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At least 433 records · Page 24
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Neural units with time-dependent functionality

We show that the time-resolved dynamics of an underdamped harmonic oscillator can be used to do multifunctional computation, performing distinct computations at distinct times within a single dynamical trajectory. We consider the amplitude of an oscillator whose inputs influence its frequency. The activity of the oscillator at fixed times is a nonmonotonic function of its inputs, so it can solve problems such as XOR that are not linearly separable. The activity of the oscillator at fixed input is a nonmonotonic function of time, so it is multifunctional in a temporal sense, and able to carry out distinct nonlinear computations at distinct times within the same dynamical trajectory. We show that a single oscillator, observed at different times, can act as all of the elementary logic gates and perform binary addition, the latter usually implemented in hardware using five logic gates. We show that a set of n oscillators, observed at different times, can perform an arbitrary number of analog-to-n-bit digital conversions. We also show that oscillators can be trained by gradient descent to perform distinct classification tasks at distinct times. Computing with time-dependent functionality can be done in or out of equilibrium, and suggests a way of reducing the number of parameters or devices required to do nonlinear computations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Nonlinear dynamics and dissipation of a curvilinear vortex driven by a strong time-dependent Meissner current

Here, we report numerical simulations of large-amplitude oscillations of a trapped vortex line under a strong ac magnetic field $\textit{H(t) = H}$ sin$\textit{ωt}$ parallel to the surface. The power dissipated by an oscillating vortex segment driven by the surface ac Meissner currents was calculated by taking into account the nonlinear vortex line tension, vortex mass, and a nonlinear Larkin-Ovchinnikov (LO) viscous drag coefficient $\textit{η(v)}$. We show that the LO decrease of $\textit{η(v)}$ with the vortex velocity $\textit{v}$ can radically change the field dependence of the surface resistance R i ( H ) caused by trapped vortices. At low frequencies, $R_i(H)$ exhibits a conventional increase with $\textit{H}$, but as $\textit{ω}$ increases, the surface resistance becomes a nonmonotonic function of $\textit{H}$ which decreases with $\textit{H}$ at higher fields. The effects of frequency, pin spacing, and the mean-free path $l_i$ on the field dependence of $R_i(H)$ were calculated. It is shown that, as the surface gets dirtier and $l_i$ decreases, the anomalous drop of $R_i(H)$ with $\textit{H}$ shifts to lower fields which can be much smaller than the lower critical magnetic field. Our numerical simulations also show that the LO decrease of $\textit{η(v)}$ with $\textit{v}$ can cause a vortex bending instability at high field amplitudes and frequencies, giving rise to the formation of dynamic kinks along the vortex. Measurements of $R_i(H)$ caused by sparse vortices trapped perpendicular to the surface can offer opportunities to investigate an extreme nonlinear dynamics of vortices driven by strong current densities up to the depairing limit at low temperatures. The behavior of $R_i(H)$, which can be tuned by varying the rf frequency or concentration of nonmagnetic impurities, is not masked by strong heating effects characteristic of dc or pulse transport measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1977

Application of the TRPLT1 element to large amplitude free vibrations of plates

A finite element formulation is developed for analyzing large amplitude free flexural vibrations of thin plates in NASTRAN. Stress distributions in the plate, in addition to deflection shapes and nonlinear frequencies are determined. Linearized equations of motion governing large amplitude oscillations of plates and a linearized geometrical stiffness matrix are presented. The solution procedure and convergence characteristics are discussed. The quasi-linear geometrical stiffness matrix for an eighteen degree-of-freedom higher order triangular plate element is evaluated by using a seven-point numerical integration. Nonlinear frequencies for square, rectangular, rhombic, and isosceles triangular plates, with edges simply supported or clamped, are compared with earlier solutions. The present formulation is found to give results entirely adequate for engineering purposes.

Mei, C.↗
NASA NTRS1974

Experimental determination of airplane mass and inertial characteristics

Current practices are evaluated for experimentally determining airplane center of gravity, moments of inertia, and products of inertia. The techniques discussed are applicable to bodies other than airplanes. In pitching- and rolling-moment-of-inertia investigations with the airplane mounted on and pivoted about knife edges, the nonlinear spring moments that occur at large amplitudes of oscillation can be eliminated by using the proper spring configuration. The single-point suspension double-pendulum technique for obtaining yawing moments of inertia, products of inertia, and the inclination of the principal axis provides accurate results from yaw-mode oscillation data, provided that the sway-mode effects are minimized by proper suspension rig design. Rocking-mode effects in the data can be isolated.

Wolowicz, C. H.↗
NASA NTRS1975

Relationships among classes of self-oscillating transistor parallel inverters

It recently has been shown in the literature that many dc-to-square-wave parallel inverters which are widely used in power-conditioning applications can be grouped into one of two families. Each family is characterized by an equivalent RLC network. Based on this approach, a classification procedure is presented for self-oscillating parallel inverters which makes evident natural relationships which exist between various inverter configurations. By utilizing concepts from the basic theory of negative resistance oscillators and the principle of duality as applied to nonlinear networks, a chain of relationships is established which enables a methodical transfer of knowledge gained about one family of inverters to any of the other families in the classification array.

Wilson, T. G.↗
NASA NTRS1976

Unsteady aerodynamic flow field analysis of the space shuttle configuration. Part 2: Launch vehicle aeroelastic analysis

An exploratory analysis has been made of the aeroelastic stability of the Space Shuttle Launch Configuration, with the objective of defining critical flow phenomena with adverse aeroelastic effects and developing simple analytic means of describing the time-dependent flow-interference effects so that they can be incorporated into a computer program to predict the aeroelastic stability of all free-free modes of the shuttle launch configuration. Three critical flow phenomana have been identified: (1) discontinuous jump of orbiter wing shock, (2) inlet flow between orbiter and booster, and (3) H.O. tank base flow. All involve highly nonlinear and often discontinuous aerodynamics which cause limit cycle oscillations of certain critical modes. Given the appropriate static data, the dynamic effects of the wing shock jump and the HO tank bulbous base effect can be analyzed using the developed quasi-steady techniques. However, further analytic and experimental efforts are required before the dynamic effects of the inlet flow phenomenon can be predicted for the shuttle launch configuration.

Reding, J. P.↗
NASA NTRS1989

Numerical Study of Three-dimensional Spatial Instability of a Supersonic Flat Plate Boundary Layer

The behavior of spatially growing three-dimensional waves in a supersonic boundary layer was studied numerically by solving the complete Navier-Stokes equations. Satisfactory comparison with linear parallel and non-parallel stability theories, and experiment are obtained when a small amplitude inflow disturbance is used. The three-dimensional unsteady Navier-Stokes equations are solved by a finite difference method which is fourth-order and second-order accurate in the convection and viscous terms respectively, and second-order accurate in time. Spanwise periodicity is assumed. The inflow disturbance is composed of eigenfunctions from linear stability theory. By increasing the amplitude of the inflow disturbance, nonlinear effects in the form of a relaxation type oscillation of the time signal of rho(u) are observed.

Maestrello, Lucio↗
NASA NTRS2014

Nonlinear Aeroelastic Analysis of the HIAD TPS Coupon in the NASA 8' High Temperature Tunnel: Theory and Experiment

The purpose of this work is to develop a set of theoretical and experimental techniques to characterize the aeroelasticity of the thermal protection system (TPS) on the NASA Hypersonic Inflatable Aerodynamic Decelerator (HIAD). A square TPS coupon experiences trailing edge oscillatory behavior during experimental testing in the 8' High Temperature Tunnel (HTT), which may indicate the presence of aeroelastic flutter. Several theoretical aeroelastic models have been developed, each corresponding to a different experimental test configuration. Von Karman large deflection theory is used for the plate-like components of the TPS, along with piston theory for the aerodynamics. The constraints between the individual TPS layers and the presence of a unidirectional foundation at the back of the coupon are included by developing the necessary energy expressions and using the Rayleigh Ritz method to derive the nonlinear equations of motion. Free vibrations and limit cycle oscillations are computed and the frequencies and amplitudes are compared with accelerometer and photogrammetry data from the experiments.

Benjamin D. Goldman↗
NASA NTRS1988

The centring dynamics of a thin liquid shell in capillary oscillations

The physical mechanism governing the centring of a hollow liquid shell in capillary oscillations, which has been observed in experiments, is investigated theoretically. First, the shell is assumed to be inviscid and to have a thickness that is much less than its spherical radius. A system of one-dimensional nonlinear equations of motion is derived using a thin-sheet model. From a numerical study the nonlinear effects of the wave are found to cause the core to oscillate slowly relative to the shell while the centre of mass of the whole system remains stationary. The effects of small viscosity are then considered in an approximation. Finally the strength of the centring mechanism is compared with that of the decentring effect due to buoyancy. The findings are consistent with the limited experimental information available.

Lee, Chun P.↗
NASA NTRS2004

All-optical Photonic Oscillator with High-Q Whispering Gallery Mode Resonators

We demonstrated low threshold optical photonic hyper-parametric oscillator in a high-Q 10(exp 10) CaF2 whispering gallery mode resonator which generates stable 8.5 GHz signal. The oscillations result from the resonantly enhanced four wave mixing occurring due to Kerr nonlinearity of the material.

optical oscillator↗
NASA NTRS1995

Low-frequency oscillations in radiative-convective systems. Part 2: An idealized model

A simple model is used to examine the hypothesis that nonlinear interactions among atmospheric radiation, cumulus convection, and the surface moisture flux can result in a stationary, low-frequency (30-60 day period) oscillating heat source in the tropical atmosphere. The model produces low-frequency oscillations of temperature, moisture, and precipitation. The mechanism that produces these oscillations is identified through analyses of the model and its results. The relevance of this mechanism to understand the observed Madden-Julian oscillation in the tropical atmosphere over the Indian and western Pacific Oceans is discussed.

Hu, QI↗
DOE OSTI2025

Materials Selection Principles for Designing Electro‐Thermal Neurons

Artificial neurons exhibiting volatile threshold switching and action potential‐like oscillations are crucial for brain‐inspired computing. While Complimentary Metal‐Oxide‐Semiconductor (CMOS)‐based strategies require hundreds of transistors to simulate each neuron, neuronal oscillations arise spontaneously in individual electro‐thermal devices due to nonlinearities like the Mott transition in VO 2 . Despite improved understanding of the physics, quantitative connections between neuronal performance and material properties remain under‐explored, preventing predictive neuron design and rational materials selection. In this work, a physics‐aware forward design methodology is developed for interrogating a wide palette of materials with properties varying by orders of magnitude, and their performance (high frequency, high dynamical reconfigurability and low power) under external circuit and device geometry constraints is assessed. The space of viable materials is identified to be much larger than previously recognized, with candidates from a range of materials classes, including Ge, GaP and MoS 2 . CMOS‐compatible performance (such as 100 GHz oscillating frequencies) can be achieved with CMOS‐compatible node sizes (≈10 nm). Finally, combinations of material properties yielding desired neuronal performance under uncertain design constraints are considered. This work solidifies forward design principles for electro‐thermal neuron devices, a necessary pre‐condition for inverse design from desired neuronal performance to required materials properties.

compact model↗
DOE OSTI2020

Pattern formation in a coupled membrane-bulk reaction-diffusion model for intracellular polarization and oscillations

Reaction-diffusion systems have been widely used to study spatio-temporal phenomena in cell biology, such as cell polarization. Coupled bulk-surface models naturally include compartmentalization of cytosolic and membrane-bound polarity molecules. Here we study the distribution of the polarity protein Cdc42 in a mass-conserved membrane-bulk model, and explore the effects of diffusion and spatial dimensionality on spatio-temporal pattern formation. We first analyze a one-dimensional (1-D) model for Cdc42 oscillations in fission yeast, consisting of two diffusion equations in the bulk domain coupled to nonlinear ODEs for binding kinetics at each end of the cell. In 1-D, our analysis reveals the existence of symmetric and asymmetric steady states, as well as anti-phase relaxation oscillations typical of slow-fast systems. We then extend our analysis to a two-dimensional (2-D) model with circular bulk geometry, for which species can either diffuse inside the cell or become bound to the membrane and undergo a nonlinear reaction-diffusion process. We also consider a nonlocal system of PDEs approximating the dynamics of the 2-D membrane-bulk model in the limit of fast bulk diffusion. In all three model variants we find that mass conservation selects perturbations of spatial modes that simply redistribute mass. In 1-D, only anti-phase oscillations between the two ends of the cell can occur, and in-phase oscillations are excluded. In higher dimensions, no radially symmetric oscillations are observed. Instead, the only instabilities are symmetry-breaking, either corresponding to stationary Turing instabilities, leading to the formation of stationary patterns, or to oscillatory Turing instabilities, leading to traveling and standing waves. Codimension-two Bogdanov—Takens bifurcations occur when the two distinct instabilities coincide, causing traveling waves to slow down and to eventually become stationary patterns. Our work clarifies the effect of geometry and dimensionality on behaviors observed in ma.ss-conserved cell polarity models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Super-resonant four-photon collinear laser frequency multiplication in plasma

Resonant four-photon scattering could nearly double frequencies of intense laser pulses in plasma. However, transverse slippage between pulses presents a technological challenge, while collinear four-photon scattering is forbidden for classical light dispersion in plasma. Nonlinear renormalization of intense laser pulses can enable collinear four-photon resonance. However, such a very intensity-sensitive resonance is difficult to maintain for evolving pulses. Remarkably, there is a lower-dimensionality submanifold of the resonant four-photon manifold where the evolving pulses stay in resonance. Furthermore this could enable an all-optical frequency doubling of mildly relativistic-intense laser pulses in collinear geometry, advantageously free of the transverse slippage challenges.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2010

Measuring a Fiber-Optic Delay Line Using a Mode-Locked Laser

The figure schematically depicts a laboratory setup for determining the optical length of a fiber-optic delay line at a precision greater than that obtainable by use of optical time-domain reflectometry or of mechanical measurement of length during the delay-line-winding process. In this setup, the delay line becomes part of the resonant optical cavity that governs the frequency of oscillation of a mode-locked laser. The length can then be determined from frequency-domain measurements, as described below. The laboratory setup is basically an all-fiber ring laser in which the delay line constitutes part of the ring. Another part of the ring - the laser gain medium - is an erbium-doped fiber amplifier pumped by a diode laser at a wavelength of 980 nm. The loop also includes an optical isolator, two polarization controllers, and a polarizing beam splitter. The optical isolator enforces unidirectional lasing. The polarization beam splitter allows light in only one polarization mode to pass through the ring; light in the orthogonal polarization mode is rejected from the ring and utilized as a diagnostic output, which is fed to an optical spectrum analyzer and a photodetector. The photodetector output is fed to a radio-frequency spectrum analyzer and an oscilloscope. The fiber ring laser can generate continuous-wave radiation in non-mode-locked operation or ultrashort optical pulses in mode-locked operation. The mode-locked operation exhibited by this ring is said to be passive in the sense that no electro-optical modulator or other active optical component is used to achieve it. Passive mode locking is achieved by exploiting optical nonlinearity of passive components in such a manner as to obtain ultra-short optical pulses. In this setup, the particular nonlinear optical property exploited to achieve passive mode locking is nonlinear polarization rotation. This or any ring laser can support oscillation in multiple modes as long as sufficient gain is present to overcome losses in the ring. When mode locking is achieved, oscillation occurs in all the modes having the same phase and same polarization. The frequency interval between modes, often denoted the free spectral range (FSR), is given by c/nL, where c is the speed of light in vacuum, n is the effective index of refraction of the fiber, and L is the total length of optical path around the ring. Therefore, the length of the fiber-optic delay line, as part of the length around the ring, can be calculated from the FSRs measured with and without the delay line incorporated into the ring. For this purpose, the FSR measurements are made by use of the optical and radio-frequency spectrum analyzers. In experimentation on a 10-km-long fiber-optic delay line, it was found that this setup made it possible to measure the length to within a fractional error of about 3 10(exp -6), corresponding to a length error of 3 cm. In contrast, measurements by optical time-domain reflectometry and mechanical measurement were found to be much less precise: For optical time-domain reflectometry, the fractional error was found no less than 10(exp -4) (corresponding to a length error of 1 m) and for mechanical measurement, the fractional error was found to be about 10(exp -2) (corresponding to a length error of 100 m).

Tu, Meirong↗
NASA NTRS2019

Aeroelastic Indicial Response Reduced-Order Modeling for Flexible Flight Vehicles

A reduced-order modeling method capable of providing computationally efficient predictions of the nonlinear, unsteady aerodynamics encountered by flexible flight vehicles under- going forced oscillations is presented. Models are developed using indicial response theory, which characterizes a vehicle’s dynamics through identification of time-accurate aerodynamic responses due to step changes in the vehicle-state parameters, e.g., angle-of-attack, pitch rate. A coupled computational fluid dynamics aeroelastic analysis is proposed for identifying step (indicial) responses of flexible vehicles. In this approach, aeroelastic indicial responses are simulated via prescribed rigid body motions, while fluid-structure interactions are captured at the subiterative level through coupling to a linear modal structural solver. A nonlinear extension of indicial response theory is applied through time-dependent linear interpolation of a database of locally linear aeroelastic step responses. Reduced-order models are then created using the mathematical principle of convolution applied to the interpolated aeroelastic indicial responses to predict the time-dependent aerodynamic response of a flexible vehicle to any arbitrary prescribed flight maneuver. The NASA FUN3D computational fluid dynamics solver is utilized for simulating full-order trajectories and indicial response functions. Aerodynamic predictions were generated for the X-56A aircraft undergoing a series of harmonic forced oscillations. The s are shown to provide a practical option for evaluating the unsteady aerodynamics of flexible vehicles using high-fidelity simulations.

Hiller, Brett↗
NASA NTRS2014

A Modular Approach to Model Oscillating Control Surfaces Using Navier Stokes Equations

The use of active controls for rotorcraft is becoming more important for modern aerospace configurations. Efforts to reduce the vibrations of helicopter blades with use of active-controls are in progress. Modeling oscillating control surfaces using the linear aerodynamics theory is well established. However, higher-fidelity methods are needed to account for nonlinear effects, such as those that occur in transonic flow. The aeroelastic responses of a wing with an oscillating control surface, computed using the transonic small perturbation (TSP) theory, have been shown to cause important transonic flow effects such as a reversal of control surface effectiveness that occurs as the shock wave crosses the hinge line. In order to account for flow complexities such as blade-vortex interactions of rotor blades higher-fidelity methods based on the Navier-Stokes equations are used. Reference 6 presents a procedure that uses the Navier-Stokes equations with moving-sheared grids and demonstrates up to 8 degrees of control-surface amplitude, using a single grid. Later, this procedure was extended to accommodate larger amplitudes, based on sliding grid zones. The sheared grid method implemented in EulerlNavier-Stokes-based aeroelastic code ENS AERO was successfully applied to active control design by industry. Recently there are several papers that present results for oscillating control surface using Reynolds Averaged Navier-Stokes (RANS) equations. References 9 and 10 report 2-D cases by filling gaps with overset grids. Reference 9 compares integrated forces with the experiment at low oscillating frequencies whereas Ref. 10 reports parametric studies but with no validation. Reference II reports results for a 3D case by modeling the gap region with a deformed grid and compares force results with the experiment only at the mid-span of flap. In Ref. II grid is deformed to match the control surface deflections at the section where the measurements are made. However, there is no indication in Ref. II that the gaps are explicitly modeled as in Ref. 6. Computations using overset grids are reported in Ref. 12 for a case by adding moving control surface to an existing blade but with no validation either with an experiment or another computation.

Navier↗