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NASA NTRS1990

On the numerical computation of nonlinear force-free magnetic fields

An algorithm has been developed to extrapolate nonlinear force-free magnetic fields from the photosphere, given the proper boundary conditions. This paper presents the results of this work, describing the mathematical formalism that was developed, the numerical techniques employed, and comments on the stability criteria and accuracy developed for these numerical schemes. An analytical solution is used for a benchmark test; the results show that the computational accuracy for the case of a nonlinear force-free magnetic field was on the order of a few percent (less than 5 percent). This newly developed scheme was applied to analyze a solar vector magnetogram, and the results were compared with the results deduced from the classical potential field method. The comparison shows that additional physical features of the vector magnetogram were revealed in the nonlinear force-free case.

Wu, S. T.↗

NASA NTRS1990

A two-step iterative method for evolving nonlinear acoustic systems to a steady-state

A new approach for evolving two-dimensional nonlinear acoustic systems with flow to a steady state is presented. The approach is a two-step iterative method which is tested on a benchmark acoustic problem for which an exact analytical solution is available. Results are also calculated for a nonlinear acoustic problem for which an exact analytical solution is not known. Results indicate that the two-step method represents a powerful, efficient, and stable method for evolving two-dimensional acoustic systems to a steady state, and that the method is applicable to any number of spatial dimensions and to other hyperbolic systems. It is noted that for the benchmark problem only a single iteration on the method is required when the transient and steady-state field are of the same order of magnitude; however, four iterations are required when the steady-state field is several orders of magnitude smaller than the transient field. This method requires six iterations before achieving a steady state for the nonlinear test problem.

Watson, Willie R.↗

NASA NTRS1990

Spatial evolution of nonlinear acoustic mode instabilities on hypersonic boundary layers

The effects are considered of strong critical layer nonlinearity on the spatial evolution of an initially linear acoustic mode instability wave on a hypersonic flat plate boundary layer. The analysis shows that nonlinearity, which is initially confined to a thin critical layer, first becomes important when the amplitude of the pressure fluctuations become O(1/M exp 4 in M exp 2), where M is the free stream Mach number. The flow outside the critical layer is still determined by linear dynamics and therefore takes the form of a linear instability wave, but with its amplitude completely determined by the flow within the critical layer. The latter flow is determined by a coupled set of nonlinear equations, which were solved numerically.

Goldstein, M. E.↗

NASA NTRS1990

Nonlinear development of crossflow vortices

Nonlinear crossflow vortices in an incompressible three-dimensional boundary layer are computed by weakly nonlinear theory and direct numerical simulations. The parallel basic flow is defined by Falkner-Skan-Cooke similarity profiles. The temporal evolution of spanwise periodic, quasi-two-dimensional disturbances without variations along the vortex axis is considered. The nonlinear theory is based on the approach of Herbert (1980, 1983). The theory predicts the existence of the finite amplitude equilibrium states seen in earlier simulations. When the disturbance amplitudes are small, there is very good quantitative agreement in the fundamental disturbance velocity components between the theory and the simulations.

Singer, Bart A.↗

NASA NTRS1991

Numerical simulations of the nonlinear kink modes in linearly stable supersonic slip surfaces

High-resolution numerical simulations of supersonic slip surfaces were performed using the Cray 2 at the Minnesota Supercomputer Center to confirm earlier analytic nonlinear stability calculations of such structures. The present study presents a numerical solution for the problem solved analytically by Artola and Majda (1987) and follows growing modes well into the large-amplitude regime. The response of an equal-density Mach-4 slip surface to a variety of impinging nonlinear sound wave trains is computed using the piecewise-parabolic method (PPM). The nature of the nonlinear kink modes observed in the simulations was found to be similar to that discussed by Artola and Majda. Most of the speeds moved in either direction, with speeds near the predicted value. It is suggested that the stationary modes will eventually dominate the flow at much later times, and it is argued that the stationary modes are more disruptive than the propagating kink modes.

Pedelty, Jeffrey A.↗

NASA NTRS1990

Nonlinear breakdowns in boundary layer transition

Theoretical studies of boundary-layer transition are described, based on high Reynolds numbers and with attention drawn to nonlinear interactions, breakdowns and scales. The article notes in particular truly nonlinear theories for which the mean-flow profile is completely altered from its original state. Two- and three-dimensional flow theory and conjectures on turbulent boundary-layer structures are included. Specific recent findings noted, and in qualitative agreement with experiments, are: nonlinear finite-time break-ups in unsteady interactive boundary layers; strong vortex/wave interactions; and prediction of turbulent boundary-layer displacement- and stress sublayer-thicknesses.

Smith, Frank T.↗

NASA NTRS1991

Linear prediction filters for linear and nonlinear modeled geomagnetic activity

It is shown that the Faraday loop analog model of geomagnetic activity exhibits both the directly driven and loading-unloading magnetospheric responses to solar wind input. It is further shown that the directly driven component is a linear response to loading while the loading-unloading response is nonlinear. Linear prediction filters which relate model input to output are discussed. By either allowing or suppressing the loading-unloading model response filters that relate to nonlinear or linear dynamics, respectively, have been computed. Filters that described the directly driven response are finite ranged; they asymptote to zero with increasing lag on a time scale that is fixed by the dissipation rate of the model. Filters that describe the nonlinear total response are infinite ranged; they asymptote with increasing lag to large amplitude periodic oscillations. Some implications of these infinite ranged filters are discussed.

Klimas, A. J.↗

NASA NTRS1991

Application of a robust linear control design to a truss structure with nonlinear joints

An efficient nonlinear equivalent beam finite-element method for the application of a full state feedback design is described, which is robust to plant uncertainties to a beamlike truss structure with nonlinear elements. The method may be extended to model nonlinear structures with other types of control systems, such as model-based compensators.

Webster, Mark↗

NASA NTRS1991

Nonlinear optical effects on the surface of acridine yellow-doped lead-tin fluorophosphate glass

The second- and third-order nonlinear optical properties of acridine yellow-doped lead-tin fluorophosphate (LTF) glass have been directly studied by measurement of surface enhanced second harmonic generation and third harmonic generation. The three photon excitation fluorescence is also observed. Based on these results, the large nonlinearities of the acridine LTF system which is a new nonlinear optical material are experimentally demonstrated.

He, K. X.↗

NASA NTRS1992

Spurious Solutions Of Nonlinear Differential Equations

Report utilizes nonlinear-dynamics approach to investigate possible sources of errors and slow convergence and non-convergence of steady-state numerical solutions when using time-dependent approach for problems containing nonlinear source terms. Emphasizes implications for development of algorithms in CFD and computational sciences in general. Main fundamental conclusion of study is that qualitative features of nonlinear differential equations cannot be adequately represented by finite-difference method and vice versa.

Yee, H. C.↗

NASA NTRS1991

Baseband pulse shaping techniques for nonlinearly amplified pi/4-QPSK and QAM systems

A new generation of multi-stage pi/4-shifted QPSK and of superposed quadrature-amplitude-modulated (SQAM) modulators-coherent demodulators (modems) and of continuous phase modulated (CPM)-gaussian premodulation filtered minimum-shift-keying (MGMSK) systems is proposed and studied. These modems will lead to bandwidth and power efficient satellite communications systems designs. As an illustrative application, a baseband processing technique pi/4-controlled transition PSK (pi/4-CTPSK) is described. To develop a cost and power efficient design strategy, we assume that nonlinear, fully saturated high power amplifiers (HPA) are utilized in the satellite earth station transmitter and in the satellite transponder. Modem structures which could lead to application specific integrated circuit (ASIC) satellite on-board processing universal modem applications are also considered. Multistate GMSK (i.e., MGMSK) signal generation methods by means of two or more RF combined nonlinearly amplified SQAM modems and by one multistate (in-phase and quadrature-baseband premodulation filtered-superposed) SQAM architecture and one RF nonlinear amplifier are studied. During the SQAM modem development phase we investigate the potential system advantages of the pi/4-shifted logic. The bandwidth efficiency of the proposed multistate GMSK and baseband filtered PAM-FM modulator (a new class in the CPM family) will be significantly higher than that of conventional G-MSK systems. To optimize the practical P(sub e) = f((E sub b)/(N sub o)) performance we consider improved coherent demodulation MGMSK structures such as deviated-frequency locking coherent demodulators. For relative low bit rate SATCOM applications, e.g., bit rates less than 300 kb/s, phase noise tracking cancellation (for fixed site earth station) and phase noise cancellation as well as Doppler compensation (for satellite to mobile earth station) applications may be required. We study digital channel sounding methods which could cancel the phase noise-caused degradations of CPM and GMSK modems.

Feher, Kamilo↗

NASA NTRS1991

Nonlinear rotordynamics analysis

Effective analysis tools were developed for predicting the nonlinear rotordynamic behavior of the Space Shuttle Main Engine (SSME) turbopumps under steady and transient operating conditions. Using these methods, preliminary parametric studies were conducted on both generic and actual HPOTP (high pressure oxygen turbopump) models. In particular, a novel modified harmonic balance/alternating Fourier transform (HB/AFT) method was developed and used to conduct a preliminary study of the effects of fluid, bearing and seal forces on the unbalanced response of a multi-disk rotor in the presence of bearing clearances. The method makes it possible to determine periodic, sub-, super-synchronous and chaotic responses of a rotor system. The method also yields information about the stability of the obtained response, thus allowing bifurcation analyses. This provides a more effective capability for predicting the response under transient conditions by searching in proximity of resonance peaks. Preliminary results were also obtained for the nonlinear transient response of an actual HPOTP model using an efficient, newly developed numerical method based on convolution integration. Currently, the HB/AFT is being extended for determining the aperiodic response of nonlinear systems. Initial results show the method to be promising.

Noah, Sherif T.↗

NASA NTRS1991

Nonlinear optical properties of organic materials: A theoretical study

Replacement of electronic switching circuits in computing and telecommunication systems with purely optical devices offers the potential for extremely high throughput and compact information processing systems. The potential application of organic materials containing molecules with large nonresonant nonlinear effects in this area have triggered intensive research during the last decade. Interest on this area was due to two facts: (1) that many organic materials show nonlinearities that are orders of magnitude larger than those of conventional inorganic materials such as lithium niobate and potassium dihydrogen phosphate; and (2) that organic materials show much flexibility in terms of molecular designs. Some of the desirable characteristics that these materials should have are that they be transparent to the frequency of the incident laser and its second or third harmonic, that they have a high damage threshold, and, in the case of second-order effects, that their crystal structure or molecular orientation be accentric. Since polymeric assemblages can enhance the nonlinear response of organic molecules severalfold, efforts have been directed toward the synthesis of thin films with interpenetrating lattices of electroactive molecules. The goal of this theoretical investigation is to predict the magnitude of the molecular polarizabilities of organic molecules that could be incorporated into films. These calculations are intended to become a powerful tool to assist material scientists in screening for the best candidates for optical applications. The procedure that was developed for the present calculations is based on the static-field approach, and is a modification to the method developed by Dewar and Stewart, 1984 for calculating molecular linear polarizabilities.

Cardelino, Beatriz H.↗

NASA NTRS1991

Linear and nonlinear dynamic analysis by boundary element method

An advanced implementation of the direct boundary element method (BEM) applicable to free-vibration, periodic (steady-state) vibration and linear and nonlinear transient dynamic problems involving two and three-dimensional isotropic solids of arbitrary shape is presented. Interior, exterior, and half-space problems can all be solved by the present formulation. For the free-vibration analysis, a new real variable BEM formulation is presented which solves the free-vibration problem in the form of algebraic equations (formed from the static kernels) and needs only surface discretization. In the area of time-domain transient analysis, the BEM is well suited because it gives an implicit formulation. Although the integral formulations are elegant, because of the complexity of the formulation it has never been implemented in exact form. In the present work, linear and nonlinear time domain transient analysis for three-dimensional solids has been implemented in a general and complete manner. The formulation and implementation of the nonlinear, transient, dynamic analysis presented here is the first ever in the field of boundary element analysis. Almost all the existing formulation of BEM in dynamics use the constant variation of the variables in space and time which is very unrealistic for engineering problems and, in some cases, it leads to unacceptably inaccurate results. In the present work, linear and quadratic isoparametric boundary elements are used for discretization of geometry and functional variations in space. In addition, higher order variations in time are used. These methods of analysis are applicable to piecewise-homogeneous materials, such that not only problems of the layered media and the soil-structure interaction can be analyzed but also a large problem can be solved by the usual sub-structuring technique. The analyses have been incorporated in a versatile, general-purpose computer program. Some numerical problems are solved and, through comparisons with available analytical and numerical results, the stability and high accuracy of these dynamic analysis techniques are established.

Ahmad, Shahid↗

NASA NTRS1991

Nonlinear optical polymers for electro-optic signal processing

Photonics is an emerging technology, slated for rapid growth in communications systems, sensors, imagers, and computers. Its growth is driven by the need for speed, reliability, and low cost. New nonlinear polymeric materials will be a key technology in the new wave of photonics devices. Electron-conjubated polymeric materials offer large electro-optic figures of merit, ease of processing into films and fibers, ruggedness, low cost, and a plethora of design options. Several new broad classes of second-order nonlinear optical polymers were developed at the Navy's Michelson Laboratory at China Lake, California. Polar alignment in thin film waveguides was achieved by electric-field poling and Langmuir-Blodgett processing. Our polymers have high softening temperatures and good aging properties. While most of the films can be photobleached with ultraviolet (UV) light, some have excellent stability in the 500-1600 nm range, and UV stability in the 290-310 nm range. The optical nonlinear response of these polymers is subpicosecond. Electro-optic switches, frequency doublers, light modulators, and optical data storage media are some of the device applications anticipated for these polymers.

Lindsay, Geoffrey A.↗

NASA NTRS1991

On the nonlinear development of the most unstable Goertler vortex mode

The nonlinear development of the most unstable Gortler vortex mode in boundary layer flows over curved walls is investigated. The most unstable Gortler mode is confined to a viscous wall layer of thickness O(G -1/5) and has spanwise wavelength O(G 11/5); it is, of course, most relevant to flow situations where the Gortler number G is much greater than 1. The nonlinear equations covering the evolution of this mode over an O(G -3/5) streamwise lengthscale are derived and are found to be of a fully nonparallel nature. The solution of these equations is achieved by making use of the numerical scheme used by Hall (1988) for the numerical solution of the nonlinear Gortler equations valid for O(1) Gortler numbers. Thus, the spanwise dependence of the flow is described by a Fourier expansion, whereas the streamwise and normal variations of the flow are dealt with by employing a suitable finite difference discretization of the governing equations. Our calculations demonstrate that, given a suitable initial disturbance, after a brief interval of decay, the energy in all the higher harmonics grows until a singularity is encountered at some downstream position. The structure of the flowfield as this singularity is approached suggests that the singularity is responsible for the vortices, which are initially confined to the thin viscous wall layer, moving away from the wall and into the core of the boundary layer.

Denier, James P.↗

NASA NTRS1992

Nonlinear analyses of composite aerospace structures in sonic fatigue

The primary research effort of this project is the development of analytical methods for the prediction of nonlinear random response of composite aerospace structures subjected to combined acoustic and thermal loads. The progress, accomplishments, and future plans of three random response research topics are discussed, namely acoustics-structure interactions using boundary/finite element methods, nonlinear vibrations of beams and composite plates under harmonic and random excitations, and numerical simulation of the nonlinear response of composite plates under combined thermal and acoustic loading.

Mei, Chuh↗

NASA NTRS1991

Nonlinear baroclinic adjustment

The concept of baroclinic adjustment is reexamined in the context of a fully nonlinear two-layer model on a beta-plane. Based on the results, a single, conceptually very simple mechanism of the nonlinear equilibration of waves and the mean flow is proposed, which is termed 'nonlinear baroclinic adjustment'. The new concept appears applicable to cases that currently require different explanations, varying from case to case, to account for the equilibration of the mean temperature gradient in the presence of external driving.

Cehelsky, Priscilla↗