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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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At least 505 records · Page 28
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

On the nonlinear dissipative dynamics of weakly overdamped oscillators

We consider the motion of weakly overdamped linear oscillators. Weak overdamping of an oscillator is defined as a slight excess of the damping decrement over its natural frequency. Exact solutions are obtained for a certain relation between the decrement and the natural frequency and qualitatively different regimes of motion are analyzed. The threshold conditions corresponding to changes of regimes are established; one-component models with an arbitrary degree of nonlinearity are analyzed, and quadratic and cubic nonlinearities are considered in detail. If the nonlinearity in a multicomponent model is determined by a homogeneous function, transformations of the Kummer-Liouville type can be reduced to an autonomous system of second-order differential equations in the case when the relation between the decrement and the natural frequency has been established. Some integrable multicomponent models with quadratic and cubic nonlinearities are analyzed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1989

Parallel processors and nonlinear structural dynamics algorithms and software

The adaptation of a finite element program with explicit time integration to a massively parallel SIMD (single instruction multiple data) computer, the CONNECTION Machine is described. The adaptation required the development of a new algorithm, called the exchange algorithm, in which all nodal variables are allocated to the element with an exchange of nodal forces at each time step. The architectural and C* programming language features of the CONNECTION Machine are also summarized. Various alternate data structures and associated algorithms for nonlinear finite element analysis are discussed and compared. Results are presented which demonstrate that the CONNECTION Machine is capable of outperforming the CRAY XMP/14.

Belytschko, Ted↗
DOE OSTI2025

Dynamic Modeling, Trajectory Optimization, and Linear Control of Cable-Driven Parallel Robots for Automated Panelized Building Retrofits

The construction industry faces a growing need for automation to reduce costs, improve accuracy and productivity, and address labor shortages. One area that stands to benefit significantly from automation is panelized prefabricated building envelope retrofits, which can improve a building’s energy efficiency in heating and cooling interior spaces. In this paper, we propose using cable-driven parallel robots (CDPRs), which can effectively lift and handle large objects, to install these panels. However, implementing CDPRs presents significant challenges because of their nonlinear dynamics, complex trajectory planning, and precise control requirements. To tackle these challenges, this work focuses on a new application of established control and trajectory optimization theories in a CDPR simulation of a building envelope retrofit under real-world conditions. We first model the dynamics of CDPRs, highlighting the critical role of damping in system behavior. Building on this dynamic model, we formulate a trajectory optimization problem to generate feasible and efficient motion plans for the robot under operational and environmental constraints. Given the high precision required in the construction industry, accurately tracking the optimized trajectory is essential. However, challenges such as partial observability and external vibrations complicate this task. To address these issues, a Linear Quadratic Gaussian control framework is applied, enabling the robot to track the optimized trajectories with precision. Simulation results show that the proposed controller enables precise end effector positioning with errors under 4 mm, even in the presence of external wind disturbances. Through comprehensive simulations, our approach allows for an in-depth exploration of the system’s nonlinear dynamics, trajectory optimization, and control strategies under controlled yet highly realistic conditions. The results demonstrate the feasibility of CDPRs for automating panel installation and provide insights into their practical deployment.

CDPR↗
DOE OSTI2014

Comparison of analytic models of instability of rarefied gas flow in a channel

Numerical and analytical results are compared concerning the limit properties of the trajectories, attractors and bifurcations of rarefied gas flows in channels. The cascade of bifurcations obtained in our previous analytical and numerical investigations is simulated numerically for different scattering functions V generalizing the ray-diffuse reflection of gas particles from the surface. The main purpose of numerical simulation by Monte Carlo method is the investigation of the properties of different analytic nonlinear dynamic systems corresponding to rarefied gas flow in a channel. The results are compared as well for the models suggested originally by R. N. Miroshin, as for the approximations considered for the first time or for studied in our subsequent papers. Analytical solutions we obtained earlier for the ray reflection which means only one determined velocity of scattered from the walls gas atoms, generally different from the specular reflection. The nonlinear iterative equation describing a rarefied gas flow in a long channel becomes unstable in some regions of corresponding parameters of V (it means the sensitivity to boundary conditions). The values of the parameters are found from analytical approximations in these regions. Numerical results show that the chaotic behavior of the nonlinear dynamic system corresponds to strange attractors and distinguishes clearly from Maxwellian distribution and from the equilibrium on the whole. In the regions of instability (as the dimension of the attractor increases) the search for a corresponding state requires a lot more computation time and a lot of data (the amount of data required increases exponentially with embedding dimension). Therefore the main complication in the computation is reducing as well the computing time as the amount of data to find a suitably close solution. To reduce the computing time our analytical results are applied. Flow conditions satisfying the requirements to the experiment are indicated where the instability of considered type can be detected. The advantages and the drawbacks of considered approximations are detected and the features of obtained solutions are indicated. The recommendations are given for applying the results in practical applications and in numerical calculations of rarefied gas flows.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Bifurcations and chaos of a vibration isolation system with magneto-rheological damper

Magneto-rheological (MR) damper possesses inherent hysteretic characteristics. We investigate the resulting nonlinear behaviors of a two degree-of-freedom (2-DoF) MR vibration isolation system under harmonic external excitation. A MR damper is identified by employing the modified Bouc-wen hysteresis model. By numerical simulation, we characterize the nonlinear dynamic evolution of period-doubling, saddle node bifurcating and inverse period-doubling using bifurcation diagrams of variations in frequency with a fixed amplitude of the harmonic excitation. The strength of chaos is determined by the Lyapunov exponent (LE) spectrum. Semi-physical experiment on the 2-DoF MR vibration isolation system is proposed. We trace the time history and phase trajectory under certain values of frequency of the harmonic excitation to verify the nonlinear dynamical evolution of period-doubling bifurcations to chaos. The largest LEs computed with the experimental data are also presented, confirming the chaotic motion in the experiment. We validate the chaotic motion caused by the hysteresis of the MR damper, and show the transitions between distinct regimes of stable motion and chaotic motion of the 2-DoF MR vibration isolation system for variations in frequency of external excitation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Linear and nonlinear evolution of the ion resonance instability in cylindrical traps: A numerical study

Numerical experiments have been performed to investigate the linear and nonlinear dynamics, and energetics of the ion resonance instability in cylindrically confined nonneutral plasma. The instability is excited on a set of parametrically different unstable equilibria of a cylindrical nonneutral cloud, composed of electrons partially neutralized by a much heavier ion species of single ionization. A particle-in-cell code has been developed and employed to carry out these simulations. The results obtained from the initial exponential growth phase of the instability in these numerical experiments are in agreement with the linearised analytical model of the ion resonance instability. As the simulations delve much further in time beyond the exponential growth phase, very interesting nonlinear phenomena of the ion resonance instability are revealed, such as a process of simultaneous wave breaking of the excited poloidal mode on the ion cloud and pinching of the poloidal perturbations on the electron cloud. This simultaneous nonlinear dynamics of the two components is associated with an energy transfer process from the electrons to the ions. At later stages there is heating induced cross-field transport of the heavier ions and tearing across the pinches on the electron cloud followed by an inverse cascade of the torn sections.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1994

EEG and chaos: Description of underlying dynamics and its relation to dissociative states

The goal of this work is the identification of states especially as related to the process of error production and lapses of awareness as might be experienced during aviation. Given the need for further articulation of the characteristics of 'error prone state' or 'hazardous state of awareness,' this NASA grant focused on basic ground work for the study of the psychophysiology of these states. In specific, the purpose of this grant was to establish the necessary methodology for addressing three broad questions. The first is how the error prone state should be conceptualized, and whether it is similar to a dissociative state, a hypnotic state, or absent mindedness. Over 1200 subjects completed a variety of psychometric measures reflecting internal states and proneness to mental lapses and absent mindedness; the study suggests that there exists a consistency of patterns displayed by individuals who self-report dissociative experiences such that those individuals who score high on measures of dissociation also score high on measures of absent mindedness, errors, and absorption, but not on scales of hypnotizability. The second broad question is whether some individuals are more prone to enter these states than others. A study of 14 young adults who scored either high or low on the dissociation experiences scale performed a series of six tasks. This study suggests that high and low dissociative individuals arrive at the experiment in similar electrocortical states and perform cognitive tasks (e.g., mental math) in a similar manner; it is in the processing of internal emotional states that differences begin to emerge. The third question to be answered is whether recent research in nonlinear dynamics, i.e., chaos, offer an addition and/or alternative to traditional signal processing methods, i.e., fast Fourier transforms, and whether chaos procedures can be modified to offer additional information useful in identifying brain states. A preliminary review suggests that current nonlinear dynamical techniques such as dimensional analysis can be successfully applied to electrocortical activity. Using the data set developed in the study of the young adults, chaos analyses using the Farmer algorithm were performed; it is concluded that dimensionality measures reflect information not contained in traditional EEG Fourier analysis.

Ray, William J.↗
NASA NTRS1993

Adaptive methods for nonlinear structural dynamics and crashworthiness analysis

The objective is to describe three research thrusts in crashworthiness analysis: adaptivity; mixed time integration, or subcycling, in which different timesteps are used for different parts of the mesh in explicit methods; and methods for contact-impact which are highly vectorizable. The techniques are being developed to improve the accuracy of calculations, ease-of-use of crashworthiness programs, and the speed of calculations. The latter is still of importance because crashworthiness calculations are often made with models of 20,000 to 50,000 elements using explicit time integration and require on the order of 20 to 100 hours on current supercomputers. The methodologies are briefly reviewed and then some example calculations employing these methods are described. The methods are also of value to other nonlinear transient computations.

Belytschko, Ted↗
DOE OSTI2021

Excited-State Dynamics and Nonlinear Optical Properties of Hyperpolarizable Chromophores Based on Conjugated Bis(terpyridyl)Ru(II) and Palladium and Platinum Porphyrinic Components: Impact of Heavy Metals upon Supermolecular Electro-Optic Properties

A new series of strongly coupled oscillators based upon (porphinato)Pd, (porphinato)Pt, and bis(terpyridyl)-ruthenium(II) building blocks is described. These RuPPd, RuPPt, RuPPdRu, and RuPPtRu chromophores feature bis- (terpyridyl)Ru(II) moieties connected to the (porphinato)metal unit via an ethyne linker that bridges the 4!-terpyridyl and porphyrin macrocycle meso-carbon positions. Pump–probe transient optical data demonstrate sub-picosecond excited singlet-to-triplet-state relaxation. The relaxed lowest-energy triplet (T 1 ) excited states of these chromophores feature absorption manifolds that span the 800–1200 nm spectral region, microsecond triplet-state lifetimes, and large absorptive extinction coefficients [ε(T 1 → T n ) > 4 × 10 4 M –1 cm –1 ]. Dynamic hyperpolarizability (β λ ) values were determined from hyper-Rayleigh light scattering (HRS) measurements carried out at several incident irradiation wavelengths over the 800–1500 nm spectral region. Relative to benchmark RuPZn and RuPZnRu chromophores which showed large βHRS values over the 1200–1600 nm range, RuPPd, RuPPt, RuPPdRu, and RuPPtRu displayed large βHRS values over the 850–1200 nm region. Generalized Thomas–Kuhn sum (TKS) rules and experimental hyperpolarizability values were utilized to determine excited state-to-excited state transition dipole terms from experimental electronic absorption data and thus assessed frequency-dependent β λ values, including two- and three-level contributions for both β zzz and β xzx tensor components to the RuPPd, RuPPt, RuPPdRu, and RuPPtRu hyperpolarizability spectra. Furthermore, these analyses qualitatively rationalize how the βzzz and βxzx tensor elements influence the observed irradiation wavelength-dependent hyperpolarizability magnitudes. The TKS analysis suggests that supermolecules related to RuPPd, RuPPt, RuPPdRu, and RuPPtRu will likely feature intricate dependences of experimentally determined βHRS values as a function of irradiation wavelength that derive from substantial singlet–triplet mixing, and complex interactions among multiple different β tensor components that modulate the long wavelength regime of the nonlinear optical response.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Local Voltage Control in Distribution Networks: A Game-Theoretic Perspective

Inverter-based voltage regulation is gaining importance to alleviate emerging reliability and power-quality concerns related to distribution systems with high penetration of photovoltaic (PV) systems. This paper seeks contribution in the domain of reactive power compensation by establishing stability of local Volt/VAr controllers. In lieu of the approximate linear surrogate used in the existing work, the paper establishes existence and uniqueness of an equilibrium point using nonlinear AC power flow model. Key to this end is to consider a nonlinear dynamical system with non-incremental local Volt/VAr control, cast the Volt/VAr dynamics as a game, and leverage the fixed-point theorem as well as pertinent contraction mapping argument. Numerical examples are provided to complement the analytical results.

14 SOLAR ENERGY↗
DOE OSTI2020

Nonlinear ionization dynamics of hot dense plasma observed in a laser-plasma amplifier

Understanding the behaviour of matter under conditions of extreme temperature, pressure, density and electromagnetic fields has profound effects on our understanding of cosmologic objects and the formation of the universe. Lacking direct access to such objects, our interpretation of observed data mainly relies on theoretical models. However, such models, which need to encompass nuclear physics, atomic physics and plasma physics over a huge dynamic range in the dimensions of energy and time, can only provide reliable information if we can benchmark them to experiments under well-defined laboratory conditions. Due to the plethora of effects occurring in this kind of highly excited matter, characterizing isolated dynamics or obtaining direct insight remains challenging. High-density plasmas are turbulent and opaque for radiation below the plasma frequency and allow only near-surface insight into ionization processes with visible wavelengths. Here, the output of a high-harmonic seeded laser-plasma amplifier using eight-fold ionized krypton as the gain medium operating at a 32.8 nm wavelength is ptychographically imaged. A complex-valued wavefront is observed in the extreme ultraviolet (XUV) beam with high resolution. Ab initio spatio-temporal Maxwell–Bloch simulations show excellent agreement with the experimental observations, revealing overionization of krypton in the plasma channel due to nonlinear laser-plasma interactions, successfully validating this four-dimensional multiscale model. This constitutes the first experimental observation of the laser ion abundance reshaping a laser-plasma amplifier. The presented approach shows the possibility of directly modelling light-plasma interactions in extreme conditions, such as those present during the early times of the universe, with direct experimental verification.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Implementing Inertial Control for PMSG-WTG in Region 2 Using Virtual Synchronous Generator with Multiple Virtual Rotating Masses

With the increasing integration of renewable energy, the problems associated with a deteriorating grid frequency profile and potential power system instability have become more significant. In this paper, the inertial control algorithm using a virtual synchronous generator (VSG) is implemented on a Type 4 permanent magnet synchronous generator (PMSG) wind turbine generator (WTG). The overall nonlinear dynamic model and its small-signal linearization of the PMSG-WTG using a VSG is established and comprehensively analyzed. Inevitably, the direct application of the VSG introduces a large inertia, which causes conflict between the fast variance of available wind power and inverter control with slow dynamics, particularly in Region 2 of the wind turbine. Aiming to address such issues, a VSG with multiple virtual rotating masses is proposed to improve the active power tracking performance as well as to boost the inertial control of a VSG. The inertial responses are verified in a modified 10-MVA IEEE 14-bus microgrid system. The assessment of the simulation results demonstrates the applicability of the VSG on renewable energy generation units.

17 WIND ENERGY↗
DOE OSTI2018

A Novel Interfacing Technique for Distributed Hybrid Simulations Combining EMT and Transient Stability Models

With steady increase of power electronic devices and nonlinear dynamic loads in large scale AC/DC systems, the traditional hybrid simulation method, which incorporates these components into a single EMT subsystem and hence causes great difficulty for network partitioning and significant deterioration in simulation efficiency. To resolve these issues, a novel distributed hybrid simulation method is proposed in this paper. The key to realize this method is a distinct interfacing technique, which includes: i) a new approach based on the two-level Schur complement to update the interfaces by taking full consideration of the couplings between different EMT subsystems; and ii) a combined interaction protocol to further improve the efficiency while guaranteeing the simulation accuracy. The advantages of the proposed method in terms of both efficiency and accuracy have been verified by using it for the simulation study of an AC/DC hybrid system including a two-terminal VSC-HVDC and nonlinear dynamic loads.

Distributed hybrid simulation↗
DOE OSTI2022

Asymptotic optimality of twist-untwist protocols for Heisenberg scaling in atom-based sensing

Twist-untwist protocols for quantum metrology consist of a serial application of (1) unitary nonlinear dynamics (e.g., spin squeezing or Kerr nonlinearity), (2) parameterized dynamics U ( φ ) (e.g., a collective rotation or phase space displacement), and (3) time reversed application of step 1. Such protocols are known to produce states that allow Heisenberg scaling for experimentally accessible estimators of φ even when the nonlinearities are applied for times much shorter than required to produce Schrödinger cat states. In this work, we prove that, asymptotically in the number of particles, twist-untwist protocols provide the lowest estimation error among quantum metrology protocols that utilize two calls to a weakly nonlinear evolution and a readout involving only first and second moments of a total spin operator n → · J → . We consider the following physical settings: all-to-all interactions generated by one-axis twisting J z 2 (e.g., interacting Bose gases), constant finite range spin-spin interactions of distinguishable or bosonic atoms (e.g., trapped ions or Rydberg atoms, or lattice bosons). In these settings, we further show that the optimal twist-untwist protocols asymptotically achieve 85% and 92% of the respective quantum Cramér-Rao bounds. We show that the error of a twist-untwist protocol can be decreased by a factor of L without an increase in the noise of the spin measurement if the twist-untwist protocol can be noiselessly iterated as an L layer quantum alternating operator ansatz.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2013

Higher order harmonic detection for exploring nonlinear interactions

Nonlinear dynamics underpin a vast array of physical phenomena ranging from interfacial motion to jamming transitions. In many cases, decoupling the contributions of competing or co-existing mechanisms to the system response can be achieved through investigation of higher order harmonics. Here, a method using band excitation scanning probe microscopy to investigate higher order harmonics of the electromechanical response, with nanometer scale spatial resolution is presented. The utility of the technique is demonstrated by probing the first three harmonics of strain for a well-known system, a model Pb(Zr1-xTix)O3 ferroelectric capacitor. It is shown that the second order harmonic response is correlated with the first harmonic response, whereas the third harmonic is not. Additionally, nanoscale measurements of the second harmonic response with field reveal significant deviations from Rayleigh-type models in the form of a much more complicated field dependence than is observed in the spatially averaged data. These results illustrate the versatility of combining proximal probe techniques with nth harmonic detection methods in exploring and decoupling nonlinear dynamics in a wide variety of nanoscale materials.

ferroelectric↗
DOE OSTI2023

gLaSDI: Parametric physics-informed greedy latent space dynamics identification

A parametric adaptive physics-informed greedy Latent Space Dynamics Identification (gLaSDI) method is proposed for accurate, efficient, and robust data-driven reduced-order modeling of high-dimensional nonlinear dynamical systems. In the proposed gLaSDI framework, an autoencoder discovers intrinsic nonlinear latent representations of high-dimensional data, while dynamics identification (DI) models capture local latent-space dynamics. Here, an interactive training algorithm is adopted for the autoencoder and local DI models, which enables identification of simple latent-space dynamics and enhances accuracy and efficiency of data-driven reduced-order modeling. To maximize and accelerate the exploration of the parameter space for the optimal model performance, an adaptive greedy sampling algorithm integrated with a physics-informed residual-based error indicator and random-subset evaluation is introduced to search for the optimal training samples on the fly. Further, to exploit local latent-space dynamics captured by the local DI models for an improved modeling accuracy with a minimum number of local DI models in the parameter space, a -nearest neighbor convex interpolation scheme is employed. The effectiveness of the proposed framework is demonstrated by modeling various nonlinear dynamical problems, including Burgers equations, nonlinear heat conduction, and radial advection. The proposed adaptive greedy sampling outperforms the conventional predefined uniform sampling in terms of accuracy. Compared with the high-fidelity models, gLaSDI achieves 17 to 2,658× speed-up with 1 to 5% relative errors.

97 MATHEMATICS AND COMPUTING↗