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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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NASA NTRS1995

Lyapunov exponents from CHUA's circuit time series using artificial neural networks

In this paper we present the general problem of identifying if a nonlinear dynamic system has a chaotic behavior. If the answer is positive the system will be sensitive to small perturbations in the initial conditions which will imply that there is a chaotic attractor in its state space. A particular problem would be that of identifying a chaotic oscillator. We present an example of three well known different chaotic oscillators where we have knowledge of the equations that govern the dynamical systems and from there we can obtain the corresponding time series. In a similar example we assume that we only know the time series and, finally, in another example we have to take measurements in the Chua's circuit to obtain sample points of the time series. With the knowledge about the time series the phase plane portraits are plotted and from them, by visual inspection, it is concluded whether or not the system is chaotic. This method has the problem of uncertainty and subjectivity and for that reason a different approach is needed. A quantitative approach is the computation of the Lyapunov exponents. We describe several methods for obtaining them and apply a little known method of artificial neural networks to the different examples mentioned above. We end the paper discussing the importance of the Lyapunov exponents in the interpretation of the dynamic behavior of biological neurons and biological neural networks.

Gonzalez, J. Jesus↗
NASA NTRS1995

Wavenumber selection and hysteresis in nonlinear baroclinic flow

Wavenumber transition and hysteresis in a highly unstable baroclinic flow are investigated using a high-resolution spectral numerical model. As the flow becomes more supercritical, the dominant wave gradually shifts from the most unstable wave predicted by the linear theory to a longer wave with a larger time-averaged amplitude, while the rectified mean flow attains a stronger shear at the center of the channel. The numerical results display a complex hysteresis behavior, which occurs not only between the states of different dominant wavenumbers, but also between the states of identical dominant wavenumber but of different dynamic characteristics. In a certain parameter range three stable states, each with different dominant wavenumber, are possible, and in another parameter range four stable states are possible, among them three stable states with an identical dominant wave. The numerical results suggest that a multiple weather regime exists even without external forcing in which the flow aperiodically varies between two distinct behaviors. The effects of stable higher harmonics are assessed and it is found that their presence contributes not only to the better approximation of the model solutions but also to the selection of the final equilibrium state, due to the chaotic nature of the initial transient period.

Chou, Shih-Hung↗
NASA NTRS2011

Verification and Validation Plan for Flight Performance Requirements on the CEV Parachute Assembly System

The Crew Exploration Vehicle Parachute Assembly System (CPAS) is engaged in a multi-year design and test campaign aimed at qualifying a parachute recovery system for human use on the Orion Spacecraft. Orion has parachute flight performance requirements that will ultimately be verified through the use of Monte Carlo multi-degree of freedom flight simulations. These simulations will be anchored by real world flight test data and iteratively improved to provide a closer approximation to the real physics observed in the inherently chaotic inflation and steady state flight of the CPAS parachutes. This paper will examine the processes necessary to verify the flight performance requirements of the human rated spacecraft. The focus will be on the requirements verification and model validation planned on CPAS.

Morris, Aaron L.↗
NASA NTRS1994

Convection in the Physical Vapor Transport Process: Thermosolutal - Part 2

We consider the effect of an inert gas on the diffusive-convective physical vapor transport process. We investigate the case when the temperature gradient is stabilizing and the concentration gradient is destabilizing for a wide parametric range. When an inert gas is present, the thermal and solutal convection oppose each other. The solutal field is destabilizing while the thermal field and the advective-diffusive flux stabilize the flow field. When the pressure of the inert component is increased, the stabilizing effect of the advective-diffusive flux is decreased. The intensity of convection as well as the oscillatory transient time increases. Below, the critical Rayleigh number, the nonlinear dynamics of the flow field show an oscillatory approach to steady state. For parametric values in the neighborhood of the critical Rayleigh number, the flow field undergoes a chaotic transient which settles to a periodic state. The asymptotic state of the flow field shows that growth and amalgamation of cells yields an overturning motion which results in an asymmetric cellular structure. The low gravity environment yields the stabilizing advective-diffusive flow which results in uniform temperature and concentration gradients near the crystal interface.

Duval, Walter M. B.↗
NASA NTRS1995

A FFT Method for the Quasiclassical Selection of Initial Ro-Vibrational States of Triatomic Molecules

This paper describes the use of an exact fast Fourier transform (FFT) method to prepare specified vibrational-rotational states of triatomic molecules. The method determines the Fourier coefficients needed to describe the coordinates and momenta of a vibrating-rotating triatomic molecule. Once the Fourier coefficients of a particular state are determined, it is possible to easily generate as many random sets of initial cartesian coordinates and momenta as desired. All the members of each set will correspond to the particular vibrational-rotational state selected. For example, in the case of the ground vibrational state of a non-rotating water molecule, the calculated actions of 100 sets of initial conditions produced actions within 0.001 h(bar) of the specified quantization values and energies within 5 cm(sup -1) of the semiclassical eigenvalue. The numerical procedure is straightforward for states in which all the fundamental frequencies are independent. However for states for which the fundamental frequencies become commensurate (resonance states), there are additional complications. In these cases it is necessary to determine a new set of "fundamental" frequencies and to modify the quantization conditions. Once these adjustments are made, good results are obtained for resonance states. The major problems are in labelling the large number of Fourier coefficients and the presence of regions of chaotic motion. Results are presented for the vibrational states of H2O and HCN and the ro-vibrational states of H2O.

Eaker, Charles W.↗
NASA NTRS1995

Controlling Chaotic Lasers

Irregular fluctuations in intensity have long plagued the operation of a wide variety of solid-state lasers. We are exploring the possibility of exploiting rather than avoiding a laser's chaotic output. As an important step in that direction, we have applied a novel control technique to stabilize a solid state laser. By making small periodic changes in only one input parameter of the laser, we are able to stabilize complex periodic waveforms and steady state behavior in the laser output. We demonstrate the application of this approach in a diode pumped Nd:/YAG laser system.

Gills, Zelda↗
NASA NTRS2016

Least Squares Shadowing Sensitivity Analysis of Chaotic Flow Around a Two-Dimensional Airfoil

Gradient-based sensitivity analysis has proven to be an enabling technology for many applications, including design of aerospace vehicles. However, conventional sensitivity analysis methods break down when applied to long-time averages of chaotic systems. This breakdown is a serious limitation because many aerospace applications involve physical phenomena that exhibit chaotic dynamics, most notably high-resolution large-eddy and direct numerical simulations of turbulent aerodynamic flows. A recently proposed methodology, Least Squares Shadowing (LSS), avoids this breakdown and advances the state of the art in sensitivity analysis for chaotic flows. The first application of LSS to a chaotic flow simulated with a large-scale computational fluid dynamics solver is presented. The LSS sensitivity computed for this chaotic flow is verified and shown to be accurate, but the computational cost of the current LSS implementation is high.

Blonigan, Patrick J.↗
NASA NTRS1990

Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. Part 1: The ODE connection and its implications for algorithm development in computational fluid dynamics

Spurious stable as well as unstable steady state numerical solutions, spurious asymptotic numerical solutions of higher period, and even stable chaotic behavior can occur when finite difference methods are used to solve nonlinear differential equations (DE) numerically. The occurrence of spurious asymptotes is independent of whether the DE possesses a unique steady state or has additional periodic solutions and/or exhibits chaotic phenomena. The form of the nonlinear DEs and the type of numerical schemes are the determining factor. In addition, the occurrence of spurious steady states is not restricted to the time steps that are beyond the linearized stability limit of the scheme. In many instances, it can occur below the linearized stability limit. Therefore, it is essential for practitioners in computational sciences to be knowledgeable about the dynamical behavior of finite difference methods for nonlinear scalar DEs before the actual application of these methods to practical computations. It is also important to change the traditional way of thinking and practices when dealing with genuinely nonlinear problems. In the past, spurious asymptotes were observed in numerical computations but tended to be ignored because they all were assumed to lie beyond the linearized stability limits of the time step parameter delta t. As can be seen from the study, bifurcations to and from spurious asymptotic solutions and transitions to computational instability not only are highly scheme dependent and problem dependent, but also initial data and boundary condition dependent, and not limited to time steps that are beyond the linearized stability limit.

Yee, H. C.↗
NASA NTRS1991

Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. I - The dynamics of time discretization and its implications for algorithm development in computational fluid dynamics

Spurious stable as well as unstable steady state numerical solutions, spurious asymptotic numerical solutions of higher period, and even stable chaotic behavior can occur when finite difference methods are used to solve nonlinear differential equations (DE) numerically. The occurrence of spurious asymptotes is independent of whether the DE possesses a unique steady state or has additional periodic solutions and/or exhibits chaotic phenomena. The form of the nonlinear DEs and the type of numerical schemes are the determining factor. In addition, the occurrence of spurious steady states is not restricted to the time steps that are beyond the linearized stability limit of the scheme. In many instances, it can occur below the linearized stability limit. Therefore, it is essential for practitioners in computational sciences to be knowledgeable about the dynamical behavior of finite difference methods for nonlinear scalar DEs before the actual application of these methods to practical computations. It is also important to change the traditional way of thinking and practices when dealing with genuinely nonlinear problems. In the past, spurious asymptotes were observed in numerical computations but tended to be ignored because they all were assumed to lie beyond the linearized stability limits of the time step parameter delta t. As can be seen from the study, bifurcations to and from spurious asymptotic solutions and transitions to computational instability not only are highly scheme dependent and problem dependent, but also initial data and boundary condition dependent, and not limited to time steps that are beyond the linearized stability limit.

Yee, H. C.↗
NASA NTRS1994

Chaotic dynamics of corotating magnetospheric convection

The corotating plasma convection system of the Jovian magnetosphere is analyzed. The macroscopic (mhd) model introduced by Summers and Mu, (1992) that incorporates the effects of microdiffusion is extended by including previously neglected density effects. We reduce the governing partial differential equations to a third-order ordinary differential system by the Galerkin technique of mode truncation. We carry out such a severe truncation partly in the interests of tractability, and leave open the question of the efficacy of adding additional modes. Exhaustive numerical integrations are carried out to calculate the long-term solutions, and we discover that a rich array of plasma motions is possible, dependent on the value of the height-integrated ionospheric Pederson conductivity Sigma. If Sigma is less than a certain critical value Sigma(sub c), then plasma motion can be expected to be chaotic (or periodic), while if Sigma is greater than Sigma(sub c), then steady state convection is expected. In the former case, whether the plasma motion is chaotic or periodic (and, if periodic, the magnitude of the period) can be very sensitive to the value of Sigma. The value of Sigma(sub c), which is a function of a parameter q that occurs in the assumed form of the stationary radial profile (varies as L(exp -q) of the plasma mass per unit magnetic flux, lies well within the accepted range of values of Sigma for Jupiter, i.e. Sigma greater than or equal to 0.1 mho and less than or equal to 10 mho.

Summers, Danny↗
NASA NTRS2002

Phase Synchronization and Desynchronization of Structural Response Induced by Turbulent and External Sound

Acoustic and turbulent boundary layer flow loadings over a flexible structure are used to study the spatial-temporal dynamics of the response of the structure. The stability of the spatial synchronization and desynchronization by an active external force is investigated with an array of coupled transducers on the structure. In the synchronous state, the structural phase is locked, which leads to the formation of spatial patterns while the amplitude peaks exhibit chaotic behaviors. Large amplitude, spatially symmetric loading is superimposed on broadband, but in the desynchronized state, the spectrum broadens and the phase space is lost. The resulting pattern bears a striking resemblance to phase turbulence. The transition is achieved by using a low power external actuator to trigger broadband behaviors from the knowledge of the external acoustic load inducing synchronization. The changes are made favorably and efficiently to alter the frequency distribution of power, not the total power level. Before synchronization effects are seen, the panel response to the turbulent boundary layer loading is discontinuously spatio-temporally correlated. The stability develops from different competing wavelengths; the spatial scale is significantly shorter than when forced with the superimposed external sound. When the external sound level decreases and the synchronized phases are lost, changes in the character of the spectra can be linked to the occurrence of spatial phase transition. These changes can develop broadband response. Synchronized responses of fuselage structure panels have been observed in subsonic and supersonic aircraft; results from two flights tests are discussed.

Maestrello, Lucio↗
NASA NTRS1989

Inhibition of quantum transport due to 'scars' of unstable periodic orbits

A new quantum mechanism for the suppression of chaotic ionization of highly excited hydrogen atoms explains the appearance of anomalously stable states in the microwave ionization experiments of Koch et al. A novel phase-space representation of the perturbed wave functions reveals that the inhibition of quantum transport is due to the selective excitation of wave functions that are highly localized near unstable periodic orbits in the chaotic classical phase space. The 'scarred' wave functions provide a new basis for the quantum description of a variety of classically chaotic systems.

Jensen, R. V.↗
NASA NTRS1986

Orbital resonances, unusual configurations and exotic rotation states among planetary satellites

The origin of orbital resonances is shown in the demonstration of the evolution of a pair of planetary satellites through a commensurability of the mean motions by a sequence of diagrams of constant energy curves in a two-dimensional phase space; the closed curve corresponding to the motion in each successive diagram is identified by its adiabatically conserved area. It is found that two-body resonances serve as a basis in the solution of the problem of the origin and evolution of the three-body Laplace resonance among the Galilean satellites of Jupiter. The unusual rotation state of Saturn's satellite Hyperion which is expected to tumble chaotically for an indefinite amount of time is discussed.

Peale, S. J.↗
NASA NTRS2011

Radiolysis of Sulfuric Acid, Sulfuric Acid Monohydrate, and Sulfuric Acid Tetrahydrate and Its Relevance to Europa

We report laboratory studies on the 0.8 MeV proton irradiation of ices composed of sulfuric acid (H2SO4), sulfuric acid monohydrate (H2SO4 H2O), and sulfuric acid tetrahydrate (H2SO4 4H2O) between 10 and 180 K. Using infrared spectroscopy, we identify the main radiation products as H2O, SO2, (S2O3)x, H3O+, HSO4(exp -), and SO4(exp 2-). At high radiation doses, we find that H2SO4 molecules are destroyed completely and that H2SO4 H2O is formed on subsequent warming. This hydrate is significantly more stable to radiolytic destruction than pure H2SO4, falling to an equilibrium relative abundance of 50% of its original value on prolonged irradiation. Unlike either pure H2SO4 or H2SO4 H2O, the loss of H2SO4 4H2O exhibits a strong temperature dependence, as the tetrahydrate is essentially unchanged at the highest irradiation temperatures and completely destroyed at the lowest ones, which we speculate is due to a combination of radiolytic destruction and amorphization. Furthermore, at the lower temperatures it is clear that irradiation causes the tetrahydrate spectrum to transition to one that closely resembles the monohydrate spectrum. Extrapolating our results to Europa s surface, we speculate that the variations in SO2 concentrations observed in the chaotic terrains are a result of radiation processing of lower hydration states of sulfuric acid and that the monohydrate will remain stable on the surface over geological times, while the tetrahydrate will remain stable in the warmer regions but be destroyed in the colder regions, unless it can be reformed by other processes, such as thermal reactions induced by diurnal cycling.

Loeffler, M. J.↗
NASA NTRS1990

An investigation of chaotic Kolmogorov flows

A two dimensional flow governed by the incompressible Navier-Stokes equations with a steady spatially periodic forcing (known as the Kolmogorov flow) is numerically simulated. The behavior of the flow and its transition states as the Reynolds number (Re) varies is investigated in detail, as well as a number of the flow features. A sequence of bifurcations is shown to take place in the flow as Re varied. Two main regimes of the flow were observed: small and large scale structure regimes corresponding to different ranges of Re. Each of the regimes includes a number of quasiperiodic, chaotic, and relaminarization windows. In addition, each range contains a chaotic window with non-ergodic chaotic attractors. Spatially disordered, but temporally steady states were discovered in large scale structure regime. Features of the diverse cases are displayed in terms of the temporal power spectrum, Poincare sections and, where possible, Lyapunov exponents and Kaplan-Yorke dimension.

Platt, N.↗
NASA NTRS1991

An investigation of chaotic Kolmogorov flows

A two dimensional flow governed by the incompressible Navier-Stokes equations with a steady spatially periodic forcing (known as the Kolmogorov flow) is numerically simulated. The behavior of the flow and its transition states as the Reynolds number (Re) varies is investigated in detail, as well as a number of the flow features. A sequence of bifurcations is shown to take place in the flow as Re varied. Two main regimes of the flow were observed: small and large scale structure regimes corresponding to different ranges of Re. Each of the regimes includes a number of quasiperiodic, chaotic, and relaminarization windows. In addition, each range contains a chaotic window with non-ergodic chaotic attractors. Spatially disordered, but temporally steady states were discovered in large scale structure regime. Features of the diverse cases are displayed in terms of the temporal power spectrum, Poincare sections and, where possible, Lyapunov exponents and Kaplan-Yorke dimension.

Platt, N.↗
NASA NTRS1996

Computational Study of Chaotic and Ordered Solutions of the Kuramoto-Sivashinsky Equation

We report the results of extensive numerical experiments on the Kuramoto-Sivashinsky equation in the strongly chaotic regime as the viscosity parameter is decreased and increasingly more linearly unstable modes enter the dynamics. General initial conditions are used and evolving states do not assume odd-parity. A large number of numerical experiments are employed in order to obtain quantitative characteristics of the dynamics. We report on different routes to chaos and provide numerical evidence and construction of strange attractors with self-similar characteristics. As the 'viscosity' parameter decreases the dynamics becomes increasingly more complicated and chaotic. In particular it is found that regular behavior in the form of steady state or steady state traveling waves is supported amidst the time-dependent and irregular motions. We show that multimodal steady states emerge and are supported on decreasing windows in parameter space. In addition we invoke a self-similarity property of the equation, to show that these profiles are obtainable from global fixed point attractors of the Kuramoto-Sivashinsky equation at much larger values of the viscosity.

Smyrlis, Yiorgos S.↗