theories for advanced high-temperature materials

Complex states of stress and strain are introduced into components during service in engineering applications. It follows that analysis of such components requires material descriptions, or constitutive theories, which reflect the tensorial nature of stress and strain. For applications involving stress levels above yield, the situation is more complex in that material response is both nonlinear and history dependent. This has led to the development of viscoplastic constitutive theories which introduce time by expressing the flow and evolutionary equation in the form of time derivatives. Models were developed here which can be used to analyze high temperature components manufactured from advanced composite materials. In parallel with these studies, effort was directed at developing multiaxial testing techniques to verify the various theories. Recent progress in the development of constitutive theories from both the theoretical and experimental viewpoints are outlined. One important aspect is that material descriptions for advanced composite materials which can be implemented in general purpose finite element codes and used for practical design are verified.

Ellis, J. R.↗

NASA NTRS1988

An approximation theory for the identification of nonlinear distributed parameter systems

An abstract approximation framework for the identification of nonlinear distributed parameter systems is developed. Inverse problems for nonlinear systems governed by strongly maximal monotone operators (satisfying a mild continuous dependence condition with respect to the unknown parameters to be identified) are treated. Convergence of Galerkin approximations and the corresponding solutions of finite dimensional approximating identification problems to a solution of the original finite dimensional identification problem is demonstrated using the theory of nonlinear evolution systems and a nonlinear analog of the Trotter-Kato approximation result for semigroups of bounded linear operators. The nonlinear theory developed here is shown to subsume an existing linear theory as a special case. It is also shown to be applicable to a broad class of nonlinear elliptic operators and the corresponding nonlinear parabolic partial differential equations to which they lead. An application of the theory to a quasilinear model for heat conduction or mass transfer is discussed.

Banks, H. T.↗

NASA NTRS1988

A theory for the radiation at the third to fifth harmonics of the plasma frequency upstream from the earth's bow shock

A theory involving the process L + T' - T is proposed for the observed third to fifth harmonics of the plasma frequency observed upstream from the earth's bow shock. The conditions for which the theory may explain the observed radiation are determined, and the viability of the theory is discussed. The theory is found to require L waves with temperature between about 10 to the 21st and 10 to the 22nd K in the source regions to account for the levels and number of harmonics of the observed radiation. Such L wave temperatures are theoretically possible in the foreshock, but are not consistent with the most intense observed L waves.

Cairns, Iver H.↗

NASA NTRS1988

Significance of vapor phase chemical reactions on CVD rates predicted by chemically frozen and local thermochemical equilibrium boundary layer theories

This paper investigates the role played by vapor-phase chemical reactions on CVD rates by comparing the results of two extreme theories developed to predict CVD mass transport rates in the absence of interfacial kinetic barrier: one based on chemically frozen boundary layer and the other based on local thermochemical equilibrium. Both theories consider laminar convective-diffusion boundary layers at high Reynolds numbers and include thermal (Soret) diffusion and variable property effects. As an example, Na2SO4 deposition was studied. It was found that gas phase reactions have no important role on Na2SO4 deposition rates and on the predictions of the theories. The implications of the predictions of the two theories to other CVD systems are discussed.

Gokoglu, Suleyman A.↗

NASA NTRS1986

A multiaxial theory of viscoplasticity for isotropic materials

Many viscoplastic constitutive models for high temperature structural alloys are based exclusively on uniaxial test data. Generalization to multiaxial states of stress is made by assuming the stress dependence to be on the second principal invariant (J sub 2) of the deviatoric stress, frequently called the effective stress. If such a J sub 2 theory, based on uniaxial testing, is called upon to predict behavior under conditions other than uniaxial, e.g., pure shear, and it does so poorly, nothing is left to adjust in the theory. For a fully isotropic material whose inelastic deformation behavior is relatively independent of hydrostatic stress, the most general stress dependence is on the two (non-zero) principal invariants of the deviatoric stress, J sub 2 and J sub 3. These invariants constitute what is known as an integrity basis for the material. A time dependent constitutive theory with stress dependence on J sub 2 and J sub 3 is presented, that reduces to a known J sub 2 theory as a special case.

Robinson, D. N.↗

NASA NTRS1989

The minimum drag of thin wings at supersonic speed according to Kogan's theory

In the theory of thin lifting surfaces the minimum drag consistent with a given total lift occurs when the downwash, averaged between forward and reversed motion of the wing, has the same value at all points of the wing planform. In Kogan's theory the conditions for minimum drag are determined on the forward sloping characteristic surface touching the trailing edge of the wing and it is shown that such a surface plays the role of the Trefftz plane familiar in subsonic wing theory. This paper shows how Kogan's theory may be applied to determine the drag of elliptic wings at supersonic speed. It appears that such wings have lower drag than the conventional 'delta' wing.

Jones, Robert T.↗

NASA NTRS1989

Potential theory of radiation

A theoretical method is being developed by which the structure of a radiation field can be predicted by a radiation potential theory, similar to a classical potential theory. The introduction of a scalar potential is justified on the grounds that the spectral intensity vector is irrotational. The vector is also solenoidal in the limits of a radiation field in complete radiative equilibrium or in a vacuum. This method provides an exact, elliptic type equation that will upgrade the accuracy and the efficiency of the current CFD programs required for the prediction of radiation and flow fields. A number of interesting results emerge from the present study. First, a steady state radiation field exhibits an optically modulated inverse square law distribution character. Secondly, the unsteady radiation field is structured with two conjugate scalar potentials. Each is governed by a Klein-Gordon equation with a frictional force and a restoring force. This steady potential field structure and the propagation of radiation potentials are consistent with the well known results of classical electromagnetic theory. The extension of the radiation potential theory for spray combustion and hypersonic flow is also recommended.

Chiu, Huei-Huang↗