Seismic assessment of WSDOT bridges with prestressed hollow core piles : part II.

DOT National Transportation Integrated Search

2009-12-01

This report investigates the seismic performance of a reinforced concrete : bridge with prestressed hollow core piles. Both nonlinear static and nonlinear dynamic : analyses were carried out. A three-dimensional spine model of the bridge was : ...

Numerical and Experimental Dynamic Characteristics of Thin-Film Membranes

NASA Technical Reports Server (NTRS)

Young, Leyland G.; Ramanathan, Suresh; Hu, Jia-Zhu; Pai, P. Frank

2004-01-01

Presented is a total-Lagrangian displacement-based non-linear finite-element model of thin-film membranes for static and dynamic large-displacement analyses. The membrane theory fully accounts for geometric non-linearities. Fully non-linear static analysis followed by linear modal analysis is performed for an inflated circular cylindrical Kapton membrane tube under different pressures, and for a rectangular membrane under different tension loads at four comers. Finite element results show that shell modes dominate the dynamics of the inflated tube when the inflation pressure is low, and that vibration modes localized along four edges dominate the dynamics of the rectangular membrane. Numerical dynamic characteristics of the two membrane structures were experimentally verified using a Polytec PI PSV-200 scanning laser vibrometer and an EAGLE-500 8-camera motion analysis system.

Application of Quasi-Linearization Techniques to Rail Vehicle Dynamic Analyses

DOT National Transportation Integrated Search

1978-11-01

The objective of the work reported here was to define methods for applying the describing function technique to realistic models of nonlinear rail cars. The describing function method offers a compromise between the accuracy of nonlinear digital simu...

Nonlinear equations for dynamics of pretwisted beams undergoing small strains and large rotations

NASA Technical Reports Server (NTRS)

Hodges, D. H.

1985-01-01

Nonlinear beam kinematics are developed and applied to the dynamic analysis of a pretwisted, rotating beam element. The common practice of assuming moderate rotations caused by structural deformation in geometric nonlinear analyses of rotating beams was abandoned in the present analysis. The kinematic relations that described the orientation of the cross section during deformation are simplified by systematically ignoring the extensional strain compared to unity in those relations. Open cross section effects such as warping rigidity and dynamics are ignored, but other influences of warp are retained. The beam cross section is not allowed to deform in its own plane. Various means of implementation are discussed, including a finite element formulation. Numerical results obtained for nonlinear static problems show remarkable agreement with experiment.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Milani, Gabriele, E-mail: milani@stru.polimi.it, E-mail: gabriele.milani@polimi.it; Valente, Marco

This study presents some FE results regarding the behavior under horizontal loads of eight existing masonry towers located in the North-East of Italy. The towers, albeit unique for geometric and architectural features, show some affinities which justify a comparative analysis, as for instance the location and the similar masonry material. Their structural behavior under horizontal loads is therefore influenced by geometrical issues, such as slenderness, walls thickness, perforations, irregularities, presence of internal vaults, etc., all features which may be responsible for a peculiar output. The geometry of the towers is deduced from both existing available documentation and in-situ surveys. Onmore » the basis of such geometrical data, a detailed 3D realistic mesh is conceived, with a point by point characterization of each single geometric element. The FE models are analysed under seismic loads acting along geometric axes of the plan section, both under non-linear static (pushover) and non-linear dynamic excitation assumptions. A damage-plasticity material model exhibiting softening in both tension and compression, already available in the commercial code Abaqus, is used for masonry. Pushover analyses are performed with both G1 and G2 horizontal loads distribution, according to Italian code requirements, along X+/− and Y+/− directions. Non-linear dynamic analyses are performed along both X and Y directions with a real accelerogram scaled to different peak ground accelerations. Some few results are presented in this paper. It is found that the results obtained with pushover analyses reasonably well fit expensive non-linear dynamic simulations, with a slightly less conservative trend.« less

Using complexity metrics with R-R intervals and BPM heart rate measures.

PubMed

Wallot, Sebastian; Fusaroli, Riccardo; Tylén, Kristian; Jegindø, Else-Marie

2013-01-01

Lately, growing attention in the health sciences has been paid to the dynamics of heart rate as indicator of impending failures and for prognoses. Likewise, in social and cognitive sciences, heart rate is increasingly employed as a measure of arousal, emotional engagement and as a marker of interpersonal coordination. However, there is no consensus about which measurements and analytical tools are most appropriate in mapping the temporal dynamics of heart rate and quite different metrics are reported in the literature. As complexity metrics of heart rate variability depend critically on variability of the data, different choices regarding the kind of measures can have a substantial impact on the results. In this article we compare linear and non-linear statistics on two prominent types of heart beat data, beat-to-beat intervals (R-R interval) and beats-per-min (BPM). As a proof-of-concept, we employ a simple rest-exercise-rest task and show that non-linear statistics-fractal (DFA) and recurrence (RQA) analyses-reveal information about heart beat activity above and beyond the simple level of heart rate. Non-linear statistics unveil sustained post-exercise effects on heart rate dynamics, but their power to do so critically depends on the type data that is employed: While R-R intervals are very susceptible to non-linear analyses, the success of non-linear methods for BPM data critically depends on their construction. Generally, "oversampled" BPM time-series can be recommended as they retain most of the information about non-linear aspects of heart beat dynamics.

Nonlinear effects of climate and density in the dynamics of a fluctuating population of reindeer.

PubMed

Tyler, Nicholas J C; Forchhammer, Mads C; Øritsland, Nils Are

2008-06-01

Nonlinear and irregular population dynamics may arise as a result of phase dependence and coexistence of multiple attractors. Here we explore effects of climate and density in the dynamics of a highly fluctuating population of wild reindeer (Rangifer tarandus platyrhynchus) on Svalbard observed over a period of 29 years. Time series analyses revealed that density dependence and the effects of local climate (measured as the degree of ablation [melting] of snow during winter) on numbers were both highly nonlinear: direct negative density dependence was found when the population was growing (Rt > 0) and during phases of the North Atlantic Oscillation (NAO) characterized by winters with generally high (1979-1995) and low (1996-2007) indices, respectively. A growth-phase-dependent model explained the dynamics of the population best and revealed the influence of density-independent processes on numbers that a linear autoregressive model missed altogether. In particular, the abundance of reindeer was enhanced by ablation during phases of growth (Rt > 0), an observation that contrasts with the view that periods of mild weather in winter are normally deleterious for reindeer owing to icing of the snowpack. Analyses of vital rates corroborated the nonlinearity described in the population time series and showed that both starvation mortality in winter and fecundity were nonlinearly related to fluctuations in density and the level of ablation. The erratic pattern of growth of the population of reindeer in Adventdalen seems, therefore, to result from a combination of the effects of nonlinear density dependence, strong density-dependent mortality, and variable density independence related to ablation in winter.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rodriguez, Mario E.

An area in earthquake risk reduction that needs an urgent examination is the selection of earthquake records for nonlinear dynamic analysis of structures. An often-mentioned shortcoming from results of nonlinear dynamic analyses of structures is that these results are limited to the type of records that these analyses use as input data. This paper proposes a procedure for selecting earthquake records for nonlinear dynamic analysis of structures. This procedure uses a seismic damage index evaluated using the hysteretic energy dissipated by a Single Degree of Freedom System (SDOF) representing a multi-degree-of freedom structure responding to an earthquake record, and themore » plastic work capacity of the system at collapse. The type of structural system is considered using simple parameters. The proposed method is based on the evaluation of the damage index for a suite of earthquake records and a selected type of structural system. A set of 10 strong ground motion records is analyzed to show an application of the proposed procedure for selecting earthquake records for structural design.« less

Standard representation and unified stability analysis for dynamic artificial neural network models.

PubMed

Kim, Kwang-Ki K; Patrón, Ernesto Ríos; Braatz, Richard D

2018-02-01

An overview is provided of dynamic artificial neural network models (DANNs) for nonlinear dynamical system identification and control problems, and convex stability conditions are proposed that are less conservative than past results. The three most popular classes of dynamic artificial neural network models are described, with their mathematical representations and architectures followed by transformations based on their block diagrams that are convenient for stability and performance analyses. Classes of nonlinear dynamical systems that are universally approximated by such models are characterized, which include rigorous upper bounds on the approximation errors. A unified framework and linear matrix inequality-based stability conditions are described for different classes of dynamic artificial neural network models that take additional information into account such as local slope restrictions and whether the nonlinearities within the DANNs are odd. A theoretical example shows reduced conservatism obtained by the conditions. Copyright © 2017. Published by Elsevier Ltd.

Structural Dynamic Analyses And Test Predictions For Spacecraft Structures With Non-Linearities

NASA Astrophysics Data System (ADS)

Vergniaud, Jean-Baptiste; Soula, Laurent; Newerla, Alfred

2012-07-01

The overall objective of the mechanical development and verification process is to ensure that the spacecraft structure is able to sustain the mechanical environments encountered during launch. In general the spacecraft structures are a-priori assumed to behave linear, i.e. the responses to a static load or dynamic excitation, respectively, will increase or decrease proportionally to the amplitude of the load or excitation induced. However, past experiences have shown that various non-linearities might exist in spacecraft structures and the consequences of their dynamic effects can significantly affect the development and verification process. Current processes are mainly adapted to linear spacecraft structure behaviour. No clear rules exist for dealing with major structure non-linearities. They are handled outside the process by individual analysis and margin policy, and analyses after tests to justify the CLA coverage. Non-linearities can primarily affect the current spacecraft development and verification process on two aspects. Prediction of flights loads by launcher/satellite coupled loads analyses (CLA): only linear satellite models are delivered for performing CLA and no well-established rules exist how to properly linearize a model when non- linearities are present. The potential impact of the linearization on the results of the CLA has not yet been properly analyzed. There are thus difficulties to assess that CLA results will cover actual flight levels. Management of satellite verification tests: the CLA results generated with a linear satellite FEM are assumed flight representative. If the internal non- linearities are present in the tested satellite then there might be difficulties to determine which input level must be passed to cover satellite internal loads. The non-linear behaviour can also disturb the shaker control, putting the satellite at risk by potentially imposing too high levels. This paper presents the results of a test campaign performed in the frame of an ESA TRP study [1]. A bread-board including typical non-linearities has been designed, manufactured and tested through a typical spacecraft dynamic test campaign. The study has demonstrate the capabilities to perform non-linear dynamic test predictions on a flight representative spacecraft, the good correlation of test results with respect to Finite Elements Model (FEM) prediction and the possibility to identify modal behaviour and to characterize non-linearities characteristics from test results. As a synthesis for this study, overall guidelines have been derived on the mechanical verification process to improve level of expertise on tests involving spacecraft including non-linearity.

Sexual affordances, perceptual-motor invariance extraction and intentional nonlinear dynamics: sexually deviant and non-deviant patterns in male subjects.

PubMed

Renaud, Patrice; Goyette, Mathieu; Chartier, Sylvain; Zhornitski, Simon; Trottier, Dominique; Rouleau, Joanne-L; Proulx, Jean; Fedoroff, Paul; Bradford, John-P; Dassylva, Benoit; Bouchard, Stephane

2010-10-01

Sexual arousal and gaze behavior dynamics are used to characterize deviant sexual interests in male subjects. Pedophile patients and non-deviant subjects are immersed with virtual characters depicting relevant sexual features. Gaze behavior dynamics as indexed from correlation dimensions (D2) appears to be fractal in nature and significantly different from colored noise (surrogate data tests and recurrence plot analyses were performed). This perceptual-motor fractal dynamics parallels sexual arousal and differs from pedophiles to non-deviant subjects when critical sexual information is processed. Results are interpreted in terms of sexual affordance, perceptual invariance extraction and intentional nonlinear dynamics.

Non-linear quantum-classical scheme to simulate non-equilibrium strongly correlated fermionic many-body dynamics

PubMed Central

Kreula, J. M.; Clark, S. R.; Jaksch, D.

2016-01-01

We propose a non-linear, hybrid quantum-classical scheme for simulating non-equilibrium dynamics of strongly correlated fermions described by the Hubbard model in a Bethe lattice in the thermodynamic limit. Our scheme implements non-equilibrium dynamical mean field theory (DMFT) and uses a digital quantum simulator to solve a quantum impurity problem whose parameters are iterated to self-consistency via a classically computed feedback loop where quantum gate errors can be partly accounted for. We analyse the performance of the scheme in an example case. PMID:27609673

Vowel selection and its effects on perturbation and nonlinear dynamic measures.

PubMed

Maccallum, Julia K; Zhang, Yu; Jiang, Jack J

2011-01-01

Acoustic analysis of voice is typically conducted on recordings of sustained vowel phonation. This study applied perturbation and nonlinear dynamic analyses to the vowels /a/, /i/, and /u/ in order to determine vowel selection effects on analysis. Forty subjects (20 males and 20 females) with normal voices participated in recording. Traditional parameters of fundamental frequency, signal-to-noise ratio, percent jitter, and percent shimmer were calculated for the signals using CSpeech. Nonlinear dynamic parameters of correlation dimension and second-order entropy were also calculated. Perturbation analysis results were largely incongruous in this study and in previous research. Fundamental frequency results corroborated previous work, indicating higher fundamental frequency for /i/ and /u/ and lower fundamental frequency for /a/. Signal-to-noise ratio results showed that /i/ and /u/ have greater harmonic levels than /a/. Results of nonlinear dynamic analysis suggested that more complex activity may be evident in /a/ than in /i/ or /u/. Percent jitter and percent shimmer may not be useful for description of acoustic differences between vowels. Fundamental frequency, signal-to-noise ratio, and nonlinear dynamic parameters may be applied to characterize /a/ as having lower frequency, higher noise, and greater nonlinear components than /i/ and /u/. Copyright © 2010 S. Karger AG, Basel.

Dynamics of elastic nonlinear rotating composite beams with embedded actuators

NASA Astrophysics Data System (ADS)

Ghorashi, Mehrdaad

2009-08-01

A comprehensive study of the nonlinear dynamics of composite beams is presented. The study consists of static and dynamic solutions with and without active elements. The static solution provides the initial conditions for the dynamic analysis. The dynamic problems considered include the analyses of clamped (hingeless) and articulated (hinged) accelerating rotating beams. Numerical solutions for the steady state and transient responses have been obtained. It is shown that the transient solution of the nonlinear formulation of accelerating rotating beam converges to the steady state solution obtained by the shooting method. The effect of perturbing the steady state solution has also been calculated and the results are shown to be compatible with those of the accelerating beam analysis. Next, the coupled flap-lag rigid body dynamics of a rotating articulated beam with hinge offset and subjected to aerodynamic forces is formulated. The solution to this rigid-body problem is then used, together with the finite difference method, in order to produce the nonlinear elasto-dynamic solution of an accelerating articulated beam. Next, the static and dynamic responses of nonlinear composite beams with embedded Anisotropic Piezo-composite Actuators (APA) are presented. The effect of activating actuators at various directions on the steady state force and moments generated in a rotating composite beam has been presented. With similar results for the transient response, this analysis can be used in controlling the response of adaptive rotating beams.

Nonlinear static and dynamic finite element analysis of an eccentrically loaded graphite-epoxy beam

NASA Technical Reports Server (NTRS)

Fasanella, Edwin L.; Jackson, Karen E.; Jones, Lisa E.

1991-01-01

The Dynamic Crash Analysis of Structures (DYCAT) and NIKE3D nonlinear finite element codes were used to model the static and implulsive response of an eccentrically loaded graphite-epoxy beam. A 48-ply unidirectional composite beam was tested under an eccentric axial compressive load until failure. This loading configuration was chosen to highlight the capabilities of two finite element codes for modeling a highly nonlinear, large deflection structural problem which has an exact solution. These codes are currently used to perform dynamic analyses of aircraft structures under impact loads to study crashworthiness and energy absorbing capabilities. Both beam and plate element models were developed to compare with the experimental data using the DYCAST and NIKE3D codes.

The brain as a dynamic physical system.

PubMed

McKenna, T M; McMullen, T A; Shlesinger, M F

1994-06-01

The brain is a dynamic system that is non-linear at multiple levels of analysis. Characterization of its non-linear dynamics is fundamental to our understanding of brain function. Identifying families of attractors in phase space analysis, an approach which has proven valuable in describing non-linear mechanical and electrical systems, can prove valuable in describing a range of behaviors and associated neural activity including sensory and motor repertoires. Additionally, transitions between attractors may serve as useful descriptors for analysing state changes in neurons and neural ensembles. Recent observations of synchronous neural activity, and the emerging capability to record the spatiotemporal dynamics of neural activity by voltage-sensitive dyes and electrode arrays, provide opportunities for observing the population dynamics of neural ensembles within a dynamic systems context. New developments in the experimental physics of complex systems, such as the control of chaotic systems, selection of attractors, attractor switching and transient states, can be a source of powerful new analytical tools and insights into the dynamics of neural systems.

Nonlinear vibrations and dynamic stability of viscoelastic orthotropic rectangular plates

NASA Astrophysics Data System (ADS)

Eshmatov, B. Kh.

2007-03-01

This paper describes the analyses of the nonlinear vibrations and dynamic stability of viscoelastic orthotropic plates. The models are based on the Kirchhoff-Love (K.L.) hypothesis and Reissner-Mindlin (R.M.) generalized theory (with the incorporation of shear deformation and rotatory inertia) in geometrically nonlinear statements. It provides justification for the choice of the weakly singular Koltunov-Rzhanitsyn type kernel, with three rheological parameters. In addition, the implication of each relaxation kernel parameter has been studied. To solve problems of viscoelastic systems with weakly singular kernels of relaxation, a numerical method has been used, based on quadrature formulae. With a combination of the Bubnov-Galerkin and the presented method, problems of nonlinear vibrations and dynamic stability in viscoelastic orthotropic rectangular plates have been solved, according to the K.L. and R.M. hypotheses. A comparison of the results obtained via these theories is also presented. In all problems, the convergence of the Bubnov-Galerkin method has been investigated. The implications of material viscoelasticity on vibration and dynamic stability are presented graphically.

Nonlinear dynamics of homeothermic temperature control in skunk cabbage, Symplocarpus foetidus

NASA Astrophysics Data System (ADS)

Ito, Takanori; Ito, Kikukatsu

2005-11-01

Certain primitive plants undergo orchestrated temperature control during flowering. Skunk cabbage, Symplocarpus foetidus, has been demonstrated to maintain an internal temperature of around 20 °C even when the ambient temperature drops below freezing. However, it is not clear whether a unique algorithm controls the homeothermic behavior of S. foetidus, or whether such an algorithm might exhibit linear or nonlinear thermoregulatory dynamics. Here we report the underlying dynamics of temperature control in S. foetidus using nonlinear forecasting, attractor and correlation dimension analyses. It was shown that thermoregulation in S. foetidus was governed by low-dimensional chaotic dynamics, the geometry of which showed a strange attractor named the “Zazen attractor.” Our data suggest that the chaotic thermoregulation in S. foetidus is inherent and that it is an adaptive response to the natural environment.

Nonlinear vibration of a coupled high- Tc superconducting levitation system

NASA Astrophysics Data System (ADS)

Sugiura, T.; Inoue, T.; Ura, H.

2004-10-01

High- Tc superconducting levitation can be applied to electro-mechanical systems, such as flywheel energy storage and linear-drive transportation. Such a system can be modeled as a magnetically coupled system of many permanent magnets and high- Tc superconducting bulks. It is a multi-degree-of-freedom dynamical system coupled by nonlinear interaction between levitated magnets and superconducting bulks. This nonlinearly coupled system, with small damping due to no contact support, can easily show complicated phenomena of nonlinear dynamics. In mechanical design, it is important to evaluate this nonlinear dynamics, though it has not been well studied so far. This research deals with forced vibration of a coupled superconducting levitation system. As a simple modeling of a coupled system, a permanent magnet levitated above a superconducting bulk is placed between two fixed permanent magnets without contact. Frequency response of the levitated magnet under excitation of one of the fixed magnets was examined theoretically. The results show typical nonlinear vibration, such as jump, hysteresis, and parametric resonance, which were confirmed in our numerical analyses and experiments.

Nonlinear oscillation of a rigid body over high- Tc superconductors supported by electro-magnetic forces

NASA Astrophysics Data System (ADS)

Sugiura, T.; Ogawa, S.; Ura, H.

2005-10-01

Characteristics of high- Tc superconducting levitation systems are no contact support and stable levitation without control. They can be applied to supporting mechanisms in machines, such as linear-drives and magnetically levitated trains. But small damping due to noncontact support and nonlinearity in the magnetic force can easily cause complicated phenomena of nonlinear dynamics. This research deals with nonlinear oscillation of a rigid bar supported at its both ends by electro-magnetic forces between superconductors and permanent magnets as a simple modeling of the above application. Deriving the equation of motion, we discussed an effect of nonlinearity in the magnetic force on dynamics of the levitated body: occurrence of combination resonance in the asymmetrical system. Numerical analyses and experiments were also carried out, and their results confirmed the above theoretical prediction.

Nonlinear dynamic analysis of D α signals for type I edge localized modes characterization on JET with a carbon wall

NASA Astrophysics Data System (ADS)

Cannas, Barbara; Fanni, Alessandra; Murari, Andrea; Pisano, Fabio; Contributors, JET

2018-02-01

In this paper, the dynamic characteristics of type-I ELM time-series from the JET tokamak, the world’s largest magnetic confinement plasma physics experiment, have been investigated. The dynamic analysis has been focused on the detection of nonlinear structure in D α radiation time series. Firstly, the method of surrogate data has been applied to evaluate the statistical significance of the null hypothesis of static nonlinear distortion of an underlying Gaussian linear process. Several nonlinear statistics have been evaluated, such us the time delayed mutual information, the correlation dimension and the maximal Lyapunov exponent. The obtained results allow us to reject the null hypothesis, giving evidence of underlying nonlinear dynamics. Moreover, no evidence of low-dimensional chaos has been found; indeed, the analysed time series are better characterized by the power law sensitivity to initial conditions which can suggest a motion at the ‘edge of chaos’, at the border between chaotic and regular non-chaotic dynamics. This uncertainty makes it necessary to further investigate about the nature of the nonlinear dynamics. For this purpose, a second surrogate test to distinguish chaotic orbits from pseudo-periodic orbits has been applied. In this case, we cannot reject the null hypothesis which means that the ELM time series is possibly pseudo-periodic. In order to reproduce pseudo-periodic dynamical properties, a periodic state-of-the-art model, proposed to reproduce the ELM cycle, has been corrupted by a dynamical noise, obtaining time series qualitatively in agreement with experimental time series.

Finite element for rotor/stator interactive forces in general engine dynamic simulation. Part 1: Development of bearing damper element

NASA Technical Reports Server (NTRS)

Adams, M. L.; Padovan, J.; Fertis, D. G.

1980-01-01

A general purpose squeeze-film damper interactive force element was developed, coded into a software package (module) and debugged. This software package was applied to nonliner dynamic analyses of some simple rotor systems. Results for pressure distributions show that the long bearing (end sealed) is a stronger bearing as compared to the short bearing as expected. Results of the nonlinear dynamic analysis, using a four degree of freedom simulation model, showed that the orbit of the rotating shaft increases nonlinearity to fill the bearing clearance as the unbalanced weight increases.

Nonlinear Recurrent Dynamics and Long-Term Nonstationarities in EEG Alpha Cortical Activity: Implications for Choosing Adequate Segment Length in Nonlinear EEG Analyses.

PubMed

Cerquera, Alexander; Vollebregt, Madelon A; Arns, Martijn

2018-03-01

Nonlinear analysis of EEG recordings allows detection of characteristics that would probably be neglected by linear methods. This study aimed to determine a suitable epoch length for nonlinear analysis of EEG data based on its recurrence rate in EEG alpha activity (electrodes Fz, Oz, and Pz) from 28 healthy and 64 major depressive disorder subjects. Two nonlinear metrics, Lempel-Ziv complexity and scaling index, were applied in sliding windows of 20 seconds shifted every 1 second and in nonoverlapping windows of 1 minute. In addition, linear spectral analysis was carried out for comparison with the nonlinear results. The analysis with sliding windows showed that the cortical dynamics underlying alpha activity had a recurrence period of around 40 seconds in both groups. In the analysis with nonoverlapping windows, long-term nonstationarities entailed changes over time in the nonlinear dynamics that became significantly different between epochs across time, which was not detected with the linear spectral analysis. Findings suggest that epoch lengths shorter than 40 seconds neglect information in EEG nonlinear studies. In turn, linear analysis did not detect characteristics from long-term nonstationarities in EEG alpha waves of control subjects and patients with major depressive disorder patients. We recommend that application of nonlinear metrics in EEG time series, particularly of alpha activity, should be carried out with epochs around 60 seconds. In addition, this study aimed to demonstrate that long-term nonlinearities are inherent to the cortical brain dynamics regardless of the presence or absence of a mental disorder.

Finite element analyses of railroad tank car head impacts

DOT National Transportation Integrated Search

2008-09-24

This paper describes engineering analyses of a railroad : tank car impacted at its head by a rigid punch. This type of : collision, referred to as a head impact, is examined using : dynamic, nonlinear finite element analysis (FEA). : Commercial softw...

Nonlinear dynamic analysis of voices before and after surgical excision of vocal polyps

NASA Astrophysics Data System (ADS)

Zhang, Yu; McGilligan, Clancy; Zhou, Liang; Vig, Mark; Jiang, Jack J.

2004-05-01

Phase space reconstruction, correlation dimension, and second-order entropy, methods from nonlinear dynamics, are used to analyze sustained vowels generated by patients before and after surgical excision of vocal polyps. Two conventional acoustic perturbation parameters, jitter and shimmer, are also employed to analyze voices before and after surgery. Presurgical and postsurgical analyses of jitter, shimmer, correlation dimension, and second-order entropy are statistically compared. Correlation dimension and second-order entropy show a statistically significant decrease after surgery, indicating reduced complexity and higher predictability of postsurgical voice dynamics. There is not a significant postsurgical difference in shimmer, although jitter shows a significant postsurgical decrease. The results suggest that jitter and shimmer should be applied to analyze disordered voices with caution; however, nonlinear dynamic methods may be useful for analyzing abnormal vocal function and quantitatively evaluating the effects of surgical excision of vocal polyps.

The contribution of reorientational nonlinearity of CS2 liquid in supercontinuum generation

NASA Astrophysics Data System (ADS)

Porsezian, K.; Raja, R. Vasantha Jayakantha; Husakou, Anton; Hermann, Joachim

2011-08-01

We aim to study the nonlinear optical phenomena with femtosecond pulse propagation in liquid-core photonic crystal fibers filled with CS2. In particular, we intend to study the effect of slow nonlinearity due to reorientational contribution of liquid molecules on broadband supercontinuum generation in the femtosecond regime using appropriately modified nonlinear Schrödinger equation. We show that the response of the slow nonlinearity enhances broadening of the pulse and changes the dynamics of the generated solitons. To analyse the quality of the pulse, the stability analysis and coherence of the SCG are studied numerically.

The landscape of nonlinear structural dynamics: an introduction

PubMed Central

Butlin, T.; Woodhouse, J.; Champneys, A. R.

2015-01-01

Nonlinear behaviour is ever-present in vibrations and other dynamical motions of engineering structures. Manifestations of nonlinearity include amplitude-dependent natural frequencies, buzz, squeak and rattle, self-excited oscillation and non-repeatability. This article primarily serves as an extended introduction to a theme issue in which such nonlinear phenomena are highlighted through diverse case studies. More ambitiously though, there is another goal. Both the engineering context and the mathematical techniques that can be used to identify, analyse, control or exploit these phenomena in practice are placed in the context of a mind-map, which has been created through expert elicitation. This map, which is available in software through the electronic supplementary material, attempts to provide a practitioner’s guide to what hitherto might seem like a vast and complex research landscape. PMID:26303925

The landscape of nonlinear structural dynamics: an introduction.

PubMed

Butlin, T; Woodhouse, J; Champneys, A R

2015-09-28

Nonlinear behaviour is ever-present in vibrations and other dynamical motions of engineering structures. Manifestations of nonlinearity include amplitude-dependent natural frequencies, buzz, squeak and rattle, self-excited oscillation and non-repeatability. This article primarily serves as an extended introduction to a theme issue in which such nonlinear phenomena are highlighted through diverse case studies. More ambitiously though, there is another goal. Both the engineering context and the mathematical techniques that can be used to identify, analyse, control or exploit these phenomena in practice are placed in the context of a mind-map, which has been created through expert elicitation. This map, which is available in software through the electronic supplementary material, attempts to provide a practitioner's guide to what hitherto might seem like a vast and complex research landscape. © 2015 The Authors.

Use of recurrence plots in the analysis of pupil diameter dynamics in narcoleptics

NASA Astrophysics Data System (ADS)

Keegan, Andrew P.; Zbilut, J. P.; Merritt, S. L.; Mercer, P. J.

1993-11-01

Recurrence plots were used to evaluate pupil dynamics of subjects with narcolepsy. Preliminary data indicate that this nonlinear method of analyses may be more useful in revealing underlying deterministic differences than traditional methods like FFT and counting statistics.

Computational Results for the KTH-NASA Wind-Tunnel Model Used for Acquisition of Transonic Nonlinear Aeroelastic Data

NASA Technical Reports Server (NTRS)

Silva, Walter A.; Chwalowski, Pawel; Wieseman, Carol D.; Eller, David; Ringertz, Ulf

2017-01-01

A status report is provided on the collaboration between the Royal Institute of Technology (KTH) in Sweden and the NASA Langley Research Center regarding the aeroelastic analyses of a full-span fighter configuration wind-tunnel model. This wind-tunnel model was tested in the Transonic Dynamics Tunnel (TDT) in the summer of 2016. Large amounts of data were acquired including steady/unsteady pressures, accelerations, strains, and measured dynamic deformations. The aeroelastic analyses presented include linear aeroelastic analyses, CFD steady analyses, and analyses using CFD-based reduced-order models (ROMs).

Quantification of Interactions between Dynamic Cellular Network Functionalities by Cascaded Layering

PubMed Central

Prescott, Thomas P.; Lang, Moritz; Papachristodoulou, Antonis

2015-01-01

Large, naturally evolved biomolecular networks typically fulfil multiple functions. When modelling or redesigning such systems, functional subsystems are often analysed independently first, before subsequent integration into larger-scale computational models. In the design and analysis process, it is therefore important to quantitatively analyse and predict the dynamics of the interactions between integrated subsystems; in particular, how the incremental effect of integrating a subsystem into a network depends on the existing dynamics of that network. In this paper we present a framework for simulating the contribution of any given functional subsystem when integrated together with one or more other subsystems. This is achieved through a cascaded layering of a network into functional subsystems, where each layer is defined by an appropriate subset of the reactions. We exploit symmetries in our formulation to exhaustively quantify each subsystem’s incremental effects with minimal computational effort. When combining subsystems, their isolated behaviour may be amplified, attenuated, or be subject to more complicated effects. We propose the concept of mutual dynamics to quantify such nonlinear phenomena, thereby defining the incompatibility and cooperativity between all pairs of subsystems when integrated into any larger network. We exemplify our theoretical framework by analysing diverse behaviours in three dynamic models of signalling and metabolic pathways: the effect of crosstalk mechanisms on the dynamics of parallel signal transduction pathways; reciprocal side-effects between several integral feedback mechanisms and the subsystems they stabilise; and consequences of nonlinear interactions between elementary flux modes in glycolysis for metabolic engineering strategies. Our analysis shows that it is not sufficient to just specify subsystems and analyse their pairwise interactions; the environment in which the interaction takes place must also be explicitly defined. Our framework provides a natural representation of nonlinear interaction phenomena, and will therefore be an important tool for modelling large-scale evolved or synthetic biomolecular networks. PMID:25933116

Non-linear dynamic characteristics and optimal control of giant magnetostrictive film subjected to in-plane stochastic excitation

NASA Astrophysics Data System (ADS)

Zhu, Z. W.; Zhang, W. D.; Xu, J.

2014-03-01

The non-linear dynamic characteristics and optimal control of a giant magnetostrictive film (GMF) subjected to in-plane stochastic excitation were studied. Non-linear differential items were introduced to interpret the hysteretic phenomena of the GMF, and the non-linear dynamic model of the GMF subjected to in-plane stochastic excitation was developed. The stochastic stability was analysed, and the probability density function was obtained. The condition of stochastic Hopf bifurcation and noise-induced chaotic response were determined, and the fractal boundary of the system's safe basin was provided. The reliability function was solved from the backward Kolmogorov equation, and an optimal control strategy was proposed in the stochastic dynamic programming method. Numerical simulation shows that the system stability varies with the parameters, and stochastic Hopf bifurcation and chaos appear in the process; the area of the safe basin decreases when the noise intensifies, and the boundary of the safe basin becomes fractal; the system reliability improved through stochastic optimal control. Finally, the theoretical and numerical results were proved by experiments. The results are helpful in the engineering applications of GMF.

Nonlinear flight dynamics and stability of hovering model insects

PubMed Central

Liang, Bin; Sun, Mao

2013-01-01

Current analyses on insect dynamic flight stability are based on linear theory and limited to small disturbance motions. However, insects' aerial environment is filled with swirling eddies and wind gusts, and large disturbances are common. Here, we numerically solve the equations of motion coupled with the Navier–Stokes equations to simulate the large disturbance motions and analyse the nonlinear flight dynamics of hovering model insects. We consider two representative model insects, a model hawkmoth (large size, low wingbeat frequency) and a model dronefly (small size, high wingbeat frequency). For small and large initial disturbances, the disturbance motion grows with time, and the insects tumble and never return to the equilibrium state; the hovering flight is inherently (passively) unstable. The instability is caused by a pitch moment produced by forward/backward motion and/or a roll moment produced by side motion of the insect. PMID:23697714

Cluster Synchronization of Diffusively Coupled Nonlinear Systems: A Contraction-Based Approach

NASA Astrophysics Data System (ADS)

Aminzare, Zahra; Dey, Biswadip; Davison, Elizabeth N.; Leonard, Naomi Ehrich

2018-04-01

Finding the conditions that foster synchronization in networked nonlinear systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in nonlinear systems with linear coupling, such as has been used to model neuronal networks, are in general not strict enough to accurately determine the system behavior. We leverage contraction theory to derive new sufficient conditions for cluster synchronization in terms of the network structure, for a network where the intrinsic nonlinear dynamics of each node may differ. Our result requires that network connections satisfy a cluster-input-equivalence condition, and we explore the influence of this requirement on network dynamics. For application to networks of nodes with FitzHugh-Nagumo dynamics, we show that our new sufficient condition is tighter than those found in previous analyses that used smooth or nonsmooth Lyapunov functions. Improving the analytical conditions for when cluster synchronization will occur based on network configuration is a significant step toward facilitating understanding and control of complex networked systems.

Nonlinear Dynamics in Gene Regulation Promote Robustness and Evolvability of Gene Expression Levels.

PubMed

Steinacher, Arno; Bates, Declan G; Akman, Ozgur E; Soyer, Orkun S

2016-01-01

Cellular phenotypes underpinned by regulatory networks need to respond to evolutionary pressures to allow adaptation, but at the same time be robust to perturbations. This creates a conflict in which mutations affecting regulatory networks must both generate variance but also be tolerated at the phenotype level. Here, we perform mathematical analyses and simulations of regulatory networks to better understand the potential trade-off between robustness and evolvability. Examining the phenotypic effects of mutations, we find an inverse correlation between robustness and evolvability that breaks only with nonlinearity in the network dynamics, through the creation of regions presenting sudden changes in phenotype with small changes in genotype. For genotypes embedding low levels of nonlinearity, robustness and evolvability correlate negatively and almost perfectly. By contrast, genotypes embedding nonlinear dynamics allow expression levels to be robust to small perturbations, while generating high diversity (evolvability) under larger perturbations. Thus, nonlinearity breaks the robustness-evolvability trade-off in gene expression levels by allowing disparate responses to different mutations. Using analytical derivations of robustness and system sensitivity, we show that these findings extend to a large class of gene regulatory network architectures and also hold for experimentally observed parameter regimes. Further, the effect of nonlinearity on the robustness-evolvability trade-off is ensured as long as key parameters of the system display specific relations irrespective of their absolute values. We find that within this parameter regime genotypes display low and noisy expression levels. Examining the phenotypic effects of mutations, we find an inverse correlation between robustness and evolvability that breaks only with nonlinearity in the network dynamics. Our results provide a possible solution to the robustness-evolvability trade-off, suggest an explanation for the ubiquity of nonlinear dynamics in gene expression networks, and generate useful guidelines for the design of synthetic gene circuits.

Reconstruction of dynamic structures of experimental setups based on measurable experimental data only

NASA Astrophysics Data System (ADS)

Chen, Tian-Yu; Chen, Yang; Yang, Hu-Jiang; Xiao, Jing-Hua; Hu, Gang

2018-03-01

Nowadays, massive amounts of data have been accumulated in various and wide fields, it has become today one of the central issues in interdisciplinary fields to analyze existing data and extract as much useful information as possible from data. It is often that the output data of systems are measurable while dynamic structures producing these data are hidden, and thus studies to reveal system structures by analyzing available data, i.e., reconstructions of systems become one of the most important tasks of information extractions. In the past, most of the works in this respect were based on theoretical analyses and numerical verifications. Direct analyses of experimental data are very rare. In physical science, most of the analyses of experimental setups were based on the first principles of physics laws, i.e., so-called top-down analyses. In this paper, we conducted an experiment of “Boer resonant instrument for forced vibration” (BRIFV) and inferred the dynamic structure of the experimental set purely from the analysis of the measurable experimental data, i.e., by applying the bottom-up strategy. Dynamics of the experimental set is strongly nonlinear and chaotic, and itʼs subjects to inevitable noises. We proposed to use high-order correlation computations to treat nonlinear dynamics; use two-time correlations to treat noise effects. By applying these approaches, we have successfully reconstructed the structure of the experimental setup, and the dynamic system reconstructed with the measured data reproduces good experimental results in a wide range of parameters.

Shape Distributions of Nonlinear Dynamical Systems for Video-Based Inference.

PubMed

Venkataraman, Vinay; Turaga, Pavan

2016-12-01

This paper presents a shape-theoretic framework for dynamical analysis of nonlinear dynamical systems which appear frequently in several video-based inference tasks. Traditional approaches to dynamical modeling have included linear and nonlinear methods with their respective drawbacks. A novel approach we propose is the use of descriptors of the shape of the dynamical attractor as a feature representation of nature of dynamics. The proposed framework has two main advantages over traditional approaches: a) representation of the dynamical system is derived directly from the observational data, without any inherent assumptions, and b) the proposed features show stability under different time-series lengths where traditional dynamical invariants fail. We illustrate our idea using nonlinear dynamical models such as Lorenz and Rossler systems, where our feature representations (shape distribution) support our hypothesis that the local shape of the reconstructed phase space can be used as a discriminative feature. Our experimental analyses on these models also indicate that the proposed framework show stability for different time-series lengths, which is useful when the available number of samples are small/variable. The specific applications of interest in this paper are: 1) activity recognition using motion capture and RGBD sensors, 2) activity quality assessment for applications in stroke rehabilitation, and 3) dynamical scene classification. We provide experimental validation through action and gesture recognition experiments on motion capture and Kinect datasets. In all these scenarios, we show experimental evidence of the favorable properties of the proposed representation.

Characterization of doctor-patient communication using heartbeat nonlinear dynamics: A preliminary study using Lagged Poincaré Plots.

PubMed

Nardelli, M; Del Piccolo, L; Danzi, Op; Perlini, C; Tedeschi, F; Greco, A; Scilingo, Ep; Valenza, G

2017-07-01

Emphatic doctor-patient communication has been associated with an improved psycho-physiological well-being involving cardiovascular and neuroendocrine responses. Nevertheless, a comprehensive assessment of heartbeat linear and nonlinear/complex dynamics throughout the communication of a life-threatening disease has not been performed yet. To this extent, we here study heart rate variability (HRV) series gathered from 17 subjects while watching a video where an oncologist discloses the diagnosis of a cancer metastasis to a patient. Further 17 subjects watched the same video including additional affective emphatic contents. For the assessment of the two groups, linear heartbeat dynamics was quantified through measures defined in the time and frequency domains, whereas nonlinear/complex dynamics referred to measures of entropy, and combined Lagged Poincare Plots (LPP) and symbolic analyses. Considering differences between the beginning and the end of the video, results from non-parametric statistical tests demonstrated that the group watching emphatic contents showed HRV changes in the LF/HF ratio exclusively. Conversely, the group watching the purely informative video showed changes in vagal activity (i.e., HF power), LF/HF ratio, as well as LPP measures. Additionally, a Support Vector Machine algorithm including HRV nonlinear/complex information was able to automatically discern between groups with an accuracy of 76.47%. We therefore propose the use of heartbeat nonlinear/complex dynamics to objectively assess the empathy level of healthy women.

Analyses of Multishaft Rotor-Bearing Response

NASA Technical Reports Server (NTRS)

Nelson, H. D.; Meacham, W. L.

1985-01-01

Method works for linear and nonlinear systems. Finite-element-based computer program developed to analyze free and forced response of multishaft rotor-bearing systems. Acronym, ARDS, denotes Analysis of Rotor Dynamic Systems. Systems with nonlinear interconnection or support bearings or both analyzed by numerically integrating reduced set of coupledsystem equations. Linear systems analyzed in closed form for steady excitations and treated as equivalent to nonlinear systems for transient excitation. ARDS is FORTRAN program developed on an Amdahl 470 (similar to IBM 370).

Nonlinear dynamics of cardiovascular ageing

PubMed Central

Shiogai, Y.; Stefanovska, A.; McClintock, P.V.E.

2010-01-01

The application of methods drawn from nonlinear and stochastic dynamics to the analysis of cardiovascular time series is reviewed, with particular reference to the identification of changes associated with ageing. The natural variability of the heart rate (HRV) is considered in detail, including the respiratory sinus arrhythmia (RSA) corresponding to modulation of the instantaneous cardiac frequency by the rhythm of respiration. HRV has been intensively studied using traditional spectral analyses, e.g. by Fourier transform or autoregressive methods, and, because of its complexity, has been used as a paradigm for testing several proposed new methods of complexity analysis. These methods are reviewed. The application of time–frequency methods to HRV is considered, including in particular the wavelet transform which can resolve the time-dependent spectral content of HRV. Attention is focused on the cardio-respiratory interaction by introduction of the respiratory frequency variability signal (RFV), which can be acquired simultaneously with HRV by use of a respiratory effort transducer. Current methods for the analysis of interacting oscillators are reviewed and applied to cardio-respiratory data, including those for the quantification of synchronization and direction of coupling. These reveal the effect of ageing on the cardio-respiratory interaction through changes in the mutual modulation of the instantaneous cardiac and respiratory frequencies. Analyses of blood flow signals recorded with laser Doppler flowmetry are reviewed and related to the current understanding of how endothelial-dependent oscillations evolve with age: the inner lining of the vessels (the endothelium) is shown to be of crucial importance to the emerging picture. It is concluded that analyses of the complex and nonlinear dynamics of the cardiovascular system can illuminate the mechanisms of blood circulation, and that the heart, the lungs and the vascular system function as a single entity in dynamical terms. Clear evidence is found for dynamical ageing. PMID:20396667

Nonlinear dynamics of cardiovascular ageing

NASA Astrophysics Data System (ADS)

Shiogai, Y.; Stefanovska, A.; McClintock, P. V. E.

2010-03-01

The application of methods drawn from nonlinear and stochastic dynamics to the analysis of cardiovascular time series is reviewed, with particular reference to the identification of changes associated with ageing. The natural variability of the heart rate (HRV) is considered in detail, including the respiratory sinus arrhythmia (RSA) corresponding to modulation of the instantaneous cardiac frequency by the rhythm of respiration. HRV has been intensively studied using traditional spectral analyses, e.g. by Fourier transform or autoregressive methods, and, because of its complexity, has been used as a paradigm for testing several proposed new methods of complexity analysis. These methods are reviewed. The application of time-frequency methods to HRV is considered, including in particular the wavelet transform which can resolve the time-dependent spectral content of HRV. Attention is focused on the cardio-respiratory interaction by introduction of the respiratory frequency variability signal (RFV), which can be acquired simultaneously with HRV by use of a respiratory effort transducer. Current methods for the analysis of interacting oscillators are reviewed and applied to cardio-respiratory data, including those for the quantification of synchronization and direction of coupling. These reveal the effect of ageing on the cardio-respiratory interaction through changes in the mutual modulation of the instantaneous cardiac and respiratory frequencies. Analyses of blood flow signals recorded with laser Doppler flowmetry are reviewed and related to the current understanding of how endothelial-dependent oscillations evolve with age: the inner lining of the vessels (the endothelium) is shown to be of crucial importance to the emerging picture. It is concluded that analyses of the complex and nonlinear dynamics of the cardiovascular system can illuminate the mechanisms of blood circulation, and that the heart, the lungs and the vascular system function as a single entity in dynamical terms. Clear evidence is found for dynamical ageing.

Structural health monitoring based on sensitivity vector fields and attractor morphing.

PubMed

Yin, Shih-Hsun; Epureanu, Bogdan I

2006-09-15

The dynamic responses of a thermo-shielding panel forced by unsteady aerodynamic loads and a classical Duffing oscillator are investigated to detect structural damage. A nonlinear aeroelastic model is obtained for the panel by using third-order piston theory to model the unsteady supersonic flow, which interacts with the panel. To identify damage, we analyse the morphology (deformation and movement) of the attractor of the dynamics of the aeroelastic system and the Duffing oscillator. Damages of various locations, extents and levels are shown to be revealed by the attractor-based analysis. For the panel, the type of damage considered is a local reduction in the bending stiffness. For the Duffing oscillator, variations in the linear and nonlinear stiffnesses and damping are considered as damage. Present studies of such problems are based on linear theories. In contrast, the presented approach using nonlinear dynamics has the potential of enhancing accuracy and sensitivity of detection.

The coupled nonlinear dynamics of a lift system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Crespo, Rafael Sánchez, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Kaczmarczyk, Stefan, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Picton, Phil, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk

2014-12-10

Coupled lateral and longitudinal vibrations of suspension and compensating ropes in a high-rise lift system are often induced by the building motions due to wind or seismic excitations. When the frequencies of the building become near the natural frequencies of the ropes, large resonance motions of the system may result. This leads to adverse coupled dynamic phenomena involving nonplanar motions of the ropes, impact loads between the ropes and the shaft walls, as well as vertical vibrations of the car, counterweight and compensating sheave. Such an adverse dynamic behaviour of the system endangers the safety of the installation. This papermore » presents two mathematical models describing the nonlinear responses of a suspension/ compensating rope system coupled with the elevator car / compensating sheave motions. The models accommodate the nonlinear couplings between the lateral and longitudinal modes, with and without longitudinal inertia of the ropes. The partial differential nonlinear equations of motion are derived using Hamilton Principle. Then, the Galerkin method is used to discretise the equations of motion and to develop a nonlinear ordinary differential equation model. Approximate numerical solutions are determined and the behaviour of the system is analysed.« less

Non-linear dynamic characteristics and optimal control of giant magnetostrictive film subjected to in-plane stochastic excitation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhu, Z. W., E-mail: zhuzhiwen@tju.edu.cn; Tianjin Key Laboratory of Non-linear Dynamics and Chaos Control, 300072, Tianjin; Zhang, W. D., E-mail: zhangwenditju@126.com

2014-03-15

The non-linear dynamic characteristics and optimal control of a giant magnetostrictive film (GMF) subjected to in-plane stochastic excitation were studied. Non-linear differential items were introduced to interpret the hysteretic phenomena of the GMF, and the non-linear dynamic model of the GMF subjected to in-plane stochastic excitation was developed. The stochastic stability was analysed, and the probability density function was obtained. The condition of stochastic Hopf bifurcation and noise-induced chaotic response were determined, and the fractal boundary of the system's safe basin was provided. The reliability function was solved from the backward Kolmogorov equation, and an optimal control strategy was proposedmore » in the stochastic dynamic programming method. Numerical simulation shows that the system stability varies with the parameters, and stochastic Hopf bifurcation and chaos appear in the process; the area of the safe basin decreases when the noise intensifies, and the boundary of the safe basin becomes fractal; the system reliability improved through stochastic optimal control. Finally, the theoretical and numerical results were proved by experiments. The results are helpful in the engineering applications of GMF.« less

Using nonlinear methods to quantify changes in infant limb movements and vocalizations.

PubMed

Abney, Drew H; Warlaumont, Anne S; Haussman, Anna; Ross, Jessica M; Wallot, Sebastian

2014-01-01

The pairing of dynamical systems theory and complexity science brings novel concepts and methods to the study of infant motor development. Accordingly, this longitudinal case study presents a new approach to characterizing the dynamics of infant limb and vocalization behaviors. A single infant's vocalizations and limb movements were recorded from 51-days to 305-days of age. On each recording day, accelerometers were placed on all four of the infant's limbs and an audio recorder was worn on the child's chest. Using nonlinear time series analysis methods, such as recurrence quantification analysis and Allan factor, we quantified changes in the stability and multiscale properties of the infant's behaviors across age as well as how these dynamics relate across modalities and effectors. We observed that particular changes in these dynamics preceded or coincided with the onset of various developmental milestones. For example, the largest changes in vocalization dynamics preceded the onset of canonical babbling. The results show that nonlinear analyses can help to understand the functional co-development of different aspects of infant behavior.

Using nonlinear methods to quantify changes in infant limb movements and vocalizations

PubMed Central

Abney, Drew H.; Warlaumont, Anne S.; Haussman, Anna; Ross, Jessica M.; Wallot, Sebastian

2014-01-01

The pairing of dynamical systems theory and complexity science brings novel concepts and methods to the study of infant motor development. Accordingly, this longitudinal case study presents a new approach to characterizing the dynamics of infant limb and vocalization behaviors. A single infant's vocalizations and limb movements were recorded from 51-days to 305-days of age. On each recording day, accelerometers were placed on all four of the infant's limbs and an audio recorder was worn on the child's chest. Using nonlinear time series analysis methods, such as recurrence quantification analysis and Allan factor, we quantified changes in the stability and multiscale properties of the infant's behaviors across age as well as how these dynamics relate across modalities and effectors. We observed that particular changes in these dynamics preceded or coincided with the onset of various developmental milestones. For example, the largest changes in vocalization dynamics preceded the onset of canonical babbling. The results show that nonlinear analyses can help to understand the functional co-development of different aspects of infant behavior. PMID:25161629

Application of GRASP (General Rotorcraft Aeromechanical Stability Program) to nonlinear analysis of a cantilever beam

NASA Technical Reports Server (NTRS)

Hinnant, Howard E.; Hodges, Dewey H.

1987-01-01

The General Rotorcraft Aeromechanical Stability Program (GRASP) was developed to analyse the steady-state and linearized dynamic behavior of rotorcraft in hovering and axial flight conditions. Because of the nature of problems GRASP was created to solve, the geometrically nonlinear behavior of beams is one area in which the program must perform well in order to be of any value. Numerical results obtained from GRASP are compared to both static and dynamic experimental data obtained for a cantilever beam undergoing large displacements and rotations caused by deformations. The correlation is excellent in all cases.

Advances and trends in structures and dynamics; Proceedings of the Symposium, Washington, DC, October 22-25, 1984

NASA Technical Reports Server (NTRS)

Noor, A. K. (Editor); Hayduk, R. J. (Editor)

1985-01-01

Among the topics discussed are developments in structural engineering hardware and software, computation for fracture mechanics, trends in numerical analysis and parallel algorithms, mechanics of materials, advances in finite element methods, composite materials and structures, determinations of random motion and dynamic response, optimization theory, automotive tire modeling methods and contact problems, the damping and control of aircraft structures, and advanced structural applications. Specific topics covered include structural design expert systems, the evaluation of finite element system architectures, systolic arrays for finite element analyses, nonlinear finite element computations, hierarchical boundary elements, adaptive substructuring techniques in elastoplastic finite element analyses, automatic tracking of crack propagation, a theory of rate-dependent plasticity, the torsional stability of nonlinear eccentric structures, a computation method for fluid-structure interaction, the seismic analysis of three-dimensional soil-structure interaction, a stress analysis for a composite sandwich panel, toughness criterion identification for unidirectional composite laminates, the modeling of submerged cable dynamics, and damping synthesis for flexible spacecraft structures.

Nonlinear and Synchronous Dissolved Organic Matter Dynamics in Streams Across an Agriculture Land Use and Climate Setting

NASA Astrophysics Data System (ADS)

Xenopoulos, M. A.; Vogt, R. J.

2014-12-01

There is now increasing evidence that non-linearity is a common response in ecological systems to pressures caused by human activities. There is also increasing evidence that exogenous environmental drivers, such as climate, induce spatial and temporal synchrony in a wide range of ecological variables. Using Moran's I and Pearson's correlation, we quantified the synchrony of dissolved organic carbon concentration (DOC) and quality (DOM; e.g., specific UV absorbance, Fluorescence Index, PARAFAC), nutrients, discharge and temperature in 40 streams that span an agriculture gradient (0 to >70% cropland), over 10 years. We then used breakpoint regression, 2D-Kolmogorov-Smirnov test and significant zero crossings (SiZer) analyses to quantify the prevalence of nonlinearity and ecological thresholds (breakpoints) where applicable. There was a high degree of synchrony in DOM quality (r > 0.7) but not DOC (r < 0.4). The degree of synchrony was driven in part by the catchment's land use. With respect to the nonlinear analyses we found non-linearity in ~50% of bivariate datasets analyzed. Non-linearity was also driven in part by the catchment's land use. Breakpoints defined different DOM properties. Nonlinearity and synchronous behaviour in DOM are intimately linked to land use.

Potential for wind extraction from 4D-Var assimilation of aerosols and moisture

NASA Astrophysics Data System (ADS)

Zaplotnik, Žiga; Žagar, Nedjeljka

2017-04-01

We discuss the potential of the four-dimensional variational data assimilation (4D-Var) to retrieve the unobserved wind field from observations of atmospheric tracers and the mass field through internal model dynamics and the multivariate relationships in the background-error term for 4D-Var. The presence of non-linear moist dynamics makes the wind retrieval from tracers very difficult. On the other hand, it has been shown that moisture observations strongly influence both tropical and mid-latitude wind field in 4D-Var. We present an intermediate complexity model that describes nonlinear interactions between the wind, temperature, aerosols and moisture including their sinks and sources in the framework of the so-called first baroclinic mode atmosphere envisaged by A. Gill. Aerosol physical processes, which are included in the model, are the non-linear advection, diffusion and sources and sinks that exist as dry and wet deposition and diffusion. Precipitation is parametrized according to the Betts-Miller scheme. The control vector for 4D-Var includes aerosols, moisture and the three dynamical variables. The former is analysed univariately whereas wind field and mass field are analysed in a multivariate fashion taking into account quasi-geostrophic and unbalanced dynamics. The OSSE type of studies are performed for the tropical region to assess the ability of 4D-Var to extract wind-field information from the time series of observations of tracers as a function of the flow nonlinearity, the observations density and the length of the assimilation window (12 hours and 24 hours), in dry and moist environment. Results show that the 4D-Var assimilation of aerosols and temperature data is beneficial for the wind analysis with analysis errors strongly dependent on the moist processes and reliable background-error covariances.

"Speaking Volumes": A Longitudinal Study of Lexical and Grammatical Growth between 17 and 42 Months

ERIC Educational Resources Information Center

Labrell, Florence; van Geert, Paul; Declercq, Christelle; Baltazart, Véronique; Caillies, Stéphanie; Olivier, Marie; Le Sourn-Bissaoui, Sandrine

2014-01-01

Dynamic analyses of language growth tell us how vocabulary and grammar develop and how the two might be intertwined. Analyses of growth curves between 17 and 42 months, based on longitudinal data for 34 children, revealed interesting patterns of vocabulary and grammatical developments. They showed that these patterns were nonlinear, but with…

Hierarchical nonlinear dynamics of human attention.

PubMed

Rabinovich, Mikhail I; Tristan, Irma; Varona, Pablo

2015-08-01

Attention is the process of focusing mental resources on a specific cognitive/behavioral task. Such brain dynamics involves different partially overlapping brain functional networks whose interconnections change in time according to the performance stage, and can be stimulus-driven or induced by an intrinsically generated goal. The corresponding activity can be described by different families of spatiotemporal discrete patterns or sequential dynamic modes. Since mental resources are finite, attention modalities compete with each other at all levels of the hierarchy, from perception to decision making and behavior. Cognitive activity is a dynamical process and attention possesses some universal dynamical characteristics. Thus, it is time to apply nonlinear dynamical theory for the description and prediction of hierarchical attentional tasks. Such theory has to include the analyses of attentional control stability, the time cost of attention switching, the finite capacity of informational resources in the brain, and the normal and pathological bifurcations of attention sequential dynamics. In this paper we have integrated today's knowledge, models and results in these directions. Copyright © 2015 Elsevier Ltd. All rights reserved.

Using complexity metrics with R-R intervals and BPM heart rate measures

PubMed Central

Wallot, Sebastian; Fusaroli, Riccardo; Tylén, Kristian; Jegindø, Else-Marie

2013-01-01

Lately, growing attention in the health sciences has been paid to the dynamics of heart rate as indicator of impending failures and for prognoses. Likewise, in social and cognitive sciences, heart rate is increasingly employed as a measure of arousal, emotional engagement and as a marker of interpersonal coordination. However, there is no consensus about which measurements and analytical tools are most appropriate in mapping the temporal dynamics of heart rate and quite different metrics are reported in the literature. As complexity metrics of heart rate variability depend critically on variability of the data, different choices regarding the kind of measures can have a substantial impact on the results. In this article we compare linear and non-linear statistics on two prominent types of heart beat data, beat-to-beat intervals (R-R interval) and beats-per-min (BPM). As a proof-of-concept, we employ a simple rest-exercise-rest task and show that non-linear statistics—fractal (DFA) and recurrence (RQA) analyses—reveal information about heart beat activity above and beyond the simple level of heart rate. Non-linear statistics unveil sustained post-exercise effects on heart rate dynamics, but their power to do so critically depends on the type data that is employed: While R-R intervals are very susceptible to non-linear analyses, the success of non-linear methods for BPM data critically depends on their construction. Generally, “oversampled” BPM time-series can be recommended as they retain most of the information about non-linear aspects of heart beat dynamics. PMID:23964244

Deployment Simulation of Ultra-Lightweight Inflatable Structures

NASA Technical Reports Server (NTRS)

Wang, John T.; Johnson, Arthur R.

2002-01-01

Dynamic deployment analyses of folded inflatable tubes are conducted to investigate modeling issues related to the deployment of solar sail booms. The analyses are necessary because ground tests include gravity effects and may poorly represent deployment in space. A control volume approach, available in the LS-DYNA nonlinear dynamic finite element code, and the ideal gas law are used to simulate the dynamic inflation deployment process. Three deployment issues are investigated for a tube packaged in a Z-fold configuration. The issues are the effect of the rate of inflation, the effect of residual air, and the effect of gravity. The results of the deployment analyses reveal that the time and amount of inflation gas required to achieve a full deployment are related to these issues.

Linear and nonlinear dynamic analysis of redundant load path bearingless rotor systems

NASA Technical Reports Server (NTRS)

Murthy, V. R.; Shultz, Louis A.

1994-01-01

The goal of this research is to develop the transfer matrix method to treat nonlinear autonomous boundary value problems with multiple branches. The application is the complete nonlinear aeroelastic analysis of multiple-branched rotor blades. Once the development is complete, it can be incorporated into the existing transfer matrix analyses. There are several difficulties to be overcome in reaching this objective. The conventional transfer matrix method is limited in that it is applicable only to linear branch chain-like structures, but consideration of multiple branch modeling is important for bearingless rotors. Also, hingeless and bearingless rotor blade dynamic characteristics (particularly their aeroelasticity problems) are inherently nonlinear. The nonlinear equations of motion and the multiple-branched boundary value problem are treated together using a direct transfer matrix method. First, the formulation is applied to a nonlinear single-branch blade to validate the nonlinear portion of the formulation. The nonlinear system of equations is iteratively solved using a form of Newton-Raphson iteration scheme developed for differential equations of continuous systems. The formulation is then applied to determine the nonlinear steady state trim and aeroelastic stability of a rotor blade in hover with two branches at the root. A comprehensive computer program is developed and is used to obtain numerical results for the (1) free vibration, (2) nonlinearly deformed steady state, (3) free vibration about the nonlinearly deformed steady state, and (4) aeroelastic stability tasks. The numerical results obtained by the present method agree with results from other methods.

Foldover effect and energy output from a nonlinear pseudo-maglev harvester

NASA Astrophysics Data System (ADS)

Kecik, Krzysztof; Mitura, Andrzej; Warminski, Jerzy; Lenci, Stefano

2018-01-01

Dynamics analysis and energy harvesting of a nonlinear magnetic pseudo-levitation (pseudo-maglev) harvester under harmonic excitation is presented in this paper. The system, for selected parameters, has two stable possible solutions with different corresponding energy outputs. The main goal is to analyse the influence of resistance load on the multi-stability zones and energy recovery which can help to tune the system to improve the energy harvesting efficiency.

Method of performing computational aeroelastic analyses

NASA Technical Reports Server (NTRS)

Silva, Walter A. (Inventor)

2011-01-01

Computational aeroelastic analyses typically use a mathematical model for the structural modes of a flexible structure and a nonlinear aerodynamic model that can generate a plurality of unsteady aerodynamic responses based on the structural modes for conditions defining an aerodynamic condition of the flexible structure. In the present invention, a linear state-space model is generated using a single execution of the nonlinear aerodynamic model for all of the structural modes where a family of orthogonal functions is used as the inputs. Then, static and dynamic aeroelastic solutions are generated using computational interaction between the mathematical model and the linear state-space model for a plurality of periodic points in time.

Further Results of Soft-Inplane Tiltrotor Aeromechanics Investigation Using Two Multibody Analyses

NASA Technical Reports Server (NTRS)

Masarati, Pierangelo; Quaranta, Giuseppe; Piatak, David J.; Singleton, Jeffrey D.

2004-01-01

This investigation focuses on the development of multibody analytical models to predict the dynamic response, aeroelastic stability, and blade loading of a soft-inplane tiltrotor wind-tunnel model. Comprehensive rotorcraft-based multibody analyses enable modeling of the rotor system to a high level of detail such that complex mechanics and nonlinear effects associated with control system geometry and joint deadband may be considered. The influence of these and other nonlinear effects on the aeromechanical behavior of the tiltrotor model are examined. A parametric study of the design parameters which may have influence on the aeromechanics of the soft-inplane rotor system are also included in this investigation.

Computational Aeroelastic Modeling of Airframes and TurboMachinery: Progress and Challenges

NASA Technical Reports Server (NTRS)

Bartels, R. E.; Sayma, A. I.

2006-01-01

Computational analyses such as computational fluid dynamics and computational structural dynamics have made major advances toward maturity as engineering tools. Computational aeroelasticity is the integration of these disciplines. As computational aeroelasticity matures it too finds an increasing role in the design and analysis of aerospace vehicles. This paper presents a survey of the current state of computational aeroelasticity with a discussion of recent research, success and continuing challenges in its progressive integration into multidisciplinary aerospace design. This paper approaches computational aeroelasticity from the perspective of the two main areas of application: airframe and turbomachinery design. An overview will be presented of the different prediction methods used for each field of application. Differing levels of nonlinear modeling will be discussed with insight into accuracy versus complexity and computational requirements. Subjects will include current advanced methods (linear and nonlinear), nonlinear flow models, use of order reduction techniques and future trends in incorporating structural nonlinearity. Examples in which computational aeroelasticity is currently being integrated into the design of airframes and turbomachinery will be presented.

Spatiotemporal chaos of fractional order logistic equation in nonlinear coupled lattices

NASA Astrophysics Data System (ADS)

Zhang, Ying-Qian; Wang, Xing-Yuan; Liu, Li-Yan; He, Yi; Liu, Jia

2017-11-01

We investigate a new spatiotemporal dynamics with fractional order differential logistic map and spatial nonlinear coupling. The spatial nonlinear coupling features such as the higher percentage of lattices in chaotic behaviors for most of parameters and none periodic windows in bifurcation diagrams are held, which are more suitable for encryptions than the former adjacent coupled map lattices. Besides, the proposed model has new features such as the wider parameter range and wider range of state amplitude for ergodicity, which contributes a wider range of key space when applied in encryptions. The simulations and theoretical analyses are developed in this paper.

Assessment of Walking Stability of Elderly by Means of Nonlinear Time-Series Analysis and Simple Accelerometry

NASA Astrophysics Data System (ADS)

Ohtaki, Yasuaki; Arif, Muhammad; Suzuki, Akihiro; Fujita, Kazuki; Inooka, Hikaru; Nagatomi, Ryoichi; Tsuji, Ichiro

This study presents an assessment of walking stability in elderly people, focusing on local dynamic stability of walking. Its main objectives were to propose a technique to quantify local dynamic stability using nonlinear time-series analyses and a portable instrument, and to investigate their reliability in revealing the efficacy of an exercise training intervention for elderly people for improvement of walking stability. The method measured three-dimensional acceleration of the upper body, and computation of Lyapunov exponents, thereby directly quantifying the local stability of the dynamic system. Straight level walking of young and elderly subjects was investigated in the experimental study. We compared Lyapunov exponents of young and the elderly subjects, and of groups before and after the exercise intervention. Experimental results demonstrated that the exercise intervention improved local dynamic stability of walking. The proposed method was useful in revealing effects and efficacies of the exercise intervention for elderly people.

Coexistence of Multiple Nonlinear States in a Tristable Passive Kerr Resonator

NASA Astrophysics Data System (ADS)

Anderson, Miles; Wang, Yadong; Leo, François; Coen, Stéphane; Erkintalo, Miro; Murdoch, Stuart G.

2017-07-01

Passive Kerr cavities driven by coherent laser fields display a rich landscape of nonlinear physics, including bistability, pattern formation, and localized dissipative structures (solitons). Their conceptual simplicity has for several decades offered an unprecedented window into nonlinear cavity dynamics, providing insights into numerous systems and applications ranging from all-optical memory devices to microresonator frequency combs. Yet despite the decades of study, a recent theoretical work has surprisingly alluded to an entirely new and unexplored paradigm in the regime where nonlinearly tilted cavity resonances overlap with one another [T. Hansson and S. Wabnitz, J. Opt. Soc. Am. B 32, 1259 (2015), 10.1364/JOSAB.32.001259]. We use synchronously driven fiber ring resonators to experimentally access this regime and observe the rise of new nonlinear dissipative states. Specifically, we observe, for the first time to the best of our knowledge, the stable coexistence of temporal Kerr cavity solitons and extended modulation instability (Turing) patterns, and perform real-time measurements that unveil the dynamics of the ensuing nonlinear structure. When operating in the regime of continuous wave tristability, we further observe the coexistence of two distinct cavity soliton states, one of which can be identified as a "super" cavity soliton, as predicted by Hansson and Wabnitz. Our experimental findings are in excellent agreement with theoretical analyses and numerical simulations of the infinite-dimensional Ikeda map that governs the cavity dynamics. The results from our work reveal that experimental systems can support complex combinations of distinct nonlinear states, and they could have practical implications to future microresonator-based frequency comb sources.

Experimental Nonlinear Dynamics and Snap-Through of Post-Buckled Thin Laminated Composite Plates

NASA Astrophysics Data System (ADS)

Kim, Han-Gyu

Modern aerospace systems are increasingly being designed with composite panels and plates to achieve light weight and high specific strength and stiffness. For constrained panels, thermally-induced axial loading may cause buckling of the structure, which can lead to nonlinear and potentially chaotic behavior. When post-buckled composite plates experience snap-through, they are subjected to large-amplitude deformations and in-plane compressive loading. These phenomena pose a potential threat to the structural integrity of composite structures. In this work, the nonlinear dynamic behavior of post-buckled composite plates was investigated experimentally and computationally. For the experimental work, an electrodynamic shaker was used to apply harmonic loads and the dynamic response of plate specimens was measured using a single-point displacement-sensing laser, a double-point laser vibrometer (velocity-sensing), and a set of digital image correlation cameras. Both chaotic and periodic steady-state snap-through behaviors were investigated. The experimental data were used to characterize snap-through behaviors of the post-buckled specimens and their boundaries in the harmonic forcing parameter space. The nonlinear behavior of post-buckled plates was modeled using the classical laminated plate theory (CLPT) and the von Karman strain-displacement relations. The static equilibrium paths of the post-buckled plates were analyzed using an arc-length method with a branch-switching technique. For the dynamic analysis, the nonlinear equations of motion were derived based on CLPT and the nonlinear finite element model of the equations was constructed using the Hermite cubic interpolation functions for both conforming and nonconforming elements. The numerical analyses were conducted using the model and were compared with the experimental data.

Multiscale volatility duration characteristics on financial multi-continuum percolation dynamics

NASA Astrophysics Data System (ADS)

Wang, Min; Wang, Jun

A random stock price model based on the multi-continuum percolation system is developed to investigate the nonlinear dynamics of stock price volatility duration, in an attempt to explain various statistical facts found in financial data, and have a deeper understanding of mechanisms in the financial market. The continuum percolation system is usually referred to be a random coverage process or a Boolean model, it is a member of a class of statistical physics systems. In this paper, the multi-continuum percolation (with different values of radius) is employed to model and reproduce the dispersal of information among the investors. To testify the rationality of the proposed model, the nonlinear analyses of return volatility duration series are preformed by multifractal detrending moving average analysis and Zipf analysis. The comparison empirical results indicate the similar nonlinear behaviors for the proposed model and the actual Chinese stock market.

Experimental evaluation of four ground-motion scaling methods for dynamic response-history analysis of nonlinear structures

USGS Publications Warehouse

O'Donnell, Andrew P.; Kurama, Yahya C.; Kalkan, Erol; Taflanidis, Alexandros A.

2017-01-01

This paper experimentally evaluates four methods to scale earthquake ground-motions within an ensemble of records to minimize the statistical dispersion and maximize the accuracy in the dynamic peak roof drift demand and peak inter-story drift demand estimates from response-history analyses of nonlinear building structures. The scaling methods that are investigated are based on: (1) ASCE/SEI 7–10 guidelines; (2) spectral acceleration at the fundamental (first mode) period of the structure, Sa(T1); (3) maximum incremental velocity, MIV; and (4) modal pushover analysis. A total of 720 shake-table tests of four small-scale nonlinear building frame specimens with different static and dynamic characteristics are conducted. The peak displacement demands from full suites of 36 near-fault ground-motion records as well as from smaller “unbiased” and “biased” design subsets (bins) of ground-motions are included. Out of the four scaling methods, ground-motions scaled to the median MIV of the ensemble resulted in the smallest dispersion in the peak roof and inter-story drift demands. Scaling based on MIValso provided the most accurate median demands as compared with the “benchmark” demands for structures with greater nonlinearity; however, this accuracy was reduced for structures exhibiting reduced nonlinearity. The modal pushover-based scaling (MPS) procedure was the only method to conservatively overestimate the median drift demands.

Modal Substructuring of Geometrically Nonlinear Finite Element Models with Interface Reduction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.

Substructuring methods have been widely used in structural dynamics to divide large, complicated finite element models into smaller substructures. For linear systems, many methods have been developed to reduce the subcomponents down to a low order set of equations using a special set of component modes, and these are then assembled to approximate the dynamics of a large scale model. In this paper, a substructuring approach is developed for coupling geometrically nonlinear structures, where each subcomponent is drastically reduced to a low order set of nonlinear equations using a truncated set of fixedinterface and characteristic constraint modes. The method usedmore » to extract the coefficients of the nonlinear reduced order model (NLROM) is non-intrusive in that it does not require any modification to the commercial FEA code, but computes the NLROM from the results of several nonlinear static analyses. The NLROMs are then assembled to approximate the nonlinear differential equations of the global assembly. The method is demonstrated on the coupling of two geometrically nonlinear plates with simple supports at all edges. The plates are joined at a continuous interface through the rotational degrees-of-freedom (DOF), and the nonlinear normal modes (NNMs) of the assembled equations are computed to validate the models. The proposed substructuring approach reduces a 12,861 DOF nonlinear finite element model down to only 23 DOF, while still accurately reproducing the first three NNMs of the full order model.« less

Modal Substructuring of Geometrically Nonlinear Finite Element Models with Interface Reduction

DOE PAGES

Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.

2017-03-29

Substructuring methods have been widely used in structural dynamics to divide large, complicated finite element models into smaller substructures. For linear systems, many methods have been developed to reduce the subcomponents down to a low order set of equations using a special set of component modes, and these are then assembled to approximate the dynamics of a large scale model. In this paper, a substructuring approach is developed for coupling geometrically nonlinear structures, where each subcomponent is drastically reduced to a low order set of nonlinear equations using a truncated set of fixedinterface and characteristic constraint modes. The method usedmore » to extract the coefficients of the nonlinear reduced order model (NLROM) is non-intrusive in that it does not require any modification to the commercial FEA code, but computes the NLROM from the results of several nonlinear static analyses. The NLROMs are then assembled to approximate the nonlinear differential equations of the global assembly. The method is demonstrated on the coupling of two geometrically nonlinear plates with simple supports at all edges. The plates are joined at a continuous interface through the rotational degrees-of-freedom (DOF), and the nonlinear normal modes (NNMs) of the assembled equations are computed to validate the models. The proposed substructuring approach reduces a 12,861 DOF nonlinear finite element model down to only 23 DOF, while still accurately reproducing the first three NNMs of the full order model.« less

Investigating multiphoton phenomena using nonlinear dynamics

NASA Astrophysics Data System (ADS)

Huang, Shu

Many seemingly simple systems can display extraordinarily complex dynamics which has been studied and uncovered through nonlinear dynamical theory. The leitmotif of this thesis is changing phase-space structures and their (linear or non-linear) stabilities by adding control functions (which act on the system as external perturbations) to the relevant Hamiltonians. These phase-space structures may be periodic orbits, invariant tori or their stable and unstable manifolds. One-electron systems and diatomic molecules are fundamental and important staging ground for new discoveries in nonlinear dynamics. In past years, increasing emphasis and effort has been put on the control or manipulation of these systems. Recent developments of nonlinear dynamical tools can provide efficient ways of doing so. In the first subtopic of the thesis, we are adding a control function to restore tori at prescribed locations in phase space. In the remainder of the thesis, a control function with parameters is used to change the linear stability of the periodic orbits which govern the processes in question. In this thesis, we report our theoretical analyses on multiphoton ionization of Rydberg atoms exposed to strong microwave fields and the dissociation of diatomic molecules exposed to bichromatic lasers using nonlinear dynamical tools. This thesis is composed of three subtopics. In the first subtopic, we employ local control theory to reduce the stochastic ionization of hydrogen atom in a strong microwave field by adding a relatively small control term to the original Hamiltonian. In the second subtopic, we perform periodic orbit analysis to investigate multiphoton ionization driven by a bichromatic microwave field. Our results show quantitative and qualitative agreement with previous studies, and hence identify the mechanism through which short periodic orbits organize the dynamics in multiphoton ionization. In addition, we achieve substantial time savings with this approach. In the third subtopic we extend our periodic orbit analysis to the dissociation of diatomic molecules driven by a bichromatic laser. In this problem, our results based on periodic orbit analysis again show good agreement with previous work, and hence promise more potential applications of this approach in molecular physics.

Analysis of complex neural circuits with nonlinear multidimensional hidden state models

PubMed Central

Friedman, Alexander; Slocum, Joshua F.; Tyulmankov, Danil; Gibb, Leif G.; Altshuler, Alex; Ruangwises, Suthee; Shi, Qinru; Toro Arana, Sebastian E.; Beck, Dirk W.; Sholes, Jacquelyn E. C.; Graybiel, Ann M.

2016-01-01

A universal need in understanding complex networks is the identification of individual information channels and their mutual interactions under different conditions. In neuroscience, our premier example, networks made up of billions of nodes dynamically interact to bring about thought and action. Granger causality is a powerful tool for identifying linear interactions, but handling nonlinear interactions remains an unmet challenge. We present a nonlinear multidimensional hidden state (NMHS) approach that achieves interaction strength analysis and decoding of networks with nonlinear interactions by including latent state variables for each node in the network. We compare NMHS to Granger causality in analyzing neural circuit recordings and simulations, improvised music, and sociodemographic data. We conclude that NMHS significantly extends the scope of analyses of multidimensional, nonlinear networks, notably in coping with the complexity of the brain. PMID:27222584

Finite Element Analysis of Wrinkled Membrane Structures for Sunshield Applications

NASA Technical Reports Server (NTRS)

Johnston, John D.; Brodeur, Stephen J. (Technical Monitor)

2002-01-01

The deployable sunshield is an example of a gossamer structure envisioned for use on future space telescopes. The basic structure consists of multiple layers of pretensioned, thin-film membranes supported by deployable booms. The prediction and verification of sunshield dynamics has been identified as an area in need of technology development due to the difficulties inherent in predicting nonlinear structural behavior of the membranes and because of the challenges involved. in ground testing of the full-scale structure. This paper describes a finite element analysis of a subscale sunshield that has been subjected to ground testing in support of the Next Generation Space Telescope (NGST) program. The analysis utilizes a nonlinear material model that accounts for wrinkling of the membranes. Results are presented from a nonlinear static preloading analysis and subsequent dynamics analyses to illustrate baseline sunshield structural characteristics. Studies are then described which provide further insight into the effect of membrane. preload on sunshield dynamics and the performance of different membrane modeling techniques. Lastly, a comparison of analytical predictions and ground test results is presented.

Super Nonlinear Electrodeposition-Diffusion-Controlled Thin-Film Selector.

PubMed

Ji, Xinglong; Song, Li; He, Wei; Huang, Kejie; Yan, Zhiyuan; Zhong, Shuai; Zhang, Yishu; Zhao, Rong

2018-03-28

Selector elements with high nonlinearity are an indispensable part in constructing high density, large-scale, 3D stackable emerging nonvolatile memory and neuromorphic network. Although significant efforts have been devoted to developing novel thin-film selectors, it remains a great challenge in achieving good switching performance in the selectors to satisfy the stringent electrical criteria of diverse memory elements. In this work, we utilized high-defect-density chalcogenide glass (Ge 2 Sb 2 Te 5 ) in conjunction with high mobility Ag element (Ag-GST) to achieve a super nonlinear selective switching. A novel electrodeposition-diffusion dynamic selector based on Ag-GST exhibits superior selecting performance including excellent nonlinearity (<5 mV/dev), ultra-low leakage (<10 fA), and bidirectional operation. With the solid microstructure evidence and dynamic analyses, we attributed the selective switching to the competition between the electrodeposition and diffusion of Ag atoms in the glassy GST matrix under electric field. A switching model is proposed, and the in-depth understanding of the selective switching mechanism offers an insight of switching dynamics for the electrodeposition-diffusion-controlled thin-film selector. This work opens a new direction of selector designs by combining high mobility elements and high-defect-density chalcogenide glasses, which can be extended to other materials with similar properties.

Dynamics of heart rate variability analysed through nonlinear and linear dynamics is already impaired in young type 1 diabetic subjects.

PubMed

Souza, Naiara M; Giacon, Thais R; Pacagnelli, Francis L; Barbosa, Marianne P C R; Valenti, Vitor E; Vanderlei, Luiz C M

2016-10-01

Autonomic diabetic neuropathy is one of the most common complications of type 1 diabetes mellitus, and studies using heart rate variability to investigate these individuals have shown inconclusive results regarding autonomic nervous system activation. Aims To investigate the dynamics of heart rate in young subjects with type 1 diabetes mellitus through nonlinear and linear methods of heart rate variability. We evaluated 20 subjects with type 1 diabetes mellitus and 23 healthy control subjects. We obtained the following nonlinear indices from the recurrence plot: recurrence rate (REC), determinism (DET), and Shanon entropy (ES), and we analysed indices in the frequency (LF and HF in ms2 and normalised units - nu - and LF/HF ratio) and time domains (SDNN and RMSSD), through analysis of 1000 R-R intervals, captured by a heart rate monitor. There were reduced values (p<0.05) for individuals with type 1 diabetes mellitus compared with healthy subjects in the following indices: DET, REC, ES, RMSSD, SDNN, LF (ms2), and HF (ms2). In relation to the recurrence plot, subjects with type 1 diabetes mellitus demonstrated lower recurrence and greater variation in their plot, inter-group and intra-group, respectively. Young subjects with type 1 diabetes mellitus have autonomic nervous system behaviour that tends to randomness compared with healthy young subjects. Moreover, this behaviour is related to reduced sympathetic and parasympathetic activity of the autonomic nervous system.

NONLINEAR AND FIBER OPTICS: Transient stimulated thermal scattering in a field of quasiplanar counterpropagating pump beams

NASA Astrophysics Data System (ADS)

Arutyunov, Yu A.; Bagan, A. A.; Gerasimov, V. B.; Golyanov, A. V.; Ogluzdin, Valerii E.; Sugrobov, V. A.; Khizhnyak, A. I.

1990-04-01

Theoretical analyses and experimental studies are made of transient stimulated thermal scattering in a thermal nonlinear medium subjected to a field of counterpropagating quasiplane waves. The equations for the counterpropagating four-beam interaction are solved analytically for pairwise counterpropagating scattered waves using the constant pump wave intensity approximation. The conditions for the occurrence of an absolute instability of the scattered waves are determined and the angular dependence of their increment is obtained; these results are in good agreement with experimental data. An investigation is reported of the dynamics of spiky lasing in a laser with resonators coupled by a dynamic hologram in which stimulated thermal scattering is a source of radiation initiating lasing in the system as a whole.

Dynamic Analyses Including Joints Of Truss Structures

NASA Technical Reports Server (NTRS)

Belvin, W. Keith

1991-01-01

Method for mathematically modeling joints to assess influences of joints on dynamic response of truss structures developed in study. Only structures with low-frequency oscillations considered; only Coulomb friction and viscous damping included in analysis. Focus of effort to obtain finite-element mathematical models of joints exhibiting load-vs.-deflection behavior similar to measured load-vs.-deflection behavior of real joints. Experiments performed to determine stiffness and damping nonlinearities typical of joint hardware. Algorithm for computing coefficients of analytical joint models based on test data developed to enable study of linear and nonlinear effects of joints on global structural response. Besides intended application to large space structures, applications in nonaerospace community include ground-based antennas and earthquake-resistant steel-framed buildings.

Effects of a hydrotherapy programme on symbolic and complexity dynamics of heart rate variability and aerobic capacity in fibromyalgia patients.

PubMed

Zamunér, Antonio Roberto; Andrade, Carolina P; Forti, Meire; Marchi, Andrea; Milan, Juliana; Avila, Mariana Arias; Catai, Aparecida Maria; Porta, Alberto; Silva, Ester

2015-01-01

To evaluate the effects of a hydrotherapy programme on aerobic capacity and linear and non-linear dynamics of heart rate variability (HRV) in women with fibromyalgia syndrome (FMS). 20 women with FMS and 20 healthy controls (HC) took part in the study. The FMS group was evaluated at baseline and after a 16-week hydrotherapy programme. All participants underwent cardiopulmonary exercise testing on a cycle ergometer and RR intervals recording in supine and standing positions. The HRV was analysed by linear and non-linear methods. The current level of pain, the tender points, the pressure pain threshold and the impact of FMS on quality of life were assessed. The FMS patients presented higher cardiac sympathetic modulation, lower vagal modulation and lower complexity of HRV in supine position than the HC. Only the HC decreased the complexity indices of HRV during orthostatic stimulus. After a 16-week hydrotherapy programme, the FMS patients increased aerobic capacity, decreased cardiac sympathetic modulation and increased vagal modulation and complexity dynamics of HRV in supine. The FMS patients also improved their cardiac autonomic adjustments to the orthostatic stimulus. Associations between improvements in non-linear dynamics of HRV and improvements in pain and in the impact of FMS on quality of life were found. A 16-week hydrotherapy programme proved to be effective in ameliorating symptoms, aerobic functional capacity and cardiac autonomic control in FMS patients. Improvements in the non-linear dynamics of HRV were related to improvements in pain and in the impact of FMS on quality of life.

Analytical investigations of seismic responses for reinforced concrete bridge columns subjected to strong near-fault ground motion

NASA Astrophysics Data System (ADS)

Su, Chin-Kuo; Sung, Yu-Chi; Chang, Shuenn-Yih; Huang, Chao-Hsun

2007-09-01

Strong near-fault ground motion, usually caused by the fault-rupture and characterized by a pulse-like velocity-wave form, often causes dramatic instantaneous seismic energy (Jadhav and Jangid 2006). Some reinforced concrete (RC) bridge columns, even those built according to ductile design principles, were damaged in the 1999 Chi-Chi earthquake. Thus, it is very important to evaluate the seismic response of a RC bridge column to improve its seismic design and prevent future damage. Nonlinear time history analysis using step-by-step integration is capable of tracing the dynamic response of a structure during the entire vibration period and is able to accommodate the pulsing wave form. However, the accuracy of the numerical results is very sensitive to the modeling of the nonlinear load-deformation relationship of the structural member. FEMA 273 and ATC-40 provide the modeling parameters for structural nonlinear analyses of RC beams and RC columns. They use three parameters to define the plastic rotation angles and a residual strength ratio to describe the nonlinear load-deformation relationship of an RC member. Structural nonlinear analyses are performed based on these parameters. This method provides a convenient way to obtain the nonlinear seismic responses of RC structures. However, the accuracy of the numerical solutions might be further improved. For this purpose, results from a previous study on modeling of the static pushover analyses for RC bridge columns (Sung et al. 2005) is adopted for the nonlinear time history analysis presented herein to evaluate the structural responses excited by a near-fault ground motion. To ensure the reliability of this approach, the numerical results were compared to experimental results. The results confirm that the proposed approach is valid.

Multibody dynamic simulation of knee contact mechanics

PubMed Central

Bei, Yanhong; Fregly, Benjamin J.

2006-01-01

Multibody dynamic musculoskeletal models capable of predicting muscle forces and joint contact pressures simultaneously would be valuable for studying clinical issues related to knee joint degeneration and restoration. Current three-dimensional multi-body knee models are either quasi-static with deformable contact or dynamic with rigid contact. This study proposes a computationally efficient methodology for combining multibody dynamic simulation methods with a deformable contact knee model. The methodology requires preparation of the articular surface geometry, development of efficient methods to calculate distances between contact surfaces, implementation of an efficient contact solver that accounts for the unique characteristics of human joints, and specification of an application programming interface for integration with any multibody dynamic simulation environment. The current implementation accommodates natural or artificial tibiofemoral joint models, small or large strain contact models, and linear or nonlinear material models. Applications are presented for static analysis (via dynamic simulation) of a natural knee model created from MRI and CT data and dynamic simulation of an artificial knee model produced from manufacturer’s CAD data. Small and large strain natural knee static analyses required 1 min of CPU time and predicted similar contact conditions except for peak pressure, which was higher for the large strain model. Linear and nonlinear artificial knee dynamic simulations required 10 min of CPU time and predicted similar contact force and torque but different contact pressures, which were lower for the nonlinear model due to increased contact area. This methodology provides an important step toward the realization of dynamic musculoskeletal models that can predict in vivo knee joint motion and loading simultaneously. PMID:15564115

Observation of dynamic interactions between fundamental and second-harmonic modes in a high-power sub-terahertz gyrotron operating in regimes of soft and hard self-excitation.

PubMed

Saito, Teruo; Tatematsu, Yoshinori; Yamaguchi, Yuusuke; Ikeuchi, Shinji; Ogasawara, Shinya; Yamada, Naoki; Ikeda, Ryosuke; Ogawa, Isamu; Idehara, Toshitaka

2012-10-12

Dynamic mode interaction between fundamental and second-harmonic modes has been observed in high-power sub-terahertz gyrotrons [T. Notake et al., Phys. Rev. Lett. 103, 225002 (2009); T. Saito et al. Phys. Plasmas 19, 063106 (2012)]. Interaction takes place between a parasitic fundamental or first-harmonic (FH) mode and an operating second-harmonic (SH) mode, as well as among SH modes. In particular, nonlinear excitation of the parasitic FH mode in the hard self-excitation regime with assistance of a SH mode in the soft self-excitation regime was clearly observed. Moreover, both cases of stable two-mode oscillation and oscillation of the FH mode only were observed. These observations and theoretical analyses of the dynamic behavior of the mode interaction verify the nonlinear hard self-excitation of the FH mode.

Equivalent model construction for a non-linear dynamic system based on an element-wise stiffness evaluation procedure and reduced analysis of the equivalent system

NASA Astrophysics Data System (ADS)

Kim, Euiyoung; Cho, Maenghyo

2017-11-01

In most non-linear analyses, the construction of a system matrix uses a large amount of computation time, comparable to the computation time required by the solving process. If the process for computing non-linear internal force matrices is substituted with an effective equivalent model that enables the bypass of numerical integrations and assembly processes used in matrix construction, efficiency can be greatly enhanced. A stiffness evaluation procedure (STEP) establishes non-linear internal force models using polynomial formulations of displacements. To efficiently identify an equivalent model, the method has evolved such that it is based on a reduced-order system. The reduction process, however, makes the equivalent model difficult to parameterize, which significantly affects the efficiency of the optimization process. In this paper, therefore, a new STEP, E-STEP, is proposed. Based on the element-wise nature of the finite element model, the stiffness evaluation is carried out element-by-element in the full domain. Since the unit of computation for the stiffness evaluation is restricted by element size, and since the computation is independent, the equivalent model can be constructed efficiently in parallel, even in the full domain. Due to the element-wise nature of the construction procedure, the equivalent E-STEP model is easily characterized by design parameters. Various reduced-order modeling techniques can be applied to the equivalent system in a manner similar to how they are applied in the original system. The reduced-order model based on E-STEP is successfully demonstrated for the dynamic analyses of non-linear structural finite element systems under varying design parameters.

Differences in postural tremor dynamics with age and neurological disease.

PubMed

Morrison, Steven; Newell, Karl M; Kavanagh, Justin J

2017-06-01

The overlap of dominant tremor frequencies and similarly amplified tremor observed for Parkinson's disease (PD) and essential tremor (ET) means differentiating between these pathologies is often difficult. As tremor exhibits non-linear properties, employing both linear and non-linear analyses may help distinguish between the tremor dynamics of aging, PD and ET. This study was designed to examine postural tremor in healthy older adults, PD and ET using standard linear and non-linear metrics. Hand and finger postural tremor was recorded in 15 healthy older adults (64 ± 6 years), 15 older individuals with PD (63 ± 6 years), and 10 persons with ET (68 ± 7 years). Linear measures of amplitude, frequency, and between-limb coupling (coherence) were performed. Non-linear measures of regularity (ApEn) and coupling (Cross-ApEn) were also used. Additionally, receiver operating characteristic analyses were performed for those measures that were significantly different between all groups. The results revealed that the linear measures only showed significant differences between the healthy adults and ET/PD persons, but no differences between the two neurological groups. Coherence showed higher bilateral coupling for ET but no differences in inter-limb coupling between PD and healthy subjects. However, ApEn values for finger tremor revealed significant differences between all groups, with tremor for ET persons being more regular (lower ApEn) overall. Similarly, Cross-ApEn results also showed differences between all groups, with ET persons showing strongest inter-limb coupling followed by PD and elderly. Overall, our findings point to the diagnostic potential for non-linear measures of coupling and tremor structure as biomarkers for discriminating between ET, PD and healthy persons.

Modeling and complexity of stochastic interacting Lévy type financial price dynamics

NASA Astrophysics Data System (ADS)

Wang, Yiduan; Zheng, Shenzhou; Zhang, Wei; Wang, Jun; Wang, Guochao

2018-06-01

In attempt to reproduce and investigate nonlinear dynamics of security markets, a novel nonlinear random interacting price dynamics, which is considered as a Lévy type process, is developed and investigated by the combination of lattice oriented percolation and Potts dynamics, which concerns with the instinctive random fluctuation and the fluctuation caused by the spread of the investors' trading attitudes, respectively. To better understand the fluctuation complexity properties of the proposed model, the complexity analyses of random logarithmic price return and corresponding volatility series are preformed, including power-law distribution, Lempel-Ziv complexity and fractional sample entropy. In order to verify the rationality of the proposed model, the corresponding studies of actual security market datasets are also implemented for comparison. The empirical results reveal that this financial price model can reproduce some important complexity features of actual security markets to some extent. The complexity of returns decreases with the increase of parameters γ1 and β respectively, furthermore, the volatility series exhibit lower complexity than the return series

Three-Dimensional Numerical Analyses of Earth Penetration Dynamics

DTIC Science & Technology

1979-01-31

Lagrangian formulation based on the HEMP method and has been adapted and validated for treatment of normal-incidence (axisymmetric) impact and...code, is a detailed analysis of the structural response of the EPW. This analysis is generated using a nonlinear dynamic, elastic- plastic finite element...based on the HEMP scheme. Thus, the code has the same material modeling capabilities and abilities to track large scale motion found in the WAVE-L code

Modal and Impact Dynamics Analysis of an Aluminum Cylinder

NASA Technical Reports Server (NTRS)

Lessard, Wendy B.

2002-01-01

This paper presents analyses for the modal characteristics and impact response of an all-aluminum cylinder. The analyses were performed in preparation for impact tests of the cylinder at The Impact Dynamics Research Facility (IDRF) at the NASA Langley Research Center. Mode shapes and frequencies were computed using NASTRAN and compared with existing experimental data to assess the overall accuracy of the mass and stiffness of the finite element model. A series of non-linear impact analyses were then performed using MSC Dytran in which the weight distribution on the floor and the impact velocity of the cylinder were varied. The effects of impact velocity and mass on the rebound and gross deformation of the cylinder were studied in this investigation.

Non-linear modelling and control of semi-active suspensions with variable damping

NASA Astrophysics Data System (ADS)

Chen, Huang; Long, Chen; Yuan, Chao-Chun; Jiang, Hao-Bin

2013-10-01

Electro-hydraulic dampers can provide variable damping force that is modulated by varying the command current; furthermore, they offer advantages such as lower power, rapid response, lower cost, and simple hardware. However, accurate characterisation of non-linear f-v properties in pre-yield and force saturation in post-yield is still required. Meanwhile, traditional linear or quarter vehicle models contain various non-linearities. The development of a multi-body dynamics model is very complex, and therefore, SIMPACK was used with suitable improvements for model development and numerical simulations. A semi-active suspension was built based on a belief-desire-intention (BDI)-agent model framework. Vehicle handling dynamics were analysed, and a co-simulation analysis was conducted in SIMPACK and MATLAB to evaluate the BDI-agent controller. The design effectively improved ride comfort, handling stability, and driving safety. A rapid control prototype was built based on dSPACE to conduct a real vehicle test. The test and simulation results were consistent, which verified the simulation.

Turbine blade forced response prediction using FREPS

NASA Technical Reports Server (NTRS)

Murthy, Durbha, V.; Morel, Michael R.

1993-01-01

This paper describes a software system called FREPS (Forced REsponse Prediction System) that integrates structural dynamic, steady and unsteady aerodynamic analyses to efficiently predict the forced response dynamic stresses in axial flow turbomachinery blades due to aerodynamic and mechanical excitations. A flutter analysis capability is also incorporated into the system. The FREPS system performs aeroelastic analysis by modeling the motion of the blade in terms of its normal modes. The structural dynamic analysis is performed by a finite element code such as MSC/NASTRAN. The steady aerodynamic analysis is based on nonlinear potential theory and the unsteady aerodynamic analyses is based on the linearization of the non-uniform potential flow mean. The program description and presentation of the capabilities are reported herein. The effectiveness of the FREPS package is demonstrated on the High Pressure Oxygen Turbopump turbine of the Space Shuttle Main Engine. Both flutter and forced response analyses are performed and typical results are illustrated.

The development and validation of a numerical integration method for non-linear viscoelastic modeling

PubMed Central

Ramo, Nicole L.; Puttlitz, Christian M.

2018-01-01

Compelling evidence that many biological soft tissues display both strain- and time-dependent behavior has led to the development of fully non-linear viscoelastic modeling techniques to represent the tissue’s mechanical response under dynamic conditions. Since the current stress state of a viscoelastic material is dependent on all previous loading events, numerical analyses are complicated by the requirement of computing and storing the stress at each step throughout the load history. This requirement quickly becomes computationally expensive, and in some cases intractable, for finite element models. Therefore, we have developed a strain-dependent numerical integration approach for capturing non-linear viscoelasticity that enables calculation of the current stress from a strain-dependent history state variable stored from the preceding time step only, which improves both fitting efficiency and computational tractability. This methodology was validated based on its ability to recover non-linear viscoelastic coefficients from simulated stress-relaxation (six strain levels) and dynamic cyclic (three frequencies) experimental stress-strain data. The model successfully fit each data set with average errors in recovered coefficients of 0.3% for stress-relaxation fits and 0.1% for cyclic. The results support the use of the presented methodology to develop linear or non-linear viscoelastic models from stress-relaxation or cyclic experimental data of biological soft tissues. PMID:29293558

Effects of unbalance location on dynamic characteristics of high-speed gasoline engine turbocharger with floating ring bearings

NASA Astrophysics Data System (ADS)

Wang, Longkai; Bin, Guangfu; Li, Xuejun; Liu, Dingqu

2016-03-01

For the high-speed gasoline engine turbocharger rotor, due to the heterogeneity of multiple parts material, manufacturing and assembly errors, running wear in impeller and uneven carbon of turbine, the random unbalance usually can be developed which will induce excessive rotor vibration, and even lead to nonlinear vibration accidents. However, the investigation of unbalance location on the nonlinear high-speed turbocharger rotordynamic characteristics is less. In order to discuss the rotor unbalance location effects of turbocharger with nonlinear floating ring bearings(FRBs), the realistic turbocharger of gasoline engine is taken as a research object. The rotordynamic equations of motion under the condition of unbalance are derived by applied unbalance force and nonlinear oil film force of FRBs. The FE model of turbocharger rotor-bearing system is modeled which includes the unbalance excitation and nonlinear FRBs. Under the conditions of four different applied locations of unbalance, the nonlinear transient analyses are performed based on the rotor FEM. The differences of dynamic behavior are obvious to the turbocharger rotor systems for four conditions, and the bifurcation phenomena are different. From the results of waterfall and transient response analysis, the speed for the appearance of fractional frequency is not identical and the amplitude magnitude is different from the different unbalance locations, and the non-synchronous vibration does not occur in the turbocharger and the amplitude is relative stable and minimum under the condition 4. The turbocharger vibration and non-synchronous components could be reduced or suppressed by controlling the applied location of unbalance, which is helpful for the dynamic design, fault diagnosis and vibration control of the high-speed gasoline engine turbochargers.

State Space Formulation of Nonlinear Vibration Responses Collected from a Dynamic Rotor-Bearing System: An Extension of Bearing Diagnostics to Bearing Prognostics

PubMed Central

Tse, Peter W.; Wang, Dong

2017-01-01

Bearings are widely used in various industries to support rotating shafts. Their failures accelerate failures of other adjacent components and may cause unexpected machine breakdowns. In recent years, nonlinear vibration responses collected from a dynamic rotor-bearing system have been widely analyzed for bearing diagnostics. Numerous methods have been proposed to identify different bearing faults. However, these methods are unable to predict the future health conditions of bearings. To extend bearing diagnostics to bearing prognostics, this paper reports the design of a state space formulation of nonlinear vibration responses collected from a dynamic rotor-bearing system in order to intelligently predict bearing remaining useful life (RUL). Firstly, analyses of nonlinear vibration responses were conducted to construct a bearing health indicator (BHI) so as to assess the current bearing health condition. Secondly, a state space model of the BHI was developed to mathematically track the health evolution of the BHI. Thirdly, unscented particle filtering was used to predict bearing RUL. Lastly, a new bearing acceleration life testing setup was designed to collect natural bearing degradation data, which were used to validate the effectiveness of the proposed bearing prognostic method. Results show that the prediction accuracy of the proposed bearing prognostic method is promising and the proposed bearing prognostic method is able to reflect future bearing health conditions. PMID:28216586

State Space Formulation of Nonlinear Vibration Responses Collected from a Dynamic Rotor-Bearing System: An Extension of Bearing Diagnostics to Bearing Prognostics.

PubMed

Tse, Peter W; Wang, Dong

2017-02-14

Bearings are widely used in various industries to support rotating shafts. Their failures accelerate failures of other adjacent components and may cause unexpected machine breakdowns. In recent years, nonlinear vibration responses collected from a dynamic rotor-bearing system have been widely analyzed for bearing diagnostics. Numerous methods have been proposed to identify different bearing faults. However, these methods are unable to predict the future health conditions of bearings. To extend bearing diagnostics to bearing prognostics, this paper reports the design of a state space formulation of nonlinear vibration responses collected from a dynamic rotor-bearing system in order to intelligently predict bearing remaining useful life (RUL). Firstly, analyses of nonlinear vibration responses were conducted to construct a bearing health indicator (BHI) so as to assess the current bearing health condition. Secondly, a state space model of the BHI was developed to mathematically track the health evolution of the BHI. Thirdly, unscented particle filtering was used to predict bearing RUL. Lastly, a new bearing acceleration life testing setup was designed to collect natural bearing degradation data, which were used to validate the effectiveness of the proposed bearing prognostic method. Results show that the prediction accuracy of the proposed bearing prognostic method is promising and the proposed bearing prognostic method is able to reflect future bearing health conditions.

Nonlinear modelling of high-speed catenary based on analytical expressions of cable and truss elements

NASA Astrophysics Data System (ADS)

Song, Yang; Liu, Zhigang; Wang, Hongrui; Lu, Xiaobing; Zhang, Jing

2015-10-01

Due to the intrinsic nonlinear characteristics and complex structure of the high-speed catenary system, a modelling method is proposed based on the analytical expressions of nonlinear cable and truss elements. The calculation procedure for solving the initial equilibrium state is proposed based on the Newton-Raphson iteration method. The deformed configuration of the catenary system as well as the initial length of each wire can be calculated. Its accuracy and validity of computing the initial equilibrium state are verified by comparison with the separate model method, absolute nodal coordinate formulation and other methods in the previous literatures. Then, the proposed model is combined with a lumped pantograph model and a dynamic simulation procedure is proposed. The accuracy is guaranteed by the multiple iterative calculations in each time step. The dynamic performance of the proposed model is validated by comparison with EN 50318, the results of the finite element method software and SIEMENS simulation report, respectively. At last, the influence of the catenary design parameters (such as the reserved sag and pre-tension) on the dynamic performance is preliminarily analysed by using the proposed model.

A study of vocal nonlinearities in humpback whale songs: from production mechanisms to acoustic analysis.

PubMed

Cazau, Dorian; Adam, Olivier; Aubin, Thierry; Laitman, Jeffrey T; Reidenberg, Joy S

2016-10-10

Although mammalian vocalizations are predominantly harmonically structured, they can exhibit an acoustic complexity with nonlinear vocal sounds, including deterministic chaos and frequency jumps. Such sounds are normative events in mammalian vocalizations, and can be directly traceable to the nonlinear nature of vocal-fold dynamics underlying typical mammalian sound production. In this study, we give qualitative descriptions and quantitative analyses of nonlinearities in the song repertoire of humpback whales from the Ste Marie channel (Madagascar) to provide more insight into the potential communication functions and underlying production mechanisms of these features. A low-dimensional biomechanical modeling of the whale's U-fold (vocal folds homolog) is used to relate specific vocal mechanisms to nonlinear vocal features. Recordings of living humpback whales were searched for occurrences of vocal nonlinearities (instabilities). Temporal distributions of nonlinearities were assessed within sound units, and between different songs. The anatomical production sources of vocal nonlinearities and the communication context of their occurrences in recordings are discussed. Our results show that vocal nonlinearities may be a communication strategy that conveys information about the whale's body size and physical fitness, and thus may be an important component of humpback whale songs.

A study of vocal nonlinearities in humpback whale songs: from production mechanisms to acoustic analysis

NASA Astrophysics Data System (ADS)

Cazau, Dorian; Adam, Olivier; Aubin, Thierry; Laitman, Jeffrey T.; Reidenberg, Joy S.

2016-10-01

Although mammalian vocalizations are predominantly harmonically structured, they can exhibit an acoustic complexity with nonlinear vocal sounds, including deterministic chaos and frequency jumps. Such sounds are normative events in mammalian vocalizations, and can be directly traceable to the nonlinear nature of vocal-fold dynamics underlying typical mammalian sound production. In this study, we give qualitative descriptions and quantitative analyses of nonlinearities in the song repertoire of humpback whales from the Ste Marie channel (Madagascar) to provide more insight into the potential communication functions and underlying production mechanisms of these features. A low-dimensional biomechanical modeling of the whale’s U-fold (vocal folds homolog) is used to relate specific vocal mechanisms to nonlinear vocal features. Recordings of living humpback whales were searched for occurrences of vocal nonlinearities (instabilities). Temporal distributions of nonlinearities were assessed within sound units, and between different songs. The anatomical production sources of vocal nonlinearities and the communication context of their occurrences in recordings are discussed. Our results show that vocal nonlinearities may be a communication strategy that conveys information about the whale’s body size and physical fitness, and thus may be an important component of humpback whale songs.

Disequilibrium dynamics in a Keynesian model with time delays

NASA Astrophysics Data System (ADS)

Gori, Luca; Guerrini, Luca; Sodini, Mauro

2018-05-01

The aim of this research is to analyse a Keynesian goods market closed economy by considering a continuous-time setup with fixed delays. The work compares dynamic results based on linear and nonlinear adjustment mechanisms through which the aggregate supply (production) reacts to a disequilibrium in the goods market and consumption depends on income at a preceding date. Both analytical and geometrical (stability switching curves) techniques are used to characterise the stability properties of the stationary equilibrium.

Predicting Mood Changes in Bipolar Disorder through Heartbeat Nonlinear Dynamics.

PubMed

Valenza, Gaetano; Nardelli, Mimma; Lanata', Antonio; Gentili, Claudio; Bertschy, Gilles; Kosel, Markus; Scilingo, Enzo Pasquale

2016-04-20

Bipolar Disorder (BD) is characterized by an alternation of mood states from depression to (hypo)mania. Mixed states, i.e., a combination of depression and mania symptoms at the same time, can also be present. The diagnosis of this disorder in the current clinical practice is based only on subjective interviews and questionnaires, while no reliable objective psychophysiological markers are available. Furthermore, there are no biological markers predicting BD outcomes, or providing information about the future clinical course of the phenomenon. To overcome this limitation, here we propose a methodology predicting mood changes in BD using heartbeat nonlinear dynamics exclusively, derived from the ECG. Mood changes are here intended as transitioning between two mental states: euthymic state (EUT), i.e., the good affective balance, and non-euthymic (non-EUT) states. Heart Rate Variability (HRV) series from 14 bipolar spectrum patients (age: 33.439.76, age range: 23-54; 6 females) involved in the European project PSYCHE, undergoing whole night ECG monitoring were analyzed. Data were gathered from a wearable system comprised of a comfortable t-shirt with integrated fabric electrodes and sensors able to acquire ECGs. Each patient was monitored twice a week, for 14 weeks, being able to perform normal (unstructured) activities. From each acquisition, the longest artifact-free segment of heartbeat dynamics was selected for further analyses. Sub-segments of 5 minutes of this segment were used to estimate trends of HRV linear and nonlinear dynamics. Considering data from a current observation at day t0, and past observations at days (t1, t2,...,), personalized prediction accuracies in forecasting a mood state (EUT/non-EUT) at day t+1 were 69% on average, reaching values as high as 83.3%. This approach opens to the possibility of predicting mood states in bipolar patients through heartbeat nonlinear dynamics exclusively.

Applied Nonlinear Dynamics and Stochastic Systems Near The Millenium. Proceedings

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kadtke, J.B.; Bulsara, A.

These proceedings represent papers presented at the Applied Nonlinear Dynamics and Stochastic Systems conference held in San Diego, California in July 1997. The conference emphasized the applications of nonlinear dynamical systems theory in fields as diverse as neuroscience and biomedical engineering, fluid dynamics, chaos control, nonlinear signal/image processing, stochastic resonance, devices and nonlinear dynamics in socio{minus}economic systems. There were 56 papers presented at the conference and 5 have been abstracted for the Energy Science and Technology database.(AIP)

Reservoir Computing Beyond Memory-Nonlinearity Trade-off.

PubMed

Inubushi, Masanobu; Yoshimura, Kazuyuki

2017-08-31

Reservoir computing is a brain-inspired machine learning framework that employs a signal-driven dynamical system, in particular harnessing common-signal-induced synchronization which is a widely observed nonlinear phenomenon. Basic understanding of a working principle in reservoir computing can be expected to shed light on how information is stored and processed in nonlinear dynamical systems, potentially leading to progress in a broad range of nonlinear sciences. As a first step toward this goal, from the viewpoint of nonlinear physics and information theory, we study the memory-nonlinearity trade-off uncovered by Dambre et al. (2012). Focusing on a variational equation, we clarify a dynamical mechanism behind the trade-off, which illustrates why nonlinear dynamics degrades memory stored in dynamical system in general. Moreover, based on the trade-off, we propose a mixture reservoir endowed with both linear and nonlinear dynamics and show that it improves the performance of information processing. Interestingly, for some tasks, significant improvements are observed by adding a few linear dynamics to the nonlinear dynamical system. By employing the echo state network model, the effect of the mixture reservoir is numerically verified for a simple function approximation task and for more complex tasks.

Nonlinear Site Response Validation Studies Using KIK-net Strong Motion Data

NASA Astrophysics Data System (ADS)

Asimaki, D.; Shi, J.

2014-12-01

Earthquake simulations are nowadays producing realistic ground motion time-series in the range of engineering design applications. Of particular significance to engineers are simulations of near-field motions and large magnitude events, for which observations are scarce. With the engineering community slowly adopting the use of simulated ground motions, site response models need to be re-evaluated in terms of their capabilities and limitations to 'translate' the simulated time-series from rock surface output to structural analyses input. In this talk, we evaluate three one-dimensional site response models: linear viscoelastic, equivalent linear and nonlinear. We evaluate the performance of the models by comparing predictions to observations at 30 downhole stations of the Japanese network KIK-Net that have recorded several strong events, including the 2011 Tohoku earthquake. Velocity profiles are used as the only input to all models, while additional parameters such as quality factor, density and nonlinear dynamic soil properties are estimated from empirical correlations. We quantify the differences of ground surface predictions and observations in terms of both seismological and engineering intensity measures, including bias ratios of peak ground response and visual comparisons of elastic spectra, and inelastic to elastic deformation ratio for multiple ductility ratios. We observe that PGV/Vs,30 — as measure of strain— is a better predictor of site nonlinearity than PGA, and that incremental nonlinear analyses are necessary to produce reliable estimates of high-frequency ground motion components at soft sites. We finally discuss the implications of our findings on the parameterization of nonlinear amplification factors in GMPEs, and on the extensive use of equivalent linear analyses in probabilistic seismic hazard procedures.

Lindemann histograms as a new method to analyse nano-patterns and phases

NASA Astrophysics Data System (ADS)

Makey, Ghaith; Ilday, Serim; Tokel, Onur; Ibrahim, Muhamet; Yavuz, Ozgun; Pavlov, Ihor; Gulseren, Oguz; Ilday, Omer

The detection, observation, and analysis of material phases and atomistic patterns are of great importance for understanding systems exhibiting both equilibrium and far-from-equilibrium dynamics. As such, there is intense research on phase transitions and pattern dynamics in soft matter, statistical and nonlinear physics, and polymer physics. In order to identify phases and nano-patterns, the pair correlation function is commonly used. However, this approach is limited in terms of recognizing competing patterns in dynamic systems, and lacks visualisation capabilities. In order to solve these limitations, we introduce Lindemann histogram quantification as an alternative method to analyse solid, liquid, and gas phases, along with hexagonal, square, and amorphous nano-pattern symmetries. We show that the proposed approach based on Lindemann parameter calculated per particle maps local number densities to material phase or particles pattern. We apply the Lindemann histogram method on dynamical colloidal self-assembly experimental data and identify competing patterns.

On the seismic behavior of the main tower of the San Felice sul Panaro (Italy) fortress

NASA Astrophysics Data System (ADS)

Castellazzi, Giovanni; D'Altri, Antonio Maria; de Miranda, Stefano; Magagnini, Stefano; Tralli, Antonio

2016-12-01

The medieval fortresses are a very common and distinctive type among the Emilian historical constructions and the earthquakes of May 20th and 29th, 2012 underlined their high vulnerability. Among those heavily damaged, there is the fortress of San Felice sul Panaro located between the two epicenters. This study presents some FE results regarding the behavior under seismic actions of the main tower (Mastio tower). The Mastio has peculiar geometric features and represents a typical example of non-isolated tower. In fact, it is constrained in very different ways by the surrounding parts of the fortress along two of its sides: on the north side it is constrained by the perimeter wall until one third of his high, while a stiffer building constrains it on the west side. In order to remodel the entire fortress, a multidisciplinary project involving the Municipality of San Felice sul Panaro and four Universities of the Emilia- Romagna (Bologna, Ferrara, Parma and Modena) together with the University of Genoa is going on. The study, oriented to the structural restoration, produced an accurate survey of the entire building including a fine definition of architectural peculiarities, historical stages and materials evolution. Based on such geometrical data, we developed a detailed 3D realistic mesh, with a point-by-point characterization of each single geometric element. We performed both pushover and nonlinear dynamic analyses using accelerograms data measured near the fortress on May 29th. A damage-plasticity material model exhibiting softening in both tension and compression, already available in the commercial code Abaqus, has been used for masonry in nonlinear dynamic analyses. On the other hand, pushover analyses have been performed utilizing similar constitutive equations available on code DIANA. The effects of higher modes of vibration have been taken into account by means of the modal pushover analysis technique. For the sake of conciseness, only some preliminary findings are presented in this paper. The results obtained with pushover analyses fit reasonably well with nonlinear dynamic simulations.

Stochasticity Favoring the Effects of the R&D Strategies of the Firms

NASA Astrophysics Data System (ADS)

Pinto, Alberto A.; Oliveira, Bruno M. P. M.; Ferreira, Fernanda A.; Ferreira, Flávio

We present stochastic dynamics on the production costs of Cournot competitions, based on perfect Nash equilibria of nonlinear R&D investment strategies to reduce the production costs of the firms at every period of the game. We analyse the effects that the R&D investment strategies can have in the profits of the firms along the time. We observe that, in certain cases, the uncertainty can improve the effects of the R&D strategies in the profits of the firms due to the non-linearity of the profit functions and also of the R&D parameters.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Coleman, Justin; Slaughter, Andrew; Veeraraghavan, Swetha

Multi-hazard Analysis for STOchastic time-DOmaiN phenomena (MASTODON) is a finite element application that aims at analyzing the response of 3-D soil-structure systems to natural and man-made hazards such as earthquakes, floods and fire. MASTODON currently focuses on the simulation of seismic events and has the capability to perform extensive ‘source-to-site’ simulations including earthquake fault rupture, nonlinear wave propagation and nonlinear soil-structure interaction (NLSSI) analysis. MASTODON is being developed to be a dynamic probabilistic risk assessment framework that enables analysts to not only perform deterministic analyses, but also easily perform probabilistic or stochastic simulations for the purpose of risk assessment.

The use of normal forms for analysing nonlinear mechanical vibrations

PubMed Central

Neild, Simon A.; Champneys, Alan R.; Wagg, David J.; Hill, Thomas L.; Cammarano, Andrea

2015-01-01

A historical introduction is given of the theory of normal forms for simplifying nonlinear dynamical systems close to resonances or bifurcation points. The specific focus is on mechanical vibration problems, described by finite degree-of-freedom second-order-in-time differential equations. A recent variant of the normal form method, that respects the specific structure of such models, is recalled. It is shown how this method can be placed within the context of the general theory of normal forms provided the damping and forcing terms are treated as unfolding parameters. The approach is contrasted to the alternative theory of nonlinear normal modes (NNMs) which is argued to be problematic in the presence of damping. The efficacy of the normal form method is illustrated on a model of the vibration of a taut cable, which is geometrically nonlinear. It is shown how the method is able to accurately predict NNM shapes and their bifurcations. PMID:26303917

The cortical focus in childhood absence epilepsy; evidence from nonlinear analysis of scalp EEG recordings.

PubMed

Sarrigiannis, Ptolemaios G; Zhao, Yifan; He, Fei; Billings, Stephen A; Baster, Kathleen; Rittey, Chris; Yianni, John; Zis, Panagiotis; Wei, Hualiang; Hadjivassiliou, Marios; Grünewald, Richard

2018-03-01

To determine the origin and dynamic characteristics of the generalised hyper-synchronous spike and wave (SW) discharges in childhood absence epilepsy (CAE). We applied nonlinear methods, the error reduction ratio (ERR) causality test and cross-frequency analysis, with a nonlinear autoregressive exogenous (NARX) model, to electroencephalograms (EEGs) from CAE, selected with stringent electro-clinical criteria (17 cases, 42 absences). We analysed the pre-ictal and ictal strength of association between homologous and heterologous EEG derivations and estimated the direction of synchronisation and corresponding time lags. A frontal/fronto-central onset of the absences is detected in 13 of the 17 cases with the highest ictal strength of association between homologous frontal followed by centro-temporal and fronto-central areas. Delays consistently in excess of 4 ms occur at the very onset between these regions, swiftly followed by the emergence of "isochronous" (0-2 ms) synchronisation but dynamic time lag changes occur during SW discharges. In absences an initial cortico-cortical spread leads to dynamic lag changes to include periods of isochronous interhemispheric synchronisation, which we hypothesize is mediated by the thalamus. Absences from CAE show ictal epileptic network dynamics remarkably similar to those observed in WAG/Rij rats which guided the formulation of the cortical focus theory. Copyright © 2017 International Federation of Clinical Neurophysiology. Published by Elsevier B.V. All rights reserved.

Model-free inference of direct network interactions from nonlinear collective dynamics.

PubMed

Casadiego, Jose; Nitzan, Mor; Hallerberg, Sarah; Timme, Marc

2017-12-19

The topology of interactions in network dynamical systems fundamentally underlies their function. Accelerating technological progress creates massively available data about collective nonlinear dynamics in physical, biological, and technological systems. Detecting direct interaction patterns from those dynamics still constitutes a major open problem. In particular, current nonlinear dynamics approaches mostly require to know a priori a model of the (often high dimensional) system dynamics. Here we develop a model-independent framework for inferring direct interactions solely from recording the nonlinear collective dynamics generated. Introducing an explicit dependency matrix in combination with a block-orthogonal regression algorithm, the approach works reliably across many dynamical regimes, including transient dynamics toward steady states, periodic and non-periodic dynamics, and chaos. Together with its capabilities to reveal network (two point) as well as hypernetwork (e.g., three point) interactions, this framework may thus open up nonlinear dynamics options of inferring direct interaction patterns across systems where no model is known.

Nonlinear Theory of The Geostrophic Adjustment

NASA Astrophysics Data System (ADS)

Zeitlin, V.

Nonlinear geostrophic adjustment and splitting of the fast and slow dynamical vari- ables are analysed in the framework of multi-layer and continuously stratified prim- itive equations by means of the multi-scale perturbation theory in the Rossby num- ber applied to localized initial disturbances. Two basic dynamical regimes: the quasi- geostrophic (QG) and the frontal geostrophic (FG) with small and large deviations of the isopycnal surfaces, respectively, are considered and differences in corresponding adjustment scenarios are displayed. Decoupling of the fast component of the flow is proven up to the third order in Rossby number and long-time corrections to the stan- dard balanced QG and FG models are found. Peculiarities of splitting in the FG regime due to the quasi-inertial oscillations are displayed and a Schrodinger-like modulation equations for the envelope of these latter are derived.

Connected cruise control: modelling, delay effects, and nonlinear behaviour

NASA Astrophysics Data System (ADS)

Orosz, Gábor

2016-08-01

Connected vehicle systems (CVS) are considered in this paper where vehicles exchange information using wireless vehicle-to-vehicle (V2V) communication. The concept of connected cruise control (CCC) is established that allows control design at the level of individual vehicles while exploiting V2V connectivity. Due to its high level of modularity the proposed design can be applied to large heterogeneous traffic systems. The dynamics of a simple CVS is analysed in detail while taking into account nonlinearities in the vehicle dynamics as well as in the controller. Time delays that arise due to intermittencies and packet drops in the communication channels are also incorporated. The results are summarised using stability charts which allow one to select control gains to maintain stability and ensure disturbance attenuation when the delay is below a critical value.

Structure and Dynamics of Replication-Mutation Systems

NASA Astrophysics Data System (ADS)

Schuster, Peter

1987-03-01

The kinetic equations of polynucleotide replication can be brought into fairly simple form provided certain environmental conditions are fulfilled. Two flow reactors, the continuously stirred tank reactor (CSTR) and a special dialysis reactor are particularly suitable for the analysis of replication kinetics. An experimental setup to study the chemical reaction network of RNA synthesis was derived from the bacteriophage Qβ. It consists of a virus specific RNA polymerase, Qβ replicase, the activated ribonucleosides GTP, ATP, CTP and UTP as well as a template suitable for replication. The ordinary differential equations for replication and mutation under the conditions of the flow reactors were analysed by the qualitative methods of bifurcation theory as well as by numerical integration. The various kinetic equations are classified according to their dynamical properties: we distinguish "quasilinear systems" which have uniquely stable point attractors and "nonlinear systems" with inherent nonlinearities which lead to multiple steady states, Hopf bifuractions, Feigenbaum-like sequences and chaotic dynamics for certain parameter ranges. Some examples which are relevant in molecular evolution and population genetics are discussed in detail.

General high-order breathers and rogue waves in the (3 + 1) -dimensional KP-Boussinesq equation

NASA Astrophysics Data System (ADS)

Sun, Baonan; Wazwaz, Abdul-Majid

2018-11-01

In this work, we investigate the (3 + 1) -dimensional KP-Boussinesq equation, which can be used to describe the nonlinear dynamic behavior in scientific and engineering applications. We derive general high-order soliton solutions by using the Hirota's bilinear method combined with the perturbation expansion technique. We also obtain periodic solutions comprising of high-order breathers, periodic line waves, and mixed solutions consisting of breathers and periodic line waves upon selecting particular parameter constraints of the obtained soliton solutions. Furthermore, smooth rational solutions are generated by taking a long wave limit of the soliton solutions. These smooth rational solutions include high-order rogue waves, high-order lumps, and hybrid solutions consisting of lumps and line rogue waves. To better understand the dynamical behaviors of these solutions, we discuss some illustrative graphical analyses. It is expected that our results can enrich the dynamical behavior of the (3 + 1) -dimensional nonlinear evolution equations of other forms.

Design considerations for a Space Shuttle Main Engine turbine blade made of single crystal material

NASA Technical Reports Server (NTRS)

Abdul-Aziz, A.; August, R.; Nagpal, V.

1993-01-01

Nonlinear finite-element structural analyses were performed on the first stage high-pressure fuel turbopump blade of the Space Shuttle Main Engine. The analyses examined the structural response and the dynamic characteristics at typical operating conditions. Single crystal material PWA-1480 was considered for the analyses. Structural response and the blade natural frequencies with respect to the crystal orientation were investigated. The analyses were conducted based on typical test stand engine cycle. Influence of combined thermal, aerodynamic, and centrifugal loadings was considered. Results obtained showed that the single crystal secondary orientation effects on the maximum principal stresses are not highly significant.

Mid-frequency Band Dynamics of Large Space Structures

NASA Technical Reports Server (NTRS)

Coppolino, Robert N.; Adams, Douglas S.

2004-01-01

High and low intensity dynamic environments experienced by a spacecraft during launch and on-orbit operations, respectively, induce structural loads and motions, which are difficult to reliably predict. Structural dynamics in low- and mid-frequency bands are sensitive to component interface uncertainty and non-linearity as evidenced in laboratory testing and flight operations. Analytical tools for prediction of linear system response are not necessarily adequate for reliable prediction of mid-frequency band dynamics and analysis of measured laboratory and flight data. A new MATLAB toolbox, designed to address the key challenges of mid-frequency band dynamics, is introduced in this paper. Finite-element models of major subassemblies are defined following rational frequency-wavelength guidelines. For computational efficiency, these subassemblies are described as linear, component mode models. The complete structural system model is composed of component mode subassemblies and linear or non-linear joint descriptions. Computation and display of structural dynamic responses are accomplished employing well-established, stable numerical methods, modern signal processing procedures and descriptive graphical tools. Parametric sensitivity and Monte-Carlo based system identification tools are used to reconcile models with experimental data and investigate the effects of uncertainties. Models and dynamic responses are exported for employment in applications, such as detailed structural integrity and mechanical-optical-control performance analyses.

Spin-current emission governed by nonlinear spin dynamics.

PubMed

Tashiro, Takaharu; Matsuura, Saki; Nomura, Akiyo; Watanabe, Shun; Kang, Keehoon; Sirringhaus, Henning; Ando, Kazuya

2015-10-16

Coupling between conduction electrons and localized magnetization is responsible for a variety of phenomena in spintronic devices. This coupling enables to generate spin currents from dynamical magnetization. Due to the nonlinearity of magnetization dynamics, the spin-current emission through the dynamical spin-exchange coupling offers a route for nonlinear generation of spin currents. Here, we demonstrate spin-current emission governed by nonlinear magnetization dynamics in a metal/magnetic insulator bilayer. The spin-current emission from the magnetic insulator is probed by the inverse spin Hall effect, which demonstrates nontrivial temperature and excitation power dependences of the voltage generation. The experimental results reveal that nonlinear magnetization dynamics and enhanced spin-current emission due to magnon scatterings are triggered by decreasing temperature. This result illustrates the crucial role of the nonlinear magnon interactions in the spin-current emission driven by dynamical magnetization, or nonequilibrium magnons, from magnetic insulators.

Spin-current emission governed by nonlinear spin dynamics

PubMed Central

Tashiro, Takaharu; Matsuura, Saki; Nomura, Akiyo; Watanabe, Shun; Kang, Keehoon; Sirringhaus, Henning; Ando, Kazuya

2015-01-01

Coupling between conduction electrons and localized magnetization is responsible for a variety of phenomena in spintronic devices. This coupling enables to generate spin currents from dynamical magnetization. Due to the nonlinearity of magnetization dynamics, the spin-current emission through the dynamical spin-exchange coupling offers a route for nonlinear generation of spin currents. Here, we demonstrate spin-current emission governed by nonlinear magnetization dynamics in a metal/magnetic insulator bilayer. The spin-current emission from the magnetic insulator is probed by the inverse spin Hall effect, which demonstrates nontrivial temperature and excitation power dependences of the voltage generation. The experimental results reveal that nonlinear magnetization dynamics and enhanced spin-current emission due to magnon scatterings are triggered by decreasing temperature. This result illustrates the crucial role of the nonlinear magnon interactions in the spin-current emission driven by dynamical magnetization, or nonequilibrium magnons, from magnetic insulators. PMID:26472712

Nonlinearities of heart rate variability in animal models of impaired cardiac control: contribution of different time scales.

PubMed

Silva, Luiz Eduardo Virgilio; Lataro, Renata Maria; Castania, Jaci Airton; Silva, Carlos Alberto Aguiar; Salgado, Helio Cesar; Fazan, Rubens; Porta, Alberto

2017-08-01

Heart rate variability (HRV) has been extensively explored by traditional linear approaches (e.g., spectral analysis); however, several studies have pointed to the presence of nonlinear features in HRV, suggesting that linear tools might fail to account for the complexity of the HRV dynamics. Even though the prevalent notion is that HRV is nonlinear, the actual presence of nonlinear features is rarely verified. In this study, the presence of nonlinear dynamics was checked as a function of time scales in three experimental models of rats with different impairment of the cardiac control: namely, rats with heart failure (HF), spontaneously hypertensive rats (SHRs), and sinoaortic denervated (SAD) rats. Multiscale entropy (MSE) and refined MSE (RMSE) were chosen as the discriminating statistic for the surrogate test utilized to detect nonlinearity. Nonlinear dynamics is less present in HF animals at both short and long time scales compared with controls. A similar finding was found in SHR only at short time scales. SAD increased the presence of nonlinear dynamics exclusively at short time scales. Those findings suggest that a working baroreflex contributes to linearize HRV and to reduce the likelihood to observe nonlinear components of the cardiac control at short time scales. In addition, an increased sympathetic modulation seems to be a source of nonlinear dynamics at long time scales. Testing nonlinear dynamics as a function of the time scales can provide a characterization of the cardiac control complementary to more traditional markers in time, frequency, and information domains. NEW & NOTEWORTHY Although heart rate variability (HRV) dynamics is widely assumed to be nonlinear, nonlinearity tests are rarely used to check this hypothesis. By adopting multiscale entropy (MSE) and refined MSE (RMSE) as the discriminating statistic for the nonlinearity test, we show that nonlinear dynamics varies with time scale and the type of cardiac dysfunction. Moreover, as complexity metrics and nonlinearities provide complementary information, we strongly recommend using the test for nonlinearity as an additional index to characterize HRV. Copyright © 2017 the American Physiological Society.

Multibody dynamic analysis using a rotation-free shell element with corotational frame

NASA Astrophysics Data System (ADS)

Shi, Jiabei; Liu, Zhuyong; Hong, Jiazhen

2018-03-01

Rotation-free shell formulation is a simple and effective method to model a shell with large deformation. Moreover, it can be compatible with the existing theories of finite element method. However, a rotation-free shell is seldom employed in multibody systems. Using a derivative of rigid body motion, an efficient nonlinear shell model is proposed based on the rotation-free shell element and corotational frame. The bending and membrane strains of the shell have been simplified by isolating deformational displacements from the detailed description of rigid body motion. The consistent stiffness matrix can be obtained easily in this form of shell model. To model the multibody system consisting of the presented shells, joint kinematic constraints including translational and rotational constraints are deduced in the context of geometric nonlinear rotation-free element. A simple node-to-surface contact discretization and penalty method are adopted for contacts between shells. A series of analyses for multibody system dynamics are presented to validate the proposed formulation. Furthermore, the deployment of a large scaled solar array is presented to verify the comprehensive performance of the nonlinear shell model.

The linear and non-linear characterization of dust ion acoustic mode in complex plasma in presence of dynamical charging of dust

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bhattacharjee, Saurav, E-mail: sauravtsk.bhattacharjee@gmail.com; Das, Nilakshi

2015-10-15

A systematic theoretical investigation has been carried out on the role of dust charging dynamics on the nature and stability of DIA (Dust Ion Acoustic) mode in complex plasma. The study has been made for both linear and non-linear scale regime of DIA mode. The observed results have been characterized in terms of background plasma responses towards dust surface responsible for dust charge fluctuation, invoking important dusty plasma parameters, especially the ion flow speed and dust size. The linear analyses confirm the nature of instability in DIA mode in presence of dust charge fluctuation. The instability shows a damping ofmore » DIA mode in subsonic flow regime followed by a gradual growth in instability in supersonic limit of ion flow. The strength of non-linearity and their existence domain is found to be driven by different dusty plasma parameters. As dust is ubiquitous in interstellar medium with plasma background, the study also addresses the possible effect of dust charging dynamics in gravito-electrostatic characterization and the stability of dust molecular clouds especially in proto-planetary disc. The observations are influential and interesting towards the understanding of dust settling mechanism and formation of dust environments in different regions in space.« less

The Nonlinear Magnetosphere: Expressions in MHD and in Kinetic Models

NASA Technical Reports Server (NTRS)

Hesse, Michael; Birn, Joachim

2011-01-01

Like most plasma systems, the magnetosphere of the Earth is governed by nonlinear dynamic evolution equations. The impact of nonlinearities ranges from large scales, where overall dynamics features are exhibiting nonlinear behavior, to small scale, kinetic, processes, where nonlinear behavior governs, among others, energy conversion and dissipation. In this talk we present a select set of examples of such behavior, with a specific emphasis on how nonlinear effects manifest themselves in MHD and in kinetic models of magnetospheric plasma dynamics.

Nonlinear dynamics and numerical uncertainties in CFD

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sweby, P. K.

1996-01-01

The application of nonlinear dynamics to improve the understanding of numerical uncertainties in computational fluid dynamics (CFD) is reviewed. Elementary examples in the use of dynamics to explain the nonlinear phenomena and spurious behavior that occur in numerics are given. The role of dynamics in the understanding of long time behavior of numerical integrations and the nonlinear stability, convergence, and reliability of using time-marching, approaches for obtaining steady-state numerical solutions in CFD is explained. The study is complemented with spurious behavior observed in CFD computations.

Effectiveness of modified pushover analysis procedure for the estimation of seismic demands of buildings subjected to near-fault ground motions having fling step

NASA Astrophysics Data System (ADS)

Mortezaei, A.; Ronagh, H. R.

2013-06-01

Near-fault ground motions with long-period pulses have been identified as being critical in the design of structures. These motions, which have caused severe damage in recent disastrous earthquakes, are characterized by a short-duration impulsive motion that transmits large amounts of energy into the structures at the beginning of the earthquake. In nearly all of the past near-fault earthquakes, significant higher mode contributions have been evident in building structures near the fault rupture, resulting in the migration of dynamic demands (i.e. drifts) from the lower to the upper stories. Due to this, the static nonlinear pushover analysis (which utilizes a load pattern proportional to the shape of the fundamental mode of vibration) may not produce accurate results when used in the analysis of structures subjected to near-fault ground motions. The objective of this paper is to improve the accuracy of the pushover method in these situations by introducing a new load pattern into the common pushover procedure. Several pushover analyses are performed for six existing reinforced concrete buildings that possess a variety of natural periods. Then, a comparison is made between the pushover analyses' results (with four new load patterns) and those of FEMA (Federal Emergency Management Agency)-356 with reference to nonlinear dynamic time-history analyses. The comparison shows that, generally, the proposed pushover method yields better results than all FEMA-356 pushover analysis procedures for all investigated response quantities and is a closer match to the nonlinear time-history responses. In general, the method is able to reproduce the essential response features providing a reasonable measure of the likely contribution of higher modes in all phases of the response.

Distinguishing Error from Chaos in Ecological Time Series

NASA Astrophysics Data System (ADS)

Sugihara, George; Grenfell, Bryan; May, Robert M.

1990-11-01

Over the years, there has been much discussion about the relative importance of environmental and biological factors in regulating natural populations. Often it is thought that environmental factors are associated with stochastic fluctuations in population density, and biological ones with deterministic regulation. We revisit these ideas in the light of recent work on chaos and nonlinear systems. We show that completely deterministic regulatory factors can lead to apparently random fluctuations in population density, and we then develop a new method (that can be applied to limited data sets) to make practical distinctions between apparently noisy dynamics produced by low-dimensional chaos and population variation that in fact derives from random (high-dimensional)noise, such as environmental stochasticity or sampling error. To show its practical use, the method is first applied to models where the dynamics are known. We then apply the method to several sets of real data, including newly analysed data on the incidence of measles in the United Kingdom. Here the additional problems of secular trends and spatial effects are explored. In particular, we find that on a city-by-city scale measles exhibits low-dimensional chaos (as has previously been found for measles in New York City), whereas on a larger, country-wide scale the dynamics appear as a noisy two-year cycle. In addition to shedding light on the basic dynamics of some nonlinear biological systems, this work dramatizes how the scale on which data is collected and analysed can affect the conclusions drawn.

WARP3D-Release 10.8: Dynamic Nonlinear Analysis of Solids using a Preconditioned Conjugate Gradient Software Architecture

NASA Technical Reports Server (NTRS)

Koppenhoefer, Kyle C.; Gullerud, Arne S.; Ruggieri, Claudio; Dodds, Robert H., Jr.; Healy, Brian E.

1998-01-01

This report describes theoretical background material and commands necessary to use the WARP3D finite element code. WARP3D is under continuing development as a research code for the solution of very large-scale, 3-D solid models subjected to static and dynamic loads. Specific features in the code oriented toward the investigation of ductile fracture in metals include a robust finite strain formulation, a general J-integral computation facility (with inertia, face loading), an element extinction facility to model crack growth, nonlinear material models including viscoplastic effects, and the Gurson-Tver-gaard dilatant plasticity model for void growth. The nonlinear, dynamic equilibrium equations are solved using an incremental-iterative, implicit formulation with full Newton iterations to eliminate residual nodal forces. The history integration of the nonlinear equations of motion is accomplished with Newmarks Beta method. A central feature of WARP3D involves the use of a linear-preconditioned conjugate gradient (LPCG) solver implemented in an element-by-element format to replace a conventional direct linear equation solver. This software architecture dramatically reduces both the memory requirements and CPU time for very large, nonlinear solid models since formation of the assembled (dynamic) stiffness matrix is avoided. Analyses thus exhibit the numerical stability for large time (load) steps provided by the implicit formulation coupled with the low memory requirements characteristic of an explicit code. In addition to the much lower memory requirements of the LPCG solver, the CPU time required for solution of the linear equations during each Newton iteration is generally one-half or less of the CPU time required for a traditional direct solver. All other computational aspects of the code (element stiffnesses, element strains, stress updating, element internal forces) are implemented in the element-by- element, blocked architecture. This greatly improves vectorization of the code on uni-processor hardware and enables straightforward parallel-vector processing of element blocks on multi-processor hardware.

Mastodon

DOE Office of Scientific and Technical Information (OSTI.GOV)

Coleman, Justin Leigh; Veeraraghavan, Swetha; Bolisetti, Chandrakanth

MASTODON has the capability to model stochastic nonlinear soil-structure interaction (NLSSI) in a dynamic probabilistic risk assessment framework. The NLSSI simulations include structural dynamics, time integration, dynamic porous media flow, nonlinear hysteretic soil constitutive models, geometric nonlinearities (gapping, sliding, and uplift). MASTODON is also the MOOSE based master application for dynamic PRA of external hazards.

Nonlinear dynamics that appears in the dynamical model of drying process of a polymer solution coated on a flat substrate

NASA Astrophysics Data System (ADS)

Kagami, Hiroyuki

2007-01-01

We have proposed and modified the dynamical model of drying process of polymer solution coated on a flat substrate for flat polymer film fabrication and have presented the fruits through some meetings and so on. Though basic equations of the dynamical model have characteristic nonlinearity, character of the nonlinearity has not been studied enough yet. In this paper, at first, we derive nonlinear equations from the dynamical model of drying process of polymer solution. Then we introduce results of numerical simulations of the nonlinear equations and consider roles of various parameters. Some of them are indirectly concerned in strength of non-equilibriumity. Through this study, we approach essential qualities of nonlinearity in non-equilibrium process of drying process.

Memory-induced nonlinear dynamics of excitation in cardiac diseases.

PubMed

Landaw, Julian; Qu, Zhilin

2018-04-01

Excitable cells, such as cardiac myocytes, exhibit short-term memory, i.e., the state of the cell depends on its history of excitation. Memory can originate from slow recovery of membrane ion channels or from accumulation of intracellular ion concentrations, such as calcium ion or sodium ion concentration accumulation. Here we examine the effects of memory on excitation dynamics in cardiac myocytes under two diseased conditions, early repolarization and reduced repolarization reserve, each with memory from two different sources: slow recovery of a potassium ion channel and slow accumulation of the intracellular calcium ion concentration. We first carry out computer simulations of action potential models described by differential equations to demonstrate complex excitation dynamics, such as chaos. We then develop iterated map models that incorporate memory, which accurately capture the complex excitation dynamics and bifurcations of the action potential models. Finally, we carry out theoretical analyses of the iterated map models to reveal the underlying mechanisms of memory-induced nonlinear dynamics. Our study demonstrates that the memory effect can be unmasked or greatly exacerbated under certain diseased conditions, which promotes complex excitation dynamics, such as chaos. The iterated map models reveal that memory converts a monotonic iterated map function into a nonmonotonic one to promote the bifurcations leading to high periodicity and chaos.

Nonlinear dynamics of global atmospheric and Earth-system processes

NASA Technical Reports Server (NTRS)

Saltzman, Barry; Ebisuzaki, Wesley; Maasch, Kirk A.; Oglesby, Robert; Pandolfo, Lionel

1990-01-01

Researchers are continuing their studies of the nonlinear dynamics of global weather systems. Sensitivity analyses of large-scale dynamical models of the atmosphere (i.e., general circulation models i.e., GCM's) were performed to establish the role of satellite-signatures of soil moisture, sea surface temperature, snow cover, and sea ice as crucial boundary conditions determining global weather variability. To complete their study of the bimodality of the planetary wave states, they are using the dynamical systems approach to construct a low-order theoretical explanation of this phenomenon. This work should have important implications for extended range forecasting of low-frequency oscillations, elucidating the mechanisms for the transitions between the two wave modes. Researchers are using the methods of jump analysis and attractor dimension analysis to examine the long-term satellite records of significant variables (e.g., long wave radiation, and cloud amount), to explore the nature of mode transitions in the atmosphere, and to determine the minimum number of equations needed to describe the main weather variations with a low-order dynamical system. Where feasible they will continue to explore the applicability of the methods of complex dynamical systems analysis to the study of the global earth-system from an integrative viewpoint involving the roles of geochemical cycling and the interactive behavior of the atmosphere, hydrosphere, and biosphere.

Memory-induced nonlinear dynamics of excitation in cardiac diseases

NASA Astrophysics Data System (ADS)

Landaw, Julian; Qu, Zhilin

2018-04-01

Excitable cells, such as cardiac myocytes, exhibit short-term memory, i.e., the state of the cell depends on its history of excitation. Memory can originate from slow recovery of membrane ion channels or from accumulation of intracellular ion concentrations, such as calcium ion or sodium ion concentration accumulation. Here we examine the effects of memory on excitation dynamics in cardiac myocytes under two diseased conditions, early repolarization and reduced repolarization reserve, each with memory from two different sources: slow recovery of a potassium ion channel and slow accumulation of the intracellular calcium ion concentration. We first carry out computer simulations of action potential models described by differential equations to demonstrate complex excitation dynamics, such as chaos. We then develop iterated map models that incorporate memory, which accurately capture the complex excitation dynamics and bifurcations of the action potential models. Finally, we carry out theoretical analyses of the iterated map models to reveal the underlying mechanisms of memory-induced nonlinear dynamics. Our study demonstrates that the memory effect can be unmasked or greatly exacerbated under certain diseased conditions, which promotes complex excitation dynamics, such as chaos. The iterated map models reveal that memory converts a monotonic iterated map function into a nonmonotonic one to promote the bifurcations leading to high periodicity and chaos.

Some Aspects of Nonlinear Dynamics and CFD

NASA Technical Reports Server (NTRS)

Yee, Helen C.; Merriam, Marshal (Technical Monitor)

1996-01-01

The application of nonlinear dynamics to improve the understanding of numerical uncertainties in computational fluid dynamics (CFD) is reviewed. Elementary examples in the use of dynamics to explain the nonlinear phenomena and spurious behavior that occur in numerics are given. The role of dynamics in the understanding of long time behavior of numerical integrations and the nonlinear stability, convergence, and reliability of using time-marching approaches for obtaining steady-state numerical solutions in CFD is explained. The study is complemented with examples of spurious behavior observed in CFD computations.

Implementation of an integrated op-amp based chaotic neuron model and observation of its chaotic dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jung, Jinwoo; Lee, Jewon; Song, Hanjung

2011-03-15

This paper presents a fully integrated circuit implementation of an operational amplifier (op-amp) based chaotic neuron model with a bipolar output function, experimental measurements, and analyses of its chaotic behavior. The proposed chaotic neuron model integrated circuit consists of several op-amps, sample and hold circuits, a nonlinear function block for chaotic signal generation, a clock generator, a nonlinear output function, etc. Based on the HSPICE (circuit program) simulation results, approximated empirical equations for analyses were formulated. Then, the chaotic dynamical responses such as bifurcation diagrams, time series, and Lyapunov exponent were calculated using these empirical equations. In addition, we performedmore » simulations about two chaotic neuron systems with four synapses to confirm neural network connections and got normal behavior of the chaotic neuron such as internal state bifurcation diagram according to the synaptic weight variation. The proposed circuit was fabricated using a 0.8-{mu}m single poly complementary metal-oxide semiconductor technology. Measurements of the fabricated single chaotic neuron with {+-}2.5 V power supplies and a 10 kHz sampling clock frequency were carried out and compared with the simulated results.« less

Optimal non-linear health insurance.

PubMed

Blomqvist, A

1997-06-01

Most theoretical and empirical work on efficient health insurance has been based on models with linear insurance schedules (a constant co-insurance parameter). In this paper, dynamic optimization techniques are used to analyse the properties of optimal non-linear insurance schedules in a model similar to one originally considered by Spence and Zeckhauser (American Economic Review, 1971, 61, 380-387) and reminiscent of those that have been used in the literature on optimal income taxation. The results of a preliminary numerical example suggest that the welfare losses from the implicit subsidy to employer-financed health insurance under US tax law may be a good deal smaller than previously estimated using linear models.

A phenomenological approach to modeling chemical dynamics in nonlinear and two-dimensional spectroscopy.

PubMed

Ramasesha, Krupa; De Marco, Luigi; Horning, Andrew D; Mandal, Aritra; Tokmakoff, Andrei

2012-04-07

We present an approach for calculating nonlinear spectroscopic observables, which overcomes the approximations inherent to current phenomenological models without requiring the computational cost of performing molecular dynamics simulations. The trajectory mapping method uses the semi-classical approximation to linear and nonlinear response functions, and calculates spectra from trajectories of the system's transition frequencies and transition dipole moments. It rests on identifying dynamical variables important to the problem, treating the dynamics of these variables stochastically, and then generating correlated trajectories of spectroscopic quantities by mapping from the dynamical variables. This approach allows one to describe non-Gaussian dynamics, correlated dynamics between variables of the system, and nonlinear relationships between spectroscopic variables of the system and the bath such as non-Condon effects. We illustrate the approach by applying it to three examples that are often not adequately treated by existing analytical models--the non-Condon effect in the nonlinear infrared spectra of water, non-Gaussian dynamics inherent to strongly hydrogen bonded systems, and chemical exchange processes in barrier crossing reactions. The methods described are generally applicable to nonlinear spectroscopy throughout the optical, infrared and terahertz regions.

Effects of Inertial and Geometric Nonlinearities in the Simulation of Flexible Aircraft Dynamics

NASA Astrophysics Data System (ADS)

Bun Tse, Bosco Chun

This thesis examines the relative importance of the inertial and geometric nonlinearities in modelling the dynamics of a flexible aircraft. Inertial nonlinearities are derived by employing an exact definition of the velocity distribution and lead to coupling between the rigid body and elastic motions. The geometric nonlinearities are obtained by applying nonlinear theory of elasticity to the deformations. Peters' finite state unsteady aerodynamic model is used to evaluate the aerodynamic forces. Three approximate models obtained by excluding certain combinations of nonlinear terms are compared with that of the complete dynamics equations to obtain an indication of which terms are required for an accurate representation of the flexible aircraft behavior. A generic business jet model is used for the analysis. The results indicate that the nonlinear terms have a significant effect for more flexible aircraft, especially the geometric nonlinearities which leads to increased damping in the dynamics.

Virtual-pulse time integral methodology: A new explicit approach for computational dynamics - Theoretical developments for general nonlinear structural dynamics

NASA Technical Reports Server (NTRS)

Chen, Xiaoqin; Tamma, Kumar K.; Sha, Desong

1993-01-01

The present paper describes a new explicit virtual-pulse time integral methodology for nonlinear structural dynamics problems. The purpose of the paper is to provide the theoretical basis of the methodology and to demonstrate applicability of the proposed formulations to nonlinear dynamic structures. Different from the existing numerical methods such as direct time integrations or mode superposition techniques, the proposed methodology offers new perspectives and methodology of development, and possesses several unique and attractive computational characteristics. The methodology is tested and compared with the implicit Newmark method (trapezoidal rule) through a nonlinear softening and hardening spring dynamic models. The numerical results indicate that the proposed explicit virtual-pulse time integral methodology is an excellent alternative for solving general nonlinear dynamic problems.

Nonaxisymmetric Dynamic Instabilities of Rotating Polytropes. II. Torques, Bars, and Mode Saturation with Applications to Protostars and Fizzlers

NASA Astrophysics Data System (ADS)

Imamura, James N.; Durisen, Richard H.; Pickett, Brian K.

2000-01-01

Dynamic nonaxisymmetric instabilities in rapidly rotating stars and protostars have a range of potential applications in astrophysics, including implications for binary formation during protostellar cloud collapse and for the possibility of aborted collapse to neutron star densities at late stages of stellar evolution (``fizzlers''). We have recently presented detailed linear analyses for polytropes of the most dynamically unstable global modes, the barlike modes. These produce bar distortions in the regions near the rotation axis but have trailing spiral arms toward the equator. In this paper, we use our linear eigenfunctions to predict the early nonlinear behavior of the dynamic instability and compare these ``quasi-linear'' predictions with several fully nonlinear hydrodynamics simulations. The comparisons demonstrate that the nonlinear saturation of the barlike instability is due to the self-interaction gravitational torques between the growing central bar and the spiral arms, where angular momentum is transferred outward from bar to arms. We also find a previously unsuspected resonance condition that accurately predicts the mass of the bar regions in our own simulations and in those published by other researchers. The quasi-linear theory makes other accurate predictions about consequences of instability, including properties of possible end-state bars and increases in central density, which can be large under some conditions. We discuss in some detail the application of our results to binary formation during protostellar collapse and to the formation of massive rotating black holes.

Linear and nonlinear dynamic analysis by boundary element method. Ph.D. Thesis, 1986 Final Report

NASA Technical Reports Server (NTRS)

Ahmad, Shahid

1991-01-01

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.

Overview of Sensitivity Analysis and Shape Optimization for Complex Aerodynamic Configurations

NASA Technical Reports Server (NTRS)

Newman, Perry A.; Newman, James C., III; Barnwell, Richard W.; Taylor, Arthur C., III; Hou, Gene J.-W.

1998-01-01

This paper presents a brief overview of some of the more recent advances in steady aerodynamic shape-design sensitivity analysis and optimization, based on advanced computational fluid dynamics. The focus here is on those methods particularly well- suited to the study of geometrically complex configurations and their potentially complex associated flow physics. When nonlinear state equations are considered in the optimization process, difficulties are found in the application of sensitivity analysis. Some techniques for circumventing such difficulties are currently being explored and are included here. Attention is directed to methods that utilize automatic differentiation to obtain aerodynamic sensitivity derivatives for both complex configurations and complex flow physics. Various examples of shape-design sensitivity analysis for unstructured-grid computational fluid dynamics algorithms are demonstrated for different formulations of the sensitivity equations. Finally, the use of advanced, unstructured-grid computational fluid dynamics in multidisciplinary analyses and multidisciplinary sensitivity analyses within future optimization processes is recommended and encouraged.

Sierra/Solid Mechanics 4.48 User's Guide.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Merewether, Mark Thomas; Crane, Nathan K; de Frias, Gabriel Jose

Sierra/SolidMechanics (Sierra/SM) is a Lagrangian, three-dimensional code for finite element analysis of solids and structures. It provides capabilities for explicit dynamic, implicit quasistatic and dynamic analyses. The explicit dynamics capabilities allow for the efficient and robust solution of models with extensive contact subjected to large, suddenly applied loads. For implicit problems, Sierra/SM uses a multi-level iterative solver, which enables it to effectively solve problems with large deformations, nonlinear material behavior, and contact. Sierra/SM has a versatile library of continuum and structural elements, and a large library of material models. The code is written for parallel computing environments enabling scalable solutionsmore » of extremely large problems for both implicit and explicit analyses. It is built on the SIERRA Framework, which facilitates coupling with other SIERRA mechanics codes. This document describes the functionality and input syntax for Sierra/SM.« less

Nonlinear distortion of thin liquid sheets

NASA Astrophysics Data System (ADS)

Mehring, Carsten Ralf

Thin planar, annular and conical liquid sheets or films are analyzed, in a unified manner, by means of a reduced- dimension approach providing governing equations for the nonlinear motion of planar and swirling annular thin inviscid and incompressible liquid sheets in zero gravity and with axial disturbances only. Temporal analyses of periodically disturbed infinite sheets are considered, as well as spatial analyses of semi-infinite sheets modulated at the nozzle exit. Results on planar and swirling annular or conical sheets are presented for a zero density ambient gas. Here, conical sheets are obtained in the nearfield of the nozzle exit by considering sheets or films with swirl in excess of that needed to stabilize the discharging stream in its annular configuration. For nonswirling annular sheets a spatially and/or temporally constant gas-core pressure is assumed. A model extension considering the influence of aerodynamic effects on planar sheets is proposed. For planar and annular sheets, linear analyses of the pure initial- and pure boundary-value problem provide insight into the propagation characteristics of dilational and sinuous waves, the (linear) coupling between both wave modes, the stability limits for the annular configuration, as well as the appearance of particular waves on semi-infinite modulated sheets downstream from the nozzle exit. Nonlinear steady-state solutions for the conical configuration (without modulation) are illustrated. Comparison between nonlinear and linear numerical and linear analytical solutions for temporally or spatially developing sheets provides detailed information on the nonlinear distortion characteristics including nonlinear wave propagation and mode-coupling for all the considered geometric configurations and for a variety of parameter configurations. Sensitivity studies on the influence of Weber number, modulation frequency, annular radius, forcing amplitude and sheet divergence on breakup or collapse length and times are reported for modulated semi-infinite annular and conical sheets. Comparisons between the different geometric configurations are made. For periodically disturbed planar sheets, accuracy of the employed reduced-dimension approach is demonstrated by comparison with more accurate two-dimensional vortex dynamics simulations.

The influence of track modelling options on the simulation of rail vehicle dynamics

NASA Astrophysics Data System (ADS)

Di Gialleonardo, Egidio; Braghin, Francesco; Bruni, Stefano

2012-09-01

This paper investigates the effect of different models for track flexibility on the simulation of railway vehicle running dynamics on tangent and curved track. To this end, a multi-body model of the rail vehicle is defined including track flexibility effects on three levels of detail: a perfectly rigid pair of rails, a sectional track model and a three-dimensional finite element track model. The influence of the track model on the calculation of the nonlinear critical speed is pointed out and it is shown that neglecting the effect of track flexibility results in an overestimation of the critical speed by more than 10%. Vehicle response to stochastic excitation from track irregularity is also investigated, analysing the effect of track flexibility models on the vertical and lateral wheel-rail contact forces. Finally, the effect of the track model on the calculation of dynamic forces produced by wheel out-of-roundness is analysed, showing that peak dynamic loads are very sensitive to the track model used in the simulation.

Aeroelastic characteristics of composite bearingless rotor blades

NASA Technical Reports Server (NTRS)

Bielawa, R. L.

1976-01-01

Owing to the inherent unique structural features of composite bearingless rotors, various assumptions upon which conventional rotor aeroelastic analyses are formulated, are violated. Three such features identified are highly nonlinear and time-varying structural twist, structural redundancy in bending and torsion, and for certain configurations a strongly coupled low frequency bending-torsion mode. An examination of these aeroelastic considerations and appropriate formulations required for accurate analyses of such rotor systems is presented. Also presented are test results from a dynamically scaled model rotor and complementary analytic results obtained with the appropriately reformulated aeroelastic analysis.

Dynamic interaction of monowheel inclined vehicle-vibration platform coupled system with quadratic and cubic nonlinearities

NASA Astrophysics Data System (ADS)

Zhou, Shihua; Song, Guiqiu; Sun, Maojun; Ren, Zhaohui; Wen, Bangchun

2018-01-01

In order to analyze the nonlinear dynamics and stability of a novel design for the monowheel inclined vehicle-vibration platform coupled system (MIV-VPCS) with intermediate nonlinearity support subjected to a harmonic excitation, a multi-degree of freedom lumped parameter dynamic model taking into account the dynamic interaction of the MIV-VPCS with quadratic and cubic nonlinearities is presented. The dynamical equations of the coupled system are derived by applying the displacement relationship, interaction force relationship at the contact position and Lagrange's equation, which are further discretized into a set of nonlinear ordinary differential equations with coupled terms by Galerkin's truncation. Based on the mathematical model, the coupled multi-body nonlinear dynamics of the vibration system is investigated by numerical method, and the parameters influences of excitation amplitude, mass ratio and inclined angle on the dynamic characteristics are precisely analyzed and discussed by bifurcation diagram, Largest Lyapunov exponent and 3-D frequency spectrum. Depending on different ranges of system parameters, the results show that the different motions and jump discontinuity appear, and the coupled system enters into chaotic behavior through different routes (period-doubling bifurcation, inverse period-doubling bifurcation, saddle-node bifurcation and Hopf bifurcation), which are strongly attributed to the dynamic interaction of the MIV-VPCS. The decreasing excitation amplitude and inclined angle could reduce the higher order bifurcations, and effectively control the complicated nonlinear dynamic behaviors under the perturbation of low rotational speed. The first bifurcation and chaotic motion occur at lower value of inclined angle, and the chaotic behavior lasts for larger intervals with higher rotational speed. The investigation results could provide a better understanding of the nonlinear dynamic behaviors for the dynamic interaction of the MIV-VPCS.

Short Time Impulse Response Function (STIRF) for automatic evaluation of the variation of the dynamic parameters of reinforced concrete framed structures during strong earthquakes.

NASA Astrophysics Data System (ADS)

Carlo Ponzo, Felice; Ditommaso, Rocco

2015-04-01

This study presents an innovative strategy for automatic evaluation of the variable fundamental frequency and related damping factor of nonlinear structures during strong motion phases. Most of methods for damage detection are based on the assessment of the variations of the dynamic parameters characterizing the monitored structure. A crucial aspect of these methods is the automatic and accurate estimation of both structural eigen-frequencies and related damping factors also during the nonlinear behaviour. A new method, named STIRF (Short-Time Impulse Response Function - STIRF), based on the nonlinear interferometric analysis combined with the Fourier Transform (FT) here is proposed in order to allow scientists and engineers to characterize frequencies and damping variations of a monitored structure. The STIRF approach helps to overcome some limitation derived from the use of techniques based on simple Fourier Transform. These latter techniques provide good results when the response of the monitored system is stationary, but fails when the system exhibits a non-stationary, time-varying behaviour: even non-stationary input, soil-foundation and/or adjacent structures interaction phenomena can show the inadequacy of classic techniques to analysing the nonlinear and/or non-stationary behaviour of structures. In fact, using this kind of approach it is possible to improve some of the existing methods for the automatic damage detection providing stable results also during the strong motion phase. Results are consistent with those expected if compared with other techniques. The main advantage derived from the use of the proposed approach (STIRF) for Structural Health Monitoring is based on the simplicity of the interpretation of the nonlinear variations of the fundamental frequency and the related equivalent viscous damping factor. The proposed methodology has been tested on both numerical and experimental models also using data retrieved from shaking table tests. Based on the results provided in this study, the methodology seems to be able to evaluate fast variations (over time) of dynamic parameters of a generic reinforced concrete framed structure. Further analyses are necessary to better calibrate the length of the moving time-window (in order to minimize the spurious frequency within each Interferometric Response Function evaluated on both weak and strong motion phases) and to verify the possibility to use the STIRF to analyse the nonlinear behaviour of general systems. Acknowledgements This study was partially funded by the Italian Civil Protection Department within the project DPC-RELUIS 2014 - RS4 ''Seismic observatory of structures and health monitoring''. References R. Ditommaso, F.C. Ponzo (2015). Automatic evaluation of the fundamental frequency variations and related damping factor of reinforced concrete framed structures using the Short Time Impulse Response Function (STIRF). Engineering Structures, 82 (2015), 104-112. http://dx.doi.org/10.1016/j.engstruct.2014.10.023.

Theoretical investigation of the force and dynamically coupled torsional-axial-lateral dynamic response of eared rotors

NASA Technical Reports Server (NTRS)

David, J. W.; Mitchell, L. D.

1982-01-01

Difficulties in solution methodology to be used to deal with the potentially higher nonlinear rotor equations when dynamic coupling is included. A solution methodology is selected to solve the nonlinear differential equations. The selected method was verified to give good results even at large nonlinearity levels. The transfer matrix methodology is extended to the solution of nonlinear problems.

Dynamics of a bistable Miura-origami structure

NASA Astrophysics Data System (ADS)

Fang, Hongbin; Li, Suyi; Ji, Huimin; Wang, K. W.

2017-05-01

Origami-inspired structures and materials have shown extraordinary properties and performances originating from the intricate geometries of folding. However, current state of the art studies have mostly focused on static and quasistatic characteristics. This research performs a comprehensive experimental and analytical study on the dynamics of origami folding through investigating a stacked Miura-Ori (SMO) structure with intrinsic bistability. We fabricate and experimentally investigated a bistable SMO prototype with rigid facets and flexible crease lines. Under harmonic base excitation, the SMO exhibits both intrawell and interwell oscillations. Spectrum analyses reveal that the dominant nonlinearities of SMO are quadratic and cubic, which generate rich dynamics including subharmonic and chaotic oscillations. The identified nonlinearities indicate that a third-order polynomial can be employed to approximate the measured force-displacement relationship. Such an approximation is validated via numerical study by qualitatively reproducing the phenomena observed in the experiments. The dynamic characteristics of the bistable SMO resemble those of a Helmholtz-Duffing oscillator (HDO); this suggests the possibility of applying the established tools and insights of HDO to predict origami dynamics. We also show that the bistability of SMO can be programmed within a large design space via tailoring the crease stiffness and initial stress-free configurations. The results of this research offer a wealth of fundamental insights into the dynamics of origami folding, and provide a solid foundation for developing foldable and deployable structures and materials with embedded dynamic functionalities.

Complex nonlinear dynamics in the limit of weak coupling of a system of microcantilevers connected by a geometrically nonlinear tunable nanomembrane.

PubMed

Jeong, Bongwon; Cho, Hanna; Keum, Hohyun; Kim, Seok; Michael McFarland, D; Bergman, Lawrence A; King, William P; Vakakis, Alexander F

2014-11-21

Intentional utilization of geometric nonlinearity in micro/nanomechanical resonators provides a breakthrough to overcome the narrow bandwidth limitation of linear dynamic systems. In past works, implementation of intentional geometric nonlinearity to an otherwise linear nano/micromechanical resonator has been successfully achieved by local modification of the system through nonlinear attachments of nanoscale size, such as nanotubes and nanowires. However, the conventional fabrication method involving manual integration of nanoscale components produced a low yield rate in these systems. In the present work, we employed a transfer-printing assembly technique to reliably integrate a silicon nanomembrane as a nonlinear coupling component onto a linear dynamic system with two discrete microcantilevers. The dynamics of the developed system was modeled analytically and investigated experimentally as the coupling strength was finely tuned via FIB post-processing. The transition from the linear to the nonlinear dynamic regime with gradual change in the coupling strength was experimentally studied. In addition, we observed for the weakly coupled system that oscillation was asynchronous in the vicinity of the resonance, thus exhibiting a nonlinear complex mode. We conjectured that the emergence of this nonlinear complex mode could be attributed to the nonlinear damping arising from the attached nanomembrane.

COMPARISON OF NONLINEAR DYNAMICS OPTIMIZATION METHODS FOR APS-U

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sun, Y.; Borland, Michael

Many different objectives and genetic algorithms have been proposed for storage ring nonlinear dynamics performance optimization. These optimization objectives include nonlinear chromaticities and driving/detuning terms, on-momentum and off-momentum dynamic acceptance, chromatic detuning, local momentum acceptance, variation of transverse invariant, Touschek lifetime, etc. In this paper, the effectiveness of several different optimization methods and objectives are compared for the nonlinear beam dynamics optimization of the Advanced Photon Source upgrade (APS-U) lattice. The optimized solutions from these different methods are preliminarily compared in terms of the dynamic acceptance, local momentum acceptance, chromatic detuning, and other performance measures.

Neurobiologically Inspired Approaches to Nonlinear Process Control and Modeling

DTIC Science & Technology

1999-12-31

incorporates second messenger reaction kinetics and calcium dynamics to represent the nonlinear dynamics and the crucial role of neuromodulation in local...reflex). The dynamic neuromodulation as a mechanism for the nonlinear attenuation is the novel result of this study. Ear- lier simulations have shown

Sustainability science: accounting for nonlinear dynamics in policy and social-ecological systems

EPA Science Inventory

Resilience is an emergent property of complex systems. Understanding resilience is critical for sustainability science, as linked social-ecological systems and the policy process that governs them are characterized by non-linear dynamics. Non-linear dynamics in these systems mean...

Order reduction, identification and localization studies of dynamical systems

NASA Astrophysics Data System (ADS)

Ma, Xianghong

In this thesis methods are developed for performing order reduction, system identification and induction of nonlinear localization in complex mechanical dynamic systems. General techniques are proposed for constructing low-order models of linear and nonlinear mechanical systems; in addition, novel mechanical designs are considered for inducing nonlinear localization phenomena for the purpose of enhancing their dynamical performance. The thesis is in three major parts. In the first part, the transient dynamics of an impulsively loaded multi-bay truss is numerically computed by employing the Direct Global Matrix (DGM) approach. The approach is applicable to large-scale flexible structures with periodicity. Karhunen-Loeve (K-L) decomposition is used to discretize the dynamics of the truss and to create the low-order models of the truss. The leading order K-L modes are recovered by an experiment, which shows the feasibility of K-L based order reduction technique. In the second part of the thesis, nonlinear localization in dynamical systems is studied through two applications. In the seismic base isolation study, it is shown that the dynamics are sensitive to the presence of nonlinear elements and that passive motion confinement can be induced under proper design. In the coupled rod system, numerical simulation of the transient dynamics shows that a nonlinear backlash spring can induce either nonlinear localization or delocalization in the form of beat phenomena. K-L decomposition and poincare maps are utilized to study the nonlinear effects. The study shows that nonlinear localization can be induced in complex structures through backlash. In the third and final part of the thesis, a new technique based on Green!s function method is proposed to identify the dynamics of practical bolted joints. By modeling the difference between the dynamics of the bolted structure and the corresponding unbolted one, one constructs a nonparametric model for the joint dynamics. Two applications are given with a bolted beam and a truss joint in order to show the applicability of the technique.

Nonlinear dynamic mechanism of vocal tremor from voice analysis and model simulations

NASA Astrophysics Data System (ADS)

Zhang, Yu; Jiang, Jack J.

2008-09-01

Nonlinear dynamic analysis and model simulations are used to study the nonlinear dynamic characteristics of vocal folds with vocal tremor, which can typically be characterized by low-frequency modulation and aperiodicity. Tremor voices from patients with disorders such as paresis, Parkinson's disease, hyperfunction, and adductor spasmodic dysphonia show low-dimensional characteristics, differing from random noise. Correlation dimension analysis statistically distinguishes tremor voices from normal voices. Furthermore, a nonlinear tremor model is proposed to study the vibrations of the vocal folds with vocal tremor. Fractal dimensions and positive Lyapunov exponents demonstrate the evidence of chaos in the tremor model, where amplitude and frequency play important roles in governing vocal fold dynamics. Nonlinear dynamic voice analysis and vocal fold modeling may provide a useful set of tools for understanding the dynamic mechanism of vocal tremor in patients with laryngeal diseases.

Databases for the Global Dynamics of Multiparameter Nonlinear Systems

DTIC Science & Technology

2014-03-05

AFRL-OSR-VA-TR-2014-0078 DATABASES FOR THE GLOBAL DYNAMICS OF MULTIPARAMETER NONLINEAR SYSTEMS Konstantin Mischaikow RUTGERS THE STATE UNIVERSITY OF...University of New Jersey ASB III, Rutgers Plaza New Brunswick, NJ 08807 DATABASES FOR THE GLOBAL DYNAMICS OF MULTIPARAMETER NONLINEAR SYSTEMS ...dynamical systems . We refer to the output as a Database for Global Dynamics since it allows the user to query for information about the existence and

Transient Vibration Prediction for Rotors on Ball Bearings Using Load-dependent Non-linear Bearing Stiffness

NASA Technical Reports Server (NTRS)

Fleming, David P.; Poplawski, J. V.

2002-01-01

Rolling-element bearing forces vary nonlinearly with bearing deflection. Thus an accurate rotordynamic transient analysis requires bearing forces to be determined at each step of the transient solution. Analyses have been carried out to show the effect of accurate bearing transient forces (accounting for non-linear speed and load dependent bearing stiffness) as compared to conventional use of average rolling-element bearing stiffness. Bearing forces were calculated by COBRA-AHS (Computer Optimized Ball and Roller Bearing Analysis - Advanced High Speed) and supplied to the rotordynamics code ARDS (Analysis of Rotor Dynamic Systems) for accurate simulation of rotor transient behavior. COBRA-AHS is a fast-running 5 degree-of-freedom computer code able to calculate high speed rolling-element bearing load-displacement data for radial and angular contact ball bearings and also for cylindrical and tapered roller beatings. Results show that use of nonlinear bearing characteristics is essential for accurate prediction of rotordynamic behavior.

A review on non-linear aeroelasticity of high aspect-ratio wings

NASA Astrophysics Data System (ADS)

Afonso, Frederico; Vale, José; Oliveira, Éder; Lau, Fernando; Suleman, Afzal

2017-02-01

Current economic constraints and environmental regulations call for design of more efficient aircraft configurations. An observed trend in aircraft design to reduce the lift induced drag and improve fuel consumption and emissions is to increase the wing aspect-ratio. However, a slender wing is more flexible and subject to higher deflections under the same operating conditions. This effect may lead to changes in dynamic behaviour and in aeroelastic response, potentially resulting in instabilities. Therefore, it is important to take into account geometric non-linearities in the design of high aspect-ratio wings, as well as having accurate computational codes that couple the aerodynamic and structural models in the presence of non-linearities. Here, a review on the state-of-the-art on non-linear aeroelasticity of high aspect-ratio wings is presented. The methodologies employed to analyse high aspect-ratio wings are presented and their applications discussed. Important observations from the state-of-the-art studies are drawn and the current challenges in the field are identified.

Nonlinear dynamic analysis of traveling wave-type ultrasonic motors.

PubMed

Nakagawa, Yosuke; Saito, Akira; Maeno, Takashi

2008-03-01

In this paper, nonlinear dynamic response of a traveling wave-type ultrasonic motor was investigated. In particular, understanding the transient dynamics of a bar-type ultrasonic motor, such as starting up and stopping, is of primary interest. First, the transient response of the bar-type ultrasonic motor at starting up and stopping was measured using a laser Doppler velocimeter, and its driving characteristics are discussed in detail. The motor is shown to possess amplitude-dependent nonlinearity that greatly influences the transient dynamics of the motor. Second, a dynamical model of the motor was constructed as a second-order nonlinear oscillator, which represents the dynamics of the piezoelectric ceramic, stator, and rotor. The model features nonlinearities caused by the frictional interface between the stator and the rotor, and cubic nonlinearity in the dynamics of the stator. Coulomb's friction model was employed for the interface model, and a stick-slip phenomenon is considered. Lastly, it was shown that the model is capable of representing the transient dynamics of the motor accurately. The critical parameters in the model were identified from measured results, and numerical simulations were conducted using the model with the identified parameters. Good agreement between the results of measurements and numerical simulations is observed.

Nonlinear quasi-static finite element simulations predict in vitro strength of human proximal femora assessed in a dynamic sideways fall setup.

PubMed

Varga, Peter; Schwiedrzik, Jakob; Zysset, Philippe K; Fliri-Hofmann, Ladina; Widmer, Daniel; Gueorguiev, Boyko; Blauth, Michael; Windolf, Markus

2016-04-01

Osteoporotic proximal femur fractures are caused by low energy trauma, typically when falling on the hip from standing height. Finite element simulations, widely used to predict the fracture load of femora in fall, usually include neither mass-related inertial effects, nor the viscous part of bone׳s material behavior. The aim of this study was to elucidate if quasi-static non-linear homogenized finite element analyses can predict in vitro mechanical properties of proximal femora assessed in dynamic drop tower experiments. The case-specific numerical models of 13 femora predicted the strength (R(2)=0.84, SEE=540N, 16.2%), stiffness (R(2)=0.82, SEE=233N/mm, 18.0%) and fracture energy (R(2)=0.72, SEE=3.85J, 39.6%); and provided fair qualitative matches with the fracture patterns. The influence of material anisotropy was negligible for all predictions. These results suggest that quasi-static homogenized finite element analysis may be used to predict mechanical properties of proximal femora in the dynamic sideways fall situation. Copyright © 2015 Elsevier Ltd. All rights reserved.

An Aeroelastic Analysis of a Thin Flexible Membrane

NASA Technical Reports Server (NTRS)

Scott, Robert C.; Bartels, Robert E.; Kandil, Osama A.

2007-01-01

Studies have shown that significant vehicle mass and cost savings are possible with the use of ballutes for aero-capture. Through NASA's In-Space Propulsion program, a preliminary examination of ballute sensitivity to geometry and Reynolds number was conducted, and a single-pass coupling between an aero code and a finite element solver was used to assess the static aeroelastic effects. There remain, however, a variety of open questions regarding the dynamic aeroelastic stability of membrane structures for aero-capture, with the primary challenge being the prediction of the membrane flutter onset. The purpose of this paper is to describe and begin addressing these issues. The paper includes a review of the literature associated with the structural analysis of membranes and membrane utter. Flow/structure analysis coupling and hypersonic flow solver options are also discussed. An approach is proposed for tackling this problem that starts with a relatively simple geometry and develops and evaluates analysis methods and procedures. This preliminary study considers a computationally manageable 2-dimensional problem. The membrane structural models used in the paper include a nonlinear finite-difference model for static and dynamic analysis and a NASTRAN finite element membrane model for nonlinear static and linear normal modes analysis. Both structural models are coupled with a structured compressible flow solver for static aeroelastic analysis. For dynamic aeroelastic analyses, the NASTRAN normal modes are used in the structured compressible flow solver and 3rd order piston theories were used with the finite difference membrane model to simulate utter onset. Results from the various static and dynamic aeroelastic analyses are compared.

On the dynamics of Airy beams in nonlinear media with nonlinear losses.

PubMed

Ruiz-Jiménez, Carlos; Nóbrega, K Z; Porras, Miguel A

2015-04-06

We investigate on the nonlinear dynamics of Airy beams in a regime where nonlinear losses due to multi-photon absorption are significant. We identify the nonlinear Airy beam (NAB) that preserves the amplitude of the inward Hänkel component as an attractor of the dynamics. This attractor governs also the dynamics of finite-power (apodized) Airy beams, irrespective of the location of the entrance plane in the medium with respect to the Airy waist plane. A soft (linear) input long before the waist, however, strongly speeds up NAB formation and its persistence as a quasi-stationary beam in comparison to an abrupt input at the Airy waist plane, and promotes the formation of a new type of highly dissipative, fully nonlinear Airy beam not described so far.

Fast-Running Aeroelastic Code Based on Unsteady Linearized Aerodynamic Solver Developed

NASA Technical Reports Server (NTRS)

Reddy, T. S. R.; Bakhle, Milind A.; Keith, T., Jr.

2003-01-01

The NASA Glenn Research Center has been developing aeroelastic analyses for turbomachines for use by NASA and industry. An aeroelastic analysis consists of a structural dynamic model, an unsteady aerodynamic model, and a procedure to couple the two models. The structural models are well developed. Hence, most of the development for the aeroelastic analysis of turbomachines has involved adapting and using unsteady aerodynamic models. Two methods are used in developing unsteady aerodynamic analysis procedures for the flutter and forced response of turbomachines: (1) the time domain method and (2) the frequency domain method. Codes based on time domain methods require considerable computational time and, hence, cannot be used during the design process. Frequency domain methods eliminate the time dependence by assuming harmonic motion and, hence, require less computational time. Early frequency domain analyses methods neglected the important physics of steady loading on the analyses for simplicity. A fast-running unsteady aerodynamic code, LINFLUX, which includes steady loading and is based on the frequency domain method, has been modified for flutter and response calculations. LINFLUX, solves unsteady linearized Euler equations for calculating the unsteady aerodynamic forces on the blades, starting from a steady nonlinear aerodynamic solution. First, we obtained a steady aerodynamic solution for a given flow condition using the nonlinear unsteady aerodynamic code TURBO. A blade vibration analysis was done to determine the frequencies and mode shapes of the vibrating blades, and an interface code was used to convert the steady aerodynamic solution to a form required by LINFLUX. A preprocessor was used to interpolate the mode shapes from the structural dynamic mesh onto the computational dynamics mesh. Then, we used LINFLUX to calculate the unsteady aerodynamic forces for a given mode, frequency, and phase angle. A postprocessor read these unsteady pressures and calculated the generalized aerodynamic forces, eigenvalues, and response amplitudes. The eigenvalues determine the flutter frequency and damping. As a test case, the flutter of a helical fan was calculated with LINFLUX and compared with calculations from TURBO-AE, a nonlinear time domain code, and from ASTROP2, a code based on linear unsteady aerodynamics.

Aeroelastic Analysis Of Joined Wing Of High Altitude Long Endurance (HALE) Aircraft Based On The Sensor-Craft Configuration

NASA Astrophysics Data System (ADS)

Marisarla, Soujanya; Ghia, Urmila; "Karman" Ghia, Kirti

2002-11-01

Towards a comprehensive aeroelastic analysis of a joined wing, fluid dynamics and structural analyses are initially performed separately. Steady flow calculations are currently performed using 3-D compressible Navier-Stokes equations. Flow analysis of M6-Onera wing served to validate the software for the fluid dynamics analysis. The complex flow field of the joined wing is analyzed and the prevailing fluid dynamic forces are computed using COBALT software. Currently, these forces are being transferred as fluid loads on the structure. For the structural analysis, several test cases were run considering the wing as a cantilever beam; these served as validation cases. A nonlinear structural analysis of the wing is being performed using ANSYS software to predict the deflections and stresses on the joined wing. Issues related to modeling, and selecting appropriate mesh for the structure were addressed by first performing a linear analysis. The frequencies and mode shapes of the deformed wing are obtained from modal analysis. Both static and dynamic analyses are carried out, and the results obtained are carefully analyzed. Loose coupling between the fluid and structural analyses is currently being examined.

Nonlinear dynamic range transformation in visual communication channels.

PubMed

Alter-Gartenberg, R

1996-01-01

The article evaluates nonlinear dynamic range transformation in the context of the end-to-end continuous-input/discrete processing/continuous-display imaging process. Dynamic range transformation is required when we have the following: (i) the wide dynamic range encountered in nature is compressed into the relatively narrow dynamic range of the display, particularly for spatially varying irradiance (e.g., shadow); (ii) coarse quantization is expanded to the wider dynamic range of the display; and (iii) nonlinear tone scale transformation compensates for the correction in the camera amplifier.

Left-Right Non-Linear Dynamical Higgs

NASA Astrophysics Data System (ADS)

Jing, Shu; Juan, Yepes

2016-12-01

All the possible CP-conserving non-linear operators up to the p4-order in the Lagrangian expansion are analysed here for the left-right symmetric model in the non-linear electroweak chiral context coupled to a light dynamical Higgs. The low energy effects will be triggered by an emerging new physics field content in the nature, more specifically, from spin-1 resonances sourced by the straightforward extension of the SM local gauge symmetry to the larger local group SU(2)L × SU(2)R × U(1)B-L. Low energy phenomenology will be altered by integrating out the resonances from the physical spectrum, being manifested through induced corrections onto the left handed operators. Such modifications are weighted by powers of the scales ratio implied by the symmetries of the model and will determine the size of the effective operator basis to be used. The recently observed diboson excess around the invariant mass 1.8 TeV-2 TeV entails a scale suppression that suggests to encode the low energy effects via a much smaller set of effective operators. J. Y. also acknowledges KITPC financial support during the completion of this work

Nonlinear finite element modeling of vibration control of plane rod-type structural members with integrated piezoelectric patches

NASA Astrophysics Data System (ADS)

Chróścielewski, Jacek; Schmidt, Rüdiger; Eremeyev, Victor A.

2018-05-01

This paper addresses modeling and finite element analysis of the transient large-amplitude vibration response of thin rod-type structures (e.g., plane curved beams, arches, ring shells) and its control by integrated piezoelectric layers. A geometrically nonlinear finite beam element for the analysis of piezolaminated structures is developed that is based on the Bernoulli hypothesis and the assumptions of small strains and finite rotations of the normal. The finite element model can be applied to static, stability, and transient analysis of smart structures consisting of a master structure and integrated piezoelectric actuator layers or patches attached to the upper and lower surfaces. Two problems are studied extensively: (i) FE analyses of a clamped semicircular ring shell that has been used as a benchmark problem for linear vibration control in several recent papers are critically reviewed and extended to account for the effects of structural nonlinearity and (ii) a smart circular arch subjected to a hydrostatic pressure load is investigated statically and dynamically in order to study the shift of bifurcation and limit points, eigenfrequencies, and eigenvectors, as well as vibration control for loading conditions which may lead to dynamic loss of stability.

Econometric testing on linear and nonlinear dynamic relation between stock prices and macroeconomy in China

NASA Astrophysics Data System (ADS)

Borjigin, Sumuya; Yang, Yating; Yang, Xiaoguang; Sun, Leilei

2018-03-01

Many researchers have realized that there is a strong correlation between stock prices and macroeconomy. In order to make this relationship clear, a lot of studies have been done. However, the causal relationship between stock prices and macroeconomy has still not been well explained. A key point is that, most of the existing research adopts linear and stable models to investigate the correlation of stock prices and macroeconomy, while the real causality of that may be nonlinear and dynamic. To fill this research gap, we investigate the nonlinear and dynamic causal relationships between stock prices and macroeconomy. Based on the case of China's stock prices and acroeconomy measures from January 1992 to March 2017, we compare the linear Granger causality test models with nonlinear ones. Results demonstrate that the nonlinear dynamic Granger causality is much stronger than linear Granger causality. From the perspective of nonlinear dynamic Granger causality, China's stock prices can be viewed as "national economic barometer". On the one hand, this study will encourage researchers to take nonlinearity and dynamics into account when they investigate the correlation of stock prices and macroeconomy; on the other hand, our research can guide regulators and investors to make better decisions.

The nonlinear dynamics of a spacecraft coupled to the vibration of a contained fluid

NASA Technical Reports Server (NTRS)

Peterson, Lee D.; Crawley, Edward F.; Hansman, R. John

1988-01-01

The dynamics of a linear spacecraft mode coupled to a nonlinear low gravity slosh of a fluid in a cylindrical tank is investigated. Coupled, nonlinear equations of motion for the fluid-spacecraft dynamics are derived through an assumed mode Lagrangian method. Unlike linear fluid slosh models, this nonlinear slosh model retains two fundamental slosh modes and three secondary modes. An approximate perturbation solution of the equations of motion indicates that the nonlinear coupled system response involves fluid-spacecraft modal resonances not predicted by either a linear, or a nonlinear, uncoupled slosh analysis. Experimental results substantiate the analytical predictions.

Parametric model of servo-hydraulic actuator coupled with a nonlinear system: Experimental validation

NASA Astrophysics Data System (ADS)

Maghareh, Amin; Silva, Christian E.; Dyke, Shirley J.

2018-05-01

Hydraulic actuators play a key role in experimental structural dynamics. In a previous study, a physics-based model for a servo-hydraulic actuator coupled with a nonlinear physical system was developed. Later, this dynamical model was transformed into controllable canonical form for position tracking control purposes. For this study, a nonlinear device is designed and fabricated to exhibit various nonlinear force-displacement profiles depending on the initial condition and the type of materials used as replaceable coupons. Using this nonlinear system, the controllable canonical dynamical model is experimentally validated for a servo-hydraulic actuator coupled with a nonlinear physical system.

Broad-band simulation of M7.2 earthquake on the North Tehran fault, considering non-linear soil effects

NASA Astrophysics Data System (ADS)

Majidinejad, A.; Zafarani, H.; Vahdani, S.

2018-05-01

The North Tehran fault (NTF) is known to be one of the most drastic sources of seismic hazard on the city of Tehran. In this study, we provide broad-band (0-10 Hz) ground motions for the city as a consequence of probable M7.2 earthquake on the NTF. Low-frequency motions (0-2 Hz) are provided from spectral element dynamic simulation of 17 scenario models. High-frequency (2-10 Hz) motions are calculated with a physics-based method based on S-to-S backscattering theory. Broad-band ground motions at the bedrock level show amplifications, both at low and high frequencies, due to the existence of deep Tehran basin in the vicinity of the NTF. By employing soil profiles obtained from regional studies, effect of shallow soil layers on broad-band ground motions is investigated by both linear and non-linear analyses. While linear soil response overestimate ground motion prediction equations, non-linear response predicts plausible results within one standard deviation of empirical relationships. Average Peak Ground Accelerations (PGAs) at the northern, central and southern parts of the city are estimated about 0.93, 0.59 and 0.4 g, respectively. Increased damping caused by non-linear soil behaviour, reduces the soil linear responses considerably, in particular at frequencies above 3 Hz. Non-linear deamplification reduces linear spectral accelerations up to 63 per cent at stations above soft thick sediments. By performing more general analyses, which exclude source-to-site effects on stations, a correction function is proposed for typical site classes of Tehran. Parameters for the function which reduces linear soil response in order to take into account non-linear soil deamplification are provided for various frequencies in the range of engineering interest. In addition to fully non-linear analyses, equivalent-linear calculations were also conducted which their comparison revealed appropriateness of the method for large peaks and low frequencies, but its shortage for small to medium peaks and motions with higher than 3 Hz frequencies.

Recurrence plot analyses suggest a novel reference system involved in newborn spontaneous movements.

PubMed

Assmann, Birte; Thiel, Marco; Romano, Maria C; Niemitz, Carsten

2006-08-01

The movements of newborns have been thoroughly studied in terms of reflexes, muscle synergies, leg coordination, and target-directed arm/hand movements. Since these approaches have concentrated mainly on separate accomplishments, there has remained a clear need for more integrated investigations. Here, we report an inquiry in which we explicitly concentrated on taking such a perspective and, additionally, were guided by the methodological concept of home base behavior, which Ilan Golani developed for studies of exploratory behavior in animals. Methods from nonlinear dynamics, such as symbolic dynamics and recurrence plot analyses of kinematic data received from audiovisual newborn recordings, yielded new insights into the spatial and temporal organization of limb movements. In the framework of home base behavior, our approach uncovered a novel reference system of spontaneous newborn movements.

Nonlinear dynamics in flow through unsaturated fractured-porous media: Status and perspectives

DOE Office of Scientific and Technical Information (OSTI.GOV)

Faybishenko, Boris

2002-11-27

The need has long been recognized to improve predictions of flow and transport in partially saturated heterogeneous soils and fractured rock of the vadose zone for many practical applications, such as remediation of contaminated sites, nuclear waste disposal in geological formations, and climate predictions. Until recently, flow and transport processes in heterogeneous subsurface media with oscillating irregularities were assumed to be random and were not analyzed using methods of nonlinear dynamics. The goals of this paper are to review the theoretical concepts, present the results, and provide perspectives on investigations of flow and transport in unsaturated heterogeneous soils and fracturedmore » rock, using the methods of nonlinear dynamics and deterministic chaos. The results of laboratory and field investigations indicate that the nonlinear dynamics of flow and transport processes in unsaturated soils and fractured rocks arise from the dynamic feedback and competition between various nonlinear physical processes along with complex geometry of flow paths. Although direct measurements of variables characterizing the individual flow processes are not technically feasible, their cumulative effect can be characterized by analyzing time series data using the models and methods of nonlinear dynamics and chaos. Identifying flow through soil or rock as a nonlinear dynamical system is important for developing appropriate short- and long-time predictive models, evaluating prediction uncertainty, assessing the spatial distribution of flow characteristics from time series data, and improving chemical transport simulations. Inferring the nature of flow processes through the methods of nonlinear dynamics could become widely used in different areas of the earth sciences.« less

Nonlinear Dynamical Modes as a Basis for Short-Term Forecast of Climate Variability

NASA Astrophysics Data System (ADS)

Feigin, A. M.; Mukhin, D.; Gavrilov, A.; Seleznev, A.; Loskutov, E.

2017-12-01

We study abilities of data-driven stochastic models constructed by nonlinear dynamical decomposition of spatially distributed data to quantitative (short-term) forecast of climate characteristics. We compare two data processing techniques: (i) widely used empirical orthogonal function approach, and (ii) nonlinear dynamical modes (NDMs) framework [1,2]. We also make comparison of two kinds of the prognostic models: (i) traditional autoregression (linear) model and (ii) model in the form of random ("stochastic") nonlinear dynamical system [3]. We apply all combinations of the above-mentioned data mining techniques and kinds of models to short-term forecasts of climate indices based on sea surface temperature (SST) data. We use NOAA_ERSST_V4 dataset (monthly SST with space resolution 20 × 20) covering the tropical belt and starting from the year 1960. We demonstrate that NDM-based nonlinear model shows better prediction skill versus EOF-based linear and nonlinear models. Finally we discuss capability of NDM-based nonlinear model for long-term (decadal) prediction of climate variability. [1] D. Mukhin, A. Gavrilov, E. Loskutov , A.Feigin, J.Kurths, 2015: Principal nonlinear dynamical modes of climate variability, Scientific Reports, rep. 5, 15510; doi: 10.1038/srep15510. [2] Gavrilov, A., Mukhin, D., Loskutov, E., Volodin, E., Feigin, A., & Kurths, J., 2016: Method for reconstructing nonlinear modes with adaptive structure from multidimensional data. Chaos: An Interdisciplinary Journal of Nonlinear Science, 26(12), 123101. [3] Ya. Molkov, D. Mukhin, E. Loskutov, A. Feigin, 2012: Random dynamical models from time series. Phys. Rev. E, Vol. 85, n.3.

Thermal runaway and microwave heating in thin cylindrical domains

NASA Astrophysics Data System (ADS)

Ward, Michael J.

2002-04-01

The behaviour of the solution to two nonlinear heating problems in a thin cylinder of revolution of variable cross-sectional area is analysed using asymptotic and numerical methods. The first problem is to calculate the fold point, corresponding to the onset of thermal runaway, for a steady-state nonlinear elliptic equation that arises in combustion theory. In the limit of thin cylindrical domains, it is shown that the onset of thermal runaway can be delayed when a circular cylindrical domain is perturbed into a dumbell shape. Numerical values for the fold point for different domain shapes are obtained asymptotically and numerically. The second problem that is analysed is a nonlinear parabolic equation modelling the microwave heating of a ceramic cylinder by a known electric field. The basic model in a thin circular cylindrical domain was analysed in Booty & Kriegsmann (Meth. Appl. Anal. 4 (1994) p. 403). Their analysis is extended to treat thin cylindrical domains of variable cross-section. It is shown that the steady-state and dynamic behaviours of localized regions of high temperature, called hot-spots, depend on a competition between the maxima of the electric field and the maximum deformation of the circular cylinder. For a dumbell-shaped region it is shown that two disconnected hot-spot regions can occur. Depending on the parameters in the model, these regions, ultimately, either merge as time increases or else remain as disconnected regions for all time.

Nonlinearity in the vertical transmissibility of seating: the role of the human body apparent mass and seat dynamic stiffness

NASA Astrophysics Data System (ADS)

Tufano, Saverio; Griffin, Michael J.

2013-01-01

The efficiency of a seat in reducing vibration depends on the characteristics of the vibration, the dynamic characteristics of the seat, and the dynamic characteristics of the person sitting on the seat. However, it is not known whether seat cushions influence the dynamic response of the human body, whether the human body influences the dynamic response of seat cushions, or the relative importance of human body nonlinearity and seat nonlinearity in causing nonlinearity in measures of seat transmissibility. This study was designed to investigate the nonlinearity of the coupled seat and human body systems and to compare the apparent mass of the human body supported on rigid and foam seats. A frequency domain model was used to identify the dynamic parameters of seat foams and investigate their dependence on the subject-sitting weight and hip breadth. With 15 subjects, the force and acceleration at the seat base and acceleration at the subject interface were measured during random vertical vibration excitation (0.25-25 Hz) at each of five vibration magnitudes, (0.25-1.6 ms-2 r.m.s.) with four seating conditions (rigid flat seat and three foam cushions). The measurements are presented in terms of the subject's apparent mass on the rigid and foam seat surfaces, and the transmissibility and dynamic stiffness of each of the foam cushions. Both the human body and the foams showed nonlinear softening behaviour, which resulted in nonlinear cushion transmissibility. The apparent masses of subjects sitting on the rigid seat and on foam cushions were similar, but with an apparent increase in damping when sitting on the foams. The foam dynamic stiffness showed complex correlations with characteristics of the human body, which differed between foams. The nonlinearities in cushion transmissibilities, expressed in terms of changes in resonance frequencies and moduli, were more dependent on human body nonlinearity than on cushion nonlinearity.

Lifespan Differences in Nonlinear Dynamics during Rest and Auditory Oddball Performance

ERIC Educational Resources Information Center

Muller, Viktor; Lindenberger, Ulman

2012-01-01

Electroencephalographic recordings (EEG) were used to assess age-associated differences in nonlinear brain dynamics during both rest and auditory oddball performance in children aged 9.0-12.8 years, younger adults, and older adults. We computed nonlinear coupling dynamics and dimensional complexity, and also determined spectral alpha power as an…

Quantitative theory of driven nonlinear brain dynamics.

PubMed

Roberts, J A; Robinson, P A

2012-09-01

Strong periodic stimuli such as bright flashing lights evoke nonlinear responses in the brain and interact nonlinearly with ongoing cortical activity, but the underlying mechanisms for these phenomena are poorly understood at present. The dominant features of these experimentally observed dynamics are reproduced by the dynamics of a quantitative neural field model subject to periodic drive. Model power spectra over a range of drive frequencies show agreement with multiple features of experimental measurements, exhibiting nonlinear effects including entrainment over a range of frequencies around the natural alpha frequency f(α), subharmonic entrainment near 2f(α), and harmonic generation. Further analysis of the driven dynamics as a function of the drive parameters reveals rich nonlinear dynamics that is predicted to be observable in future experiments at high drive amplitude, including period doubling, bistable phase-locking, hysteresis, wave mixing, and chaos indicated by positive Lyapunov exponents. Moreover, photosensitive seizures are predicted for physiologically realistic model parameters yielding bistability between healthy and seizure dynamics. These results demonstrate the applicability of neural field models to the new regime of periodically driven nonlinear dynamics, enabling interpretation of experimental data in terms of specific generating mechanisms and providing new tests of the theory. Copyright © 2012 Elsevier Inc. All rights reserved.

Nonlinear problems in flight dynamics

NASA Technical Reports Server (NTRS)

Chapman, G. T.; Tobak, M.

1984-01-01

A comprehensive framework is proposed for the description and analysis of nonlinear problems in flight dynamics. Emphasis is placed on the aerodynamic component as the major source of nonlinearities in the flight dynamic system. Four aerodynamic flows are examined to illustrate the richness and regularity of the flow structures and the nature of the flow structures and the nature of the resulting nonlinear aerodynamic forces and moments. A framework to facilitate the study of the aerodynamic system is proposed having parallel observational and mathematical components. The observational component, structure is described in the language of topology. Changes in flow structure are described via bifurcation theory. Chaos or turbulence is related to the analogous chaotic behavior of nonlinear dynamical systems characterized by the existence of strange attractors having fractal dimensionality. Scales of the flow are considered in the light of ideas from group theory. Several one and two degree of freedom dynamical systems with various mathematical models of the nonlinear aerodynamic forces and moments are examined to illustrate the resulting types of dynamical behavior. The mathematical ideas that proved useful in the description of fluid flows are shown to be similarly useful in the description of flight dynamic behavior.

An Overview of Preliminary Computational and Experimental Results for the Semi-Span Super-Sonic Transport (S4T) Wind-Tunnel Model

NASA Technical Reports Server (NTRS)

Silva, Walter A.; Perry, Boyd, III; Florance, James R.; Sanetrik, Mark D.; Wieseman, Carol D.; Stevens, William L.; Funk, Christie J.; Hur, Jiyoung; Christhilf, David M.; Coulson, David A.

2011-01-01

A summary of computational and experimental aeroelastic and aeroservoelastic (ASE) results for the Semi-Span Super-Sonic Transport (S4T) wind-tunnel model is presented. A broad range of analyses and multiple ASE wind-tunnel tests of the S4T have been performed in support of the ASE element in the Supersonics Program, part of NASA's Fundamental Aeronautics Program. The computational results to be presented include linear aeroelastic and ASE analyses, nonlinear aeroelastic analyses using an aeroelastic CFD code, and rapid aeroelastic analyses using CFD-based reduced-order models (ROMs). Experimental results from two closed-loop wind-tunnel tests performed at NASA Langley's Transonic Dynamics Tunnel (TDT) will be presented as well.

Unambiguous demonstration of soliton evolution in slow-light silicon photonic crystal waveguides with SFG-XFROG.

PubMed

Li, Xiujian; Liao, Jiali; Nie, Yongming; Marko, Matthew; Jia, Hui; Liu, Ju; Wang, Xiaochun; Wong, Chee Wei

2015-04-20

We demonstrate the temporal and spectral evolution of picosecond soliton in the slow light silicon photonic crystal waveguides (PhCWs) by sum frequency generation cross-correlation frequency resolved optical grating (SFG-XFROG) and nonlinear Schrödinger equation (NLSE) modeling. The reference pulses for the SFG-XFROG measurements are unambiguously pre-characterized by the second harmonic generation frequency resolved optical gating (SHG-FROG) assisted with the combination of NLSE simulations and optical spectrum analyzer (OSA) measurements. Regardless of the inevitable nonlinear two photon absorption, high order soliton compressions have been observed remarkably owing to the slow light enhanced nonlinear effects in the silicon PhCWs. Both the measurements and the further numerical analyses of the pulse dynamics indicate that, the free carrier dispersion (FCD) enhanced by the slow light effects is mainly responsible for the compression, the acceleration, and the spectral blue shift of the soliton.

Nonlinear flight control design using backstepping methodology

NASA Astrophysics Data System (ADS)

Tran, Thanh Trung

The subject of nonlinear flight control design using backstepping control methodology is investigated in the dissertation research presented here. Control design methods based on nonlinear models of the dynamic system provide higher utility and versatility because the design model more closely matches the physical system behavior. Obtaining requisite model fidelity is only half of the overall design process, however. Design of the nonlinear control loops can lessen the effects of nonlinearity, or even exploit nonlinearity, to achieve higher levels of closed-loop stability, performance, and robustness. The goal of the research is to improve control quality for a general class of strict-feedback dynamic systems and provide flight control architectures to augment the aircraft motion. The research is divided into two parts: theoretical control development for the strict-feedback form of nonlinear dynamic systems and application of the proposed theory for nonlinear flight dynamics. In the first part, the research is built on two components: transforming the nonlinear dynamic model to a canonical strict-feedback form and then applying backstepping control theory to the canonical model. The research considers a process to determine when this transformation is possible, and when it is possible, a systematic process to transfer the model is also considered when practical. When this is not the case, certain modeling assumptions are explored to facilitate the transformation. After achieving the canonical form, a systematic design procedure for formulating a backstepping control law is explored in the research. Starting with the simplest subsystem and ending with the full system, pseudo control concepts based on Lyapunov control functions are used to control each successive subsystem. Typically each pseudo control must be solved from a nonlinear algebraic equation. At the end of this process, the physical control input must be re-expressed in terms of the physical states by eliminating the pseudo control transformations. In the second part, the research focuses on nonlinear control design for flight dynamics of aircraft motion. Some assumptions on aerodynamics of the aircraft are addressed to transform full nonlinear flight dynamics into the canonical strict-feedback form. The assumptions are also analyzed, validated, and compared to show the advantages and disadvantages of the design models. With the achieved models, investigation focuses on formulating the backstepping control laws and provides an advanced control algorithm for nonlinear flight dynamics of the aircraft. Experimental and simulation studies are successfully implemented to validate the proposed control method. Advancement of nonlinear backstepping control theory and its application to nonlinear flight control are achieved in the dissertation research.

Influence of unbalance levels on nonlinear dynamics of a rotor-backup rolling bearing system

NASA Astrophysics Data System (ADS)

Fonseca, Cesar A.; Santos, Ilmar F.; Weber, Hans I.

2017-04-01

Rotor drops in magnetic bearing and unbalance in rotors have been objective of study for many years. The combination of these two well-known phenomena led to an interesting chaotic response, when the rotor touches the inner race of the back-up bearing. The present work explores the nonlinear rotor backup bearing dynamics both theoretically and experimentally using a fully instrumented test rig, where the position of shaft, its angular velocity and the contact forces between the shaft and the backup bearing are sampled at 25 kHz. The test rig is built by a removable passive magnetic bearing, which allows for simulation of magnetic bearing failure (loss of carrying capacity and rotor fall). The rotor is studied numerically as well as experimentally. A theoretical approach is given beforehand and supplies the basis of the study. Finally the presented results are commented on the point of view of nonlinear dynamics applied to the practical use. The theoretical and numerical analyses are shown through orbit plots, phase plans, Poincaré maps, force response in time and double sided spectrum. The latter is important to characterize the condition at different levels of unbalance between forward and backward whirl. Our preliminary results indicate that for smaller amount of unbalance the rotor swings at the bottom of the bearing, the more the unbalance increases, other dynamical behavior occur and some can be extremely harmful, since the rotor can be lifted from the contact state and return, starting to impact innumerable times without reaching a steady state.

An experimental study of nonlinear dynamic system identification

NASA Technical Reports Server (NTRS)

Stry, Greselda I.; Mook, D. Joseph

1990-01-01

A technique for robust identification of nonlinear dynamic systems is developed and illustrated using both simulations and analog experiments. The technique is based on the Minimum Model Error optimal estimation approach. A detailed literature review is included in which fundamental differences between the current approach and previous work is described. The most significant feature of the current work is the ability to identify nonlinear dynamic systems without prior assumptions regarding the form of the nonlinearities, in constrast to existing nonlinear identification approaches which usually require detailed assumptions of the nonlinearities. The example illustrations indicate that the method is robust with respect to prior ignorance of the model, and with respect to measurement noise, measurement frequency, and measurement record length.

Dynamics of cochlear nonlinearity: Automatic gain control or instantaneous damping?

PubMed

Altoè, Alessandro; Charaziak, Karolina K; Shera, Christopher A

2017-12-01

Measurements of basilar-membrane (BM) motion show that the compressive nonlinearity of cochlear mechanical responses is not an instantaneous phenomenon. For this reason, the cochlear amplifier has been thought to incorporate an automatic gain control (AGC) mechanism characterized by a finite reaction time. This paper studies the effect of instantaneous nonlinear damping on the responses of oscillatory systems. The principal results are that (i) instantaneous nonlinear damping produces a noninstantaneous gain control that differs markedly from typical AGC strategies; (ii) the kinetics of compressive nonlinearity implied by the finite reaction time of an AGC system appear inconsistent with the nonlinear dynamics measured on the gerbil basilar membrane; and (iii) conversely, those nonlinear dynamics can be reproduced using an harmonic oscillator with instantaneous nonlinear damping. Furthermore, existing cochlear models that include instantaneous gain-control mechanisms capture the principal kinetics of BM nonlinearity. Thus, an AGC system with finite reaction time appears neither necessary nor sufficient to explain nonlinear gain control in the cochlea.

A nonlinear dynamics of trunk kinematics during manual lifting tasks.

PubMed

Khalaf, Tamer; Karwowski, Waldemar; Sapkota, Nabin

2015-01-01

Human responses at work may exhibit nonlinear properties where small changes in the initial task conditions can lead to large changes in system behavior. Therefore, it is important to study such nonlinearity to gain a better understanding of human performance under a variety of physical, perceptual, and cognitive tasks conditions. The main objective of this study was to investigate whether the human trunk kinematics data during a manual lifting task exhibits nonlinear behavior in terms of determinist chaos. Data related to kinematics of the trunk with respect to the pelvis were collected using Industrial Lumbar Motion Monitor (ILMM), and analyzed applying the nonlinear dynamical systems methodology. Nonlinear dynamics quantifiers of Lyapunov exponents and Kaplan-Yorke dimensions were calculated and analyzed under different task conditions. The study showed that human trunk kinematics during manual lifting exhibits chaotic behavior in terms of trunk sagittal angular displacement, velocity and acceleration. The findings support the importance of accounting for nonlinear dynamical properties of biomechanical responses to lifting tasks.

Dark solitons, modulation instability and breathers in a chain of weakly nonlinear oscillators with cyclic symmetry

NASA Astrophysics Data System (ADS)

Fontanela, F.; Grolet, A.; Salles, L.; Chabchoub, A.; Hoffmann, N.

2018-01-01

In the aerospace industry the trend for light-weight structures and the resulting complex dynamic behaviours currently challenge vibration engineers. In many cases, these light-weight structures deviate from linear behaviour, and complex nonlinear phenomena can be expected. We consider a cyclically symmetric system of coupled weakly nonlinear undamped oscillators that could be considered a minimal model for different cyclic and symmetric aerospace structures experiencing large deformations. The focus is on localised vibrations that arise from wave envelope modulation of travelling waves. For the defocussing parameter range of the approximative nonlinear evolution equation, we show the possible existence of dark solitons and discuss their characteristics. For the focussing parameter range, we characterise modulation instability and illustrate corresponding nonlinear breather dynamics. Furthermore, we show that for stronger nonlinearity or randomness in initial conditions, transient breather-type dynamics and decay into bright solitons appear. The findings suggest that significant vibration localisation may arise due to mechanisms of nonlinear modulation dynamics.

Proposed solution methodology for the dynamically coupled nonlinear geared rotor mechanics equations

NASA Technical Reports Server (NTRS)

Mitchell, L. D.; David, J. W.

1983-01-01

The equations which describe the three-dimensional motion of an unbalanced rigid disk in a shaft system are nonlinear and contain dynamic-coupling terms. Traditionally, investigators have used an order analysis to justify ignoring the nonlinear terms in the equations of motion, producing a set of linear equations. This paper will show that, when gears are included in such a rotor system, the nonlinear dynamic-coupling terms are potentially as large as the linear terms. Because of this, one must attempt to solve the nonlinear rotor mechanics equations. A solution methodology is investigated to obtain approximate steady-state solutions to these equations. As an example of the use of the technique, a simpler set of equations is solved and the results compared to numerical simulations. These equations represent the forced, steady-state response of a spring-supported pendulum. These equations were chosen because they contain the type of nonlinear terms found in the dynamically-coupled nonlinear rotor equations. The numerical simulations indicate this method is reasonably accurate even when the nonlinearities are large.

Application of numerical optimization techniques to control system design for nonlinear dynamic models of aircraft

NASA Technical Reports Server (NTRS)

Lan, C. Edward; Ge, Fuying

1989-01-01

Control system design for general nonlinear flight dynamic models is considered through numerical simulation. The design is accomplished through a numerical optimizer coupled with analysis of flight dynamic equations. The general flight dynamic equations are numerically integrated and dynamic characteristics are then identified from the dynamic response. The design variables are determined iteratively by the optimizer to optimize a prescribed objective function which is related to desired dynamic characteristics. Generality of the method allows nonlinear effects to aerodynamics and dynamic coupling to be considered in the design process. To demonstrate the method, nonlinear simulation models for an F-5A and an F-16 configurations are used to design dampers to satisfy specifications on flying qualities and control systems to prevent departure. The results indicate that the present method is simple in formulation and effective in satisfying the design objectives.

Supercomputer use in orthopaedic biomechanics research: focus on functional adaptation of bone.

PubMed

Hart, R T; Thongpreda, N; Van Buskirk, W C

1988-01-01

The authors describe two biomechanical analyses carried out using numerical methods. One is an analysis of the stress and strain in a human mandible, and the other analysis involves modeling the adaptive response of a sheep bone to mechanical loading. The computing environment required for the two types of analyses is discussed. It is shown that a simple stress analysis of a geometrically complex mandible can be accomplished using a minicomputer. However, more sophisticated analyses of the same model with dynamic loading or nonlinear materials would require supercomputer capabilities. A supercomputer is also required for modeling the adaptive response of living bone, even when simple geometric and material models are use.

Non-linear dynamics of stable carbon and hydrogen isotope signatures based on a biological kinetic model of aerobic enzymatic methane oxidation.

PubMed

Vavilin, Vasily A; Rytov, Sergey V; Shim, Natalia; Vogt, Carsten

2016-06-01

The non-linear dynamics of stable carbon and hydrogen isotope signatures during methane oxidation by the methanotrophic bacteria Methylosinus sporium strain 5 (NCIMB 11126) and Methylocaldum gracile strain 14 L (NCIMB 11912) under copper-rich (8.9 µM Cu(2+)), copper-limited (0.3 µM Cu(2+)) or copper-regular (1.1 µM Cu(2+)) conditions has been described mathematically. The model was calibrated by experimental data of methane quantities and carbon and hydrogen isotope signatures of methane measured previously in laboratory microcosms reported by Feisthauer et al. [ 1 ] M. gracile initially oxidizes methane by a particulate methane monooxygenase and assimilates formaldehyde via the ribulose monophosphate pathway, whereas M. sporium expresses a soluble methane monooxygenase under copper-limited conditions and uses the serine pathway for carbon assimilation. The model shows that during methane solubilization dominant carbon and hydrogen isotope fractionation occurs. An increase of biomass due to growth of methanotrophs causes an increase of particulate or soluble monooxygenase that, in turn, decreases soluble methane concentration intensifying methane solubilization. The specific maximum rate of methane oxidation υm was proved to be equal to 4.0 and 1.3 mM mM(-1) h(-1) for M. sporium under copper-rich and copper-limited conditions, respectively, and 0.5 mM mM(-1) h(-1) for M. gracile. The model shows that methane oxidation cannot be described by traditional first-order kinetics. The kinetic isotope fractionation ceases when methane concentrations decrease close to the threshold value. Applicability of the non-linear model was confirmed by dynamics of carbon isotope signature for carbon dioxide that was depleted and later enriched in (13)C. Contrasting to the common Rayleigh linear graph, the dynamic curves allow identifying inappropriate isotope data due to inaccurate substrate concentration analyses. The non-linear model pretty adequately described experimental data presented in the two-dimensional plot of hydrogen versus carbon stable isotope signatures.

Modelling Nonlinear Dynamic Textures using Hybrid DWT-DCT and Kernel PCA with GPU

NASA Astrophysics Data System (ADS)

Ghadekar, Premanand Pralhad; Chopade, Nilkanth Bhikaji

2016-12-01

Most of the real-world dynamic textures are nonlinear, non-stationary, and irregular. Nonlinear motion also has some repetition of motion, but it exhibits high variation, stochasticity, and randomness. Hybrid DWT-DCT and Kernel Principal Component Analysis (KPCA) with YCbCr/YIQ colour coding using the Dynamic Texture Unit (DTU) approach is proposed to model a nonlinear dynamic texture, which provides better results than state-of-art methods in terms of PSNR, compression ratio, model coefficients, and model size. Dynamic texture is decomposed into DTUs as they help to extract temporal self-similarity. Hybrid DWT-DCT is used to extract spatial redundancy. YCbCr/YIQ colour encoding is performed to capture chromatic correlation. KPCA is applied to capture nonlinear motion. Further, the proposed algorithm is implemented on Graphics Processing Unit (GPU), which comprise of hundreds of small processors to decrease time complexity and to achieve parallelism.

Bayesian inversion analysis of nonlinear dynamics in surface heterogeneous reactions.

PubMed

Omori, Toshiaki; Kuwatani, Tatsu; Okamoto, Atsushi; Hukushima, Koji

2016-09-01

It is essential to extract nonlinear dynamics from time-series data as an inverse problem in natural sciences. We propose a Bayesian statistical framework for extracting nonlinear dynamics of surface heterogeneous reactions from sparse and noisy observable data. Surface heterogeneous reactions are chemical reactions with conjugation of multiple phases, and they have the intrinsic nonlinearity of their dynamics caused by the effect of surface-area between different phases. We adapt a belief propagation method and an expectation-maximization (EM) algorithm to partial observation problem, in order to simultaneously estimate the time course of hidden variables and the kinetic parameters underlying dynamics. The proposed belief propagation method is performed by using sequential Monte Carlo algorithm in order to estimate nonlinear dynamical system. Using our proposed method, we show that the rate constants of dissolution and precipitation reactions, which are typical examples of surface heterogeneous reactions, as well as the temporal changes of solid reactants and products, were successfully estimated only from the observable temporal changes in the concentration of the dissolved intermediate product.

Nonlinear complexity of random visibility graph and Lempel-Ziv on multitype range-intensity interacting financial dynamics

NASA Astrophysics Data System (ADS)

Zhang, Yali; Wang, Jun

2017-09-01

In an attempt to investigate the nonlinear complex evolution of financial dynamics, a new financial price model - the multitype range-intensity contact (MRIC) financial model, is developed based on the multitype range-intensity interacting contact system, in which the interaction and transmission of different types of investment attitudes in a stock market are simulated by viruses spreading. Two new random visibility graph (VG) based analyses and Lempel-Ziv complexity (LZC) are applied to study the complex behaviors of return time series and the corresponding random sorted series. The VG method is the complex network theory, and the LZC is a non-parametric measure of complexity reflecting the rate of new pattern generation of a series. In this work, the real stock market indices are considered to be comparatively studied with the simulation data of the proposed model. Further, the numerical empirical study shows the similar complexity behaviors between the model and the real markets, the research confirms that the financial model is reasonable to some extent.

Dynamical analysis of a cubic Liénard system with global parameters (II)

NASA Astrophysics Data System (ADS)

Chen, Hebai; Chen, Xingwu

2016-06-01

In this paper, we continue to study the global dynamics of a cubic Liénard system for global parameters in the case of three equilibria to follow (2015 Nonlinearity 28 3535-62), which deals with the case of two equilibria. We first analyse qualitative properties of all equilibria and judge the existences of limit cycles and homoclinic loops and their numbers. Then we obtain the bifurcation diagram and all phase portraits as our main results. Based on these results, in the case of three equilibria a positive answer to conjecture 3.2 of (1998 Nonlinearity 11 1505-19), which is about the existence of some function whose graph is exactly the surface of double limit cycles, is obtained. Moreover, a parameter region for the nonexistence of figure-eight loops is given theoretically to compensate for previous numerical results and is illustrated numerically. Supported by NSFC 11471228, 11572263, the Fundamental Research Funds for the Central Universities and Cultivation Foundation of Excellent Doctoral Dissertation of Southwest Jiaotong University (2015).

Nonlinear convective pulsation models of type II Cepheids

NASA Astrophysics Data System (ADS)

Smolec, Radoslaw

2015-08-01

We present a grid of nonlinear convective pulsation models of type-II Cepheids: BL Her stars, W Vir stars and RV Tau stars. The models cover a wide range of masses, luminosities, effective temperatures and chemical compositions. The most interesting result is detection of deterministic chaos in the models. Different routes to chaos are detected (period doubling, intermittent route) as well as variety of phenomena intrinsic to chaotic dynamics (periodic islands within chaotic bands, crisis bifurcation, type-I and type-III intermittency). Some of the phenomena (period doubling in BL Her and in RV Tau stars, irregular pulsation of RV Tau stars) are well known in the pulsation of type-II Cepheids. Prospects of discovering the other are briefly discussed. Transition from BL Her type pulsation through W Vir type till RV Tau type is analysed. In the most luminous models a dynamical instability is detected, which indicates that pulsation driven mass loss is important process occurring in type-II Cepheids.

Linear and non-linear dynamic models of a geared rotor-bearing system

NASA Technical Reports Server (NTRS)

Kahraman, Ahmet; Singh, Rajendra

1990-01-01

A three degree of freedom non-linear model of a geared rotor-bearing system with gear backlash and radial clearances in rolling element bearings is proposed here. This reduced order model can be used to describe the transverse-torsional motion of the system. It is justified by comparing the eigen solutions yielded by corresponding linear model with the finite element method results. Nature of nonlinearities in bearings is examined and two approximate nonlinear stiffness functions are proposed. These approximate bearing models are verified by comparing their frequency responses with the results given by the exact form of nonlinearity. The proposed nonlinear dynamic model of the geared rotor-bearing system can be used to investigate the dynamic behavior and chaos.

Nonlinear Light Dynamics in Multi-Core Structures

DTIC Science & Technology

2017-02-27

be generated in continuous- discrete optical media such as multi-core optical fiber or waveguide arrays; localisation dynamics in a continuous... discrete nonlinear system. Detailed theoretical analysis is presented of the existence and stability of the discrete -continuous light bullets using a very...and pulse compression using wave collapse (self-focusing) energy localisation dynamics in a continuous- discrete nonlinear system, as implemented in a

Quantum-Enhanced Sensing Based on Time Reversal of Nonlinear Dynamics.

PubMed

Linnemann, D; Strobel, H; Muessel, W; Schulz, J; Lewis-Swan, R J; Kheruntsyan, K V; Oberthaler, M K

2016-07-01

We experimentally demonstrate a nonlinear detection scheme exploiting time-reversal dynamics that disentangles continuous variable entangled states for feasible readout. Spin-exchange dynamics of Bose-Einstein condensates is used as the nonlinear mechanism which not only generates entangled states but can also be time reversed by controlled phase imprinting. For demonstration of a quantum-enhanced measurement we construct an active atom SU(1,1) interferometer, where entangled state preparation and nonlinear readout both consist of parametric amplification. This scheme is capable of exhausting the quantum resource by detecting solely mean atom numbers. Controlled nonlinear transformations widen the spectrum of useful entangled states for applied quantum technologies.

Nonlinear Dynamical Model of a Soft Viscoelastic Dielectric Elastomer

NASA Astrophysics Data System (ADS)

Zhang, Junshi; Chen, Hualing; Li, Dichen

2017-12-01

Actuated by alternating stimulation, dielectric elastomers (DEs) show a behavior of complicated nonlinear vibration, implying a potential application as dynamic electromechanical actuators. As is well known, for a vibrational system, including the DE system, the dynamic properties are significantly affected by the geometrical sizes. In this article, a nonlinear dynamical model is deduced to investigate the geometrical effects on dynamic properties of viscoelastic DEs. The DEs with square and arbitrary rectangular geometries are considered, respectively. Besides, the effects of tensile forces on dynamic performances of rectangular DEs with comparably small and large geometrical sizes are explored. Phase paths and Poincaré maps are utilized to detect the periodicity of the nonlinear vibrations of DEs. The resonance characteristics of DEs incorporating geometrical effects are also investigated. The results indicate that the dynamic properties of DEs, including deformation response, vibrational periodicity, and resonance, are tuned when the geometrical sizes vary.

Dynamics of representational change: entropy, action, and cognition.

PubMed

Stephen, Damian G; Dixon, James A; Isenhower, Robert W

2009-12-01

Explaining how the cognitive system can create new structures has been a major challenge for cognitive science. Self-organization from the theory of nonlinear dynamics offers an account of this remarkable phenomenon. Two studies provide an initial test of the hypothesis that the emergence of new cognitive structure follows the same universal principles as emergence in other domains (e.g., fluids, lasers). In both studies, participants initially solved gear-system problems by manually tracing the force across a system of gears. Subsequently, they discovered that the gears form an alternating sequence, thereby demonstrating a new cognitive structure. In both studies, dynamical analyses of action during problem solving predicted the spontaneous emergence of the new cognitive structure. Study 1 showed that a peak in entropy, followed by negentropy, key indicators of self-organization, predicted discovery of alternation. Study 2 replicated these effects, and showed that increasing environmental entropy accelerated discovery, a classic prediction from dynamics. Additional analyses based on the relationship between phase transitions and power-law behavior provide converging evidence. The studies provide an initial demonstration of the emergence of cognitive structure through self-organization.

Evolutionary optimization with data collocation for reverse engineering of biological networks.

PubMed

Tsai, Kuan-Yao; Wang, Feng-Sheng

2005-04-01

Modern experimental biology is moving away from analyses of single elements to whole-organism measurements. Such measured time-course data contain a wealth of information about the structure and dynamic of the pathway or network. The dynamic modeling of the whole systems is formulated as a reverse problem that requires a well-suited mathematical model and a very efficient computational method to identify the model structure and parameters. Numerical integration for differential equations and finding global parameter values are still two major challenges in this field of the parameter estimation of nonlinear dynamic biological systems. We compare three techniques of parameter estimation for nonlinear dynamic biological systems. In the proposed scheme, the modified collocation method is applied to convert the differential equations to the system of algebraic equations. The observed time-course data are then substituted into the algebraic system equations to decouple system interactions in order to obtain the approximate model profiles. Hybrid differential evolution (HDE) with population size of five is able to find a global solution. The method is not only suited for parameter estimation but also can be applied for structure identification. The solution obtained by HDE is then used as the starting point for a local search method to yield the refined estimates.

Multiscale functions, scale dynamics, and applications to partial differential equations

NASA Astrophysics Data System (ADS)

Cresson, Jacky; Pierret, Frédéric

2016-05-01

Modeling phenomena from experimental data always begins with a choice of hypothesis on the observed dynamics such as determinism, randomness, and differentiability. Depending on these choices, different behaviors can be observed. The natural question associated to the modeling problem is the following: "With a finite set of data concerning a phenomenon, can we recover its underlying nature? From this problem, we introduce in this paper the definition of multi-scale functions, scale calculus, and scale dynamics based on the time scale calculus [see Bohner, M. and Peterson, A., Dynamic Equations on Time Scales: An Introduction with Applications (Springer Science & Business Media, 2001)] which is used to introduce the notion of scale equations. These definitions will be illustrated on the multi-scale Okamoto's functions. Scale equations are analysed using scale regimes and the notion of asymptotic model for a scale equation under a particular scale regime. The introduced formalism explains why a single scale equation can produce distinct continuous models even if the equation is scale invariant. Typical examples of such equations are given by the scale Euler-Lagrange equation. We illustrate our results using the scale Newton's equation which gives rise to a non-linear diffusion equation or a non-linear Schrödinger equation as asymptotic continuous models depending on the particular fractional scale regime which is considered.

Development of monofilar rotor hub vibration absorber

NASA Technical Reports Server (NTRS)

Duh, J.; Miao, W.

1983-01-01

A design and ground test program was conducted to study the performance of the monofilar absorber for vibration reduction on a four-bladed helicopter. A monofilar is a centrifugal tuned two degree-of-freedom rotor hub absorber that provides force attenuation at two frequencies using the same dynamic mass. Linear and non-linear analyses of the coupled monofilar/airframe system were developed to study tuning and attenuation characteristics. Based on the analysis, a design was fabricated and impact bench tests verified the calculated non-rotating natural frequencies and mode shapes. Performance characteristics were measured using a rotating absorber test facility. These tests showed significant attenuation of fixed-system 4P hub motions due to 3P inplane rotating-system hub forces. In addition, detuning effects of the 3P monofilar modal response were small due to the nonlinearities and tuning pin slippage. However, attenuation of 4P hub motions due to 5P inplane hub forces was poor. The performance of the 5P monofilar modal response was degraded by torsional motion of the dynamic mass relative to the support arm which resulted in binding of the dynamic components. Analytical design studies were performed to evaluate this torsional motion problem. An alternative design is proposed which may alleviate the torsional motion of the dynamic mass.

Structural stability of nonlinear population dynamics.

PubMed

Cenci, Simone; Saavedra, Serguei

2018-01-01

In population dynamics, the concept of structural stability has been used to quantify the tolerance of a system to environmental perturbations. Yet, measuring the structural stability of nonlinear dynamical systems remains a challenging task. Focusing on the classic Lotka-Volterra dynamics, because of the linearity of the functional response, it has been possible to measure the conditions compatible with a structurally stable system. However, the functional response of biological communities is not always well approximated by deterministic linear functions. Thus, it is unclear the extent to which this linear approach can be generalized to other population dynamics models. Here, we show that the same approach used to investigate the classic Lotka-Volterra dynamics, which is called the structural approach, can be applied to a much larger class of nonlinear models. This class covers a large number of nonlinear functional responses that have been intensively investigated both theoretically and experimentally. We also investigate the applicability of the structural approach to stochastic dynamical systems and we provide a measure of structural stability for finite populations. Overall, we show that the structural approach can provide reliable and tractable information about the qualitative behavior of many nonlinear dynamical systems.

Structural stability of nonlinear population dynamics

NASA Astrophysics Data System (ADS)

Cenci, Simone; Saavedra, Serguei

2018-01-01

In population dynamics, the concept of structural stability has been used to quantify the tolerance of a system to environmental perturbations. Yet, measuring the structural stability of nonlinear dynamical systems remains a challenging task. Focusing on the classic Lotka-Volterra dynamics, because of the linearity of the functional response, it has been possible to measure the conditions compatible with a structurally stable system. However, the functional response of biological communities is not always well approximated by deterministic linear functions. Thus, it is unclear the extent to which this linear approach can be generalized to other population dynamics models. Here, we show that the same approach used to investigate the classic Lotka-Volterra dynamics, which is called the structural approach, can be applied to a much larger class of nonlinear models. This class covers a large number of nonlinear functional responses that have been intensively investigated both theoretically and experimentally. We also investigate the applicability of the structural approach to stochastic dynamical systems and we provide a measure of structural stability for finite populations. Overall, we show that the structural approach can provide reliable and tractable information about the qualitative behavior of many nonlinear dynamical systems.

Joint nonlinearity effects in the design of a flexible truss structure control system

NASA Technical Reports Server (NTRS)

Mercadal, Mathieu

1986-01-01

Nonlinear effects are introduced in the dynamics of large space truss structures by the connecting joints which are designed with rather important tolerances to facilitate the assembly of the structures in space. The purpose was to develop means to investigate the nonlinear dynamics of the structures, particularly the limit cycles that might occur when active control is applied to the structures. An analytical method was sought and derived to predict the occurrence of limit cycles and to determine their stability. This method is mainly based on the quasi-linearization of every joint using describing functions. This approach was proven successful when simple dynamical systems were tested. Its applicability to larger systems depends on the amount of computations it requires, and estimates of the computational task tend to indicate that the number of individual sources of nonlinearity should be limited. Alternate analytical approaches, which do not account for every single nonlinearity, or the simulation of a simplified model of the dynamical system should, therefore, be investigated to determine a more effective way to predict limit cycles in large dynamical systems with an important number of distributed nonlinearities.

Time-varying nonlinear dynamics of a deploying piezoelectric laminated composite plate under aerodynamic force

NASA Astrophysics Data System (ADS)

Lu, S. F.; Zhang, W.; Song, X. J.

2017-09-01

Using Reddy's high-order shear theory for laminated plates and Hamilton's principle, a nonlinear partial differential equation for the dynamics of a deploying cantilevered piezoelectric laminated composite plate, under the combined action of aerodynamic load and piezoelectric excitation, is introduced. Two-degree of freedom (DOF) nonlinear dynamic models for the time-varying coefficients describing the transverse vibration of the deploying laminate under the combined actions of a first-order aerodynamic force and piezoelectric excitation were obtained by selecting a suitable time-dependent modal function satisfying the displacement boundary conditions and applying second-order discretization using the Galerkin method. Using a numerical method, the time history curves of the deploying laminate were obtained, and its nonlinear dynamic characteristics, including extension speed and different piezoelectric excitations, were studied. The results suggest that the piezoelectric excitation has a clear effect on the change of the nonlinear dynamic characteristics of such piezoelectric laminated composite plates. The nonlinear vibration of the deploying cantilevered laminate can be effectively suppressed by choosing a suitable voltage and polarity.

Analysis of Nonlinear Dynamics by Square Matrix Method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yu, Li Hua

The nonlinear dynamics of a system with periodic structure can be analyzed using a square matrix. In this paper, we show that because the special property of the square matrix constructed for nonlinear dynamics, we can reduce the dimension of the matrix from the original large number for high order calculation to low dimension in the first step of the analysis. Then a stable Jordan decomposition is obtained with much lower dimension. The transformation to Jordan form provides an excellent action-angle approximation to the solution of the nonlinear dynamics, in good agreement with trajectories and tune obtained from tracking. Andmore » more importantly, the deviation from constancy of the new action-angle variable provides a measure of the stability of the phase space trajectories and their tunes. Thus the square matrix provides a novel method to optimize the nonlinear dynamic system. The method is illustrated by many examples of comparison between theory and numerical simulation. Finally, in particular, we show that the square matrix method can be used for optimization to reduce the nonlinearity of a system.« less

Nonlinear dynamics of planetary gears using analytical and finite element models

NASA Astrophysics Data System (ADS)

Ambarisha, Vijaya Kumar; Parker, Robert G.

2007-05-01

Vibration-induced gear noise and dynamic loads remain key concerns in many transmission applications that use planetary gears. Tooth separations at large vibrations introduce nonlinearity in geared systems. The present work examines the complex, nonlinear dynamic behavior of spur planetary gears using two models: (i) a lumped-parameter model, and (ii) a finite element model. The two-dimensional (2D) lumped-parameter model represents the gears as lumped inertias, the gear meshes as nonlinear springs with tooth contact loss and periodically varying stiffness due to changing tooth contact conditions, and the supports as linear springs. The 2D finite element model is developed from a unique finite element-contact analysis solver specialized for gear dynamics. Mesh stiffness variation excitation, corner contact, and gear tooth contact loss are all intrinsically considered in the finite element analysis. The dynamics of planetary gears show a rich spectrum of nonlinear phenomena. Nonlinear jumps, chaotic motions, and period-doubling bifurcations occur when the mesh frequency or any of its higher harmonics are near a natural frequency of the system. Responses from the dynamic analysis using analytical and finite element models are successfully compared qualitatively and quantitatively. These comparisons validate the effectiveness of the lumped-parameter model to simulate the dynamics of planetary gears. Mesh phasing rules to suppress rotational and translational vibrations in planetary gears are valid even when nonlinearity from tooth contact loss occurs. These mesh phasing rules, however, are not valid in the chaotic and period-doubling regions.

Converting HAZUS capacity curves to seismic hazard-compatible building fragility functions: effect of hysteretic models

USGS Publications Warehouse

Ryu, Hyeuk; Luco, Nicolas; Baker, Jack W.; Karaca, Erdem

2008-01-01

A methodology was recently proposed for the development of hazard-compatible building fragility models using parameters of capacity curves and damage state thresholds from HAZUS (Karaca and Luco, 2008). In the methodology, HAZUS curvilinear capacity curves were used to define nonlinear dynamic SDOF models that were subjected to the nonlinear time history analysis instead of the capacity spectrum method. In this study, we construct a multilinear capacity curve with negative stiffness after an ultimate (capping) point for the nonlinear time history analysis, as an alternative to the curvilinear model provided in HAZUS. As an illustration, here we propose parameter values of the multilinear capacity curve for a moderate-code low-rise steel moment resisting frame building (labeled S1L in HAZUS). To determine the final parameter values, we perform nonlinear time history analyses of SDOF systems with various parameter values and investigate their effects on resulting fragility functions through sensitivity analysis. The findings improve capacity curves and thereby fragility and/or vulnerability models for generic types of structures.

Parallel processing for nonlinear dynamics simulations of structures including rotating bladed-disk assemblies

NASA Technical Reports Server (NTRS)

Hsieh, Shang-Hsien

1993-01-01

The principal objective of this research is to develop, test, and implement coarse-grained, parallel-processing strategies for nonlinear dynamic simulations of practical structural problems. There are contributions to four main areas: finite element modeling and analysis of rotational dynamics, numerical algorithms for parallel nonlinear solutions, automatic partitioning techniques to effect load-balancing among processors, and an integrated parallel analysis system.

Equivalent reduced model technique development for nonlinear system dynamic response

NASA Astrophysics Data System (ADS)

Thibault, Louis; Avitabile, Peter; Foley, Jason; Wolfson, Janet

2013-04-01

The dynamic response of structural systems commonly involves nonlinear effects. Often times, structural systems are made up of several components, whose individual behavior is essentially linear compared to the total assembled system. However, the assembly of linear components using highly nonlinear connection elements or contact regions causes the entire system to become nonlinear. Conventional transient nonlinear integration of the equations of motion can be extremely computationally intensive, especially when the finite element models describing the components are very large and detailed. In this work, the equivalent reduced model technique (ERMT) is developed to address complicated nonlinear contact problems. ERMT utilizes a highly accurate model reduction scheme, the System equivalent reduction expansion process (SEREP). Extremely reduced order models that provide dynamic characteristics of linear components, which are interconnected with highly nonlinear connection elements, are formulated with SEREP for the dynamic response evaluation using direct integration techniques. The full-space solution will be compared to the response obtained using drastically reduced models to make evident the usefulness of the technique for a variety of analytical cases.

A solar cycle dependence of nonlinearity in magnetospheric activity

NASA Astrophysics Data System (ADS)

Johnson, Jay R.; Wing, Simon

2005-04-01

The nonlinear dependencies inherent to the historical Kp data stream (1932-2003) are examined using mutual information and cumulant-based cost as discriminating statistics. The discriminating statistics are compared with surrogate data streams that are constructed using the corrected amplitude adjustment Fourier transform (CAAFT) method and capture the linear properties of the original Kp data. Differences are regularly seen in the discriminating statistics a few years prior to solar minima, while no differences are apparent at the time of solar maxima. These results suggest that the dynamics of the magnetosphere tend to be more linear at solar maximum than at solar minimum. The strong nonlinear dependencies tend to peak on a timescale around 40-50 hours and are statistically significant up to 1 week. Because the solar wind driver variables, VBs, and dynamical pressure exhibit a much shorter decorrelation time for nonlinearities, the results seem to indicate that the nonlinearity is related to internal magnetospheric dynamics. Moreover, the timescales for the nonlinearity seem to be on the same order as that for storm/ring current relaxation. We suggest that the strong solar wind driving that occurs around solar maximum dominates the magnetospheric dynamics, suppressing the internal magnetospheric nonlinearity. On the other hand, in the descending phase of the solar cycle just prior to solar minimum, when magnetospheric activity is weaker, the dynamics exhibit a significant nonlinear internal magnetospheric response that may be related to increased solar wind speed.

Approximated Stable Inversion for Nonlinear Systems with Nonhyperbolic Internal Dynamics. Revised

NASA Technical Reports Server (NTRS)

Devasia, Santosh

1999-01-01

A technique to achieve output tracking for nonminimum phase nonlinear systems with non- hyperbolic internal dynamics is presented. The present paper integrates stable inversion techniques (that achieve exact-tracking) with approximation techniques (that modify the internal dynamics) to circumvent the nonhyperbolicity of the internal dynamics - this nonhyperbolicity is an obstruction to applying presently available stable inversion techniques. The theory is developed for nonlinear systems and the method is applied to a two-cart with inverted-pendulum example.

Nonlinear optical oscillation dynamics in high-Q lithium niobate microresonators.

PubMed

Sun, Xuan; Liang, Hanxiao; Luo, Rui; Jiang, Wei C; Zhang, Xi-Cheng; Lin, Qiang

2017-06-12

Recent advance of lithium niobate microphotonic devices enables the exploration of intriguing nonlinear optical effects. We show complex nonlinear oscillation dynamics in high-Q lithium niobate microresonators that results from unique competition between the thermo-optic nonlinearity and the photorefractive effect, distinctive to other device systems and mechanisms ever reported. The observed phenomena are well described by our theory. This exploration helps understand the nonlinear optical behavior of high-Q lithium niobate microphotonic devices which would be crucial for future application of on-chip nonlinear lithium niobate photonics.

Instantaneous nonlinear assessment of complex cardiovascular dynamics by Laguerre-Volterra point process models.

PubMed

Valenza, Gaetano; Citi, Luca; Barbieri, Riccardo

2013-01-01

We report an exemplary study of instantaneous assessment of cardiovascular dynamics performed using point-process nonlinear models based on Laguerre expansion of the linear and nonlinear Wiener-Volterra kernels. As quantifiers, instantaneous measures such as high order spectral features and Lyapunov exponents can be estimated from a quadratic and cubic autoregressive formulation of the model first order moment, respectively. Here, these measures are evaluated on heartbeat series coming from 16 healthy subjects and 14 patients with Congestive Hearth Failure (CHF). Data were gathered from the on-line repository PhysioBank, which has been taken as landmark for testing nonlinear indices. Results show that the proposed nonlinear Laguerre-Volterra point-process methods are able to track the nonlinear and complex cardiovascular dynamics, distinguishing significantly between CHF and healthy heartbeat series.

Nonlinear Oscillators in Space Physics

NASA Technical Reports Server (NTRS)

Lester,Daniel; Thronson, Harley

2011-01-01

We discuss dynamical systems that produce an oscillation without an external time dependent source. Numerical results are presented for nonlinear oscillators in the Em1h's atmosphere, foremost the quasi-biennial oscillation (QBOl. These fluid dynamical oscillators, like the solar dynamo, have in common that one of the variables in a governing equation is strongly nonlinear and that the nonlinearity, to first order, has particular form. of 3rd or odd power. It is shown that this form of nonlinearity can produce the fundamental li'equency of the internal oscillation. which has a period that is favored by the dynamical condition of the fluid. The fundamental frequency maintains the oscillation, with no energy input to the system at that particular frequency. Nonlinearities of 2nd or even power could not maintain the oscillation.

Dynamic fluctuations in single-molecule biophysics experiments. Comment on "Extracting physics of life at the molecular level: A review of single-molecule data analyses" by W. Colomb and S.K. Sarkar

NASA Astrophysics Data System (ADS)

Krapf, Diego

2015-06-01

Single-molecule biophysics includes the study of isolated molecules and that of individual molecules within living cells. In both cases, dynamic fluctuations at the nanoscale play a critical role. Colomb and Sarkar emphasize how different noise sources affect the analysis of single molecule data [1]. Fluctuations in biomolecular systems arise from two very different mechanisms. On one hand thermal fluctuations are a predominant feature in the behavior of individual molecules. On the other hand, non-Gaussian fluctuations can arise from inter- and intramolecular interactions [2], spatial heterogeneities [3], non-Poisson external perturbations [4] and complex non-linear dynamics in general [5,6].

Power capability evaluation for lithium iron phosphate batteries based on multi-parameter constraints estimation

NASA Astrophysics Data System (ADS)

Wang, Yujie; Pan, Rui; Liu, Chang; Chen, Zonghai; Ling, Qiang

2018-01-01

The battery power capability is intimately correlated with the climbing, braking and accelerating performance of the electric vehicles. Accurate power capability prediction can not only guarantee the safety but also regulate driving behavior and optimize battery energy usage. However, the nonlinearity of the battery model is very complex especially for the lithium iron phosphate batteries. Besides, the hysteresis loop in the open-circuit voltage curve is easy to cause large error in model prediction. In this work, a multi-parameter constraints dynamic estimation method is proposed to predict the battery continuous period power capability. A high-fidelity battery model which considers the battery polarization and hysteresis phenomenon is presented to approximate the high nonlinearity of the lithium iron phosphate battery. Explicit analyses of power capability with multiple constraints are elaborated, specifically the state-of-energy is considered in power capability assessment. Furthermore, to solve the problem of nonlinear system state estimation, and suppress noise interference, the UKF based state observer is employed for power capability prediction. The performance of the proposed methodology is demonstrated by experiments under different dynamic characterization schedules. The charge and discharge power capabilities of the lithium iron phosphate batteries are quantitatively assessed under different time scales and temperatures.

Nanopore Current Oscillations: Nonlinear Dynamics on the Nanoscale.

PubMed

Hyland, Brittany; Siwy, Zuzanna S; Martens, Craig C

2015-05-21

In this Letter, we describe theoretical modeling of an experimentally realized nanoscale system that exhibits the general universal behavior of a nonlinear dynamical system. In particular, we consider the description of voltage-induced current fluctuations through a single nanopore from the perspective of nonlinear dynamics. We briefly review the experimental system and its behavior observed and then present a simple phenomenological nonlinear model that reproduces the qualitative behavior of the experimental data. The model consists of a two-dimensional deterministic nonlinear bistable oscillator experiencing both dissipation and random noise. The multidimensionality of the model and the interplay between deterministic and stochastic forces are both required to obtain a qualitatively accurate description of the physical system.

Elevated nonlinearity as an indicator of shifts in the dynamics of populations under stress.

PubMed

Dakos, Vasilis; Glaser, Sarah M; Hsieh, Chih-Hao; Sugihara, George

2017-03-01

Populations occasionally experience abrupt changes, such as local extinctions, strong declines in abundance or transitions from stable dynamics to strongly irregular fluctuations. Although most of these changes have important ecological and at times economic implications, they remain notoriously difficult to detect in advance. Here, we study changes in the stability of populations under stress across a variety of transitions. Using a Ricker-type model, we simulate shifts from stable point equilibrium dynamics to cyclic and irregular boom-bust oscillations as well as abrupt shifts between alternative attractors. Our aim is to infer the loss of population stability before such shifts based on changes in nonlinearity of population dynamics. We measure nonlinearity by comparing forecast performance between linear and nonlinear models fitted on reconstructed attractors directly from observed time series. We compare nonlinearity to other suggested leading indicators of instability (variance and autocorrelation). We find that nonlinearity and variance increase in a similar way prior to the shifts. By contrast, autocorrelation is strongly affected by oscillations. Finally, we test these theoretical patterns in datasets of fisheries populations. Our results suggest that elevated nonlinearity could be used as an additional indicator to infer changes in the dynamics of populations under stress. © 2017 The Author(s).

Dynamic modeling of moment wheel assemblies with nonlinear rolling bearing supports

NASA Astrophysics Data System (ADS)

Wang, Hong; Han, Qinkai; Luo, Ruizhi; Qing, Tao

2017-10-01

Moment wheel assemblies (MWA) have been widely used in spacecraft attitude control and large angle slewing maneuvers over the years. Understanding and controlling vibration of MWAs is a crucial factor to achieving the desired level of payload performance. Dynamic modeling of a MWA with nonlinear rolling bearing supports is conducted. An improved load distribution analysis is proposed to more accurately obtain the contact deformations and angles between the rolling balls and raceways. Then, the bearing restoring forces are then obtained through iteratively solving the load distribution equations at every time step. The effects of preload condition, surface waviness, Hertz contact and elastohydrodynamic lubrication could all be reflected in the nonlinear bearing forces. Considering the mass imbalances of the flywheel, flexibility of supporting structures and rolling bearing nonlinearity, the dynamic model of a typical MWA is established based upon the energy theorem. Dynamic tests are conducted to verify the nonlinear dynamic model. The influences of flywheel mass eccentricity and inner/outer waviness amplitudes on the dynamic responses are discussed in detail. The obtained results would be useful for the design and vibration control of the MWA system.

Use of the dynamic stiffness method to interpret experimental data from a nonlinear system

NASA Astrophysics Data System (ADS)

Tang, Bin; Brennan, M. J.; Gatti, G.

2018-05-01

The interpretation of experimental data from nonlinear structures is challenging, primarily because of dependency on types and levels of excitation, and coupling issues with test equipment. In this paper, the use of the dynamic stiffness method, which is commonly used in the analysis of linear systems, is used to interpret the data from a vibration test of a controllable compressed beam structure coupled to a test shaker. For a single mode of the system, this method facilitates the separation of mass, stiffness and damping effects, including nonlinear stiffness effects. It also allows the separation of the dynamics of the shaker from the structure under test. The approach needs to be used with care, and is only suitable if the nonlinear system has a response that is predominantly at the excitation frequency. For the structure under test, the raw experimental data revealed little about the underlying causes of the dynamic behaviour. However, the dynamic stiffness approach allowed the effects due to the nonlinear stiffness to be easily determined.

Nonlinear Dynamics of Silicon Nanowire Resonator Considering Nonlocal Effect.

PubMed

Jin, Leisheng; Li, Lijie

2017-12-01

In this work, nonlinear dynamics of silicon nanowire resonator considering nonlocal effect has been investigated. For the first time, dynamical parameters (e.g., resonant frequency, Duffing coefficient, and the damping ratio) that directly influence the nonlinear dynamics of the nanostructure have been derived. Subsequently, by calculating their response with the varied nonlocal coefficient, it is unveiled that the nonlocal effect makes more obvious impacts at the starting range (from zero to a small value), while the impact of nonlocal effect becomes weaker when the nonlocal term reaches to a certain threshold value. Furthermore, to characterize the role played by nonlocal effect in exerting influence on nonlinear behaviors such as bifurcation and chaos (typical phenomena in nonlinear dynamics of nanoscale devices), we have calculated the Lyapunov exponents and bifurcation diagram with and without nonlocal effect, and results shows the nonlocal effect causes the most significant effect as the device is at resonance. This work advances the development of nanowire resonators that are working beyond linear regime.

New Perspectives: Wave Mechanical Interpretations of Dark Matter, Baryon and Dark Energy

NASA Astrophysics Data System (ADS)

Russell, Esra

We model the cosmic components: dark matter, dark energy and baryon distributions in the Cosmic Web by means of highly nonlinear Schrodinger type and reaction diffusion type wave mechanical descriptions. The construction of these wave mechanical models of the structure formation is achieved by introducing the Fisher information measure and its comparison with highly nonlinear term which has dynamical analogy to infamous quantum potential in the wave equations. Strikingly, the comparison of this nonlinear term and the Fisher information measure provides a dynamical distinction between lack of self-organization and self-organization in the dynamical evolution of the cosmic components. Mathematically equivalent to the standard cosmic fluid equations, these approaches make it possible to follow the evolution of the matter distribution even into the highly nonlinear regime by circumventing singularities. Also, numerical realizations of the emerging web-like patterns are presented from the nonlinear dynamics of the baryon component while dark energy component shows Gaussian type dynamics corresponding to soliton-like solutions.

A nonlinear dynamics approach for incorporating wind-speed patterns into wind-power project evaluation.

PubMed

Huffaker, Ray; Bittelli, Marco

2015-01-01

Wind-energy production may be expanded beyond regions with high-average wind speeds (such as the Midwest U.S.A.) to sites with lower-average speeds (such as the Southeast U.S.A.) by locating favorable regional matches between natural wind-speed and energy-demand patterns. A critical component of wind-power evaluation is to incorporate wind-speed dynamics reflecting documented diurnal and seasonal behavioral patterns. Conventional probabilistic approaches remove patterns from wind-speed data. These patterns must be restored synthetically before they can be matched with energy-demand patterns. How to accurately restore wind-speed patterns is a vexing problem spurring an expanding line of papers. We propose a paradigm shift in wind power evaluation that employs signal-detection and nonlinear-dynamics techniques to empirically diagnose whether synthetic pattern restoration can be avoided altogether. If the complex behavior of observed wind-speed records is due to nonlinear, low-dimensional, and deterministic system dynamics, then nonlinear dynamics techniques can reconstruct wind-speed dynamics from observed wind-speed data without recourse to conventional probabilistic approaches. In the first study of its kind, we test a nonlinear dynamics approach in an application to Sugarland Wind-the first utility-scale wind project proposed in Florida, USA. We find empirical evidence of a low-dimensional and nonlinear wind-speed attractor characterized by strong temporal patterns that match up well with regular daily and seasonal electricity demand patterns.

Double symbolic joint entropy in nonlinear dynamic complexity analysis

NASA Astrophysics Data System (ADS)

Yao, Wenpo; Wang, Jun

2017-07-01

Symbolizations, the base of symbolic dynamic analysis, are classified as global static and local dynamic approaches which are combined by joint entropy in our works for nonlinear dynamic complexity analysis. Two global static methods, symbolic transformations of Wessel N. symbolic entropy and base-scale entropy, and two local ones, namely symbolizations of permutation and differential entropy, constitute four double symbolic joint entropies that have accurate complexity detections in chaotic models, logistic and Henon map series. In nonlinear dynamical analysis of different kinds of heart rate variability, heartbeats of healthy young have higher complexity than those of the healthy elderly, and congestive heart failure (CHF) patients are lowest in heartbeats' joint entropy values. Each individual symbolic entropy is improved by double symbolic joint entropy among which the combination of base-scale and differential symbolizations have best complexity analysis. Test results prove that double symbolic joint entropy is feasible in nonlinear dynamic complexity analysis.

Walking dynamics of the passive compass-gait model under OGY-based control: Emergence of bifurcations and chaos

NASA Astrophysics Data System (ADS)

Gritli, Hassène; Belghith, Safya

2017-06-01

An analysis of the passive dynamic walking of a compass-gait biped model under the OGY-based control approach using the impulsive hybrid nonlinear dynamics is presented in this paper. We describe our strategy for the development of a simplified analytical expression of a controlled hybrid Poincaré map and then for the design of a state-feedback control. Our control methodology is based mainly on the linearization of the impulsive hybrid nonlinear dynamics around a desired nominal one-periodic hybrid limit cycle. Our analysis of the controlled walking dynamics is achieved by means of bifurcation diagrams. Some interesting nonlinear phenomena are displayed, such as the period-doubling bifurcation, the cyclic-fold bifurcation, the period remerging, the period bubbling and chaos. A comparison between the raised phenomena in the impulsive hybrid nonlinear dynamics and the hybrid Poincaré map under control was also presented.

Extended Kalman Filter for Estimation of Parameters in Nonlinear State-Space Models of Biochemical Networks

PubMed Central

Sun, Xiaodian; Jin, Li; Xiong, Momiao

2008-01-01

It is system dynamics that determines the function of cells, tissues and organisms. To develop mathematical models and estimate their parameters are an essential issue for studying dynamic behaviors of biological systems which include metabolic networks, genetic regulatory networks and signal transduction pathways, under perturbation of external stimuli. In general, biological dynamic systems are partially observed. Therefore, a natural way to model dynamic biological systems is to employ nonlinear state-space equations. Although statistical methods for parameter estimation of linear models in biological dynamic systems have been developed intensively in the recent years, the estimation of both states and parameters of nonlinear dynamic systems remains a challenging task. In this report, we apply extended Kalman Filter (EKF) to the estimation of both states and parameters of nonlinear state-space models. To evaluate the performance of the EKF for parameter estimation, we apply the EKF to a simulation dataset and two real datasets: JAK-STAT signal transduction pathway and Ras/Raf/MEK/ERK signaling transduction pathways datasets. The preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinear state-space equations for modeling dynamic biochemical networks. PMID:19018286

Longtime dynamics of the PDE model for the motion toward light of bacterial colonies

NASA Astrophysics Data System (ADS)

Taranets, R.; Chugunova, M.

2018-03-01

We study stationary solutions and longtime dynamics of the PDE model for cyanobacteria motion, which was recently proposed by Chavy-Waddy and Kolokolnikov (2016 Nonlinearity 29 3174). For different values of the parameter α, which controls the extent of the aggregate, we analyse a family of corresponding steady states and their stability (considering symmetric and non-symmetric cases separately). We derive the rate of convergence toward steady states, show existence of weak nonnegative solutions, and we also discover that the value α = 3 is a special case for this PDE model. Using numerical simulations we compare different regimes and illustrate convergence toward steady states.

Small-Scale Tropopause Dynamics and TOMS Total Ozone

NASA Technical Reports Server (NTRS)

Stanford, John L.

2002-01-01

This project used Earth Probe Total Ozone Mapping Spectrometer (EP TOMS) along-track ozone retrievals, in conjunction with ancillary meteorological fields and modeling studies, for high resolution investigations of upper troposphere and lower stratosphere dynamics. Specifically, high resolution along-track (Level 2) EP TOMS data were used to investigate the beautiful fine-scale structure in constituent and meteorological fields prominent in the evolution of highly non-linear baroclinic storm systems. Comparison was made with high resolution meteorological models. The analyses provide internal consistency checks and validation of the EP TOMS data which are vital for monitoring ozone depletion in both polar and midlatitude regions.

Dynamic stability experiment of Maglev systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cai, Y.; Mulcahy, T.M.; Chen, S.S.

1995-04-01

This report summarizes the research performed on Maglev vehicle dynamic stability at Argonne National Laboratory during the past few years. It also documents magnetic-force data obtained from both measurements and calculations. Because dynamic instability is not acceptable for any commercial Maglev system, it is important to consider this phenomenon in the development of all Maglev systems. This report presents dynamic stability experiments on Maglev systems and compares their numerical simulation with predictions calculated by a nonlinear dynamic computer code. Instabilities of an electrodynamic system (EDS)-type vehicle model were obtained from both experimental observations and computer simulations for a five-degree-of-freedom Maglevmore » vehicle moving on a guideway consisting of double L-shaped aluminum segments attached to a rotating wheel. The experimental and theoretical analyses developed in this study identify basic stability characteristics and future research needs of Maglev systems.« less

Dynamic stability of repulsive-force maglev suspension systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cai, Y.; Rote, D.M.; Mulcahy, T.M.

1996-11-01

This report summarizes the research performed on maglev vehicle dynamic stability at Argonne National Laboratory during the past few years. It also documents both measured and calculated magnetic-force data. Because dynamic instability is not acceptable for any commercial maglev system, it is important to consider this phenomenon in the development of all maglev systems. This report presents dynamic stability experiments on maglev systems and compares the results with predictions calculated by a nonlinear-dynamics computer code. Instabilities of an electrodynamic-suspension system type vehicle model were obtained by experimental observation and computer simulation of a five-degree-of-freedom maglev vehicle moving on a guidewaymore » that consists of a pair of L-shaped aluminum conductors attached to a rotating wheel. The experimental and theoretical analyses developed in this study identify basic stability characteristics and future research needs of maglev systems.« less

The chaotic dynamical aperture

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, S.Y.; Tepikian, S.

1985-10-01

Nonlinear magnetic forces become more important for particles in the modern large accelerators. These nonlinear elements are introduced either intentionally to control beam dynamics or by uncontrollable random errors. Equations of motion in the nonlinear Hamiltonian are usually non-integrable. Because of the nonlinear part of the Hamiltonian, the tune diagram of accelerators is a jungle. Nonlinear magnet multipoles are important in keeping the accelerator operation point in the safe quarter of the hostile jungle of resonant tunes. Indeed, all the modern accelerator design have taken advantages of nonlinear mechanics. On the other hand, the effect of the uncontrollable random multipolesmore » should be evaluated carefully. A powerful method of studying the effect of these nonlinear multipoles is using a particle tracking calculation, where a group of test particles are tracing through these magnetic multipoles in the accelerator hundreds to millions of turns in order to test the dynamical aperture of the machine. These methods are extremely useful in the design of a large accelerator such as SSC, LEP, HERA and RHIC. These calculations unfortunately take tremendous amount of computing time. In this paper, we try to apply the existing method in the nonlinear dynamics to study the possible alternative solution. When the Hamiltonian motion becomes chaotic, the tune of the machine becomes undefined. The aperture related to the chaotic orbit can be identified as chaotic dynamical aperture. We review the method of determining chaotic orbit and apply the method to nonlinear problems in accelerator physics. We then discuss the scaling properties and effect of random sextupoles.« less

Nonlinear Analyses of Elicited Modal, Raised, and Pressed Rabbit Phonation

PubMed Central

Awan, Shaheen N.; Novaleski, Carolyn K.; Rousseau, Bernard

2014-01-01

Objectives/Hypothesis The purpose of this study was to use nonlinear dynamic analysis methods such as phase space portraits and correlation dimension (D2) as well as descriptive spectrographic analyses to characterize acoustic signals produced during evoked rabbit phonation. Methods Seventeen New Zealand white breeder rabbits were used to perform the study. A Grass S-88 stimulator (SA Instrumentation, Encinitas, CA) and constant current isolation unit (Grass Telefactor, model PSIU6; West Warwick, RI) were used to provide electrical stimulation to laryngeal musculature, and transglottal airflow rate and stimulation current (mA) were manipulated to elicit modal, raised intensity, and pressed phonations. Central 1 second portions of the most stable portion of the acoustic waveform for modal, raised intensity, and pressed phonations were edited, and then analyzed via phase space portraits, Poincaré sections, and the estimation of the correlation dimension (D2). In an attempt to limit the effects of the highly variable and nonstationary characteristics of some of the signals being analyzed, D2 analysis was also performed on the most stable central 200 ms portion of the acoustic waveform. Descriptive analysis of each phonation was also conducted using sound spectrograms. Results Results showed that the complexity of phonation and the subsequent acoustic waveform is increased as transglottal airflow rate and degree of glottal adduction is manipulated in the evoked rabbit phonation model. In particular, phonatory complexity, as quantified via correlation dimension analyses and demonstrated via spectrographic characteristics, increases from “modal” (i.e., phonation elicited at just above the phonation threshold pressure) to raised intensity (phonation elicited by increasing transglottal airflow rate) to pressed (phonation elicited by increasing the stimulation current delivered to the larynx). Variations in a single dynamic dimension (airflow rate or adductory force) resulted in significantly increased productions of nonlinear phenomenon, including bifurcations from periodicity to regions of subharmonic content, F0 and harmonic jumps, and evidence of periodicity within aperiodic regions (“chaos”). Conclusions The evoked rabbit phonation model described in this study allows for the elicitation of various types of phonations under controlled conditions and therefore, has the potential to provide insight regarding important variables that may elicit examples of nonlinear phenomena such as subharmonics and deterministic chaos. PMID:24836360

A Nonlinear Dynamic Model and Free Vibration Analysis of Deployable Mesh Reflectors

NASA Technical Reports Server (NTRS)

Shi, H.; Yang, B.; Thomson, M.; Fang, H.

2011-01-01

This paper presents a dynamic model of deployable mesh reflectors, in which geometric and material nonlinearities of such a space structure are fully described. Then, by linearization around an equilibrium configuration of the reflector structure, a linearized model is obtained. With this linearized model, the natural frequencies and mode shapes of a reflector can be computed. The nonlinear dynamic model of deployable mesh reflectors is verified by using commercial finite element software in numerical simulation. As shall be seen, the proposed nonlinear model is useful for shape (surface) control of deployable mesh reflectors under thermal loads.

Testing for nonlinear dependence in financial markets.

PubMed

Dore, Mohammed; Matilla-Garcia, Mariano; Marin, Manuel Ruiz

2011-07-01

This article addresses the question of improving the detection of nonlinear dependence by means of recently developed nonparametric tests. To this end a generalized version of BDS test and a new test based on symbolic dynamics are used on realizations from a well-known artificial market for which the dynamic equation governing the market is known. Comparisons with other tests for detecting nonlinearity are also provided. We show that the test based on symbolic dynamics outperforms other tests with the advantage that it depends only on one free parameter, namely the embedding dimension. This does not hold for other tests for nonlinearity.

Nonlinear dynamics under varying temperature conditions of the resonating beams of a differential resonant accelerometer

NASA Astrophysics Data System (ADS)

Zhang, Jing; Wang, Yagang; Zega, Valentina; Su, Yan; Corigliano, Alberto

2018-07-01

In this work the nonlinear dynamic behaviour under varying temperature conditions of the resonating beams of a differential resonant accelerometer is studied from the theoretical, numerical and experimental points of view. A complete analytical model based on the Hamilton’s principle is proposed to describe the nonlinear behaviour of the resonators under varying temperature conditions and numerical solutions are presented in comparison with experimental data. This provides a novel perspective to examine the relationship between temperature and nonlinearity, which helps predicting the dynamic behaviour of resonant devices and can guide their optimal design.

Nonlinear Dynamics and Strong Cavity Cooling of Levitated Nanoparticles.

PubMed

Fonseca, P Z G; Aranas, E B; Millen, J; Monteiro, T S; Barker, P F

2016-10-21

Optomechanical systems explore and exploit the coupling between light and the mechanical motion of macroscopic matter. A nonlinear coupling offers rich new physics, in both quantum and classical regimes. We investigate a dynamic, as opposed to the usually studied static, nonlinear optomechanical system, comprising a nanosphere levitated in a hybrid electro-optical trap. The cavity offers readout of both linear-in-position and quadratic-in-position (nonlinear) light-matter coupling, while simultaneously cooling the nanosphere, for indefinite periods of time and in high vacuum. We observe the cooling dynamics via both linear and nonlinear coupling. As the background gas pressure was lowered, we observed a greater than 1000-fold reduction in temperature before temperatures fell below readout sensitivity in the present setup. This Letter opens the way to strongly coupled quantum dynamics between a cavity and a nanoparticle largely decoupled from its environment.

Nonlinear Dynamics and Strong Cavity Cooling of Levitated Nanoparticles

NASA Astrophysics Data System (ADS)

Fonseca, P. Z. G.; Aranas, E. B.; Millen, J.; Monteiro, T. S.; Barker, P. F.

2016-10-01

Optomechanical systems explore and exploit the coupling between light and the mechanical motion of macroscopic matter. A nonlinear coupling offers rich new physics, in both quantum and classical regimes. We investigate a dynamic, as opposed to the usually studied static, nonlinear optomechanical system, comprising a nanosphere levitated in a hybrid electro-optical trap. The cavity offers readout of both linear-in-position and quadratic-in-position (nonlinear) light-matter coupling, while simultaneously cooling the nanosphere, for indefinite periods of time and in high vacuum. We observe the cooling dynamics via both linear and nonlinear coupling. As the background gas pressure was lowered, we observed a greater than 1000-fold reduction in temperature before temperatures fell below readout sensitivity in the present setup. This Letter opens the way to strongly coupled quantum dynamics between a cavity and a nanoparticle largely decoupled from its environment.

Nonlinear dynamics of cortical responses to color in the human cVEP.

PubMed

Nunez, Valerie; Shapley, Robert M; Gordon, James

2017-09-01

The main finding of this paper is that the human visual cortex responds in a very nonlinear manner to the color contrast of pure color patterns. We examined human cortical responses to color checkerboard patterns at many color contrasts, measuring the chromatic visual evoked potential (cVEP) with a dense electrode array. Cortical topography of the cVEPs showed that they were localized near the posterior electrode at position Oz, indicating that the primary cortex (V1) was the major source of responses. The choice of fine spatial patterns as stimuli caused the cVEP response to be driven by double-opponent neurons in V1. The cVEP waveform revealed nonlinear color signal processing in the V1 cortex. The cVEP time-to-peak decreased and the waveform's shape was markedly narrower with increasing cone contrast. Comparison of the linear dynamics of retinal and lateral geniculate nucleus responses with the nonlinear dynamics of the cortical cVEP indicated that the nonlinear dynamics originated in the V1 cortex. The nature of the nonlinearity is a kind of automatic gain control that adjusts cortical dynamics to be faster when color contrast is greater.

Advanced development of BEM for elastic and inelastic dynamic analysis of solids

NASA Technical Reports Server (NTRS)

Banerjee, P. K.; Ahmad, S.; Wang, H. C.

1989-01-01

Direct Boundary Element formulations and their numerical implementation for periodic and transient elastic as well as inelastic transient dynamic analyses of two-dimensional, axisymmetric and three-dimensional solids are presented. The inelastic formulation is based on an initial stress approach and is the first of its kind in the field of Boundary Element Methods. This formulation employs the Navier-Cauchy equation of motion, Graffi's dynamic reciprocal theorem, Stokes' fundamental solution, and the divergence theorem, together with kinematical and constitutive equations to obtain the pertinent integral equations of the problem in the time domain within the context of the small displacement theory of elastoplasticity. The dynamic (periodic, transient as well as nonlinear transient) formulations have been applied to a range of problems. The numerical formulations presented here are included in the BEST3D and GPBEST systems.

An extended harmonic balance method based on incremental nonlinear control parameters

NASA Astrophysics Data System (ADS)

Khodaparast, Hamed Haddad; Madinei, Hadi; Friswell, Michael I.; Adhikari, Sondipon; Coggon, Simon; Cooper, Jonathan E.

2017-02-01

A new formulation for calculating the steady-state responses of multiple-degree-of-freedom (MDOF) non-linear dynamic systems due to harmonic excitation is developed. This is aimed at solving multi-dimensional nonlinear systems using linear equations. Nonlinearity is parameterised by a set of 'non-linear control parameters' such that the dynamic system is effectively linear for zero values of these parameters and nonlinearity increases with increasing values of these parameters. Two sets of linear equations which are formed from a first-order truncated Taylor series expansion are developed. The first set of linear equations provides the summation of sensitivities of linear system responses with respect to non-linear control parameters and the second set are recursive equations that use the previous responses to update the sensitivities. The obtained sensitivities of steady-state responses are then used to calculate the steady state responses of non-linear dynamic systems in an iterative process. The application and verification of the method are illustrated using a non-linear Micro-Electro-Mechanical System (MEMS) subject to a base harmonic excitation. The non-linear control parameters in these examples are the DC voltages that are applied to the electrodes of the MEMS devices.

Fluctuating interaction network and time-varying stability of a natural fish community

NASA Astrophysics Data System (ADS)

Ushio, Masayuki; Hsieh, Chih-Hao; Masuda, Reiji; Deyle, Ethan R.; Ye, Hao; Chang, Chun-Wei; Sugihara, George; Kondoh, Michio

2018-02-01

Ecological theory suggests that large-scale patterns such as community stability can be influenced by changes in interspecific interactions that arise from the behavioural and/or physiological responses of individual species varying over time. Although this theory has experimental support, evidence from natural ecosystems is lacking owing to the challenges of tracking rapid changes in interspecific interactions (known to occur on timescales much shorter than a generation time) and then identifying the effect of such changes on large-scale community dynamics. Here, using tools for analysing nonlinear time series and a 12-year-long dataset of fortnightly collected observations on a natural marine fish community in Maizuru Bay, Japan, we show that short-term changes in interaction networks influence overall community dynamics. Among the 15 dominant species, we identify 14 interspecific interactions to construct a dynamic interaction network. We show that the strengths, and even types, of interactions change with time; we also develop a time-varying stability measure based on local Lyapunov stability for attractor dynamics in non-equilibrium nonlinear systems. We use this dynamic stability measure to examine the link between the time-varying interaction network and community stability. We find seasonal patterns in dynamic stability for this fish community that broadly support expectations of current ecological theory. Specifically, the dominance of weak interactions and higher species diversity during summer months are associated with higher dynamic stability and smaller population fluctuations. We suggest that interspecific interactions, community network structure and community stability are dynamic properties, and that linking fluctuating interaction networks to community-level dynamic properties is key to understanding the maintenance of ecological communities in nature.

A Solar Cycle Dependence of Nonlinearity in Magnetospheric Activity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Johnson, Jay R; Wing, Simon

2005-03-08

The nonlinear dependencies inherent to the historical K(sub)p data stream (1932-2003) are examined using mutual information and cumulant based cost as discriminating statistics. The discriminating statistics are compared with surrogate data streams that are constructed using the corrected amplitude adjustment Fourier transform (CAAFT) method and capture the linear properties of the original K(sub)p data. Differences are regularly seen in the discriminating statistics a few years prior to solar minima, while no differences are apparent at the time of solar maximum. These results suggest that the dynamics of the magnetosphere tend to be more linear at solar maximum than at solarmore » minimum. The strong nonlinear dependencies tend to peak on a timescale around 40-50 hours and are statistically significant up to one week. Because the solar wind driver variables, VB(sub)s and dynamical pressure exhibit a much shorter decorrelation time for nonlinearities, the results seem to indicate that the nonlinearity is related to internal magnetospheric dynamics. Moreover, the timescales for the nonlinearity seem to be on the same order as that for storm/ring current relaxation. We suggest that the strong solar wind driving that occurs around solar maximum dominates the magnetospheric dynamics suppressing the internal magnetospheric nonlinearity. On the other hand, in the descending phase of the solar cycle just prior to solar minimum, when magnetospheric activity is weaker, the dynamics exhibit a significant nonlinear internal magnetospheric response that may be related to increased solar wind speed.« less

Nonlinear dynamics and quantum entanglement in optomechanical systems.

PubMed

Wang, Guanglei; Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso

2014-03-21

To search for and exploit quantum manifestations of classical nonlinear dynamics is one of the most fundamental problems in physics. Using optomechanical systems as a paradigm, we address this problem from the perspective of quantum entanglement. We uncover strong fingerprints in the quantum entanglement of two common types of classical nonlinear dynamical behaviors: periodic oscillations and quasiperiodic motion. There is a transition from the former to the latter as an experimentally adjustable parameter is changed through a critical value. Accompanying this process, except for a small region about the critical value, the degree of quantum entanglement shows a trend of continuous increase. The time evolution of the entanglement measure, e.g., logarithmic negativity, exhibits a strong dependence on the nature of classical nonlinear dynamics, constituting its signature.

Characterising non-linear dynamics in nocturnal breathing patterns of healthy infants using recurrence quantification analysis.

PubMed

Terrill, Philip I; Wilson, Stephen J; Suresh, Sadasivam; Cooper, David M; Dakin, Carolyn

2013-05-01

Breathing dynamics vary between infant sleep states, and are likely to exhibit non-linear behaviour. This study applied the non-linear analytical tool recurrence quantification analysis (RQA) to 400 breath interval periods of REM and N-REM sleep, and then using an overlapping moving window. The RQA variables were different between sleep states, with REM radius 150% greater than N-REM radius, and REM laminarity 79% greater than N-REM laminarity. RQA allowed the observation of temporal variations in non-linear breathing dynamics across a night's sleep at 30s resolution, and provides a basis for quantifying changes in complex breathing dynamics with physiology and pathology. Copyright © 2013 Elsevier Ltd. All rights reserved.

Parameter and Structure Inference for Nonlinear Dynamical Systems

NASA Technical Reports Server (NTRS)

Morris, Robin D.; Smelyanskiy, Vadim N.; Millonas, Mark

2006-01-01

A great many systems can be modeled in the non-linear dynamical systems framework, as x = f(x) + xi(t), where f() is the potential function for the system, and xi is the excitation noise. Modeling the potential using a set of basis functions, we derive the posterior for the basis coefficients. A more challenging problem is to determine the set of basis functions that are required to model a particular system. We show that using the Bayesian Information Criteria (BIC) to rank models, and the beam search technique, that we can accurately determine the structure of simple non-linear dynamical system models, and the structure of the coupling between non-linear dynamical systems where the individual systems are known. This last case has important ecological applications.

Nonlinear laser dynamics induced by frequency shifted optical feedback: application to vibration measurements.

PubMed

Girardeau, Vadim; Goloni, Carolina; Jacquin, Olivier; Hugon, Olivier; Inglebert, Mehdi; Lacot, Eric

2016-12-01

In this article, we study the nonlinear dynamics of a laser subjected to frequency shifted optical reinjection coming back from a vibrating target. More specifically, we study the nonlinear dynamical coupling between the carrier and the vibration signal. The present work shows how the nonlinear amplification of the vibration spectrum is related to the strength of the carrier and how it must be compensated to obtain accurate (i.e., without bias) vibration measurements. The theoretical predictions, confirmed by numerical simulations, are in good agreement with the experimental data. The main motivation of this study is the understanding of the nonlinear response of a laser optical feedback imaging sensor for quantitative phase measurements of small vibrations in the case of strong optical feedback.

Dynamics of a movable micromirror in a nonlinear optical cavity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kumar, Tarun; ManMohan; Bhattacherjee, Aranya B.

We consider the dynamics of a movable mirror (cantilever) of a nonlinear optical cavity. We show that a chi{sup (3)} medium with a strong Kerr nonlinearity placed inside a cavity inhibits the normal mode splitting (NMS) due to the photon blockade mechanism. This study demonstrates that the displacement spectrum of the micromirror could be used as a tool to detect the photon blockade effect. Moreover the ability to control the photon number fluctuation by tuning the Kerr nonlinearity emerges as a new handle to coherently control the dynamics of the micromirror, which further could be useful in the realization ofmore » tuneable quantum-mechanical devices. We also found that the temperature of the micromechanical mirror increases with increasing Kerr nonlinearity.« less

Coupling nonlinear optical waves to photoreactive and phase-separating soft matter: Current status and perspectives

NASA Astrophysics Data System (ADS)

Biria, Saeid; Morim, Derek R.; An Tsao, Fu; Saravanamuttu, Kalaichelvi; Hosein, Ian D.

2017-10-01

Nonlinear optics and polymer systems are distinct fields that have been studied for decades. These two fields intersect with the observation of nonlinear wave propagation in photoreactive polymer systems. This has led to studies on the nonlinear dynamics of transmitted light in polymer media, particularly for optical self-trapping and optical modulation instability. The irreversibility of polymerization leads to permanent capture of nonlinear optical patterns in the polymer structure, which is a new synthetic route to complex structured soft materials. Over time more intricate polymer systems are employed, whereby nonlinear optical dynamics can couple to nonlinear chemical dynamics, opening opportunities for self-organization. This paper discusses the work to date on nonlinear optical pattern formation processes in polymers. A brief overview of nonlinear optical phenomenon is provided to set the stage for understanding their effects. We review the accomplishments of the field on studying nonlinear waveform propagation in photopolymerizable systems, then discuss our most recent progress in coupling nonlinear optical pattern formation to polymer blends and phase separation. To this end, perspectives on future directions and areas of sustained inquiry are provided. This review highlights the significant opportunity in exploiting nonlinear optical pattern formation in soft matter for the discovery of new light-directed and light-stimulated materials phenomenon, and in turn, soft matter provides a platform by which new nonlinear optical phenomenon may be discovered.

Transient and chaotic low-energy transfers in a system with bistable nonlinearity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Romeo, F., E-mail: francesco.romeo@uniroma1.it; Manevitch, L. I.; Bergman, L. A.

2015-05-15

The low-energy dynamics of a two-dof system composed of a grounded linear oscillator coupled to a lightweight mass by means of a spring with both cubic nonlinear and negative linear components is investigated. The mechanisms leading to intense energy exchanges between the linear oscillator, excited by a low-energy impulse, and the nonlinear attachment are addressed. For lightly damped systems, it is shown that two main mechanisms arise: Aperiodic alternating in-well and cross-well oscillations of the nonlinear attachment, and secondary nonlinear beats occurring once the dynamics evolves solely in-well. The description of the former dissipative phenomenon is provided in a two-dimensionalmore » projection of the phase space, where transitions between in-well and cross-well oscillations are associated with sequences of crossings across a pseudo-separatrix. Whereas the second mechanism is described in terms of secondary limiting phase trajectories of the nonlinear attachment under certain resonance conditions. The analytical treatment of the two aformentioned low-energy transfer mechanisms relies on the reduction of the nonlinear dynamics and consequent analysis of the reduced dynamics by asymptotic techniques. Direct numerical simulations fully validate our analytical predictions.« less

Voice characteristics before versus after mandibular setback surgery in patients with mandibular prognathism using nonlinear dynamics and conventional acoustic analyses.

PubMed

Mishima, Katsuaki; Moritani, Norifumi; Nakano, Hiroyuki; Matsushita, Asuka; Iida, Seiji; Ueyama, Yoshiya

2013-12-01

The purpose of this study was to explore the voice characteristics of patients with mandibular prognathism, and to investigate the effects of mandibular setback surgery on these characteristics using nonlinear dynamics and conventional acoustic analyses. Sixteen patients (8 males and 8 females) who had skeletal 3, class III malocclusion without cleft palate, and who underwent a bilateral sagittal split ramus osteotomy (BSSRO), were enrolled. As controls, 50 healthy adults (25 males and 25 females) were enrolled. The mean first LEs (mLE1) computed for each one-second interval, and the fundamental frequency (F0) and frequencies of the first and second formant (F1, F2) were calculated for each Japanese vowel. The mLE1s for /u/ in males, and /o/ in females and the F2s for /i/ and /u/ in males, changed significantly after BSSRO. Class III voice characteristics were observed in the mLE1s for /i/ in both males and females, in the F0 for /a/, /i/, /u/ and /o/ in females, and in the F1 and F2 for /a/ in males, and the F1 for /u/ and the F2 for /i/ in females. Most of these characteristics were preserved after BSSRO. Copyright © 2013 European Association for Cranio-Maxillo-Facial Surgery. Published by Elsevier Ltd. All rights reserved.

Nonreciprocity in the dynamics of coupled oscillators with nonlinearity, asymmetry, and scale hierarchy

NASA Astrophysics Data System (ADS)

Moore, Keegan J.; Bunyan, Jonathan; Tawfick, Sameh; Gendelman, Oleg V.; Li, Shuangbao; Leamy, Michael; Vakakis, Alexander F.

2018-01-01

In linear time-invariant dynamical and acoustical systems, reciprocity holds by the Onsager-Casimir principle of microscopic reversibility, and this can be broken only by odd external biases, nonlinearities, or time-dependent properties. A concept is proposed in this work for breaking dynamic reciprocity based on irreversible nonlinear energy transfers from large to small scales in a system with nonlinear hierarchical internal structure, asymmetry, and intentional strong stiffness nonlinearity. The resulting nonreciprocal large-to-small scale energy transfers mimic analogous nonlinear energy transfer cascades that occur in nature (e.g., in turbulent flows), and are caused by the strong frequency-energy dependence of the essentially nonlinear small-scale components of the system considered. The theoretical part of this work is mainly based on action-angle transformations, followed by direct numerical simulations of the resulting system of nonlinear coupled oscillators. The experimental part considers a system with two scales—a linear large-scale oscillator coupled to a small scale by a nonlinear spring—and validates the theoretical findings demonstrating nonreciprocal large-to-small scale energy transfer. The proposed study promotes a paradigm for designing nonreciprocal acoustic materials harnessing strong nonlinearity, which in a future application will be implemented in designing lattices incorporating nonlinear hierarchical internal structures, asymmetry, and scale mixing.

Energy-momentum conserving higher-order time integration of nonlinear dynamics of finite elastic fiber-reinforced continua

NASA Astrophysics Data System (ADS)

Erler, Norbert; Groß, Michael

2015-05-01

Since many years the relevance of fibre-reinforced polymers is steadily increasing in fields of engineering, especially in aircraft and automotive industry. Due to the high strength in fibre direction, but the possibility of lightweight construction, these composites replace more and more traditional materials as metals. Fibre-reinforced polymers are often manufactured from glass or carbon fibres as attachment parts or from steel or nylon cord as force transmission parts. Attachment parts are mostly subjected to small strains, but force transmission parts usually suffer large deformations in at least one direction. Here, a geometrically nonlinear formulation is necessary. Typical examples are helicopter rotor blades, where the fibres have the function to stabilize the structure in order to counteract large centrifugal forces. For long-run analyses of rotor blade deformations, we have to apply numerically stable time integrators for anisotropic materials. This paper presents higher-order accurate and numerically stable time stepping schemes for nonlinear elastic fibre-reinforced continua with anisotropic stress behaviour.

Enhancing Security of Double Random Phase Encoding Based on Random S-Box

NASA Astrophysics Data System (ADS)

Girija, R.; Singh, Hukum

2018-06-01

In this paper, we propose a novel asymmetric cryptosystem for double random phase encoding (DRPE) using random S-Box. While utilising S-Box separately is not reliable and DRPE does not support non-linearity, so, our system unites the effectiveness of S-Box with an asymmetric system of DRPE (through Fourier transform). The uniqueness of proposed cryptosystem lies on employing high sensitivity dynamic S-Box for our DRPE system. The randomness and scalability achieved due to applied technique is an additional feature of the proposed solution. The firmness of random S-Box is investigated in terms of performance parameters such as non-linearity, strict avalanche criterion, bit independence criterion, linear and differential approximation probabilities etc. S-Boxes convey nonlinearity to cryptosystems which is a significant parameter and very essential for DRPE. The strength of proposed cryptosystem has been analysed using various parameters such as MSE, PSNR, correlation coefficient analysis, noise analysis, SVD analysis, etc. Experimental results are conferred in detail to exhibit proposed cryptosystem is highly secure.

Nonlinear dynamics as an engine of computation.

PubMed

Kia, Behnam; Lindner, John F; Ditto, William L

2017-03-06

Control of chaos teaches that control theory can tame the complex, random-like behaviour of chaotic systems. This alliance between control methods and physics-cybernetical physics-opens the door to many applications, including dynamics-based computing. In this article, we introduce nonlinear dynamics and its rich, sometimes chaotic behaviour as an engine of computation. We review our work that has demonstrated how to compute using nonlinear dynamics. Furthermore, we investigate the interrelationship between invariant measures of a dynamical system and its computing power to strengthen the bridge between physics and computation.This article is part of the themed issue 'Horizons of cybernetical physics'. © 2017 The Author(s).

Nonlinear dynamics as an engine of computation

PubMed Central

Lindner, John F.; Ditto, William L.

2017-01-01

Control of chaos teaches that control theory can tame the complex, random-like behaviour of chaotic systems. This alliance between control methods and physics—cybernetical physics—opens the door to many applications, including dynamics-based computing. In this article, we introduce nonlinear dynamics and its rich, sometimes chaotic behaviour as an engine of computation. We review our work that has demonstrated how to compute using nonlinear dynamics. Furthermore, we investigate the interrelationship between invariant measures of a dynamical system and its computing power to strengthen the bridge between physics and computation. This article is part of the themed issue ‘Horizons of cybernetical physics’. PMID:28115619

Dynamic properties of combustion instability in a lean premixed gas-turbine combustor.

PubMed

Gotoda, Hiroshi; Nikimoto, Hiroyuki; Miyano, Takaya; Tachibana, Shigeru

2011-03-01

We experimentally investigate the dynamic behavior of the combustion instability in a lean premixed gas-turbine combustor from the viewpoint of nonlinear dynamics. A nonlinear time series analysis in combination with a surrogate data method clearly reveals that as the equivalence ratio increases, the dynamic behavior of the combustion instability undergoes a significant transition from stochastic fluctuation to periodic oscillation through low-dimensional chaotic oscillation. We also show that a nonlinear forecasting method is useful for predicting the short-term dynamic behavior of the combustion instability in a lean premixed gas-turbine combustor, which has not been addressed in the fields of combustion science and physics.

Nonlinear analysis of pupillary dynamics.

PubMed

Onorati, Francesco; Mainardi, Luca Tommaso; Sirca, Fabiola; Russo, Vincenzo; Barbieri, Riccardo

2016-02-01

Pupil size reflects autonomic response to different environmental and behavioral stimuli, and its dynamics have been linked to other autonomic correlates such as cardiac and respiratory rhythms. The aim of this study is to assess the nonlinear characteristics of pupil size of 25 normal subjects who participated in a psychophysiological experimental protocol with four experimental conditions, namely “baseline”, “anger”, “joy”, and “sadness”. Nonlinear measures, such as sample entropy, correlation dimension, and largest Lyapunov exponent, were computed on reconstructed signals of spontaneous fluctuations of pupil dilation. Nonparametric statistical tests were performed on surrogate data to verify that the nonlinear measures are an intrinsic characteristic of the signals. We then developed and applied a piecewise linear regression model to detrended fluctuation analysis (DFA). Two joinpoints and three scaling intervals were identified: slope α0, at slow time scales, represents a persistent nonstationary long-range correlation, whereas α1 and α2, at middle and fast time scales, respectively, represent long-range power-law correlations, similarly to DFA applied to heart rate variability signals. Of the computed complexity measures, α0 showed statistically significant differences among experimental conditions (p<0.001). Our results suggest that (a) pupil size at constant light condition is characterized by nonlinear dynamics, (b) three well-defined and distinct long-memory processes exist at different time scales, and (c) autonomic stimulation is partially reflected in nonlinear dynamics. (c) autonomic stimulation is partially reflected in nonlinear dynamics.

Method and system for training dynamic nonlinear adaptive filters which have embedded memory

NASA Technical Reports Server (NTRS)

Rabinowitz, Matthew (Inventor)

2002-01-01

Described herein is a method and system for training nonlinear adaptive filters (or neural networks) which have embedded memory. Such memory can arise in a multi-layer finite impulse response (FIR) architecture, or an infinite impulse response (IIR) architecture. We focus on filter architectures with separate linear dynamic components and static nonlinear components. Such filters can be structured so as to restrict their degrees of computational freedom based on a priori knowledge about the dynamic operation to be emulated. The method is detailed for an FIR architecture which consists of linear FIR filters together with nonlinear generalized single layer subnets. For the IIR case, we extend the methodology to a general nonlinear architecture which uses feedback. For these dynamic architectures, we describe how one can apply optimization techniques which make updates closer to the Newton direction than those of a steepest descent method, such as backpropagation. We detail a novel adaptive modified Gauss-Newton optimization technique, which uses an adaptive learning rate to determine both the magnitude and direction of update steps. For a wide range of adaptive filtering applications, the new training algorithm converges faster and to a smaller value of cost than both steepest-descent methods such as backpropagation-through-time, and standard quasi-Newton methods. We apply the algorithm to modeling the inverse of a nonlinear dynamic tracking system 5, as well as a nonlinear amplifier 6.

Reduced-order modelling of parameter-dependent, linear and nonlinear dynamic partial differential equation models.

PubMed

Shah, A A; Xing, W W; Triantafyllidis, V

2017-04-01

In this paper, we develop reduced-order models for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space. The accuracy of the method is demonstrated on a linear and a nonlinear example, with comparisons with a global basis approach.

Reduced-order modelling of parameter-dependent, linear and nonlinear dynamic partial differential equation models

PubMed Central

Xing, W. W.; Triantafyllidis, V.

2017-01-01

In this paper, we develop reduced-order models for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space. The accuracy of the method is demonstrated on a linear and a nonlinear example, with comparisons with a global basis approach. PMID:28484327

A Nonlinear Dynamics Approach for Incorporating Wind-Speed Patterns into Wind-Power Project Evaluation

PubMed Central

Huffaker, Ray; Bittelli, Marco

2015-01-01

Wind-energy production may be expanded beyond regions with high-average wind speeds (such as the Midwest U.S.A.) to sites with lower-average speeds (such as the Southeast U.S.A.) by locating favorable regional matches between natural wind-speed and energy-demand patterns. A critical component of wind-power evaluation is to incorporate wind-speed dynamics reflecting documented diurnal and seasonal behavioral patterns. Conventional probabilistic approaches remove patterns from wind-speed data. These patterns must be restored synthetically before they can be matched with energy-demand patterns. How to accurately restore wind-speed patterns is a vexing problem spurring an expanding line of papers. We propose a paradigm shift in wind power evaluation that employs signal-detection and nonlinear-dynamics techniques to empirically diagnose whether synthetic pattern restoration can be avoided altogether. If the complex behavior of observed wind-speed records is due to nonlinear, low-dimensional, and deterministic system dynamics, then nonlinear dynamics techniques can reconstruct wind-speed dynamics from observed wind-speed data without recourse to conventional probabilistic approaches. In the first study of its kind, we test a nonlinear dynamics approach in an application to Sugarland Wind—the first utility-scale wind project proposed in Florida, USA. We find empirical evidence of a low-dimensional and nonlinear wind-speed attractor characterized by strong temporal patterns that match up well with regular daily and seasonal electricity demand patterns. PMID:25617767

An Analytical Dynamics Approach to the Control of Mechanical Systems

NASA Astrophysics Data System (ADS)

Mylapilli, Harshavardhan

A new and novel approach to the control of nonlinear mechanical systems is presented in this study. The approach is inspired by recent results in analytical dynamics that deal with the theory of constrained motion. The control requirements on the dynamical system are viewed from an analytical dynamics perspective and the theory of constrained motion is used to recast these control requirements as constraints on the dynamical system. Explicit closed form expressions for the generalized nonlinear control forces are obtained by using the fundamental equation of mechanics. The control so obtained is optimal at each instant of time and causes the constraints to be exactly satisfied. No linearizations and/or approximations of the nonlinear dynamical system are made, and no a priori structure is imposed on the nature of nonlinear controller. Three examples dealing with highly nonlinear complex dynamical systems that are chosen from diverse areas of discrete and continuum mechanics are presented to demonstrate the control approach. The first example deals with the energy control of underactuated inhomogeneous nonlinear lattices (or chains), the second example deals with the synchronization of the motion of multiple coupled slave gyros with that of a master gyro, and the final example deals with the control of incompressible hyperelastic rubber-like thin cantilever beams. Numerical simulations accompanying these examples show the ease, simplicity and the efficacy with which the control methodology can be applied and the accuracy with which the desired control objectives can be met.

Nonlinear Dynamic Models in Advanced Life Support

NASA Technical Reports Server (NTRS)

Jones, Harry

2002-01-01

To facilitate analysis, ALS systems are often assumed to be linear and time invariant, but they usually have important nonlinear and dynamic aspects. Nonlinear dynamic behavior can be caused by time varying inputs, changes in system parameters, nonlinear system functions, closed loop feedback delays, and limits on buffer storage or processing rates. Dynamic models are usually cataloged according to the number of state variables. The simplest dynamic models are linear, using only integration, multiplication, addition, and subtraction of the state variables. A general linear model with only two state variables can produce all the possible dynamic behavior of linear systems with many state variables, including stability, oscillation, or exponential growth and decay. Linear systems can be described using mathematical analysis. Nonlinear dynamics can be fully explored only by computer simulations of models. Unexpected behavior is produced by simple models having only two or three state variables with simple mathematical relations between them. Closed loop feedback delays are a major source of system instability. Exceeding limits on buffer storage or processing rates forces systems to change operating mode. Different equilibrium points may be reached from different initial conditions. Instead of one stable equilibrium point, the system may have several equilibrium points, oscillate at different frequencies, or even behave chaotically, depending on the system inputs and initial conditions. The frequency spectrum of an output oscillation may contain harmonics and the sums and differences of input frequencies, but it may also contain a stable limit cycle oscillation not related to input frequencies. We must investigate the nonlinear dynamic aspects of advanced life support systems to understand and counter undesirable behavior.

Global Optimal Trajectory in Chaos and NP-Hardness

NASA Astrophysics Data System (ADS)

Latorre, Vittorio; Gao, David Yang

This paper presents an unconventional theory and method for solving general nonlinear dynamical systems. Instead of the direct iterative methods, the discretized nonlinear system is first formulated as a global optimization problem via the least squares method. A newly developed canonical duality theory shows that this nonconvex minimization problem can be solved deterministically in polynomial time if a global optimality condition is satisfied. The so-called pseudo-chaos produced by linear iterative methods are mainly due to the intrinsic numerical error accumulations. Otherwise, the global optimization problem could be NP-hard and the nonlinear system can be really chaotic. A conjecture is proposed, which reveals the connection between chaos in nonlinear dynamics and NP-hardness in computer science. The methodology and the conjecture are verified by applications to the well-known logistic equation, a forced memristive circuit and the Lorenz system. Computational results show that the canonical duality theory can be used to identify chaotic systems and to obtain realistic global optimal solutions in nonlinear dynamical systems. The method and results presented in this paper should bring some new insights into nonlinear dynamical systems and NP-hardness in computational complexity theory.

Volterra representation enables modeling of complex synaptic nonlinear dynamics in large-scale simulations.

PubMed

Hu, Eric Y; Bouteiller, Jean-Marie C; Song, Dong; Baudry, Michel; Berger, Theodore W

2015-01-01

Chemical synapses are comprised of a wide collection of intricate signaling pathways involving complex dynamics. These mechanisms are often reduced to simple spikes or exponential representations in order to enable computer simulations at higher spatial levels of complexity. However, these representations cannot capture important nonlinear dynamics found in synaptic transmission. Here, we propose an input-output (IO) synapse model capable of generating complex nonlinear dynamics while maintaining low computational complexity. This IO synapse model is an extension of a detailed mechanistic glutamatergic synapse model capable of capturing the input-output relationships of the mechanistic model using the Volterra functional power series. We demonstrate that the IO synapse model is able to successfully track the nonlinear dynamics of the synapse up to the third order with high accuracy. We also evaluate the accuracy of the IO synapse model at different input frequencies and compared its performance with that of kinetic models in compartmental neuron models. Our results demonstrate that the IO synapse model is capable of efficiently replicating complex nonlinear dynamics that were represented in the original mechanistic model and provide a method to replicate complex and diverse synaptic transmission within neuron network simulations.

Volterra representation enables modeling of complex synaptic nonlinear dynamics in large-scale simulations

PubMed Central

Hu, Eric Y.; Bouteiller, Jean-Marie C.; Song, Dong; Baudry, Michel; Berger, Theodore W.

2015-01-01

Chemical synapses are comprised of a wide collection of intricate signaling pathways involving complex dynamics. These mechanisms are often reduced to simple spikes or exponential representations in order to enable computer simulations at higher spatial levels of complexity. However, these representations cannot capture important nonlinear dynamics found in synaptic transmission. Here, we propose an input-output (IO) synapse model capable of generating complex nonlinear dynamics while maintaining low computational complexity. This IO synapse model is an extension of a detailed mechanistic glutamatergic synapse model capable of capturing the input-output relationships of the mechanistic model using the Volterra functional power series. We demonstrate that the IO synapse model is able to successfully track the nonlinear dynamics of the synapse up to the third order with high accuracy. We also evaluate the accuracy of the IO synapse model at different input frequencies and compared its performance with that of kinetic models in compartmental neuron models. Our results demonstrate that the IO synapse model is capable of efficiently replicating complex nonlinear dynamics that were represented in the original mechanistic model and provide a method to replicate complex and diverse synaptic transmission within neuron network simulations. PMID:26441622

A Nonlinear Modal Aeroelastic Solver for FUN3D

NASA Technical Reports Server (NTRS)

Goldman, Benjamin D.; Bartels, Robert E.; Biedron, Robert T.; Scott, Robert C.

2016-01-01

A nonlinear structural solver has been implemented internally within the NASA FUN3D computational fluid dynamics code, allowing for some new aeroelastic capabilities. Using a modal representation of the structure, a set of differential or differential-algebraic equations are derived for general thin structures with geometric nonlinearities. ODEPACK and LAPACK routines are linked with FUN3D, and the nonlinear equations are solved at each CFD time step. The existing predictor-corrector method is retained, whereby the structural solution is updated after mesh deformation. The nonlinear solver is validated using a test case for a flexible aeroshell at transonic, supersonic, and hypersonic flow conditions. Agreement with linear theory is seen for the static aeroelastic solutions at relatively low dynamic pressures, but structural nonlinearities limit deformation amplitudes at high dynamic pressures. No flutter was found at any of the tested trajectory points, though LCO may be possible in the transonic regime.

Employment of CB models for non-linear dynamic analysis

NASA Technical Reports Server (NTRS)

Klein, M. R. M.; Deloo, P.; Fournier-Sicre, A.

1990-01-01

The non-linear dynamic analysis of large structures is always very time, effort and CPU consuming. Whenever possible the reduction of the size of the mathematical model involved is of main importance to speed up the computational procedures. Such reduction can be performed for the part of the structure which perform linearly. Most of the time, the classical Guyan reduction process is used. For non-linear dynamic process where the non-linearity is present at interfaces between different structures, Craig-Bampton models can provide a very rich information, and allow easy selection of the relevant modes with respect to the phenomenon driving the non-linearity. The paper presents the employment of Craig-Bampton models combined with Newmark direct integration for solving non-linear friction problems appearing at the interface between the Hubble Space Telescope and its solar arrays during in-orbit maneuvers. Theory, implementation in the FEM code ASKA, and practical results are shown.

NASA/FAA general aviation crash dynamics program

NASA Technical Reports Server (NTRS)

Thomson, R. G.; Hayduk, R. J.; Carden, H. D.

1981-01-01

The program involves controlled full scale crash testing, nonlinear structural analyses to predict large deflection elastoplastic response, and load attenuating concepts for use in improved seat and subfloor structure. Both analytical and experimental methods are used to develop expertise in these areas. Analyses include simplified procedures for estimating energy dissipating capabilities and comprehensive computerized procedures for predicting airframe response. These analyses are developed to provide designers with methods for predicting accelerations, loads, and displacements on collapsing structure. Tests on typical full scale aircraft and on full and subscale structural components are performed to verify the analyses and to demonstrate load attenuating concepts. A special apparatus was built to test emergency locator transmitters when attached to representative aircraft structure. The apparatus is shown to provide a good simulation of the longitudinal crash pulse observed in full scale aircraft crash tests.

The dynamics of a stabilised Wien bridge oscillator

NASA Astrophysics Data System (ADS)

Lerner, L.

2016-11-01

We present for the first time analytic solutions for the nonlinear dynamics of a Wien bridge oscillator stabilised by three common methods: an incandescent lamp, signal diodes, and the field effect transistor. The results can be used to optimise oscillator design, and agree well with measurements. The effect of operational amplifier marginal nonlinearity on oscillator performance at high frequencies is clarified. The oscillator circuits and their analysis can be used to demonstrate nonlinear dynamics in the undergraduate laboratory.

A comparative analysis of alternative approaches for quantifying nonlinear dynamics in cardiovascular system.

PubMed

Chen, Yun; Yang, Hui

2013-01-01

Heart rate variability (HRV) analysis has emerged as an important research topic to evaluate autonomic cardiac function. However, traditional time and frequency-domain analysis characterizes and quantify only linear and stationary phenomena. In the present investigation, we made a comparative analysis of three alternative approaches (i.e., wavelet multifractal analysis, Lyapunov exponents and multiscale entropy analysis) for quantifying nonlinear dynamics in heart rate time series. Note that these extracted nonlinear features provide information about nonlinear scaling behaviors and the complexity of cardiac systems. To evaluate the performance, we used 24-hour HRV recordings from 54 healthy subjects and 29 heart failure patients, available in PhysioNet. Three nonlinear methods are evaluated not only individually but also in combination using three classification algorithms, i.e., linear discriminate analysis, quadratic discriminate analysis and k-nearest neighbors. Experimental results show that three nonlinear methods capture nonlinear dynamics from different perspectives and the combined feature set achieves the best performance, i.e., sensitivity 97.7% and specificity 91.5%. Collectively, nonlinear HRV features are shown to have the promise to identify the disorders in autonomic cardiovascular function.

A comprehensive study of the delay vector variance method for quantification of nonlinearity in dynamical systems

PubMed Central

Mandic, D. P.; Ryan, K.; Basu, B.; Pakrashi, V.

2016-01-01

Although vibration monitoring is a popular method to monitor and assess dynamic structures, quantification of linearity or nonlinearity of the dynamic responses remains a challenging problem. We investigate the delay vector variance (DVV) method in this regard in a comprehensive manner to establish the degree to which a change in signal nonlinearity can be related to system nonlinearity and how a change in system parameters affects the nonlinearity in the dynamic response of the system. A wide range of theoretical situations are considered in this regard using a single degree of freedom (SDOF) system to obtain numerical benchmarks. A number of experiments are then carried out using a physical SDOF model in the laboratory. Finally, a composite wind turbine blade is tested for different excitations and the dynamic responses are measured at a number of points to extend the investigation to continuum structures. The dynamic responses were measured using accelerometers, strain gauges and a Laser Doppler vibrometer. This comprehensive study creates a numerical and experimental benchmark for structurally dynamical systems where output-only information is typically available, especially in the context of DVV. The study also allows for comparative analysis between different systems driven by the similar input. PMID:26909175

Research in nonlinear structural and solid mechanics

NASA Technical Reports Server (NTRS)

Mccomb, H. G., Jr. (Compiler); Noor, A. K. (Compiler)

1980-01-01

Nonlinear analysis of building structures and numerical solution of nonlinear algebraic equations and Newton's method are discussed. Other topics include: nonlinear interaction problems; solution procedures for nonlinear problems; crash dynamics and advanced nonlinear applications; material characterization, contact problems, and inelastic response; and formulation aspects and special software for nonlinear analysis.

Noise Response Data Reveal Novel Controllability Gramian for Nonlinear Network Dynamics

PubMed Central

Kashima, Kenji

2016-01-01

Control of nonlinear large-scale dynamical networks, e.g., collective behavior of agents interacting via a scale-free connection topology, is a central problem in many scientific and engineering fields. For the linear version of this problem, the so-called controllability Gramian has played an important role to quantify how effectively the dynamical states are reachable by a suitable driving input. In this paper, we first extend the notion of the controllability Gramian to nonlinear dynamics in terms of the Gibbs distribution. Next, we show that, when the networks are open to environmental noise, the newly defined Gramian is equal to the covariance matrix associated with randomly excited, but uncontrolled, dynamical state trajectories. This fact theoretically justifies a simple Monte Carlo simulation that can extract effectively controllable subdynamics in nonlinear complex networks. In addition, the result provides a novel insight into the relationship between controllability and statistical mechanics. PMID:27264780

Modeling nonlinear dynamic properties of dielectric elastomers with various crosslinks, entanglements, and finite deformations

NASA Astrophysics Data System (ADS)

Zhang, Junshi; Chen, Hualing; Li, Dichen

2018-02-01

Subject to an AC voltage, dielectric elastomers (DEs) behave as a nonlinear vibration, implying potential applications as soft dynamical actuators and robots. In this article, by utilizing the Lagrange's equation, a theoretical model is deduced to investigate the dynamic performances of DEs by considering three internal properties, including crosslinks, entanglements, and finite deformations of polymer chains. Numerical calculations are employed to describe the dynamic response, stability, periodicity, and resonance properties of DEs. It is observed that the frequency and nonlinearity of dynamic response are tuned by the internal properties of DEs. Phase paths and Poincaré maps are utilized to detect the stability and periodicity of the nonlinear vibrations of DEs, which demonstrate that transitions between aperiodic and quasi-periodic vibrations may occur when the three internal properties vary. The resonance of DEs involving the three internal properties of polymer chains is also investigated.

Dynamics of chromatic visual system processing differ in complexity between children and adults.

PubMed

Boon, Mei Ying; Suttle, Catherine M; Henry, Bruce I; Dain, Stephen J

2009-06-30

Measures of chromatic contrast sensitivity in children are lower than those of adults. This may be related to immaturities in signal processing at or near threshold. We have found that children's VEPs in response to low contrast supra-threshold chromatic stimuli are more intra-individually variable than those recorded from adults. Here, we report on linear and nonlinear analyses of chromatic VEPs recorded from children and adults. Two measures of signal-to-noise ratio are similar between the adults and children, suggesting that relatively high noise is unlikely to account for the poor clarity of negative and positive peak components in the children's VEPs. Nonlinear analysis indicates higher complexity of adults' than children's chromatic VEPs, at levels of chromatic contrast around and well above threshold.

Non-linear dynamic analysis of geared systems, part 2

NASA Technical Reports Server (NTRS)

Singh, Rajendra; Houser, Donald R.; Kahraman, Ahmet

1990-01-01

A good understanding of the steady state dynamic behavior of a geared system is required in order to design reliable and quiet transmissions. This study focuses on a system containing a spur gear pair with backlash and periodically time-varying mesh stiffness, and rolling element bearings with clearance type non-linearities. A dynamic finite element model of the linear time-invariant (LTI) system is developed. Effects of several system parameters, such as torsional and transverse flexibilities of the shafts and prime mover/load inertias, on free and force vibration characteristics are investigated. Several reduced order LTI models are developed and validated by comparing their eigen solution with the finite element model results. Several key system parameters such as mean load and damping ratio are identified and their effects on the non-linear frequency response are evaluated quantitatively. Other fundamental issues such as the dynamic coupling between non-linear modes, dynamic interactions between component non-linearities and time-varying mesh stiffness, and the existence of subharmonic and chaotic solutions including routes to chaos have also been examined in depth.

Development of an Integrated Nonlinear Aeroservoelastic Flight Dynamic Model of the NASA Generic Transport Model

NASA Technical Reports Server (NTRS)

Nguyen, Nhan; Ting, Eric

2018-01-01

This paper describes a recent development of an integrated fully coupled aeroservoelastic flight dynamic model of the NASA Generic Transport Model (GTM). The integrated model couples nonlinear flight dynamics to a nonlinear aeroelastic model of the GTM. The nonlinearity includes the coupling of the rigid-body aircraft states in the partial derivatives of the aeroelastic angle of attack. Aeroservoelastic modeling of the control surfaces which are modeled by the Variable Camber Continuous Trailing Edge Flap is also conducted. The R.T. Jones' method is implemented to approximate unsteady aerodynamics. Simulations of the GTM are conducted with simulated continuous and discrete gust loads..

An introduction to chaos theory in CFD

NASA Technical Reports Server (NTRS)

Pulliam, Thomas H.

1990-01-01

The popular subject 'chaos theory' has captured the imagination of a wide variety of scientists and engineers. CFD has always been faced with nonlinear systems and it is natural to assume that nonlinear dynamics will play a role at sometime in such work. This paper will attempt to introduce some of the concepts and analysis procedures associated with nonlinear dynamics theory. In particular, results from computations of an airfoil at high angle of attack which exhibits a sequence of bifurcations for single frequency unsteady shedding through period doublings cascading into low dimensional chaos are used to present and demonstrate various aspects of nonlinear dynamics in CFD.

A Practice-Oriented Bifurcation Analysis for Pulse Energy Converters: A Stability Margin

NASA Astrophysics Data System (ADS)

Kolokolov, Yury; Monovskaya, Anna

The popularity of systems of pulse energy conversion (PEC-systems) for practical applications is due to the heightened efficiency of energy conversion processes with comparatively simple realizations. Nevertheless, a PEC-system represents a nonlinear object with a variable structure, and the bifurcation analysis remains the basic tool to describe PEC dynamics evolution. The paper is devoted to the discussion on whether the scientific viewpoint on the natural nonlinear dynamics evolution can be involved in practical applications. We focus on the problems connected with stability boundaries of an operating regime. The results of both small-signal analysis and computational bifurcation analysis are considered in the parametrical space in comparison with the results of the experimental identification of the zonal heterogeneity of the operating process. This allows to propose an adapted stability margin as a sufficiently safe distance before the point after which the operating process begins to lose the stability. Such stability margin can extend the permissible operating domain in the parametrical space at the expense of using cause-and-effect relations in the context of natural regularities of nonlinear dynamics. Reasoning and discussion are based on the experimental and computational results for a synchronous buck converter with a pulse-width modulation. The presented results can be useful, first of all, for PEC-systems with significant variation of equivalent inductance and/or capacity. We believe that the discussion supports a viewpoint by which the contemporary methods of the computational and experimental bifurcation analyses possess both analytical abilities and experimental techniques for promising solutions which could be practice-oriented for PEC-systems.

Fuzzy model-based servo and model following control for nonlinear systems.

PubMed

Ohtake, Hiroshi; Tanaka, Kazuo; Wang, Hua O

2009-12-01

This correspondence presents servo and nonlinear model following controls for a class of nonlinear systems using the Takagi-Sugeno fuzzy model-based control approach. First, the construction method of the augmented fuzzy system for continuous-time nonlinear systems is proposed by differentiating the original nonlinear system. Second, the dynamic fuzzy servo controller and the dynamic fuzzy model following controller, which can make outputs of the nonlinear system converge to target points and to outputs of the reference system, respectively, are introduced. Finally, the servo and model following controller design conditions are given in terms of linear matrix inequalities. Design examples illustrate the utility of this approach.

An Update on Binary Formation by Rotational Fission

NASA Astrophysics Data System (ADS)

Tohline, Joel E.; Durisen, Richard H.

During the 1980s, numerical simulations showed that dynamic growth of a barlike mode in initially axisymmetric, equilibrium protostars does not lead to prompt binary formation, i. e., fission. Instead, such evolutions usually produce a dynamically stable, spinning barlike configuration. In recent years, this result has been confirmed by numerous groups using a variety of different hydrodynamical tools, and stability analyses have convincingly shown that fission does not occur in such systems because gravitational torques cause nonlinear saturation of the mode amplitude. Other possible routes to fission have been much less well scrutinized because they rely upon a detailed understanding of the structure and stability of initially nonaxisymmetric structures and/or evolutions that are driven by secular, rather than dynamic processes. Efforts are underway to examine these other fission scenarios.

A nonlinear model for top fuel dragster dynamic performance assessment

NASA Astrophysics Data System (ADS)

Spanos, P. D.; Castillo, D. H.; Kougioumtzoglou, I. A.; Tapia, R. A.

2012-02-01

The top fuel dragster is the fastest and quickest vehicle in drag racing. This vehicle is capable of travelling a quarter mile in less than 4.5 s, reaching a final speed in excess of 330 miles per hour. The average power delivered by its engine exceeds 7000 Hp. To analyse and eventually increase the performance of a top fuel dragster, a dynamic model of the vehicle is developed. Longitudinal, vertical, and pitching chassis motions are considered, as well as drive-train dynamics. The aerodynamics of the vehicle, the engine characteristics, and the force due to the combustion gases are incorporated into the model. Further, a simplified model of the traction characteristics of the rear tyres is developed where the traction is calculated as a function of the slip ratio and the velocity. The resulting nonlinear, coupled differential equations of motion are solved using a fourth-order Runge-Kutta numerical integration scheme. Several simulation runs are made to investigate the effects of the aerodynamics and of the engine's initial torque in the performance of the vehicle. The results of the computational simulations are scrutinised by comparisons with data from actual dragster races. Ultimately, the proposed dynamic model of the dragster can be used to improve the aerodynamics, the engine and clutch set-ups of the vehicle, and possibly facilitate the redesign of the dragster.

Bounded tracking for nonminimum phase nonlinear systems with fast zero dynamics

DOT National Transportation Integrated Search

1996-12-01

A PostScript file. In this paper, tracking control laws for nonminimum phase nonlinear systems with both fast and slow, possibly unstable, zero dynamics are derived. The fast zero dynamics arise from a perturbation of a nominal system. These fast zer...

Nonlinear identification of the total baroreflex arc: chronic hypertension model.

PubMed

Moslehpour, Mohsen; Kawada, Toru; Sunagawa, Kenji; Sugimachi, Masaru; Mukkamala, Ramakrishna

2016-05-01

The total baroreflex arc is the open-loop system relating carotid sinus pressure (CSP) to arterial pressure (AP). Its linear dynamic functioning has been shown to be preserved in spontaneously hypertensive rats (SHR). However, the system is known to exhibit nonlinear dynamic behaviors. The aim of this study was to establish nonlinear dynamic models of the total arc (and its subsystems) in hypertensive rats and to compare these models with previously published models for normotensive rats. Hypertensive rats were studied under anesthesia. The vagal and aortic depressor nerves were sectioned. The carotid sinus regions were isolated and attached to a servo-controlled piston pump. AP and sympathetic nerve activity were measured while CSP was controlled via the pump using Gaussian white noise stimulation. Second-order, nonlinear dynamics models were developed by application of nonparametric system identification to a portion of the measurements. The models of the total arc predicted AP 21-43% better (P < 0.005) than conventional linear dynamic models in response to a new portion of the CSP measurement. The linear and nonlinear terms of these validated models were compared with the corresponding terms of an analogous model for normotensive rats. The nonlinear gains for the hypertensive rats were significantly larger than those for the normotensive rats [-0.38 ± 0.04 (unitless) vs. -0.22 ± 0.03, P < 0.01], whereas the linear gains were similar. Hence, nonlinear dynamic functioning of the sympathetically mediated total arc may enhance baroreflex buffering of AP increases more in SHR than normotensive rats. Copyright © 2016 the American Physiological Society.

Application of dynamical systems theory to nonlinear aircraft dynamics

NASA Technical Reports Server (NTRS)

Culick, Fred E. C.; Jahnke, Craig C.

1988-01-01

Dynamical systems theory has been used to study nonlinear aircraft dynamics. A six degree of freedom model that neglects gravity has been analyzed. The aerodynamic model, supplied by NASA, is for a generic swept wing fighter and includes nonlinearities as functions of the angle of attack. A continuation method was used to calculate the steady states of the aircraft, and bifurcations of these steady states, as functions of the control deflections. Bifurcations were used to predict jump phenomena and the onset of periodic motion for roll coupling instabilities and high angle of attack maneuvers. The predictions were verified with numerical simulations.

Analysis of dynamic channel power equalization by using nonlinear amplifying Sagnac interferometer for ASK-WDM optical transmission

NASA Astrophysics Data System (ADS)

Qu, Feng; Liu, Xiaoming; Zhao, Jianhui

2004-05-01

A power equalization using an asymmetric nonlinear amplifying Sagnac interferometer (NASI) for ASK modulation is studied numerically. A nonreciprocal phase bias was proposed to be introduced into the structure. The nonreciprocal phase bias reduces not only the demanding for amplifier power or fiber non-linearity, but also increase the dynamic input power range. The power equalization is demonstrated for RZ modulation by nonlinear phase analysis and eye diagram simulation.

Chaotic Dynamics and Application of LCR Oscillators Sharing Common Nonlinearity

NASA Astrophysics Data System (ADS)

Jeevarekha, A.; Paul Asir, M.; Philominathan, P.

2016-06-01

This paper addresses the problem of sharing common nonlinearity among nonautonomous and autonomous oscillators. By choosing a suitable common nonlinear element with the driving point characteristics capable of bringing out chaotic motion in a combined system, we obtain identical chaotic states. The dynamics of the coupled system is explored through numerical and experimental studies. Employing the concept of common nonlinearity, a simple chaotic communication system is modeled and its performance is verified through Multisim simulation.

Evaluation of nonlinear properties of epileptic activity using largest Lyapunov exponent

NASA Astrophysics Data System (ADS)

Medvedeva, Tatiana M.; Lüttjohann, Annika; van Luijtelaar, Gilles; Sysoev, Ilya V.

2016-04-01

Absence seizures are known to be highly non-linear large amplitude oscillations with a well pronounced main time scale. Whilst the appearance of the main frequency is usually considered as a transition from noisy complex dynamics of baseline EEG to more regular absence activity, the dynamical properties of this type of epileptiformic activity in genetic absence models was not studied precisely. Here, the estimation of the largest Lyapunov exponent from intracranial EEGs of 10 WAG/Rij rats (genetic model of absence epilepsy) was performed. Fragments of 10 seizures and 10 episodes of on-going EEG each of 4 s length were used for each animal, 3 cortical and 2 thalamic channels were analysed. The method adapted for short noisy data was implemented. The positive values of the largest Lyapunov exponent were found as for baseline as for spike wave discharges (SWDs), with values for SWDs being significantly less than for on-going activity. Current findings may indicate that SWD is a chaotic process with a well pronounced main timescale rather than a periodic regime. Also, the absence activity was shown to be less chaotic than the baseline one.

An Estimation of a Nonlinear Dynamic Process Using Latent Class Extended Mixed Models: Affect Profiles After Terrorist Attacks.

PubMed

Burro, Roberto; Raccanello, Daniela; Pasini, Margherita; Brondino, Margherita

2018-01-01

Conceptualizing affect as a complex nonlinear dynamic process, we used latent class extended mixed models (LCMM) to understand whether there were unobserved groupings in a dataset including longitudinal measures. Our aim was to identify affect profiles over time in people vicariously exposed to terrorism, studying their relations with personality traits. The participants were 193 university students who completed online measures of affect during the seven days following two terrorist attacks (Paris, November 13, 2015; Brussels, March 22, 2016); Big Five personality traits; and antecedents of affect. After selecting students whose negative affect was influenced by the two attacks (33%), we analysed the data with the LCMM package of R. We identified two affect profiles, characterized by different trends over time: The first profile comprised students with lower positive affect and higher negative affect compared to the second profile. Concerning personality traits, conscientious-ness was lower for the first profile compared to the second profile, and vice versa for neuroticism. Findings are discussed for both their theoretical and applied relevance.

Quasilinear models through the lens of resolvent analysis

NASA Astrophysics Data System (ADS)

McKeon, Beverley; Chini, Greg

2017-11-01

Quasilinear (QL) and generalized quasilinear (GQL) analyses, e.g. Marston et al., also variously described as statistical state dynamics models, e.g., Farrell et al., restricted nonlinear models, e.g. Thomas et al., or 2D/3C models, e.g. Gayme et al., have achieved considerable success in recovering the mean velocity profile for a range of turbulent flows. In QL approaches, the portion of the velocity field that can be represented as streamwise constant, i.e. with streamwise wavenumber kx = 0 , is fully resolved, while the streamwise-varying dynamics are linearized about the streamwise-constant field; that is, only those nonlinear interactions that drive the streamwise-constant field are retained, and the non-streamwise constant ``fluctuation-fluctuation'' interactions are ignored. Here, we show how these QL approaches can be reformulated in terms of the closed-loop resolvent analysis of McKeon & Sharma (2010), which enables us to identify reasons for their evident success as well as algorithms for their efficient computation. The support of ONR through Grant No. N00014-17-2307 is gratefully acknowledged.

Investigating parameters participating in the infant respiratory control system attractor.

PubMed

Terrill, Philip I; Wilson, Stephen J; Suresh, Sadasivam; Cooper, David M; Dakin, Carolyn

2008-01-01

Theoretically, any participating parameter in a non-linear system represents the dynamics of the whole system. Taken's time delay embedding theory provides the fundamental basis for allowing non-linear analysis to be performed on physiological, time-series data. In practice, only one measurable parameter is required to be measured to convey an accurate representation of the system dynamics. In this paper, the infant respiratory control system is represented using three variables-a digitally sampled respiratory inductive plethysmography waveform, and the derived parameters tidal volume and inter-breath interval time series data. For 14 healthy infants, these data streams were analysed using recurrence plot analysis across one night of sleep. The measured attractor size of these variables followed the same qualitative trends across the nights study. Results suggest that the attractor size measures of the derived IBI and tidal volume are representative surrogates for the raw respiratory waveform. The extent to which the relative attractor sizes of IBI and tidal volume remain constant through changing sleep state could potentially be used to quantify pathology, or maturation of breathing control.

A geometrically exact formulation for three-dimensional numerical simulation of the umbilical cable in a deep-sea ROV system

NASA Astrophysics Data System (ADS)

Quan, Wei-cai; Zhang, Zhu-ying; Zhang, Ai-qun; Zhang, Qi-feng; Tian, Yu

2015-04-01

This paper proposes a geometrically exact formulation for three-dimensional static and dynamic analyses of the umbilical cable in a deep-sea remotely operated vehicle (ROV) system. The presented formulation takes account of the geometric nonlinearities of large displacement, effects of axial load and bending stiffness for modeling of slack cables. The resulting nonlinear second-order governing equations are discretized spatially by the finite element method and solved temporally by the generalized- α implicit time integration algorithm, which is adapted to the case of varying coefficient matrices. The ability to consider three-dimensional union action of ocean current and ship heave motion upon the umbilical cable is the key feature of this analysis. The presented formulation is firstly validated, and then three numerical examples for the umbilical cable in a deep-sea ROV system are demonstrated and discussed, including the steady configurations only under the action of depth-dependent ocean current, the dynamic responses in the case of the only ship heave motion, and in the case of the combined action of the ship heave motion and ocean current.

Application of non-linear dynamics to the characterization of cardiac electrical instability

NASA Technical Reports Server (NTRS)

Kaplan, D. T.; Cohen, R. J.

1987-01-01

Beat-to-beat alternation in the morphology of the ECG has been previously observed in hearts susceptible to fibrillation. In addition, fibrillation has been characterized by some as a chaotic state. Period doubling phenomena, such as alternation, and the onset of chaos have been connected by non-linear dynamical systems theory. In this paper, we describe the use of a technique from nonlinear dynamics theory, the construction of a first return nap, to assess the susceptibility to fibrillation threshhold in canine experiments.

An Unscented Kalman Filter Approach to the Estimation of Nonlinear Dynamical Systems Models

ERIC Educational Resources Information Center

Chow, Sy-Miin; Ferrer, Emilio; Nesselroade, John R.

2007-01-01

In the past several decades, methodologies used to estimate nonlinear relationships among latent variables have been developed almost exclusively to fit cross-sectional models. We present a relatively new estimation approach, the unscented Kalman filter (UKF), and illustrate its potential as a tool for fitting nonlinear dynamic models in two ways:…

Recent advances in nonlinear passive vibration isolators

NASA Astrophysics Data System (ADS)

Ibrahim, R. A.

2008-07-01

The theory of nonlinear vibration isolation has witnessed significant developments due to pressing demands for the protection of structural installations, nuclear reactors, mechanical components, and sensitive instruments from earthquake ground motion, shocks, and impact loads. In view of these demands, engineers and physicists have developed different types of nonlinear vibration isolators. This article presents a comprehensive assessment of recent developments of nonlinear isolators in the absence of active control means. It does not deal with other means of linear or nonlinear vibration absorbers. It begins with the basic concept and features of nonlinear isolators and inherent nonlinear phenomena. Specific types of nonlinear isolators are then discussed, including ultra-low-frequency isolators. For vertical vibration isolation, the treatment of the Euler spring isolator is based on the post-buckling dynamic characteristics of the column elastica and axial stiffness. Exact and approximate analyses of axial stiffness of the post-buckled Euler beam are outlined. Different techniques of reducing the resonant frequency of the isolator are described. Another group is based on the Gospodnetic-Frisch-Fay beam, which is free to slide on two supports. The restoring force of this beam resembles to a great extent the restoring roll moment of biased ships. The base isolation of buildings, bridges, and liquid storage tanks subjected to earthquake ground motion is then described. Base isolation utilizes friction elements, laminated-rubber bearings, and the friction pendulum. Nonlinear viscoelastic and composite material springs, and smart material elements are described in terms of material mechanical characteristics and the dependence of their transmissibility on temperature and excitation amplitude. The article is closed by conclusions, which highlight resolved and unresolved problems and recommendations for future research directions.

Electro-mechanical vibration analysis of functionally graded piezoelectric porous plates in the translation state

NASA Astrophysics Data System (ADS)

Wang, Yan Qing

2018-02-01

To provide reference for aerospace structural design, electro-mechanical vibrations of functionally graded piezoelectric material (FGPM) plates carrying porosities in the translation state are investigated. A modified power law formulation is employed to depict the material properties of the plates in the thickness direction. Three terms of inertial forces are taken into account due to the translation of plates. The geometrical nonlinearity is considered by adopting the von Kármán non-linear relations. Using the d'Alembert's principle, the nonlinear governing equation of the out-of-plane motion of the plates is derived. The equation is further discretized to a system of ordinary differential equations using the Galerkin method, which are subsequently solved via the harmonic balance method. Then, the approximate analytical results are validated by utilizing the adaptive step-size fourth-order Runge-Kutta technique. Additionally, the stability of the steady state responses is examined by means of the perturbation technique. Linear and nonlinear vibration analyses are both carried out and results display some interesting dynamic phenomenon for translational porous FGPM plates. Parametric study shows that the vibration characteristics of the present inhomogeneous structure depend on several key physical parameters.

Laser pulse self-compression in an active fibre with a finite gain bandwidth under conditions of a nonstationary nonlinear response

NASA Astrophysics Data System (ADS)

Balakin, A. A.; Litvak, A. G.; Mironov, V. A.; Skobelev, S. A.

2018-04-01

We study the influence of a nonstationary nonlinear response of a medium on self-compression of soliton-like laser pulses in active fibres with a finite gain bandwidth. Based on the variational approach, we qualitatively analyse the self-action of the wave packet in the system under consideration in order to classify the main evolution regimes and to determine the minimum achievable laser pulse duration during self-compression. The existence of stable soliton-type structures is shown in the framework of the parabolic approximation of the gain profile (in the approximation of the Gnizburg – Landau equation). An analysis of the self-action of laser pulses in the framework of the nonlinear Schrödinger equation with a sign-constant gain profile demonstrate a qualitative change in the dynamics of the wave field in the case of a nonsta­tionary nonlinear response that shifts the laser pulse spectrum from the amplification region and stops the pulse compression. Expressions for a minimum duration of a soliton-like laser pulse are obtained as a function of the problem parameters, which are in good agreement with the results of numerical simulation.

The Swift-Hohenberg equation with a nonlocal nonlinearity

NASA Astrophysics Data System (ADS)

Morgan, David; Dawes, Jonathan H. P.

2014-03-01

It is well known that aspects of the formation of localised states in a one-dimensional Swift-Hohenberg equation can be described by Ginzburg-Landau-type envelope equations. This paper extends these multiple scales analyses to cases where an additional nonlinear integral term, in the form of a convolution, is present. The presence of a kernel function introduces a new lengthscale into the problem, and this results in additional complexity in both the derivation of envelope equations and in the bifurcation structure. When the kernel is short-range, weakly nonlinear analysis results in envelope equations of standard type but whose coefficients are modified in complicated ways by the nonlinear nonlocal term. Nevertheless, these computations can be formulated quite generally in terms of properties of the Fourier transform of the kernel function. When the lengthscale associated with the kernel is longer, our method leads naturally to the derivation of two different, novel, envelope equations that describe aspects of the dynamics in these new regimes. The first of these contains additional bifurcations, and unexpected loops in the bifurcation diagram. The second of these captures the stretched-out nature of the homoclinic snaking curves that arises due to the nonlocal term.

Nonlinear Structural Analysis Methodology and Dynamics Scaling of Inflatable Parabolic Reflector Antenna Concepts

NASA Technical Reports Server (NTRS)

Sreekantamurthy, Tham; Gaspar, James L.; Mann, Troy; Behun, Vaughn; Pearson, James C., Jr.; Scarborough, Stephen

2007-01-01

Ultra-light weight and ultra-thin membrane inflatable antenna concepts are fast evolving to become the state-of-the-art antenna concepts for deep-space applications. NASA Langley Research Center has been involved in the structural dynamics research on antenna structures. One of the goals of the research is to develop structural analysis methodology for prediction of the static and dynamic response characteristics of the inflatable antenna concepts. This research is focused on the computational studies to use nonlinear large deformation finite element analysis to characterize the ultra-thin membrane responses of the antennas. Recently, structural analyses have been performed on a few parabolic reflector antennas of varying size and shape, which are referred in the paper as 0.3 meters subscale, 2 meters half-scale, and 4 meters full-scale antenna. The various aspects studied included nonlinear analysis methodology and solution techniques, ways to speed convergence in iterative methods, the sensitivities of responses with respect to structural loads, such as inflation pressure, gravity, and pretension loads in the ground and in-space conditions, and the ultra-thin membrane wrinkling characteristics. Several such intrinsic aspects studied have provided valuable insight into evaluation of structural characteristics of such antennas. While analyzing these structural characteristics, a quick study was also made to assess the applicability of dynamics scaling of the half-scale antenna. This paper presents the details of the nonlinear structural analysis results, and discusses the insight gained from the studies on the various intrinsic aspects of the analysis methodology. The predicted reflector surface characteristics of the three inflatable ultra-thin membrane parabolic reflector antenna concepts are presented as easily observable displacement fringe patterns with associated maximum values, and normal mode shapes and associated frequencies. Wrinkling patterns are presented to show how surface wrinkle progress with increasing tension loads. Antenna reflector surface accuracies were found to be very much dependent on the type and size of the antenna, the reflector surface curvature, reflector membrane supports in terms of spacing of catenaries, as well as the amount of applied load.

Linear and nonlinear instability in vertical counter-current laminar gas-liquid flows

NASA Astrophysics Data System (ADS)

Schmidt, Patrick; Ó Náraigh, Lennon; Lucquiaud, Mathieu; Valluri, Prashant

2016-04-01

We consider the genesis and dynamics of interfacial instability in vertical gas-liquid flows, using as a model the two-dimensional channel flow of a thin falling film sheared by counter-current gas. The methodology is linear stability theory (Orr-Sommerfeld analysis) together with direct numerical simulation of the two-phase flow in the case of nonlinear disturbances. We investigate the influence of two main flow parameters on the interfacial dynamics, namely the film thickness and pressure drop applied to drive the gas stream. To make contact with existing studies in the literature, the effect of various density contrasts is also examined. Energy budget analyses based on the Orr-Sommerfeld theory reveal various coexisting unstable modes (interfacial, shear, internal) in the case of high density contrasts, which results in mode coalescence and mode competition, but only one dynamically relevant unstable interfacial mode for low density contrast. A study of absolute and convective instability for low density contrast shows that the system is absolutely unstable for all but two narrow regions of the investigated parameter space. Direct numerical simulations of the same system (low density contrast) show that linear theory holds up remarkably well upon the onset of large-amplitude waves as well as the existence of weakly nonlinear waves. For high density contrasts, corresponding more closely to an air-water-type system, linear stability theory is also successful at determining the most-dominant features in the interfacial wave dynamics at early-to-intermediate times. Nevertheless, the short waves selected by the linear theory undergo secondary instability and the wave train is no longer regular but rather exhibits chaotic motion. The same linear stability theory predicts when the direction of travel of the waves changes — from downwards to upwards. We outline the practical implications of this change in terms of loading and flooding. The change in direction of the wave propagation is represented graphically in terms of a flow map based on the liquid and gas flow rates and the prediction carries over to the nonlinear regime with only a small deviation.

Supercritical nonlinear parametric dynamics of Timoshenko microbeams

NASA Astrophysics Data System (ADS)

Farokhi, Hamed; Ghayesh, Mergen H.

2018-06-01

The nonlinear supercritical parametric dynamics of a Timoshenko microbeam subject to an axial harmonic excitation force is examined theoretically, by means of different numerical techniques, and employing a high-dimensional analysis. The time-variant axial load is assumed to consist of a mean value along with harmonic fluctuations. In terms of modelling, a continuous expression for the elastic potential energy of the system is developed based on the modified couple stress theory, taking into account small-size effects; the kinetic energy of the system is also modelled as a continuous function of the displacement field. Hamilton's principle is employed to balance the energies and to obtain the continuous model of the system. Employing the Galerkin scheme along with an assumed-mode technique, the energy terms are reduced, yielding a second-order reduced-order model with finite number of degrees of freedom. A transformation is carried out to convert the second-order reduced-order model into a double-dimensional first order one. A bifurcation analysis is performed for the system in the absence of the axial load fluctuations. Moreover, a mean value for the axial load is selected in the supercritical range, and the principal parametric resonant response, due to the time-variant component of the axial load, is obtained - as opposed to transversely excited systems, for parametrically excited system (such as our problem here), the nonlinear resonance occurs in the vicinity of twice any natural frequency of the linear system; this is accomplished via use of the pseudo-arclength continuation technique, a direct time integration, an eigenvalue analysis, and the Floquet theory for stability. The natural frequencies of the system prior to and beyond buckling are also determined. Moreover, the effect of different system parameters on the nonlinear supercritical parametric dynamics of the system is analysed, with special consideration to the effect of the length-scale parameter.

Global warming description using Daisyworld model with greenhouse gases.

PubMed

Paiva, Susana L D; Savi, Marcelo A; Viola, Flavio M; Leiroz, Albino J K

2014-11-01

Daisyworld is an archetypal model of the earth that is able to describe the global regulation that can emerge from the interaction between life and environment. This article proposes a model based on the original Daisyworld considering greenhouse gases emission and absorption, allowing the description of the global warming phenomenon. Global and local analyses are discussed evaluating the influence of greenhouse gases in the planet dynamics. Numerical simulations are carried out showing the general qualitative behavior of the Daisyworld for different scenarios that includes solar luminosity variations and greenhouse gases effect. Nonlinear dynamics perspective is of concern discussing a way that helps the comprehension of the global warming phenomenon. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.

Two Studies of Complex Nonlinear Systems: Engineered Granular Crystals and Coarse-Graining Optimization Problems

NASA Astrophysics Data System (ADS)

Pozharskiy, Dmitry

In recent years a nonlinear, acoustic metamaterial, named granular crystals, has gained prominence due to its high accessibility, both experimentally and computationally. The observation of a wide range of dynamical phenomena in the system, due to its inherent nonlinearities, has suggested its importance in many engineering applications related to wave propagation. In the first part of this dissertation, we explore the nonlinear dynamics of damped-driven granular crystals. In one case, we consider a highly nonlinear setting, also known as a sonic vacuum, and derive a nonlinear analogue of a linear spectrum, corresponding to resonant periodic propagation and antiresonances. Experimental studies confirm the computational findings and the assimilation of experimental data into a numerical model is demonstrated. In the second case, global bifurcations in a precompressed granular crystal are examined, and their involvement in the appearance of chaotic dynamics is demonstrated. Both results highlight the importance of exploring the nonlinear dynamics, to gain insight into how a granular crystal responds to different external excitations. In the second part, we borrow established ideas from coarse-graining of dynamical systems, and extend them to optimization problems. We combine manifold learning algorithms, such as Diffusion Maps, with stochastic optimization methods, such as Simulated Annealing, and show that we can retrieve an ensemble, of few, important parameters that should be explored in detail. This framework can lead to acceleration of convergence when dealing with complex, high-dimensional optimization, and could potentially be applied to design engineered granular crystals.

Nonlinear elasticity in resonance experiments

NASA Astrophysics Data System (ADS)

Li, Xun; Sens-Schönfelder, Christoph; Snieder, Roel

2018-04-01

Resonant bar experiments have revealed that dynamic deformation induces nonlinearity in rocks. These experiments produce resonance curves that represent the response amplitude as a function of the driving frequency. We propose a model to reproduce the resonance curves with observed features that include (a) the log-time recovery of the resonant frequency after the deformation ends (slow dynamics), (b) the asymmetry in the direction of the driving frequency, (c) the difference between resonance curves with the driving frequency that is swept upward and downward, and (d) the presence of a "cliff" segment to the left of the resonant peak under the condition of strong nonlinearity. The model is based on a feedback cycle where the effect of softening (nonlinearity) feeds back to the deformation. This model provides a unified interpretation of both the nonlinearity and slow dynamics in resonance experiments. We further show that the asymmetry of the resonance curve is caused by the softening, which is documented by the decrease of the resonant frequency during the deformation; the cliff segment of the resonance curve is linked to a bifurcation that involves a steep change of the response amplitude when the driving frequency is changed. With weak nonlinearity, the difference between the upward- and downward-sweeping curves depends on slow dynamics; a sufficiently slow frequency sweep eliminates this up-down difference. With strong nonlinearity, the up-down difference results from both the slow dynamics and bifurcation; however, the presence of the bifurcation maintains the respective part of the up-down difference, regardless of the sweep rate.

A higher-order theory for geometrically nonlinear analysis of composite laminates

NASA Technical Reports Server (NTRS)

Reddy, J. N.; Liu, C. F.

1987-01-01

A third-order shear deformation theory of laminated composite plates and shells is developed, the Navier solutions are derived, and its finite element models are developed. The theory allows parabolic description of the transverse shear stresses, and therefore the shear correction factors of the usual shear deformation theory are not required in the present theory. The theory also accounts for the von Karman nonlinear strains. Closed-form solutions of the theory for rectangular cross-ply and angle-ply plates and cross-ply shells are developed. The finite element model is based on independent approximations of the displacements and bending moments (i.e., mixed finite element model), and therefore, only C sup o -approximation is required. The finite element model is used to analyze cross-ply and angle-ply laminated plates and shells for bending and natural vibration. Many of the numerical results presented here should serve as references for future investigations. Three major conclusions resulted from the research: First, for thick laminates, shear deformation theories predict deflections, stresses and vibration frequencies significantly different from those predicted by classical theories. Second, even for thin laminates, shear deformation effects are significant in dynamic and geometrically nonlinear analyses. Third, the present third-order theory is more accurate compared to the classical and firt-order theories in predicting static and dynamic response of laminated plates and shells made of high-modulus composite materials.

Nonlinear dynamics of the human lumbar intervertebral disc.

PubMed

Marini, Giacomo; Huber, Gerd; Püschel, Klaus; Ferguson, Stephen J

2015-02-05

Systems with a quasi-static response similar to the axial response of the intervertebral disc (i.e. progressive stiffening) often present complex dynamics, characterized by peculiar nonlinearities in the frequency response. However, such characteristics have not been reported for the dynamic response of the disc. The accurate understanding of disc dynamics is essential to investigate the unclear correlation between whole body vibration and low back pain. The present study investigated the dynamic response of the disc, including its potential nonlinear response, over a range of loading conditions. Human lumbar discs were tested by applying a static preload to the top and a sinusoidal displacement at the bottom of the disc. The frequency of the stimuli was set to increase linearly from a low frequency to a high frequency limit and back down. In general, the response showed nonlinear and asymmetric characteristics. For each test, the disc had different response in the frequency-increasing compared to the frequency-decreasing sweep. In particular, the system presented abrupt changes of the oscillation amplitude at specific frequencies, which differed between the two sweeps. This behaviour indicates that the system oscillation has a different equilibrium condition depending on the path followed by the stimuli. Preload and amplitude of the oscillation directly influenced the disc response by changing the nonlinear dynamics and frequency of the jump-phenomenon. These results show that the characterization of the dynamic response of physiological systems should be readdressed to determine potential nonlinearities. Their direct effect on the system function should be further investigated. Copyright © 2014 Elsevier Ltd. All rights reserved.

Dynamics of nonlinear feedback control.

PubMed

Snippe, H P; van Hateren, J H

2007-05-01

Feedback control in neural systems is ubiquitous. Here we study the mathematics of nonlinear feedback control. We compare models in which the input is multiplied by a dynamic gain (multiplicative control) with models in which the input is divided by a dynamic attenuation (divisive control). The gain signal (resp. the attenuation signal) is obtained through a concatenation of an instantaneous nonlinearity and a linear low-pass filter operating on the output of the feedback loop. For input steps, the dynamics of gain and attenuation can be very different, depending on the mathematical form of the nonlinearity and the ordering of the nonlinearity and the filtering in the feedback loop. Further, the dynamics of feedback control can be strongly asymmetrical for increment versus decrement steps of the input. Nevertheless, for each of the models studied, the nonlinearity in the feedback loop can be chosen such that immediately after an input step, the dynamics of feedback control is symmetric with respect to increments versus decrements. Finally, we study the dynamics of the output of the control loops and find conditions under which overshoots and undershoots of the output relative to the steady-state output occur when the models are stimulated with low-pass filtered steps. For small steps at the input, overshoots and undershoots of the output do not occur when the filtering in the control path is faster than the low-pass filtering at the input. For large steps at the input, however, results depend on the model, and for some of the models, multiple overshoots and undershoots can occur even with a fast control path.

Nonlinear Hysteretic Torsional Waves

NASA Astrophysics Data System (ADS)

Cabaret, J.; Béquin, P.; Theocharis, G.; Andreev, V.; Gusev, V. E.; Tournat, V.

2015-07-01

We theoretically study and experimentally report the propagation of nonlinear hysteretic torsional pulses in a vertical granular chain made of cm-scale, self-hanged magnetic beads. As predicted by contact mechanics, the torsional coupling between two beads is found to be nonlinear hysteretic. This results in a nonlinear pulse distortion essentially different from the distortion predicted by classical nonlinearities and in a complex dynamic response depending on the history of the wave particle angular velocity. Both are consistent with the predictions of purely hysteretic nonlinear elasticity and the Preisach-Mayergoyz hysteresis model, providing the opportunity to study the phenomenon of nonlinear dynamic hysteresis in the absence of other types of material nonlinearities. The proposed configuration reveals a plethora of interesting phenomena including giant amplitude-dependent attenuation, short-term memory, as well as dispersive properties. Thus, it could find interesting applications in nonlinear wave control devices such as strong amplitude-dependent filters.

Nonlinear dynamics and control of a vibrating rectangular plate

NASA Technical Reports Server (NTRS)

Shebalin, J. V.

1983-01-01

The von Karman equations of nonlinear elasticity are solved for the case of a vibrating rectangular plate by meams of a Fourier spectral transform method. The amplification of a particular Fourier mode by nonlinear transfer of energy is demonstrated for this conservative system. The multi-mode system is reduced to a minimal (two mode) system, retaining the qualitative features of the multi-mode system. The effect of a modal control law on the dynamics of this minimal nonlinear elastic system is examined.

N-soliton interactions: Effects of linear and nonlinear gain and loss

NASA Astrophysics Data System (ADS)

Carretero-González, R.; Gerdjikov, V. S.; Todorov, M. D.

2017-10-01

We analyze the dynamical behavior of the N-soliton train in the adiabatic approximation of the nonlinear Schrödinger equation perturbed simultaneously by linear and nonlinear gain/loss terms. We derive the corresponding perturbed complex Toda chain in the case of a combination of linear, cubic, and/or quintic terms. We show that the soliton interactions dynamics for this reduced PCTC model compares favorably to full numerical results of the original perturbed nonlinear Schrödinger equation.

Travelling-wave solutions of a weakly nonlinear two-dimensional higher-order Kadomtsev-Petviashvili dynamical equation for dispersive shallow-water waves

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.

2017-01-01

The propagation of three-dimensional nonlinear irrotational flow of an inviscid and incompressible fluid of the long waves in dispersive shallow-water approximation is analyzed. The problem formulation of the long waves in dispersive shallow-water approximation lead to fifth-order Kadomtsev-Petviashvili (KP) dynamical equation by applying the reductive perturbation theory. By using an extended auxiliary equation method, the solitary travelling-wave solutions of the two-dimensional nonlinear fifth-order KP dynamical equation are derived. An analytical as well as a numerical solution of the two-dimensional nonlinear KP equation are obtained and analyzed with the effects of external pressure flow.

System Identification for Nonlinear Control Using Neural Networks

NASA Technical Reports Server (NTRS)

Stengel, Robert F.; Linse, Dennis J.

1990-01-01

An approach to incorporating artificial neural networks in nonlinear, adaptive control systems is described. The controller contains three principal elements: a nonlinear inverse dynamic control law whose coefficients depend on a comprehensive model of the plant, a neural network that models system dynamics, and a state estimator whose outputs drive the control law and train the neural network. Attention is focused on the system identification task, which combines an extended Kalman filter with generalized spline function approximation. Continual learning is possible during normal operation, without taking the system off line for specialized training. Nonlinear inverse dynamic control requires smooth derivatives as well as function estimates, imposing stringent goals on the approximating technique.

Nonlinear quantum Rabi model in trapped ions

NASA Astrophysics Data System (ADS)

Cheng, Xiao-Hang; Arrazola, Iñigo; Pedernales, Julen S.; Lamata, Lucas; Chen, Xi; Solano, Enrique

2018-02-01

We study the nonlinear dynamics of trapped-ion models far away from the Lamb-Dicke regime. This nonlinearity induces a blockade on the propagation of quantum information along the Hilbert space of the Jaynes-Cummings and quantum Rabi models. We propose to use this blockade as a resource for the dissipative generation of high-number Fock states. Also, we compare the linear and nonlinear cases of the quantum Rabi model in the ultrastrong and deep strong-coupling regimes. Moreover, we propose a scheme to simulate the nonlinear quantum Rabi model in all coupling regimes. This can be done via off-resonant nonlinear red- and blue-sideband interactions in a single trapped ion, yielding applications as a dynamical quantum filter.

Nonlinear dynamic phenomena in the space shuttle thermal protection system

NASA Technical Reports Server (NTRS)

Housner, J. M.; Edighoffer, H. H.; Park, K. C.

1981-01-01

The development of an analysis for examining the nonlinear dynamic phenomena arising in the space shuttle orbiter tile/pad thermal protection system is presented. The tile/pad system consists of ceramic tiles bonded to the aluminum skin of the orbiter through a thin nylon felt pad. The pads are a soft nonlinear material which permits large strains and displays both hysteretic and nonlinear viscous damping. Application of the analysis to a square tile subjected to transverse sinusoidal motion of the orbiter skin is presented and the following nonlinear dynamic phenomena are considered: highly distorted wave forms, amplitude-dependent resonant frequencies which initially decrease and then increase with increasing amplitude of motion, magnification of substrate motion which is higher than would be expected in a similarly highly damped linear system, and classical parametric resonance instability.

Effect of motor dynamics on nonlinear feedback robot arm control

NASA Technical Reports Server (NTRS)

Tarn, Tzyh-Jong; Li, Zuofeng; Bejczy, Antal K.; Yun, Xiaoping

1991-01-01

A nonlinear feedback robot controller that incorporates the robot manipulator dynamics and the robot joint motor dynamics is proposed. The manipulator dynamics and the motor dynamics are coupled to obtain a third-order-dynamic model, and differential geometric control theory is applied to produce a linearized and decoupled robot controller. The derived robot controller operates in the robot task space, thus eliminating the need for decomposition of motion commands into robot joint space commands. Computer simulations are performed to verify the feasibility of the proposed robot controller. The controller is further experimentally evaluated on the PUMA 560 robot arm. The experiments show that the proposed controller produces good trajectory tracking performances and is robust in the presence of model inaccuracies. Compared with a nonlinear feedback robot controller based on the manipulator dynamics only, the proposed robot controller yields conspicuously improved performance.

Integrable pair-transition-coupled nonlinear Schrödinger equations.

PubMed

Ling, Liming; Zhao, Li-Chen

2015-08-01

We study integrable coupled nonlinear Schrödinger equations with pair particle transition between components. Based on exact solutions of the coupled model with attractive or repulsive interaction, we predict that some new dynamics of nonlinear excitations can exist, such as the striking transition dynamics of breathers, new excitation patterns for rogue waves, topological kink excitations, and other new stable excitation structures. In particular, we find that nonlinear wave solutions of this coupled system can be written as a linear superposition of solutions for the simplest scalar nonlinear Schrödinger equation. Possibilities to observe them are discussed in a cigar-shaped Bose-Einstein condensate with two hyperfine states. The results would enrich our knowledge on nonlinear excitations in many coupled nonlinear systems with transition coupling effects, such as multimode nonlinear fibers, coupled waveguides, and a multicomponent Bose-Einstein condensate system.

A review of human factors challenges of complex adaptive systems: discovering and understanding chaos in human performance.

PubMed

Karwowski, Waldemar

2012-12-01

In this paper, the author explores a need for a greater understanding of the true nature of human-system interactions from the perspective of the theory of complex adaptive systems, including the essence of complexity, emergent properties of system behavior, nonlinear systems dynamics, and deterministic chaos. Human performance, more often than not, constitutes complex adaptive phenomena with emergent properties that exhibit nonlinear dynamical (chaotic) behaviors. The complexity challenges in the design and management of contemporary work systems, including service systems, are explored. Examples of selected applications of the concepts of nonlinear dynamics to the study of human physical performance are provided. Understanding and applications of the concepts of theory of complex adaptive and dynamical systems should significantly improve the effectiveness of human-centered design efforts of a large system of systems. Performance of many contemporary work systems and environments may be sensitive to the initial conditions and may exhibit dynamic nonlinear properties and chaotic system behaviors. Human-centered design of emergent human-system interactions requires application of the theories of nonlinear dynamics and complex adaptive system. The success of future human-systems integration efforts requires the fusion of paradigms, knowledge, design principles, and methodologies of human factors and ergonomics with those of the science of complex adaptive systems as well as modern systems engineering.

Nonlinear dynamics of the magnetosphere and space weather

NASA Technical Reports Server (NTRS)

Sharma, A. Surjalal

1996-01-01

The solar wind-magnetosphere system exhibits coherence on the global scale and such behavior can arise from nonlinearity on the dynamics. The observational time series data were used together with phase space reconstruction techniques to analyze the magnetospheric dynamics. Analysis of the solar wind, auroral electrojet and Dst indices showed low dimensionality of the dynamics and accurate prediction can be made with an input/output model. The predictability of the magnetosphere in spite of the apparent complexity arises from its dynamical synchronism with the solar wind. The electrodynamic coupling between different regions of the magnetosphere yields its coherent, low dimensional behavior. The data from multiple satellites and ground stations can be used to develop a spatio-temporal model that identifies the coupling between different regions. These nonlinear dynamical models provide space weather forecasting capabilities.

Directed dynamical influence is more detectable with noise

PubMed Central

Jiang, Jun-Jie; Huang, Zi-Gang; Huang, Liang; Liu, Huan; Lai, Ying-Cheng

2016-01-01

Successful identification of directed dynamical influence in complex systems is relevant to significant problems of current interest. Traditional methods based on Granger causality and transfer entropy have issues such as difficulty with nonlinearity and large data requirement. Recently a framework based on nonlinear dynamical analysis was proposed to overcome these difficulties. We find, surprisingly, that noise can counterintuitively enhance the detectability of directed dynamical influence. In fact, intentionally injecting a proper amount of asymmetric noise into the available time series has the unexpected benefit of dramatically increasing confidence in ascertaining the directed dynamical influence in the underlying system. This result is established based on both real data and model time series from nonlinear ecosystems. We develop a physical understanding of the beneficial role of noise in enhancing detection of directed dynamical influence. PMID:27066763

Directed dynamical influence is more detectable with noise.

PubMed

Jiang, Jun-Jie; Huang, Zi-Gang; Huang, Liang; Liu, Huan; Lai, Ying-Cheng

2016-04-12

Successful identification of directed dynamical influence in complex systems is relevant to significant problems of current interest. Traditional methods based on Granger causality and transfer entropy have issues such as difficulty with nonlinearity and large data requirement. Recently a framework based on nonlinear dynamical analysis was proposed to overcome these difficulties. We find, surprisingly, that noise can counterintuitively enhance the detectability of directed dynamical influence. In fact, intentionally injecting a proper amount of asymmetric noise into the available time series has the unexpected benefit of dramatically increasing confidence in ascertaining the directed dynamical influence in the underlying system. This result is established based on both real data and model time series from nonlinear ecosystems. We develop a physical understanding of the beneficial role of noise in enhancing detection of directed dynamical influence.

Linear and Nonlinear Analysis of Brain Dynamics in Children with Cerebral Palsy

ERIC Educational Resources Information Center

Sajedi, Firoozeh; Ahmadlou, Mehran; Vameghi, Roshanak; Gharib, Masoud; Hemmati, Sahel

2013-01-01

This study was carried out to determine linear and nonlinear changes of brain dynamics and their relationships with the motor dysfunctions in CP children. For this purpose power of EEG frequency bands (as a linear analysis) and EEG fractality (as a nonlinear analysis) were computed in eyes-closed resting state and statistically compared between 26…

Experimental Chaos - Proceedings of the 3rd Conference

NASA Astrophysics Data System (ADS)

Harrison, Robert G.; Lu, Weiping; Ditto, William; Pecora, Lou; Spano, Mark; Vohra, Sandeep

1996-10-01

The Table of Contents for the full book PDF is as follows: * Preface * Spatiotemporal Chaos and Patterns * Scale Segregation via Formation of Domains in a Nonlinear Optical System * Laser Dynamics as Hydrodynamics * Spatiotemporal Dynamics of Human Epileptic Seizures * Experimental Transition to Chaos in a Quasi 1D Chain of Oscillators * Measuring Coupling in Spatiotemporal Dynamical Systems * Chaos in Vortex Breakdown * Dynamical Analysis * Radial Basis Function Modelling and Prediction of Time Series * Nonlinear Phenomena in Polyrhythmic Hand Movements * Using Models to Diagnose, Test and Control Chaotic Systems * New Real-Time Analysis of Time Series Data with Physical Wavelets * Control and Synchronization * Measuring and Controlling Chaotic Dynamics in a Slugging Fluidized Bed * Control of Chaos in a Laser with Feedback * Synchronization and Chaotic Diode Resonators * Control of Chaos by Continuous-time Feedback with Delay * A Framework for Communication using Chaos Sychronization * Control of Chaos in Switching Circuits * Astrophysics, Meteorology and Oceanography * Solar-Wind-Magnetospheric Dynamics via Satellite Data * Nonlinear Dynamics of the Solar Atmosphere * Fractal Dimension of Scalar and Vector Variables from Turbulence Measurements in the Atmospheric Surface Layer * Mechanics * Escape and Overturning: Subtle Transient Behavior in Nonlinear Mechanical Models * Organising Centres in the Dynamics of Parametrically Excited Double Pendulums * Intermittent Behaviour in a Heating System Driven by Phase Transitions * Hydrodynamics * Size Segregation in Couette Flow of Granular Material * Routes to Chaos in Rotational Taylor-Couette Flow * Experimental Study of the Laminar-Turbulent Transition in an Open Flow System * Chemistry * Order and Chaos in Excitable Media under External Forcing * A Chemical Wave Propagation with Accelerating Speed Accompanied by Hydrodynamic Flow * Optics * Instabilities in Semiconductor Lasers with Optical Injection * Spatio-Temporal Dynamics of a Bimode CO2 Laser with Saturable Absorber * Chaotic Homoclinic Phenomena in Opto-Thermal Devices * Observation and Characterisation of Low-Frequency Chaos in Semiconductor Lasers with External Feedback * Condensed Matter * The Application of Nonlinear Dynamics in the Study of Ferroelectric Materials * Cellular Convection in a Small Aspect Ratio Liquid Crystal Device * Driven Spin-Wave Dynamics in YIG Films * Quantum Chaology in Quartz * Small Signal Amplification Caused by Nonlinear Properties of Ferroelectrics * Composite Materials Evolved from Chaos * Electronics and Circuits * Controlling a Chaotic Array of Pulse-Coupled Fitzhugh-Nagumo Circuits * Experimental Observation of On-Off Intermittency * Phase Lock-In of Chaotic Relaxation Oscillators * Biology and Medicine * Singular Value Decomposition and Circuit Structure in Invertebrate Ganglia * Nonlinear Forecasting of Spike Trains from Neurons of a Mollusc * Ultradian Rhythm in the Sensitive Plants: Chaos or Coloured Noise? * Chaos and the Crayfish Sixth Ganglion * Hardware Coupled Nonlinear Oscillators as a Model of Retina

Adaptive nearly optimal control for a class of continuous-time nonaffine nonlinear systems with inequality constraints.

PubMed

Fan, Quan-Yong; Yang, Guang-Hong

2017-01-01

The state inequality constraints have been hardly considered in the literature on solving the nonlinear optimal control problem based the adaptive dynamic programming (ADP) method. In this paper, an actor-critic (AC) algorithm is developed to solve the optimal control problem with a discounted cost function for a class of state-constrained nonaffine nonlinear systems. To overcome the difficulties resulting from the inequality constraints and the nonaffine nonlinearities of the controlled systems, a novel transformation technique with redesigned slack functions and a pre-compensator method are introduced to convert the constrained optimal control problem into an unconstrained one for affine nonlinear systems. Then, based on the policy iteration (PI) algorithm, an online AC scheme is proposed to learn the nearly optimal control policy for the obtained affine nonlinear dynamics. Using the information of the nonlinear model, novel adaptive update laws are designed to guarantee the convergence of the neural network (NN) weights and the stability of the affine nonlinear dynamics without the requirement for the probing signal. Finally, the effectiveness of the proposed method is validated by simulation studies. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rizwan-uddin

Recently, various branches of engineering and science have seen a rapid increase in the number of dynamical analyses undertaken. This modern phenomenon often obscures the fact that such analyses were sometimes carried out even before the current trend began. Moreover, these earlier analyses, which even now seem very ingenuous, were carried out at a time when the available information about dynamical systems was not as well disseminated as it is today. One such analysis, carried out in the early 1960s, showed the existence of stable limit cycles in a simple model for space-independent xenon dynamics in nuclear reactors. The authors,more » apparently unaware of the now well-known bifurcation theorem by Hopf, could not numerically discover unstable limit cycles, though they did find regions in parameter space where the fixed points are stable for small perturbations but unstable for very large perturbations. The analysis was carried out both analytically and numerically. As a tribute to these early nonlinear dynamicists in the field of nuclear engineering, in this paper, the Hopf theorem and its conclusions are briefly described, and then the solution of the space-independent xenon oscillation problem is presented, which was obtained using the bifurcation analysis BIFDD code. These solutions are presented along with a discussion of the earlier results.« less

Nonlinear system guidance in the presence of transmission zero dynamics

NASA Technical Reports Server (NTRS)

Meyer, G.; Hunt, L. R.; Su, R.

1995-01-01

An iterative procedure is proposed for computing the commanded state trajectories and controls that guide a possibly multiaxis, time-varying, nonlinear system with transmission zero dynamics through a given arbitrary sequence of control points. The procedure is initialized by the system inverse with the transmission zero effects nulled out. Then the 'steady state' solution of the perturbation model with the transmission zero dynamics intact is computed and used to correct the initial zero-free solution. Both time domain and frequency domain methods are presented for computing the steady state solutions of the possibly nonminimum phase transmission zero dynamics. The procedure is illustrated by means of linear and nonlinear examples.

Localized nonlinear waves and dynamical stability in spinor Bose–Einstein condensates with time–space modulation

NASA Astrophysics Data System (ADS)

Yao, Yu-Qin; Han, Wei; Li, Ji; Liu, Wu-Ming

2018-05-01

Nonlinearity is one of the most remarkable characteristics of Bose–Einstein condensates (BECs). Much work has been done on one- and two-component BECs with time- or space-modulated nonlinearities, while there is little work on spinor BECs with space–time-modulated nonlinearities. In the present paper we investigate localized nonlinear waves and dynamical stability in spinor Bose–Einstein condensates with nonlinearities dependent on time and space. We solve the three coupled Gross–Pitaevskii equations by similarity transformation and obtain two families of exact matter wave solutions in terms of Jacobi elliptic functions and the Mathieu equation. The localized states of the spinor matter wave describe the dynamics of vector breathing solitons, moving breathing solitons, quasi-breathing solitons and resonant solitons. The results show that one-order vector breathing solitons, quasi-breathing solitons, resonant solitons and the moving breathing solitons ψ ±1 are all stable, but the moving breathing soliton ψ 0 is unstable. We also present the experimental parameters to realize these phenomena in future experiments.

A Study on Application of Fuzzy Adaptive Unscented Kalman Filter to Nonlinear Turbojet Engine Control

NASA Astrophysics Data System (ADS)

Han, Dongju

2018-05-01

Safe and efficient flight powered by an aircraft turbojet engine relies on the performance of the engine controller preventing compressor surge with robustness from noises or disturbances. This paper proposes the effective nonlinear controller associated with the nonlinear filter for the real turbojet engine with highly nonlinear dynamics. For the feasible controller study the nonlinearity of the engine dynamics was investigated by comparing the step responses from the linearized model with the original nonlinear dynamics. The fuzzy-based PID control logic is introduced to control the engine efficiently and FAUKF is applied for robustness from noises. The simulation results prove the effectiveness of FAUKF applied to the proposed controller such that the control performances are superior over the conventional controller and the filer performance using FAUKF indicates the satisfactory results such as clearing the defects by reducing the distortions without compressor surge, whereas the conventional UKF is not fully effective as occurring some distortions with compressor surge due to a process noise.

Finite element analysis of structural engineering problems using a viscoplastic model incorporating two back stresses

NASA Technical Reports Server (NTRS)

Arya, Vinod K.; Halford, Gary R.

1993-01-01

The feasibility of a viscoplastic model incorporating two back stresses and a drag strength is investigated for performing nonlinear finite element analyses of structural engineering problems. To demonstrate suitability for nonlinear structural analyses, the model is implemented into a finite element program and analyses for several uniaxial and multiaxial problems are performed. Good agreement is shown between the results obtained using the finite element implementation and those obtained experimentally. The advantages of using advanced viscoplastic models for performing nonlinear finite element analyses of structural components are indicated.

Influence of chemical reactions on the nonlinear dynamics of dissipative flows

NASA Astrophysics Data System (ADS)

Karimov, A. R.; Korshunov, A. M.; Beklemishev, V. V.

2015-08-01

The nonlinear dynamics of resistive flow with a chemical reaction is studied. Proceeding from the Lagrangian description, the influence of a chemical reaction on the development of fluid singularities is considered.

Nonlinear structural joint model updating based on instantaneous characteristics of dynamic responses

NASA Astrophysics Data System (ADS)

Wang, Zuo-Cai; Xin, Yu; Ren, Wei-Xin

2016-08-01

This paper proposes a new nonlinear joint model updating method for shear type structures based on the instantaneous characteristics of the decomposed structural dynamic responses. To obtain an accurate representation of a nonlinear system's dynamics, the nonlinear joint model is described as the nonlinear spring element with bilinear stiffness. The instantaneous frequencies and amplitudes of the decomposed mono-component are first extracted by the analytical mode decomposition (AMD) method. Then, an objective function based on the residuals of the instantaneous frequencies and amplitudes between the experimental structure and the nonlinear model is created for the nonlinear joint model updating. The optimal values of the nonlinear joint model parameters are obtained by minimizing the objective function using the simulated annealing global optimization method. To validate the effectiveness of the proposed method, a single-story shear type structure subjected to earthquake and harmonic excitations is simulated as a numerical example. Then, a beam structure with multiple local nonlinear elements subjected to earthquake excitation is also simulated. The nonlinear beam structure is updated based on the global and local model using the proposed method. The results show that the proposed local nonlinear model updating method is more effective for structures with multiple local nonlinear elements. Finally, the proposed method is verified by the shake table test of a real high voltage switch structure. The accuracy of the proposed method is quantified both in numerical and experimental applications using the defined error indices. Both the numerical and experimental results have shown that the proposed method can effectively update the nonlinear joint model.

Linearity and nonlinearity of basin response as a function of scale: Discussion of alternative definitions

NASA Astrophysics Data System (ADS)

Sivapalan, M.; Jothityangkoon, C.; Menabde, M.

2002-02-01

Two uses of the terms ``linearity'' and ``nonlinearity'' appear in recent literature. The first definition of nonlinearity is with respect to the dynamical property such as the rainfall-runoff response of a catchment, and nonlinearity in this sense refers to a nonlinear dependence of the storm response on the magnitude of the rainfall inputs [Minshall, 1960; Wang et al., 1981]. The second definition of nonlinearity [Huang and Willgoose, 1993; Goodrich et al., 1997] is with respect to the dependence of a catchment statistical property, such as the mean annual flood, on the area of the catchment. They are both linked to important and interconnected hydrologic concepts, and furthermore, the change of nonlinearity with area (scale) has been an important motivation for hydrologic research. While both definitions are correct mathematically, they refer to hydrologically different concepts. In this paper we show that nonlinearity in the dynamical sense and that in the statistical sense can exist independently of each other (i.e., can be unrelated). If not carefully distinguished, the existence of these two definitions can lead to a catchment's response being described as being both linear and nonlinear at the same time. We therefore recommend separating these definitions by reserving the term ``nonlinearity'' for the classical, dynamical definition with respect to rainfall inputs, while adopting the term ``scaling relationship'' for the dependence of a catchment hydrological property on catchment area.

Alternation of regular and chaotic dynamics in a simple two-degree-of-freedom system with nonlinear inertial coupling.

PubMed

Sigalov, G; Gendelman, O V; AL-Shudeifat, M A; Manevitch, L I; Vakakis, A F; Bergman, L A

2012-03-01

We show that nonlinear inertial coupling between a linear oscillator and an eccentric rotator can lead to very interesting interchanges between regular and chaotic dynamical behavior. Indeed, we show that this model demonstrates rather unusual behavior from the viewpoint of nonlinear dynamics. Specifically, at a discrete set of values of the total energy, the Hamiltonian system exhibits non-conventional nonlinear normal modes, whose shape is determined by phase locking of rotatory and oscillatory motions of the rotator at integer ratios of characteristic frequencies. Considering the weakly damped system, resonance capture of the dynamics into the vicinity of these modes brings about regular motion of the system. For energy levels far from these discrete values, the motion of the system is chaotic. Thus, the succession of resonance captures and escapes by a discrete set of the normal modes causes a sequence of transitions between regular and chaotic behavior, provided that the damping is sufficiently small. We begin from the Hamiltonian system and present a series of Poincaré sections manifesting the complex structure of the phase space of the considered system with inertial nonlinear coupling. Then an approximate analytical description is presented for the non-conventional nonlinear normal modes. We confirm the analytical results by numerical simulation and demonstrate the alternate transitions between regular and chaotic dynamics mentioned above. The origin of the chaotic behavior is also discussed.

Koopman operator theory: Past, present, and future

NASA Astrophysics Data System (ADS)

Brunton, Steven; Kaiser, Eurika; Kutz, Nathan

2017-11-01

Koopman operator theory has emerged as a dominant method to represent nonlinear dynamics in terms of an infinite-dimensional linear operator. The Koopman operator acts on the space of all possible measurement functions of the system state, advancing these measurements with the flow of the dynamics. A linear representation of nonlinear dynamics has tremendous potential to enable the prediction, estimation, and control of nonlinear systems with standard textbook methods developed for linear systems. Dynamic mode decomposition has become the leading data-driven method to approximate the Koopman operator, although there are still open questions and challenges around how to obtain accurate approximations for strongly nonlinear systems. This talk will provide an introductory overview of modern Koopman operator theory, reviewing the basics and describing recent theoretical and algorithmic developments. Particular emphasis will be placed on the use of data-driven Koopman theory to characterize and control high-dimensional fluid dynamic systems. This talk will also address key advances in the rapidly growing fields of machine learning and data science that are likely to drive future developments.

Fuzzy Counter Propagation Neural Network Control for a Class of Nonlinear Dynamical Systems

PubMed Central

Sakhre, Vandana; Jain, Sanjeev; Sapkal, Vilas S.; Agarwal, Dev P.

2015-01-01

Fuzzy Counter Propagation Neural Network (FCPN) controller design is developed, for a class of nonlinear dynamical systems. In this process, the weight connecting between the instar and outstar, that is, input-hidden and hidden-output layer, respectively, is adjusted by using Fuzzy Competitive Learning (FCL). FCL paradigm adopts the principle of learning, which is used to calculate Best Matched Node (BMN) which is proposed. This strategy offers a robust control of nonlinear dynamical systems. FCPN is compared with the existing network like Dynamic Network (DN) and Back Propagation Network (BPN) on the basis of Mean Absolute Error (MAE), Mean Square Error (MSE), Best Fit Rate (BFR), and so forth. It envisages that the proposed FCPN gives better results than DN and BPN. The effectiveness of the proposed FCPN algorithms is demonstrated through simulations of four nonlinear dynamical systems and multiple input and single output (MISO) and a single input and single output (SISO) gas furnace Box-Jenkins time series data. PMID:26366169

Fuzzy Counter Propagation Neural Network Control for a Class of Nonlinear Dynamical Systems.

PubMed

Sakhre, Vandana; Jain, Sanjeev; Sapkal, Vilas S; Agarwal, Dev P

2015-01-01

Fuzzy Counter Propagation Neural Network (FCPN) controller design is developed, for a class of nonlinear dynamical systems. In this process, the weight connecting between the instar and outstar, that is, input-hidden and hidden-output layer, respectively, is adjusted by using Fuzzy Competitive Learning (FCL). FCL paradigm adopts the principle of learning, which is used to calculate Best Matched Node (BMN) which is proposed. This strategy offers a robust control of nonlinear dynamical systems. FCPN is compared with the existing network like Dynamic Network (DN) and Back Propagation Network (BPN) on the basis of Mean Absolute Error (MAE), Mean Square Error (MSE), Best Fit Rate (BFR), and so forth. It envisages that the proposed FCPN gives better results than DN and BPN. The effectiveness of the proposed FCPN algorithms is demonstrated through simulations of four nonlinear dynamical systems and multiple input and single output (MISO) and a single input and single output (SISO) gas furnace Box-Jenkins time series data.

The Creative Chaos: Speculations on the Connection Between Non-Linear Dynamics and the Creative Process

NASA Astrophysics Data System (ADS)

Zausner, Tobi

Chaos theory may provide models for creativity and for the personality of the artist. A collection of speculative hypotheses examines the connection between art and such fundamentals of non-linear dynamics as iteration, dissipative processes, open systems, entropy, sensitivity to stimuli, autocatalysis, subsystems, bifurcations, randomness, unpredictability, irreversibility, increasing levels of organization, far-from-equilibrium conditions, strange attractors, period doubling, intermittency and self-similar fractal organization. Non-linear dynamics may also explain why certain individuals suffer mental disorders while others remain intact during a lifetime of sustained creative output.

The Dynamics of Cognitive Performance: What Has Been Learnt from Empirical Research in Science Education

ERIC Educational Resources Information Center

Stamovlasis, Dimitrios

2017-01-01

This paper discusses investigations in science education addressing the nonlinear dynamical hypothesis. Learning science is a suitable field for applying interdisciplinary research and predominately for testing psychological theories. It was demonstrated that in this area the paradigm of complexity and nonlinear dynamics have offered theoretical…

Nonlinear dynamic modeling of rotor system supported by angular contact ball bearings

NASA Astrophysics Data System (ADS)

Wang, Hong; Han, Qinkai; Zhou, Daning

2017-02-01

In current bearing dynamic models, the displacement coordinate relations are usually utilized to approximately obtain the contact deformations between the rolling element and raceways, and then the nonlinear restoring forces of the rolling bearing could be calculated accordingly. Although the calculation efficiency is relatively higher, the accuracy is lower as the contact deformations should be solved through iterative analysis. Thus, an improved nonlinear dynamic model is presented in this paper. Considering the preload condition, surface waviness, Hertz contact and elastohydrodynamic lubrication, load distribution analysis is solved iteratively to more accurately obtain the contact deformations and angles between the rolling balls and raceways. The bearing restoring forces are then obtained through iteratively solving the load distribution equations at every time step. Dynamic tests upon a typical rotor system supported by two angular contact ball bearings are conducted to verify the model. Through comparisons, the differences between the nonlinear dynamic model and current models are also pointed out. The effects of axial preload, rotor eccentricity and inner/outer waviness amplitudes on the dynamic response are discussed in detail.

A new treatment for predicting the self-excited vibrations of nonlinear systems with frictional interfaces: The Constrained Harmonic Balance Method, with application to disc brake squeal

NASA Astrophysics Data System (ADS)

Coudeyras, N.; Sinou, J.-J.; Nacivet, S.

2009-01-01

Brake squeal noise is still an issue since it generates high warranty costs for the automotive industry and irritation for customers. Key parameters must be known in order to reduce it. Stability analysis is a common method of studying nonlinear phenomena and has been widely used by the scientific and the engineering communities for solving disc brake squeal problems. This type of analysis provides areas of stability versus instability for driven parameters, thereby making it possible to define design criteria. Nevertheless, this technique does not permit obtaining the vibrating state of the brake system and nonlinear methods have to be employed. Temporal integration is a well-known method for computing the dynamic solution but as it is time consuming, nonlinear methods such as the Harmonic Balance Method (HBM) are preferred. This paper presents a novel nonlinear method called the Constrained Harmonic Balance Method (CHBM) that works for nonlinear systems subject to flutter instability. An additional constraint-based condition is proposed that omits the static equilibrium point (i.e. the trivial static solution of the nonlinear problem that would be obtained by applying the classical HBM) and therefore focuses on predicting both the Fourier coefficients and the fundamental frequency of the stationary nonlinear system. The effectiveness of the proposed nonlinear approach is illustrated by an analysis of disc brake squeal. The brake system under consideration is a reduced finite element model of a pad and a disc. Both stability and nonlinear analyses are performed and the results are compared with a classical variable order solver integration algorithm. Therefore, the objectives of the following paper are to present not only an extension of the HBM (CHBM) but also to demonstrate an application to the specific problem of disc brake squeal with extensively parametric studies that investigate the effects of the friction coefficient, piston pressure, nonlinear stiffness and structural damping.

Periodicity, chaos, and multiple attractors in a memristor-based Shinriki's circuit

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kengne, J.; Njitacke Tabekoueng, Z.; Kamdoum Tamba, V.

2015-10-15

In this contribution, a novel memristor-based oscillator, obtained from Shinriki's circuit by substituting the nonlinear positive conductance with a first order memristive diode bridge, is introduced. The model is described by a continuous time four-dimensional autonomous system with smooth nonlinearities. The basic dynamical properties of the system are investigated including equilibria and stability, phase portraits, frequency spectra, bifurcation diagrams, and Lyapunov exponents' spectrum. It is found that in addition to the classical period-doubling and symmetry restoring crisis scenarios reported in the original circuit, the memristor-based oscillator experiences the unusual and striking feature of multiple attractors (i.e., coexistence of a pairmore » of asymmetric periodic attractors with a pair of asymmetric chaotic ones) over a broad range of circuit parameters. Results of theoretical analyses are verified by laboratory experimental measurements.« less

The periodic structure of the natural record, and nonlinear dynamics.

USGS Publications Warehouse

Shaw, H.R.

1987-01-01

This paper addresses how nonlinear dynamics can contribute to interpretations of the geologic record and evolutionary processes. Background is given to explain why nonlinear concepts are important. A resume of personal research is offered to illustrate why I think nonlinear processes fit with observations on geological and cosmological time series data. The fabric of universal periodicity arrays generated by nonlinear processes is illustrated by means of a simple computer mode. I conclude with implications concerning patterns of evolution, stratigraphic boundary events, and close correlations of major geologically instantaneous events (such as impacts or massive volcanic episodes) with any sharply defined boundary in the geologic column. - from Author

From local to global measurements of nonclassical nonlinear elastic effects in geomaterials

DOE PAGES

Lott, Martin; Remillieux, Marcel C.; Le Bas, Pierre-Yves; ...

2016-09-07

Here, the equivalence between local and global measures of nonclassical nonlinear elasticity is established in a slender resonant bar. Nonlinear effects are first measured globally using nonlinear resonance ultrasound spectroscopy (NRUS), which monitors the relative shift of the resonance frequency as a function of the maximum dynamic strain in the sample. Subsequently, nonlinear effects are measured locally at various positions along the sample using dynamic acousto elasticity testing (DAET). Finally, after correcting analytically the DAET data for three-dimensional strain effects and integrating numerically these corrected data along the length of the sample, the NRUS global measures are retrieved almost exactly.

Robust adaptive cruise control of high speed trains.

PubMed

Faieghi, Mohammadreza; Jalali, Aliakbar; Mashhadi, Seyed Kamal-e-ddin Mousavi

2014-03-01

The cruise control problem of high speed trains in the presence of unknown parameters and external disturbances is considered. In particular a Lyapunov-based robust adaptive controller is presented to achieve asymptotic tracking and disturbance rejection. The system under consideration is nonlinear, MIMO and non-minimum phase. To deal with the limitations arising from the unstable zero-dynamics we do an output redefinition such that the zero-dynamics with respect to new outputs becomes stable. Rigorous stability analyses are presented which establish the boundedness of all the internal states and simultaneously asymptotic stability of the tracking error dynamics. The results are presented for two common configurations of high speed trains, i.e. the DD and PPD designs, based on the multi-body model and are verified by several numerical simulations. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Nonlinear versus Ordinary Adaptive Control of Continuous Stirred-Tank Reactor

PubMed Central

Dostal, Petr

2015-01-01

Unfortunately, the major group of the systems in industry has nonlinear behavior and control of such processes with conventional control approaches with fixed parameters causes problems and suboptimal or unstable control results. An adaptive control is one way to how we can cope with nonlinearity of the system. This contribution compares classic adaptive control and its modification with Wiener system. This configuration divides nonlinear controller into the dynamic linear part and the static nonlinear part. The dynamic linear part is constructed with the use of polynomial synthesis together with the pole-placement method and the spectral factorization. The static nonlinear part uses static analysis of the controlled plant for introducing the mathematical nonlinear description of the relation between the controlled output and the change of the control input. Proposed controller is tested by the simulations on the mathematical model of the continuous stirred-tank reactor with cooling in the jacket as a typical nonlinear system. PMID:26346878

Static Methods in the Design of Nonlinear Automatic Control Systems,

DTIC Science & Technology

1984-06-27

227 Chapter VI. Ways of Decrease of the Number of Statistical Nodes During the Research of Nonlinear Systems...at present occupies the central place. This region of research was called the statistical dynamics of nonlinear H automatic control systems...receives further development in the numerous research of Soviet and C foreign scientists. Special role in the development of the statistical dynamics of

ESTIMATION OF CONSTANT AND TIME-VARYING DYNAMIC PARAMETERS OF HIV INFECTION IN A NONLINEAR DIFFERENTIAL EQUATION MODEL.

PubMed

Liang, Hua; Miao, Hongyu; Wu, Hulin

2010-03-01

Modeling viral dynamics in HIV/AIDS studies has resulted in deep understanding of pathogenesis of HIV infection from which novel antiviral treatment guidance and strategies have been derived. Viral dynamics models based on nonlinear differential equations have been proposed and well developed over the past few decades. However, it is quite challenging to use experimental or clinical data to estimate the unknown parameters (both constant and time-varying parameters) in complex nonlinear differential equation models. Therefore, investigators usually fix some parameter values, from the literature or by experience, to obtain only parameter estimates of interest from clinical or experimental data. However, when such prior information is not available, it is desirable to determine all the parameter estimates from data. In this paper, we intend to combine the newly developed approaches, a multi-stage smoothing-based (MSSB) method and the spline-enhanced nonlinear least squares (SNLS) approach, to estimate all HIV viral dynamic parameters in a nonlinear differential equation model. In particular, to the best of our knowledge, this is the first attempt to propose a comparatively thorough procedure, accounting for both efficiency and accuracy, to rigorously estimate all key kinetic parameters in a nonlinear differential equation model of HIV dynamics from clinical data. These parameters include the proliferation rate and death rate of uninfected HIV-targeted cells, the average number of virions produced by an infected cell, and the infection rate which is related to the antiviral treatment effect and is time-varying. To validate the estimation methods, we verified the identifiability of the HIV viral dynamic model and performed simulation studies. We applied the proposed techniques to estimate the key HIV viral dynamic parameters for two individual AIDS patients treated with antiretroviral therapies. We demonstrate that HIV viral dynamics can be well characterized and quantified for individual patients. As a result, personalized treatment decision based on viral dynamic models is possible.

Modelling of the Hypothalamic-Pituitary-Adrenal Axis Perturbations by Externally Induced Cholesterol Pulses of Finite Duration and with Asymmetrically Distributed Concentration Profile

NASA Astrophysics Data System (ADS)

Stanojević, A.; Marković, V. M.; Čupić, Ž.; Vukojević, V.; Kolar-Anić, L.

2017-12-01

A model was developed that can be used to study the effect of gradual cholesterol intake by food on the HPA axis dynamics. Namely, well defined oscillatory dynamics of vital neuroendocrine hypothalamic-pituitary-adrenal (HPA) axis has proven to be necessary for maintaining regular basal physiology and formulating appropriate stress response to various types of perturbations. Cholesterol, as a precursor of all steroid HPA axis hormones, can alter the dynamics of HPA axis. To analyse its particular influence on the HPA axis dynamics we used stoichiometric model of HPA axis activity, and simulate cholesterol perturbations in the form of finite duration pulses, with asymmetrically distributed concentration profile. Our numerical simulations showed that there is a complex, nonlinear dependence between the HPA axis responsiveness and different forms of applied cholesterol concentration pulses, indicating the significance of kinetic modelling, and dynamical systems theory for the understanding of large-scale self-regulatory, and homeostatic processes within this neuroendocrine system.

Highway traffic estimation of improved precision using the derivative-free nonlinear Kalman Filter

NASA Astrophysics Data System (ADS)

Rigatos, Gerasimos; Siano, Pierluigi; Zervos, Nikolaos; Melkikh, Alexey

2015-12-01

The paper proves that the PDE dynamic model of the highway traffic is a differentially flat one and by applying spatial discretization its shows that the model's transformation into an equivalent linear canonical state-space form is possible. For the latter representation of the traffic's dynamics, state estimation is performed with the use of the Derivative-free nonlinear Kalman Filter. The proposed filter consists of the Kalman Filter recursion applied on the transformed state-space model of the highway traffic. Moreover, it makes use of an inverse transformation, based again on differential flatness theory which enables to obtain estimates of the state variables of the initial nonlinear PDE model. By avoiding approximate linearizations and the truncation of nonlinear terms from the PDE model of the traffic's dynamics the proposed filtering methods outperforms, in terms of accuracy, other nonlinear estimators such as the Extended Kalman Filter. The article's theoretical findings are confirmed through simulation experiments.

Experimental evaluation of HJB optimal controllers for the attitude dynamics of a multirotor aerial vehicle.

PubMed

Prado, Igor Afonso Acampora; Pereira, Mateus de Freitas Virgílio; de Castro, Davi Ferreira; Dos Santos, Davi Antônio; Balthazar, Jose Manoel

2018-06-01

The present paper is concerned with the design and experimental evaluation of optimal control laws for the nonlinear attitude dynamics of a multirotor aerial vehicle. Three design methods based on Hamilton-Jacobi-Bellman equation are taken into account. The first one is a linear control with guarantee of stability for nonlinear systems. The second and third are a nonlinear suboptimal control techniques. These techniques are based on an optimal control design approach that takes into account the nonlinearities present in the vehicle dynamics. The stability Proof of the closed-loop system is presented. The performance of the control system designed is evaluated via simulations and also via an experimental scheme using the Quanser 3-DOF Hover. The experiments show the effectiveness of the linear control method over the nonlinear strategy. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Rail vehicle dynamic response to a nonlinear physical 'in-service' model of its secondary suspension hydraulic dampers

NASA Astrophysics Data System (ADS)

Wang, W. L.; Zhou, Z. R.; Yu, D. S.; Qin, Q. H.; Iwnicki, S.

2017-10-01

A full nonlinear physical 'in-service' model was built for a rail vehicle secondary suspension hydraulic damper with shim-pack-type valves. In the modelling process, a shim pack deflection theory with an equivalent-pressure correction factor was proposed, and a Finite Element Analysis (FEA) approach was applied. Bench test results validated the damper model over its full velocity range and thus also proved that the proposed shim pack deflection theory and the FEA-based parameter identification approach are effective. The validated full damper model was subsequently incorporated into a detailed vehicle dynamics simulation to study how its key in-service parameter variations influence the secondary-suspension-related vehicle system dynamics. The obtained nonlinear physical in-service damper model and the vehicle dynamic response characteristics in this study could be used in the product design optimization and nonlinear optimal specifications of high-speed rail hydraulic dampers.

Temporal and Spatio-Temporal Dynamic Instabilities: Novel Computational and Experimental approaches

NASA Astrophysics Data System (ADS)

Doedel, Eusebius J.; Panayotaros, Panayotis; Lambruschini, Carlos L. Pando

2016-11-01

This special issue contains a concise account of significant research results presented at the international workshop on Advanced Computational and Experimental Techniques in Nonlinear Dynamics, which was held in Cusco, Peru in August 2015. The meeting gathered leading experts, as well as new researchers, who have contributed to different aspects of Nonlinear Dynamics. Particularly significant was the presence of many active scientists from Latin America. The topics covered in this special issue range from advanced numerical techniques to novel physical experiments, and reflect the present state of the art in several areas of Nonlinear Dynamics. It contains seven review articles, followed by twenty-one regular papers that are organized in five categories, namely (1) Nonlinear Evolution Equations and Applications, (2) Numerical Continuation in Self-sustained Oscillators, (3) Synchronization, Control and Data Analysis, (4) Hamiltonian Systems, and (5) Scaling Properties in Maps.

Analysis of helicopter flight dynamics through modeling and simulation of primary flight control actuation system

NASA Astrophysics Data System (ADS)

Nelson, Hunter Barton

A simplified second-order transfer function actuator model used in most flight dynamics applications cannot easily capture the effects of different actuator parameters. The present work integrates a nonlinear actuator model into a nonlinear state space rotorcraft model to determine the effect of actuator parameters on key flight dynamics. The completed actuator model was integrated with a swashplate kinematics where step responses were generated over a range of key hydraulic parameters. The actuator-swashplate system was then introduced into a nonlinear state space rotorcraft simulation where flight dynamics quantities such as bandwidth and phase delay analyzed. Frequency sweeps were simulated for unique actuator configurations using the coupled nonlinear actuator-rotorcraft system. The software package CIFER was used for system identification and compared directly to the linearized models. As the actuator became rate saturated, the effects on bandwidth and phase delay were apparent on the predicted handling qualities specifications.

MSC products for the simulation of tire behavior

NASA Technical Reports Server (NTRS)

Muskivitch, John C.

1995-01-01

The modeling of tires and the simulation of tire behavior are complex problems. The MacNeal-Schwendler Corporation (MSC) has a number of finite element analysis products that can be used to address the complexities of tire modeling and simulation. While there are many similarities between the products, each product has a number of capabilities that uniquely enable it to be used for a specific aspect of tire behavior. This paper discusses the following programs: (1) MSC/NASTRAN - general purpose finite element program for linear and nonlinear static and dynamic analysis; (2) MSC/ADAQUS - nonlinear statics and dynamics finite element program; (3) MSC/PATRAN AFEA (Advanced Finite Element Analysis) - general purpose finite element program with a subset of linear and nonlinear static and dynamic analysis capabilities with an integrated version of MSC/PATRAN for pre- and post-processing; and (4) MSC/DYTRAN - nonlinear explicit transient dynamics finite element program.

Theoretical and software considerations for nonlinear dynamic analysis

NASA Technical Reports Server (NTRS)

Schmidt, R. J.; Dodds, R. H., Jr.

1983-01-01

In the finite element method for structural analysis, it is generally necessary to discretize the structural model into a very large number of elements to accurately evaluate displacements, strains, and stresses. As the complexity of the model increases, the number of degrees of freedom can easily exceed the capacity of present-day software system. Improvements of structural analysis software including more efficient use of existing hardware and improved structural modeling techniques are discussed. One modeling technique that is used successfully in static linear and nonlinear analysis is multilevel substructuring. This research extends the use of multilevel substructure modeling to include dynamic analysis and defines the requirements for a general purpose software system capable of efficient nonlinear dynamic analysis. The multilevel substructuring technique is presented, the analytical formulations and computational procedures for dynamic analysis and nonlinear mechanics are reviewed, and an approach to the design and implementation of a general purpose structural software system is presented.

A geometrical approach to control and controllability of nonlinear dynamical networks

PubMed Central

Wang, Le-Zhi; Su, Ri-Qi; Huang, Zi-Gang; Wang, Xiao; Wang, Wen-Xu; Grebogi, Celso; Lai, Ying-Cheng

2016-01-01

In spite of the recent interest and advances in linear controllability of complex networks, controlling nonlinear network dynamics remains an outstanding problem. Here we develop an experimentally feasible control framework for nonlinear dynamical networks that exhibit multistability. The control objective is to apply parameter perturbation to drive the system from one attractor to another, assuming that the former is undesired and the latter is desired. To make our framework practically meaningful, we consider restricted parameter perturbation by imposing two constraints: it must be experimentally realizable and applied only temporarily. We introduce the concept of attractor network, which allows us to formulate a quantifiable controllability framework for nonlinear dynamical networks: a network is more controllable if the attractor network is more strongly connected. We test our control framework using examples from various models of experimental gene regulatory networks and demonstrate the beneficial role of noise in facilitating control. PMID:27076273

PRESS-based EFOR algorithm for the dynamic parametrical modeling of nonlinear MDOF systems

NASA Astrophysics Data System (ADS)

Liu, Haopeng; Zhu, Yunpeng; Luo, Zhong; Han, Qingkai

2017-09-01

In response to the identification problem concerning multi-degree of freedom (MDOF) nonlinear systems, this study presents the extended forward orthogonal regression (EFOR) based on predicted residual sums of squares (PRESS) to construct a nonlinear dynamic parametrical model. The proposed parametrical model is based on the non-linear autoregressive with exogenous inputs (NARX) model and aims to explicitly reveal the physical design parameters of the system. The PRESS-based EFOR algorithm is proposed to identify such a model for MDOF systems. By using the algorithm, we built a common-structured model based on the fundamental concept of evaluating its generalization capability through cross-validation. The resulting model aims to prevent over-fitting with poor generalization performance caused by the average error reduction ratio (AERR)-based EFOR algorithm. Then, a functional relationship is established between the coefficients of the terms and the design parameters of the unified model. Moreover, a 5-DOF nonlinear system is taken as a case to illustrate the modeling of the proposed algorithm. Finally, a dynamic parametrical model of a cantilever beam is constructed from experimental data. Results indicate that the dynamic parametrical model of nonlinear systems, which depends on the PRESS-based EFOR, can accurately predict the output response, thus providing a theoretical basis for the optimal design of modeling methods for MDOF nonlinear systems.

Dynamic Time Expansion and Compression Using Nonlinear Waveguides

DOEpatents

Findikoglu, Alp T.; Hahn, Sangkoo F.; Jia, Quanxi

2004-06-22

Dynamic time expansion or compression of a small amplitude input signal generated with an initial scale is performed using a nonlinear waveguide. A nonlinear waveguide having a variable refractive index is connected to a bias voltage source having a bias signal amplitude that is large relative to the input signal to vary the reflective index and concomitant speed of propagation of the nonlinear waveguide and an electrical circuit for applying the small amplitude signal and the large amplitude bias signal simultaneously to the nonlinear waveguide. The large amplitude bias signal with the input signal alters the speed of propagation of the small-amplitude signal with time in the nonlinear waveguide to expand or contract the initial time scale of the small-amplitude input signal.

Dynamic time expansion and compression using nonlinear waveguides

DOEpatents

Findikoglu, Alp T [Los Alamos, NM; Hahn, Sangkoo F [Los Alamos, NM; Jia, Quanxi [Los Alamos, NM

2004-06-22

Dynamic time expansion or compression of a small-amplitude input signal generated with an initial scale is performed using a nonlinear waveguide. A nonlinear waveguide having a variable refractive index is connected to a bias voltage source having a bias signal amplitude that is large relative to the input signal to vary the reflective index and concomitant speed of propagation of the nonlinear waveguide and an electrical circuit for applying the small-amplitude signal and the large amplitude bias signal simultaneously to the nonlinear waveguide. The large amplitude bias signal with the input signal alters the speed of propagation of the small-amplitude signal with time in the nonlinear waveguide to expand or contract the initial time scale of the small-amplitude input signal.

Quantum and semiclassical physics behind ultrafast optical nonlinearity in the midinfrared: the role of ionization dynamics within the field half cycle.

PubMed

Serebryannikov, E E; Zheltikov, A M

2014-07-25

Ultrafast ionization dynamics within the field half cycle is shown to be the key physical factor that controls the properties of optical nonlinearity as a function of the carrier wavelength and intensity of a driving laser field. The Schrödinger-equation analysis of a generic hydrogen quantum system reveals universal tendencies in the wavelength dependence of optical nonlinearity, shedding light on unusual properties of optical nonlinearities in the midinfrared. For high-intensity low-frequency fields, free-state electrons are shown to dominate over bound electrons in the overall nonlinear response of a quantum system. In this regime, semiclassical models are shown to offer useful insights into the physics behind optical nonlinearity.

COMBINED DELAY AND GRAPH EMBEDDING OF EPILEPTIC DISCHARGES IN EEG REVEALS COMPLEX AND RECURRENT NONLINEAR DYNAMICS.

PubMed

Erem, B; Hyde, D E; Peters, J M; Duffy, F H; Brooks, D H; Warfield, S K

2015-04-01

The dynamical structure of the brain's electrical signals contains valuable information about its physiology. Here we combine techniques for nonlinear dynamical analysis and manifold identification to reveal complex and recurrent dynamics in interictal epileptiform discharges (IEDs). Our results suggest that recurrent IEDs exhibit some consistent dynamics, which may only last briefly, and so individual IED dynamics may need to be considered in order to understand their genesis. This could potentially serve to constrain the dynamics of the inverse source localization problem.

Nonlinear System Identification for Aeroelastic Systems with Application to Experimental Data

NASA Technical Reports Server (NTRS)

Kukreja, Sunil L.

2008-01-01

Representation and identification of a nonlinear aeroelastic pitch-plunge system as a model of the Nonlinear AutoRegressive, Moving Average eXogenous (NARMAX) class is considered. A nonlinear difference equation describing this aircraft model is derived theoretically and shown to be of the NARMAX form. Identification methods for NARMAX models are applied to aeroelastic dynamics and its properties demonstrated via continuous-time simulations of experimental conditions. Simulation results show that (1) the outputs of the NARMAX model closely match those generated using continuous-time methods, and (2) NARMAX identification methods applied to aeroelastic dynamics provide accurate discrete-time parameter estimates. Application of NARMAX identification to experimental pitch-plunge dynamics data gives a high percent fit for cross-validated data.

Nonlinear dynamics and cavity cooling of levitated nanoparticles

NASA Astrophysics Data System (ADS)

Fonseca, P. Z. G.; Aranas, E. B.; Millen, J.; Monteiro, T. S.; Barker, P. F.

2016-09-01

We investigate a dynamic nonlinear optomechanical system, comprising a nanosphere levitated in a hybrid electro-optical trap. An optical cavity offers readout of both linear-in-position and quadratic-in-position (nonlinear) light-matter coupling, whilst simultaneously cooling the nanosphere, for indefinite periods of time and in high vacuum. Through the rich sideband structure displayed by the cavity output we can observe cooling of the linear and non-linear particle's motion. Here we present an experimental setup which allows full control over the cavity resonant frequencies, and shows cooling of the particle's motion as a function of the detuning. This work paves the way to strong-coupled quantum dynamics between a cavity and a mesoscopic object largely decoupled from its environment.

A non-linear mathematical model for dynamic analysis of spur gears including shaft and bearing dynamics

NASA Technical Reports Server (NTRS)

Ozguven, H. Nevzat

1991-01-01

A six-degree-of-freedom nonlinear semi-definite model with time varying mesh stiffness has been developed for the dynamic analysis of spur gears. The model includes a spur gear pair, two shafts, two inertias representing load and prime mover, and bearings. As the shaft and bearing dynamics have also been considered in the model, the effect of lateral-torsional vibration coupling on the dynamics of gears can be studied. In the nonlinear model developed several factors such as time varying mesh stiffness and damping, separation of teeth, backlash, single- and double-sided impacts, various gear errors and profile modifications have been considered. The dynamic response to internal excitation has been calculated by using the 'static transmission error method' developed. The software prepared (DYTEM) employs the digital simulation technique for the solution, and is capable of calculating dynamic tooth and mesh forces, dynamic factors for pinion and gear, dynamic transmission error, dynamic bearing forces and torsions of shafts. Numerical examples are given in order to demonstrate the effect of shaft and bearing dynamics on gear dynamics.

Nonlinear electromechanical modelling and dynamical behavior analysis of a satellite reaction wheel

NASA Astrophysics Data System (ADS)

Aghalari, Alireza; Shahravi, Morteza

2017-12-01

The present research addresses the satellite reaction wheel (RW) nonlinear electromechanical coupling dynamics including dynamic eccentricity of brushless dc (BLDC) motor and gyroscopic effects, as well as dry friction of shaft-bearing joints (relative small slip) and bearing friction. In contrast to other studies, the rotational velocity of the flywheel is considered to be controllable, so it is possible to study the reaction wheel dynamical behavior in acceleration stages. The RW is modeled as a three-phases BLDC motor as well as flywheel with unbalances on a rigid shaft and flexible bearings. Improved Lagrangian dynamics for electromechanical systems is used to obtain the mathematical model of the system. The developed model can properly describe electromechanical nonlinear coupled dynamical behavior of the satellite RW. Numerical simulations show the effectiveness of the presented approach.

Force and Moment Approach for Achievable Dynamics Using Nonlinear Dynamic Inversion

NASA Technical Reports Server (NTRS)

Ostroff, Aaron J.; Bacon, Barton J.

1999-01-01

This paper describes a general form of nonlinear dynamic inversion control for use in a generic nonlinear simulation to evaluate candidate augmented aircraft dynamics. The implementation is specifically tailored to the task of quickly assessing an aircraft's control power requirements and defining the achievable dynamic set. The achievable set is evaluated while undergoing complex mission maneuvers, and perfect tracking will be accomplished when the desired dynamics are achievable. Variables are extracted directly from the simulation model each iteration, so robustness is not an issue. Included in this paper is a description of the implementation of the forces and moments from simulation variables, the calculation of control effectiveness coefficients, methods for implementing different types of aerodynamic and thrust vectoring controls, adjustments for control effector failures, and the allocation approach used. A few examples illustrate the perfect tracking results obtained.

Application of dynamic recurrent neural networks in nonlinear system identification

NASA Astrophysics Data System (ADS)

Du, Yun; Wu, Xueli; Sun, Huiqin; Zhang, Suying; Tian, Qiang

2006-11-01

An adaptive identification method of simple dynamic recurrent neural network (SRNN) for nonlinear dynamic systems is presented in this paper. This method based on the theory that by using the inner-states feed-back of dynamic network to describe the nonlinear kinetic characteristics of system can reflect the dynamic characteristics more directly, deduces the recursive prediction error (RPE) learning algorithm of SRNN, and improves the algorithm by studying topological structure on recursion layer without the weight values. The simulation results indicate that this kind of neural network can be used in real-time control, due to its less weight values, simpler learning algorithm, higher identification speed, and higher precision of model. It solves the problems of intricate in training algorithm and slow rate in convergence caused by the complicate topological structure in usual dynamic recurrent neural network.

The effects of five-order nonlinear on the dynamics of dark solitons in optical fiber.

PubMed

He, Feng-Tao; Wang, Xiao-Lin; Duan, Zuo-Liang

2013-01-01

We study the influence of five-order nonlinear on the dynamic of dark soliton. Starting from the cubic-quintic nonlinear Schrodinger equation with the quadratic phase chirp term, by using a similarity transformation technique, we give the exact solution of dark soliton and calculate the precise expressions of dark soliton's width, amplitude, wave central position, and wave velocity which can describe the dynamic behavior of soliton's evolution. From two different kinds of quadratic phase chirps, we mainly analyze the effect on dark soliton's dynamics which different fiver-order nonlinear term generates. The results show the following two points with quintic nonlinearities coefficient increasing: (1) if the coefficients of the quadratic phase chirp term relate to the propagation distance, the solitary wave displays a periodic change and the soliton's width increases, while its amplitude and wave velocity reduce. (2) If the coefficients of the quadratic phase chirp term do not depend on propagation distance, the wave function only emerges in a fixed area. The soliton's width increases, while its amplitude and the wave velocity reduce.

The Effects of Five-Order Nonlinear on the Dynamics of Dark Solitons in Optical Fiber

PubMed Central

Wang, Xiao-Lin; Duan, Zuo-Liang

2013-01-01

We study the influence of five-order nonlinear on the dynamic of dark soliton. Starting from the cubic-quintic nonlinear Schrodinger equation with the quadratic phase chirp term, by using a similarity transformation technique, we give the exact solution of dark soliton and calculate the precise expressions of dark soliton's width, amplitude, wave central position, and wave velocity which can describe the dynamic behavior of soliton's evolution. From two different kinds of quadratic phase chirps, we mainly analyze the effect on dark soliton's dynamics which different fiver-order nonlinear term generates. The results show the following two points with quintic nonlinearities coefficient increasing: (1) if the coefficients of the quadratic phase chirp term relate to the propagation distance, the solitary wave displays a periodic change and the soliton's width increases, while its amplitude and wave velocity reduce. (2) If the coefficients of the quadratic phase chirp term do not depend on propagation distance, the wave function only emerges in a fixed area. The soliton's width increases, while its amplitude and the wave velocity reduce. PMID:23818814

Optical nonlinear properties and dynamics of interband transitions in multilayer MoS2 structures under femtosecond excitation at a wavelength of 514 nm

NASA Astrophysics Data System (ADS)

Khudyakov, D. V.; Borodkin, A. A.; Mazin, D. D.; Lobach, A. S.; Vartapetov, S. K.

2018-02-01

The optical nonlinear absorption and bleaching of aqueous suspensions of multilayer MoS2 sheets (structural modification 2H) under excitation by a 400-fs pulse at a wavelength of 514 nm is investigated using longitudinal scanning. The sample exhibits nonlinear absorption at intensities up to 15 GW cm-2, while a further increase in intensity to 70 GW cm-2 causes nonlinear bleaching with a relative change in transmission to 14%. The dynamics of interband transitions in the picosecond range is studied by femtosecond laser photolysis. The relaxation time of photoexcited excitons is measured to be 20 ± 2 ps. The transition dynamics is calculated in the three-level approximation, and the absorption cross sections of photoinduced electron transitions from the valence band to the conduction band and from the first to the second conduction band are estimated. It is shown that the optical nonlinear properties of suspensions of multilayer 2H MoS2 sheets are mainly determined by the dynamics of single-photon interband transitions.

Linear and nonlinear dynamics of isospectral granular chains

NASA Astrophysics Data System (ADS)

Chaunsali, R.; Xu, H.; Yang, J.; Kevrekidis, P. G.

2017-04-01

We study the dynamics of isospectral granular chains that are highly tunable due to the nonlinear Hertz contact law interaction between the granular particles. The system dynamics can thus be tuned easily from being linear to strongly nonlinear by adjusting the initial compression applied to the chain. In particular, we introduce both discrete and continuous spectral transformation schemes to generate a family of granular chains that are isospectral in their linear limit. Inspired by the principle of supersymmetry in quantum systems, we also introduce a methodology to add or remove certain eigenfrequencies, and we demonstrate numerically that the corresponding physical system can be constructed in the setting of one-dimensional granular crystals. In the linear regime, we highlight the similarities in the elastic wave transmission characteristics of such isospectral systems, and emphasize that the presented mathematical framework allows one to suitably tailor the wave transmission through a general class of granular chains, both ordered and disordered. Moreover, we show how the dynamic response of these structures deviates from its linear limit as we introduce Hertzian nonlinearity in the chain and how nonlinearity breaks the notion of linear isospectrality.

Multiscale Support Vector Learning With Projection Operator Wavelet Kernel for Nonlinear Dynamical System Identification.

PubMed

Lu, Zhao; Sun, Jing; Butts, Kenneth

2016-02-03

A giant leap has been made in the past couple of decades with the introduction of kernel-based learning as a mainstay for designing effective nonlinear computational learning algorithms. In view of the geometric interpretation of conditional expectation and the ubiquity of multiscale characteristics in highly complex nonlinear dynamic systems [1]-[3], this paper presents a new orthogonal projection operator wavelet kernel, aiming at developing an efficient computational learning approach for nonlinear dynamical system identification. In the framework of multiresolution analysis, the proposed projection operator wavelet kernel can fulfill the multiscale, multidimensional learning to estimate complex dependencies. The special advantage of the projection operator wavelet kernel developed in this paper lies in the fact that it has a closed-form expression, which greatly facilitates its application in kernel learning. To the best of our knowledge, it is the first closed-form orthogonal projection wavelet kernel reported in the literature. It provides a link between grid-based wavelets and mesh-free kernel-based methods. Simulation studies for identifying the parallel models of two benchmark nonlinear dynamical systems confirm its superiority in model accuracy and sparsity.

Onset of chaos in helical vortex breakdown at low Reynolds number

NASA Astrophysics Data System (ADS)

Pasche, S.; Avellan, F.; Gallaire, F.

2018-06-01

The nonlinear dynamics of a swirling wake flow stemming from a Graboswksi-Berger vortex [Grabowski and Berger, J. Fluid Mech. 75, 525 (1976), 10.1017/S0022112076000360] in a semi-infinite domain is addressed at low Reynolds numbers for a fixed swirl number S =1.095 , defined as the ratio between the characteristic tangential velocity and the centerline axial velocity. In this system, only pure hydrodynamic instabilities develop and interact through the quadratic nonlinearities of the Navier-Stokes equations. Such interactions lead to the onset of chaos at a Reynolds value of Re=220 . This chaotic state is reached by following a Ruelle-Takens-Newhouse scenario, which is initiated by a Hopf bifurcation (the spiral vortex breakdown) as the Reynolds number increases. At larger Reynolds value, a frequency synchronization regime appears followed by a chaotic state again. This scenario is corroborated by nonlinear time series analyses. Stability analysis around the time-average flow and temporal-azimuthal Fourier decomposition of the nonlinear flow distributions both identify successfully the developing vortices and provide deeper insight into the development of the flow patterns leading to this route to chaos. Three single-helical vortices are involved: the primary spiral associated with the spiral vortex breakdown, a downstream spiral, and a near-wake spiral. As the Reynolds number increases, the frequencies of these vortices become closer, increasing their interactions by nonlinearity to eventually generate a strong chaotic axisymmetric oscillation.

Nonlinear Time Series Analysis of Nodulation Factor Induced Calcium Oscillations: Evidence for Deterministic Chaos?

PubMed Central

Hazledine, Saul; Sun, Jongho; Wysham, Derin; Downie, J. Allan; Oldroyd, Giles E. D.; Morris, Richard J.

2009-01-01

Legume plants form beneficial symbiotic interactions with nitrogen fixing bacteria (called rhizobia), with the rhizobia being accommodated in unique structures on the roots of the host plant. The legume/rhizobial symbiosis is responsible for a significant proportion of the global biologically available nitrogen. The initiation of this symbiosis is governed by a characteristic calcium oscillation within the plant root hair cells and this signal is activated by the rhizobia. Recent analyses on calcium time series data have suggested that stochastic effects have a large role to play in defining the nature of the oscillations. The use of multiple nonlinear time series techniques, however, suggests an alternative interpretation, namely deterministic chaos. We provide an extensive, nonlinear time series analysis on the nature of this calcium oscillation response. We build up evidence through a series of techniques that test for determinism, quantify linear and nonlinear components, and measure the local divergence of the system. Chaos is common in nature and it seems plausible that properties of chaotic dynamics might be exploited by biological systems to control processes within the cell. Systems possessing chaotic control mechanisms are more robust in the sense that the enhanced flexibility allows more rapid response to environmental changes with less energetic costs. The desired behaviour could be most efficiently targeted in this manner, supporting some intriguing speculations about nonlinear mechanisms in biological signaling. PMID:19675679

Neural network based adaptive control for nonlinear dynamic regimes

NASA Astrophysics Data System (ADS)

Shin, Yoonghyun

Adaptive control designs using neural networks (NNs) based on dynamic inversion are investigated for aerospace vehicles which are operated at highly nonlinear dynamic regimes. NNs play a key role as the principal element of adaptation to approximately cancel the effect of inversion error, which subsequently improves robustness to parametric uncertainty and unmodeled dynamics in nonlinear regimes. An adaptive control scheme previously named 'composite model reference adaptive control' is further developed so that it can be applied to multi-input multi-output output feedback dynamic inversion. It can have adaptive elements in both the dynamic compensator (linear controller) part and/or in the conventional adaptive controller part, also utilizing state estimation information for NN adaptation. This methodology has more flexibility and thus hopefully greater potential than conventional adaptive designs for adaptive flight control in highly nonlinear flight regimes. The stability of the control system is proved through Lyapunov theorems, and validated with simulations. The control designs in this thesis also include the use of 'pseudo-control hedging' techniques which are introduced to prevent the NNs from attempting to adapt to various actuation nonlinearities such as actuator position and rate saturations. Control allocation is introduced for the case of redundant control effectors including thrust vectoring nozzles. A thorough comparison study of conventional and NN-based adaptive designs for a system under a limit cycle, wing-rock, is included in this research, and the NN-based adaptive control designs demonstrate their performances for two highly maneuverable aerial vehicles, NASA F-15 ACTIVE and FQM-117B unmanned aerial vehicle (UAV), operated under various nonlinearities and uncertainties.

Transient responses of phosphoric acid fuel cell power plant system. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Lu, Cheng-Yi

1983-01-01

An analytical and computerized study of the steady state and transient response of a phosphoric acid fuel cell (PAFC) system was completed. Parametric studies and sensitivity analyses of the PAFC system's operation were accomplished. Four non-linear dynamic models of the fuel cell stack, reformer, shift converters, and heat exchangers were developed based on nonhomogeneous non-linear partial differential equations, which include the material, component, energy balance, and electrochemical kinetic features. Due to a lack of experimental data for the dynamic response of the components only the steady state results were compared with data from other sources, indicating reasonably good agreement. A steady state simulation of the entire system was developed using, nonlinear ordinary differential equations. The finite difference method and trial-and-error procedures were used to obtain a solution. Using the model, a PAFC system, that was developed under NASA Grant, NCC3-17, was improved through the optimization of the heat exchanger network. Three types of cooling configurations for cell plates were evaluated to obtain the best current density and temperature distributions. The steady state solutions were used as the initial conditions in the dynamic model. The transient response of a simplified PAFC system, which included all of the major components, subjected to a load change was obtained. Due to the length of the computation time for the transient response calculations, analysis on a real-time computer was not possible. A simulation of the real-time calculations was developed on a batch type computer. The transient response characteristics are needed for the optimization of the design and control of the whole PAFC system. All of the models, procedures and simulations were programmed in Fortran and run on IBM 370 computers at Cleveland State University and the NASA Lewis Research Center.

Materials constitutive models for nonlinear analysis of thermally cycled structures

NASA Technical Reports Server (NTRS)

Kaufman, A.; Hunt, L. E.

1982-01-01

Effects of inelastic materials models on computed stress-strain solutions for thermally loaded structures were studied by performing nonlinear (elastoplastic creep) and elastic structural analyses on a prismatic, double edge wedge specimen of IN 100 alloy that was subjected to thermal cycling in fluidized beds. Four incremental plasticity creep models (isotropic, kinematic, combined isotropic kinematic, and combined plus transient creep) were exercised for the problem by using the MARC nonlinear, finite element computer program. Maximum total strain ranges computed from the elastic and nonlinear analyses agreed within 5 percent. Mean cyclic stresses, inelastic strain ranges, and inelastic work were significantly affected by the choice of inelastic constitutive model. The computing time per cycle for the nonlinear analyses was more than five times that required for the elastic analysis.

Digit replacement: A generic map for nonlinear dynamical systems.

PubMed

García-Morales, Vladimir

2016-09-01

A simple discontinuous map is proposed as a generic model for nonlinear dynamical systems. The orbit of the map admits exact solutions for wide regions in parameter space and the method employed (digit manipulation) allows the mathematical design of useful signals, such as regular or aperiodic oscillations with specific waveforms, the construction of complex attractors with nontrivial properties as well as the coexistence of different basins of attraction in phase space with different qualitative properties. A detailed analysis of the dynamical behavior of the map suggests how the latter can be used in the modeling of complex nonlinear dynamics including, e.g., aperiodic nonchaotic attractors and the hierarchical deposition of grains of different sizes on a surface.

Inferring Instantaneous, Multivariate and Nonlinear Sensitivities for the Analysis of Feedback Processes in a Dynamical System: Lorenz Model Case Study

NASA Technical Reports Server (NTRS)

Aires, Filipe; Rossow, William B.; Hansen, James E. (Technical Monitor)

2001-01-01

A new approach is presented for the analysis of feedback processes in a nonlinear dynamical system by observing its variations. The new methodology consists of statistical estimates of the sensitivities between all pairs of variables in the system based on a neural network modeling of the dynamical system. The model can then be used to estimate the instantaneous, multivariate and nonlinear sensitivities, which are shown to be essential for the analysis of the feedbacks processes involved in the dynamical system. The method is described and tested on synthetic data from the low-order Lorenz circulation model where the correct sensitivities can be evaluated analytically.

Interaction between Liénard and Ikeda dynamics in a nonlinear electro-optical oscillator with delayed bandpass feedback.

PubMed

Marquez, Bicky A; Larger, Laurent; Brunner, Daniel; Chembo, Yanne K; Jacquot, Maxime

2016-12-01

We report on experimental and theoretical analysis of the complex dynamics generated by a nonlinear time-delayed electro-optic bandpass oscillator. We investigate the interaction between the slow- and fast-scale dynamics of autonomous oscillations in the breather regime. We analyze in detail the coupling between the fast-scale behavior associated to a characteristic low-pass Ikeda behavior and the slow-scale dynamics associated to a Liénard limit-cycle. Finally, we show that when projected onto a two-dimensional phase space, the attractors corresponding to periodic and chaotic breathers display a spiral-like pattern, which strongly depends on the shape of the nonlinear function.

Unimodal dynamical systems: Comparison principles, spreading speeds and travelling waves

NASA Astrophysics Data System (ADS)

Yi, Taishan; Chen, Yuming; Wu, Jianhong

Reaction diffusion equations with delayed nonlinear reaction terms are used as prototypes to motivate an appropriate abstract formulation of dynamical systems with unimodal nonlinearity. For such non-monotone dynamical systems, we develop a general comparison principle and show how this general comparison principle, coupled with some existing results for monotone dynamical systems, can be used to establish results on the asymptotic speeds of spread and travelling waves. We illustrate our main results by an integral equation which includes a nonlocal delayed reaction diffusion equation and a nonlocal delayed lattice differential system in an unbounded domain, with the non-monotone nonlinearities including the Ricker birth function and the Mackey-Glass hematopoiesis feedback.

A Nonlinear Dynamical Systems based Model for Stochastic Simulation of Streamflow

NASA Astrophysics Data System (ADS)

Erkyihun, S. T.; Rajagopalan, B.; Zagona, E. A.

2014-12-01

Traditional time series methods model the evolution of the underlying process as a linear or nonlinear function of the autocorrelation. These methods capture the distributional statistics but are incapable of providing insights into the dynamics of the process, the potential regimes, and predictability. This work develops a nonlinear dynamical model for stochastic simulation of streamflows. In this, first a wavelet spectral analysis is employed on the flow series to isolate dominant orthogonal quasi periodic timeseries components. The periodic bands are added denoting the 'signal' component of the time series and the residual being the 'noise' component. Next, the underlying nonlinear dynamics of this combined band time series is recovered. For this the univariate time series is embedded in a d-dimensional space with an appropriate lag T to recover the state space in which the dynamics unfolds. Predictability is assessed by quantifying the divergence of trajectories in the state space with time, as Lyapunov exponents. The nonlinear dynamics in conjunction with a K-nearest neighbor time resampling is used to simulate the combined band, to which the noise component is added to simulate the timeseries. We demonstrate this method by applying it to the data at Lees Ferry that comprises of both the paleo reconstructed and naturalized historic annual flow spanning 1490-2010. We identify interesting dynamics of the signal in the flow series and epochal behavior of predictability. These will be of immense use for water resources planning and management.

Nonlinear absorption dynamics using field-induced surface hopping: zinc porphyrin in water.

PubMed

Röhr, Merle I S; Petersen, Jens; Wohlgemuth, Matthias; Bonačić-Koutecký, Vlasta; Mitrić, Roland

2013-05-10

We wish to present the application of our field-induced surface-hopping (FISH) method to simulate nonlinear absorption dynamics induced by strong nonresonant laser fields. We provide a systematic comparison of the FISH approach with exact quantum dynamics simulations on a multistate model system and demonstrate that FISH allows for accurate simulations of nonlinear excitation processes including multiphoton electronic transitions. In particular, two different approaches for simulating two-photon transitions are compared. The first approach is essentially exact and involves the solution of the time-dependent Schrödinger equation in an extended manifold of excited states, while in the second one only transiently populated nonessential states are replaced by an effective quadratic coupling term, and dynamics is performed in a considerably smaller manifold of states. We illustrate the applicability of our method to complex molecular systems by simulating the linear and nonlinear laser-driven dynamics in zinc (Zn) porphyrin in the gas phase and in water. For this purpose, the FISH approach is connected with the quantum mechanical-molecular mechanical approach (QM/MM) which is generally applicable to large classes of complex systems. Our findings that multiphoton absorption and dynamics increase the population of higher excited states of Zn porphyrin in the nonlinear regime, in particular in solution, provides a means for manipulating excited-state properties, such as transient absorption dynamics and electronic relaxation. Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Weakly nonlinear dynamics of near-CJ detonation waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bdzil, J.B.; Klein, R.

1993-01-01

The renewed interest in safety issues for large scale industrial devices and in high speed combustion has driven recent intense efforts to gain a deeper theoretical understanding of detonation wave dynamics. Linear stability analyses, weakly nonlinear bifurcation calculations as well as full scale multi-dimensional direct numerical simulations have been pursued for a standard model problem based on the reactive Euler equations for an ideal gas with constant specific heat capacities and simplified chemical reaction models. Most of these studies are concerned with overdriven detonations. This is true despite the fact that the majority of all detonations observed in nature aremore » running at speeds close to the Chapman-Jouguet (CJ) limit value. By focusing on overdriven waves one removes an array of difficulties from the analysis that is associated with the sonic flow conditions in the wake of a CJ-detonation. In particular, the proper formulation of downstream boundary conditions in the CJ-case is a yet unsolved analytical problem. A proper treatment of perturbations in the back of a Chapman-Jouguet detonation has to account for two distinct weakly nonlinear effects in the forward acoustic wave component. The first is a nonlinear interactionof highly temperature sensitive chemistry with the forward acoustic wave component in a transonic boundary layer near the end of the reaction zone. The second is a cumulative three-wave-resonance in the sense of Majda et al. which is active in the near-sonic burnt gas flow and which is essentially independent of the details of the chemical model. In this work, we consider detonations in mixtures with moderate state sensitivity of the chemical reactions. Then, the acoustic perturbations do not influence the chemistry at the order considered and we may concentrate on the second effect; the three-wave resonance.« less

Weakly nonlinear dynamics of near-CJ detonation waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bdzil, J.B.; Klein, R.

1993-02-01

The renewed interest in safety issues for large scale industrial devices and in high speed combustion has driven recent intense efforts to gain a deeper theoretical understanding of detonation wave dynamics. Linear stability analyses, weakly nonlinear bifurcation calculations as well as full scale multi-dimensional direct numerical simulations have been pursued for a standard model problem based on the reactive Euler equations for an ideal gas with constant specific heat capacities and simplified chemical reaction models. Most of these studies are concerned with overdriven detonations. This is true despite the fact that the majority of all detonations observed in nature aremore » running at speeds close to the Chapman-Jouguet (CJ) limit value. By focusing on overdriven waves one removes an array of difficulties from the analysis that is associated with the sonic flow conditions in the wake of a CJ-detonation. In particular, the proper formulation of downstream boundary conditions in the CJ-case is a yet unsolved analytical problem. A proper treatment of perturbations in the back of a Chapman-Jouguet detonation has to account for two distinct weakly nonlinear effects in the forward acoustic wave component. The first is a nonlinear interactionof highly temperature sensitive chemistry with the forward acoustic wave component in a transonic boundary layer near the end of the reaction zone. The second is a cumulative three-wave-resonance in the sense of Majda et al. which is active in the near-sonic burnt gas flow and which is essentially independent of the details of the chemical model. In this work, we consider detonations in mixtures with moderate state sensitivity of the chemical reactions. Then, the acoustic perturbations do not influence the chemistry at the order considered and we may concentrate on the second effect; the three-wave resonance.« less

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control.

PubMed

Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kutz, J Nathan

2016-01-01

In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.ork, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.

Simulation of noisy dynamical system by Deep Learning

NASA Astrophysics Data System (ADS)

Yeo, Kyongmin

2017-11-01

Deep learning has attracted huge attention due to its powerful representation capability. However, most of the studies on deep learning have been focused on visual analytics or language modeling and the capability of the deep learning in modeling dynamical systems is not well understood. In this study, we use a recurrent neural network to model noisy nonlinear dynamical systems. In particular, we use a long short-term memory (LSTM) network, which constructs internal nonlinear dynamics systems. We propose a cross-entropy loss with spatial ridge regularization to learn a non-stationary conditional probability distribution from a noisy nonlinear dynamical system. A Monte Carlo procedure to perform time-marching simulations by using the LSTM is presented. The behavior of the LSTM is studied by using noisy, forced Van der Pol oscillator and Ikeda equation.

Chaotic dynamical aperture

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, S.Y.; Tepikian, S.

1985-01-01

Nonlinear magnetic forces become more important for particles in the modern large accelerators. These nonlinear elements are introduced either intentionally to control beam dynamics or by uncontrollable random errors. Equations of motion in the nonlinear Hamiltonian are usually non-integrable. Because of the nonlinear part of the Hamiltonian, the tune diagram of accelerators is a jungle. Nonlinear magnet multipoles are important in keeping the accelerator operation point in the safe quarter of the hostile jungle of resonant tunes. Indeed, all the modern accelerator designs have taken advantages of nonlinear mechanics. On the other hand, the effect of the uncontrollable random multipolesmore » should be evaluated carefully. A powerful method of studying the effect of these nonlinear multipoles is using a particle tracking calculation, where a group of test particles are tracing through these magnetic multipoles in the accelerator hundreds to millions of turns in order to test the dynamical aperture of the machine. These methods are extremely useful in the design of a large accelerator such as SSC, LEP, HERA and RHIC. These calculations unfortunately take a tremendous amount of computing time. In this review the method of determining chaotic orbit and applying the method to nonlinear problems in accelerator physics is discussed. We then discuss the scaling properties and effect of random sextupoles.« less

Nonlinear Wave Propagation

DTIC Science & Technology

2009-02-09

grey) soliton , to a nearly linear wavetrain at the front moving with its group velocity ; like KdV the NLS DSW has two speeds. The 1-D NLS theory was...studies of wave phenomena in nonlinear optics include ultrashort pulse dynamics in mode- locked lasers, dynamics and perturbations of dark solitons ...nonlinear Kerr response and has a large normal group - velocity dispersion (GVD). This requires a set of prisms and/or mirrors specially designed to have

Non-linear relationship between maternal work hours and child body weight: Evidence from the Western Australian Pregnancy Cohort (Raine) Study.

PubMed

Li, Jianghong; Akaliyski, Plamen; Schäfer, Jakob; Kendall, Garth; Oddy, Wendy H; Stanley, Fiona; Strazdins, Lyndall

2017-08-01

Using longitudinal data from the Western Australia Pregnancy Cohort (Raine) Study and both random-effects and fixed-effects models, this study examined the connection between maternal work hours and child overweight or obesity. Following children in two-parent families from early childhood to early adolescence, multivariate analyses revealed a non-linear and developmentally dynamic relationship. Among preschool children (ages 2 to 5), we found lower likelihood of child overweight and obesity when mothers worked 24 h or less per week, compared to when mothers worked 35 or more hours. This effect was stronger in low-to-medium income families. For older children (ages 8 to 14), compared to working 35-40 h a week, working shorter hours (1-24, 25-34) or longer hours (41 or more) was both associated with increases in child overweight and obesity. These non-linear effects were more pronounced in low-to-medium income families, particularly when fathers also worked long hours. Copyright © 2017 Elsevier Ltd. All rights reserved.

A Generic Nonlinear Aerodynamic Model for Aircraft

NASA Technical Reports Server (NTRS)

Grauer, Jared A.; Morelli, Eugene A.

2014-01-01

A generic model of the aerodynamic coefficients was developed using wind tunnel databases for eight different aircraft and multivariate orthogonal functions. For each database and each coefficient, models were determined using polynomials expanded about the state and control variables, and an othgonalization procedure. A predicted squared-error criterion was used to automatically select the model terms. Modeling terms picked in at least half of the analyses, which totalled 45 terms, were retained to form the generic nonlinear aerodynamic (GNA) model. Least squares was then used to estimate the model parameters and associated uncertainty that best fit the GNA model to each database. Nonlinear flight simulations were used to demonstrate that the GNA model produces accurate trim solutions, local behavior (modal frequencies and damping ratios), and global dynamic behavior (91% accurate state histories and 80% accurate aerodynamic coefficient histories) under large-amplitude excitation. This compact aerodynamics model can be used to decrease on-board memory storage requirements, quickly change conceptual aircraft models, provide smooth analytical functions for control and optimization applications, and facilitate real-time parametric system identification.

Nonlinear coherent structures of Alfvén wave in a collisional plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jana, Sayanee; Chakrabarti, Nikhil; Ghosh, Samiran

2016-07-15

The Alfvén wave dynamics is investigated in the framework of two-fluid approach in a compressible collisional magnetized plasma. In the finite amplitude limit, the dynamics of the nonlinear Alfvén wave is found to be governed by a modified Korteweg-de Vries Burgers equation (mKdVB). In this mKdVB equation, the electron inertia is found to act as a source of dispersion, and the electron-ion collision serves as a dissipation. The collisional dissipation is eventually responsible for the Burgers term in mKdVB equation. In the long wavelength limit, this weakly nonlinear Alfvén wave is shown to be governed by a damped nonlinear Schrödingermore » equation. Furthermore, these nonlinear equations are analyzed by means of analytical calculation and numerical simulation to elucidate the various aspects of the phase-space dynamics of the nonlinear wave. Results reveal that nonlinear Alfvén wave exhibits the dissipation mediated shock, envelope, and breather like structures. Numerical simulations also predict the formation of dissipative Alfvénic rogue wave, giant breathers, and rogue wave holes. These results are discussed in the context of the space plasma.« less

Independence screening for high dimensional nonlinear additive ODE models with applications to dynamic gene regulatory networks.

PubMed

Xue, Hongqi; Wu, Shuang; Wu, Yichao; Ramirez Idarraga, Juan C; Wu, Hulin

2018-05-02

Mechanism-driven low-dimensional ordinary differential equation (ODE) models are often used to model viral dynamics at cellular levels and epidemics of infectious diseases. However, low-dimensional mechanism-based ODE models are limited for modeling infectious diseases at molecular levels such as transcriptomic or proteomic levels, which is critical to understand pathogenesis of diseases. Although linear ODE models have been proposed for gene regulatory networks (GRNs), nonlinear regulations are common in GRNs. The reconstruction of large-scale nonlinear networks from time-course gene expression data remains an unresolved issue. Here, we use high-dimensional nonlinear additive ODEs to model GRNs and propose a 4-step procedure to efficiently perform variable selection for nonlinear ODEs. To tackle the challenge of high dimensionality, we couple the 2-stage smoothing-based estimation method for ODEs and a nonlinear independence screening method to perform variable selection for the nonlinear ODE models. We have shown that our method possesses the sure screening property and it can handle problems with non-polynomial dimensionality. Numerical performance of the proposed method is illustrated with simulated data and a real data example for identifying the dynamic GRN of Saccharomyces cerevisiae. Copyright © 2018 John Wiley & Sons, Ltd.

Effect of initial strain and material nonlinearity on the nonlinear static and dynamic response of graphene sheets

NASA Astrophysics Data System (ADS)

Singh, Sandeep; Patel, B. P.

2018-06-01

Computationally efficient multiscale modelling based on Cauchy-Born rule in conjunction with finite element method is employed to study static and dynamic characteristics of graphene sheets, with/without considering initial strain, involving Green-Lagrange geometric and material nonlinearities. The strain energy density function at continuum level is established by coupling the deformation at continuum level to that at atomic level through Cauchy-Born rule. The atomic interactions between carbon atoms are modelled through Tersoff-Brenner potential. The governing equation of motion obtained using Hamilton's principle is solved through standard Newton-Raphson method for nonlinear static response and Newmark's time integration technique to obtain nonlinear transient response characteristics. Effect of initial strain on the linear free vibration frequencies, nonlinear static and dynamic response characteristics is investigated in detail. The present multiscale modelling based results are found to be in good agreement with those obtained through molecular mechanics simulation. Two different types of boundary constraints generally used in MM simulation are explored in detail and few interesting findings are brought out. The effect of initial strain is found to be greater in linear response when compared to that in nonlinear response.

Nonlinear dynamics near resonances of a rotor-active magnetic bearings system with 16-pole legs and time varying stiffness

NASA Astrophysics Data System (ADS)

Wu, R. Q.; Zhang, W.; Yao, M. H.

2018-02-01

In this paper, we analyze the complicated nonlinear dynamics of rotor-active magnetic bearings (rotor-AMB) with 16-pole legs and the time varying stiffness. The magnetic force with 16-pole legs is obtained by applying the electromagnetic theory. The governing equation of motion for rotor-active magnetic bearings is derived by using the Newton's second law. The resulting dimensionless equation of motion for the rotor-AMB system is expressed as a two-degree-of-freedom nonlinear system including the parametric excitation, quadratic and cubic nonlinearities. The averaged equation of the rotor-AMB system is obtained by using the method of multiple scales when the primary parametric resonance and 1/2 subharmonic resonance are taken into account. From the frequency-response curves, it is found that there exist the phenomena of the soft-spring type nonlinearity and the hardening-spring type nonlinearity in the rotor-AMB system. The effects of different parameters on the nonlinear dynamic behaviors of the rotor-AMB system are investigated. The numerical results indicate that the periodic, quasi-periodic and chaotic motions occur alternately in the rotor-AMB system.

The spike trains of inhibited pacemaker neurons seen through the magnifying glass of nonlinear analyses.

PubMed

Segundo, J P; Sugihara, G; Dixon, P; Stiber, M; Bersier, L F

1998-12-01

This communication describes the new information that may be obtained by applying nonlinear analytical techniques to neurobiological time-series. Specifically, we consider the sequence of interspike intervals Ti (the "timing") of trains recorded from synaptically inhibited crayfish pacemaker neurons. As reported earlier, different postsynaptic spike train forms (sets of timings with shared properties) are generated by varying the average rate and/or pattern (implying interval dispersions and sequences) of presynaptic spike trains. When the presynaptic train is Poisson (independent exponentially distributed intervals), the form is "Poisson-driven" (unperturbed and lengthened intervals succeed each other irregularly). When presynaptic trains are pacemaker (intervals practically equal), forms are either "p:q locked" (intervals repeat periodically), "intermittent" (mostly almost locked but disrupted irregularly), "phase walk throughs" (intermittencies with briefer regular portions), or "messy" (difficult to predict or describe succinctly). Messy trains are either "erratic" (some intervals natural and others lengthened irregularly) or "stammerings" (intervals are integral multiples of presynaptic intervals). The individual spike train forms were analysed using attractor reconstruction methods based on the lagged coordinates provided by successive intervals from the time-series Ti. Numerous models were evaluated in terms of their predictive performance by a trial-and-error procedure: the most successful model was taken as best reflecting the true nature of the system's attractor. Each form was characterized in terms of its dimensionality, nonlinearity and predictability. (1) The dimensionality of the underlying dynamical attractor was estimated by the minimum number of variables (coordinates Ti) required to model acceptably the system's dynamics, i.e. by the system's degrees of freedom. Each model tested was based on a different number of Ti; the smallest number whose predictions were judged successful provided the best integer approximation of the attractor's true dimension (not necessarily an integer). Dimensionalities from three to five provided acceptable fits. (2) The degree of nonlinearity was estimated by: (i) comparing the correlations between experimental results and data from linear and nonlinear models, and (ii) tuning model nonlinearity via a distance-weighting function and identifying the either local or global neighborhood size. Lockings were compatible with linear models and stammerings were marginal; nonlinear models were best for Poisson-driven, intermittent and erratic forms. (3) Finally, prediction accuracy was plotted against increasingly long sequences of intervals forecast: the accuracies for Poisson-driven, locked and stammering forms were invariant, revealing irregularities due to uncorrelated noise, but those of intermittent and messy erratic forms decayed rapidly, indicating an underlying deterministic process. The excellent reconstructions possible for messy erratic and for some intermittent forms are especially significant because of their relatively low dimensionality (around 4), high degree of nonlinearity and prediction decay with time. This is characteristic of chaotic systems, and provides evidence that nonlinear couplings between relatively few variables are the major source of the apparent complexity seen in these cases. This demonstration of different dimensions, degrees of nonlinearity and predictabilities provides rigorous support for the categorization of different synaptically driven discharge forms proposed earlier on the basis of more heuristic criteria. This has significant implications. (1) It demonstrates that heterogeneous postsynaptic forms can indeed be induced by manipulating a few presynaptic variables. (2) Each presynaptic timing induces a form with characteristic dimensionality, thus breaking up the preparation into subsystems such that the physical variables in each operate as one

Modeling dynamic interactions and coherence between marine zooplankton and fishes linked to environmental variability

NASA Astrophysics Data System (ADS)

Liu, Hui; Fogarty, Michael J.; Hare, Jonathan A.; Hsieh, Chih-hao; Glaser, Sarah M.; Ye, Hao; Deyle, Ethan; Sugihara, George

2014-03-01

The dynamics of marine fishes are closely related to lower trophic levels and the environment. Quantitatively understanding ecosystem dynamics linking environmental variability and prey resources to exploited fishes is crucial for ecosystem-based management of marine living resources. However, standard statistical models typically grounded in the concept of linear system may fail to capture the complexity of ecological processes. We have attempted to model ecosystem dynamics using a flexible, nonparametric class of nonlinear forecasting models. We analyzed annual time series of four environmental indices, 22 marine copepod taxa, and four ecologically and commercially important fish species during 1977 to 2009 on Georges Bank, a highly productive and intensively studied area of the northeast U.S. continental shelf ecosystem. We examined the underlying dynamic features of environmental indices and copepods, quantified the dynamic interactions and coherence with fishes, and explored the potential control mechanisms of ecosystem dynamics from a nonlinear perspective. We found: (1) the dynamics of marine copepods and environmental indices exhibiting clear nonlinearity; (2) little evidence of complex dynamics across taxonomic levels of copepods; (3) strong dynamic interactions and coherence between copepods and fishes; and (4) the bottom-up forcing of fishes and top-down control of copepods coexisting as target trophic levels vary. These findings highlight the nonlinear interactions among ecosystem components and the importance of marine zooplankton to fish populations which point to two forcing mechanisms likely interactively regulating the ecosystem dynamics on Georges Bank under a changing environment.

Change detection in the dynamics of an intracellular protein synthesis model using nonlinear Kalman filtering.

PubMed

Rigatos, Gerasimos G; Rigatou, Efthymia G; Djida, Jean Daniel

2015-10-01

A method for early diagnosis of parametric changes in intracellular protein synthesis models (e.g. the p53 protein - mdm2 inhibitor model) is developed with the use of a nonlinear Kalman Filtering approach (Derivative-free nonlinear Kalman Filter) and of statistical change detection methods. The intracellular protein synthesis dynamic model is described by a set of coupled nonlinear differential equations. It is shown that such a dynamical system satisfies differential flatness properties and this allows to transform it, through a change of variables (diffeomorphism), to the so-called linear canonical form. For the linearized equivalent of the dynamical system, state estimation can be performed using the Kalman Filter recursion. Moreover, by applying an inverse transformation based on the previous diffeomorphism it becomes also possible to obtain estimates of the state variables of the initial nonlinear model. By comparing the output of the Kalman Filter (which is assumed to correspond to the undistorted dynamical model) with measurements obtained from the monitored protein synthesis system, a sequence of differences (residuals) is obtained. The statistical processing of the residuals with the use of x2 change detection tests, can provide indication within specific confidence intervals about parametric changes in the considered biological system and consequently indications about the appearance of specific diseases (e.g. malignancies).

ISS method for coordination control of nonlinear dynamical agents under directed topology.

PubMed

Wang, Xiangke; Qin, Jiahu; Yu, Changbin

2014-10-01

The problems of coordination of multiagent systems with second-order locally Lipschitz continuous nonlinear dynamics under directed interaction topology are investigated in this paper. A completely nonlinear input-to-state stability (ISS)-based framework, drawing on ISS methods, with the aid of results from graph theory, matrix theory, and the ISS cyclic-small-gain theorem, is proposed for the coordination problem under directed topology, which can effectively tackle the technical challenges caused by locally Lipschitz continuous dynamics. Two coordination problems, i.e., flocking with a virtual leader and containment control, are considered. For both problems, it is assumed that only a portion of the agents can obtain the information from the leader(s). For the first problem, the proposed strategy is shown effective in driving a group of nonlinear dynamical agents reach the prespecified geometric pattern under the condition that at least one agent in each strongly connected component of the information-interconnection digraph with zero in-degree has access to the state information of the virtual leader; and the strategy proposed for the second problem can guarantee the nonlinear dynamical agents moving to the convex hull spanned by the positions of multiple leaders under the condition that for each agent there exists at least one leader that has a directed path to this agent.

A model for simulating adaptive, dynamic flows on networks: Application to petroleum infrastructure

DOE PAGES

Corbet, Thomas F.; Beyeler, Walt; Wilson, Michael L.; ...

2017-10-03

Simulation models can greatly improve decisions meant to control the consequences of disruptions to critical infrastructures. We describe a dynamic flow model on networks purposed to inform analyses by those concerned about consequences of disruptions to infrastructures and to help policy makers design robust mitigations. We conceptualize the adaptive responses of infrastructure networks to perturbations as market transactions and business decisions of operators. We approximate commodity flows in these networks by a diffusion equation, with nonlinearities introduced to model capacity limits. To illustrate the behavior and scalability of the model, we show its application first on two simple networks, thenmore » on petroleum infrastructure in the United States, where we analyze the effects of a hypothesized earthquake.« less

A model for simulating adaptive, dynamic flows on networks: Application to petroleum infrastructure

DOE Office of Scientific and Technical Information (OSTI.GOV)

Corbet, Thomas F.; Beyeler, Walt; Wilson, Michael L.

Simulation models can greatly improve decisions meant to control the consequences of disruptions to critical infrastructures. We describe a dynamic flow model on networks purposed to inform analyses by those concerned about consequences of disruptions to infrastructures and to help policy makers design robust mitigations. We conceptualize the adaptive responses of infrastructure networks to perturbations as market transactions and business decisions of operators. We approximate commodity flows in these networks by a diffusion equation, with nonlinearities introduced to model capacity limits. To illustrate the behavior and scalability of the model, we show its application first on two simple networks, thenmore » on petroleum infrastructure in the United States, where we analyze the effects of a hypothesized earthquake.« less

Non-linear controls influence functions in an aircraft dynamics simulator

NASA Technical Reports Server (NTRS)

Guerreiro, Nelson M.; Hubbard, James E., Jr.; Motter, Mark A.

2006-01-01

In the development and testing of novel structural and controls concepts, such as morphing aircraft wings, appropriate models are needed for proper system characterization. In most instances, available system models do not provide the required additional degrees of freedom for morphing structures but may be modified to some extent to achieve a compatible system. The objective of this study is to apply wind tunnel data collected for an Unmanned Air Vehicle (UAV), that implements trailing edge morphing, to create a non-linear dynamics simulator, using well defined rigid body equations of motion, where the aircraft stability derivatives change with control deflection. An analysis of this wind tunnel data, using data extraction algorithms, was performed to determine the reference aerodynamic force and moment coefficients for the aircraft. Further, non-linear influence functions were obtained for each of the aircraft s control surfaces, including the sixteen trailing edge flap segments. These non-linear controls influence functions are applied to the aircraft dynamics to produce deflection-dependent aircraft stability derivatives in a non-linear dynamics simulator. Time domain analysis of the aircraft motion, trajectory, and state histories can be performed using these nonlinear dynamics and may be visualized using a 3-dimensional aircraft model. Linear system models can be extracted to facilitate frequency domain analysis of the system and for control law development. The results of this study are useful in similar projects where trailing edge morphing is employed and will be instrumental in the University of Maryland s continuing study of active wing load control.

Dynamical principles in neuroscience

NASA Astrophysics Data System (ADS)

Rabinovich, Mikhail I.; Varona, Pablo; Selverston, Allen I.; Abarbanel, Henry D. I.

2006-10-01

Dynamical modeling of neural systems and brain functions has a history of success over the last half century. This includes, for example, the explanation and prediction of some features of neural rhythmic behaviors. Many interesting dynamical models of learning and memory based on physiological experiments have been suggested over the last two decades. Dynamical models even of consciousness now exist. Usually these models and results are based on traditional approaches and paradigms of nonlinear dynamics including dynamical chaos. Neural systems are, however, an unusual subject for nonlinear dynamics for several reasons: (i) Even the simplest neural network, with only a few neurons and synaptic connections, has an enormous number of variables and control parameters. These make neural systems adaptive and flexible, and are critical to their biological function. (ii) In contrast to traditional physical systems described by well-known basic principles, first principles governing the dynamics of neural systems are unknown. (iii) Many different neural systems exhibit similar dynamics despite having different architectures and different levels of complexity. (iv) The network architecture and connection strengths are usually not known in detail and therefore the dynamical analysis must, in some sense, be probabilistic. (v) Since nervous systems are able to organize behavior based on sensory inputs, the dynamical modeling of these systems has to explain the transformation of temporal information into combinatorial or combinatorial-temporal codes, and vice versa, for memory and recognition. In this review these problems are discussed in the context of addressing the stimulating questions: What can neuroscience learn from nonlinear dynamics, and what can nonlinear dynamics learn from neuroscience?

Dynamical principles in neuroscience

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rabinovich, Mikhail I.; Varona, Pablo; Selverston, Allen I.

Dynamical modeling of neural systems and brain functions has a history of success over the last half century. This includes, for example, the explanation and prediction of some features of neural rhythmic behaviors. Many interesting dynamical models of learning and memory based on physiological experiments have been suggested over the last two decades. Dynamical models even of consciousness now exist. Usually these models and results are based on traditional approaches and paradigms of nonlinear dynamics including dynamical chaos. Neural systems are, however, an unusual subject for nonlinear dynamics for several reasons: (i) Even the simplest neural network, with only amore » few neurons and synaptic connections, has an enormous number of variables and control parameters. These make neural systems adaptive and flexible, and are critical to their biological function. (ii) In contrast to traditional physical systems described by well-known basic principles, first principles governing the dynamics of neural systems are unknown. (iii) Many different neural systems exhibit similar dynamics despite having different architectures and different levels of complexity. (iv) The network architecture and connection strengths are usually not known in detail and therefore the dynamical analysis must, in some sense, be probabilistic. (v) Since nervous systems are able to organize behavior based on sensory inputs, the dynamical modeling of these systems has to explain the transformation of temporal information into combinatorial or combinatorial-temporal codes, and vice versa, for memory and recognition. In this review these problems are discussed in the context of addressing the stimulating questions: What can neuroscience learn from nonlinear dynamics, and what can nonlinear dynamics learn from neuroscience?.« less

Linear and non-linear analyses of Conner's Continuous Performance Test-II discriminate adult patients with attention deficit hyperactivity disorder from patients with mood and anxiety disorders.

PubMed

Fasmer, Ole Bernt; Mjeldheim, Kristin; Førland, Wenche; Hansen, Anita L; Syrstad, Vigdis Elin Giæver; Oedegaard, Ketil J; Berle, Jan Øystein

2016-08-11

Attention Deficit Hyperactivity Disorder (ADHD) is a heterogeneous disorder. Therefore it is important to look for factors that can contribute to better diagnosis and classification of these patients. The aims of the study were to characterize adult psychiatric out-patients with a mixture of mood, anxiety and attentional problems using an objective neuropsychological test of attention combined with an assessment of mood instability. Newly referred patients (n = 99; aged 18-65 years) requiring diagnostic evaluation of ADHD, mood or anxiety disorders were recruited, and were given a comprehensive diagnostic evaluation including the self-report form of the cyclothymic temperament scale and Conner's Continuous Performance Test II (CPT-II). In addition to the traditional measures from this test we have extracted raw data and analysed time series using linear and non-linear mathematical methods. Fifty patients fulfilled criteria for ADHD, while 49 did not, and were given other psychiatric diagnoses (clinical controls). When compared to the clinical controls the ADHD patients had more omission and commission errors, and higher reaction time variability. Analyses of response times showed higher values for skewness in the ADHD patients, and lower values for sample entropy and symbolic dynamics. Among the ADHD patients 59 % fulfilled criteria for a cyclothymic temperament, and this group had higher reaction time variability and lower scores on complexity than the group without this temperament. The CPT-II is a useful instrument in the assessment of ADHD in adult patients. Additional information from this test was obtained by analyzing response times using linear and non-linear methods, and this showed that ADHD patients with a cyclothymic temperament were different from those without this temperament.

Nonlinear viscoelastic characterization of polymer materials using a dynamic-mechanical methodology

NASA Technical Reports Server (NTRS)

Strganac, Thomas W.; Payne, Debbie Flowers; Biskup, Bruce A.; Letton, Alan

1995-01-01

Polymer materials retrieved from LDEF exhibit nonlinear constitutive behavior; thus the authors present a method to characterize nonlinear viscoelastic behavior using measurements from dynamic (oscillatory) mechanical tests. Frequency-derived measurements are transformed into time-domain properties providing the capability to predict long term material performance without a lengthy experimentation program. Results are presented for thin-film high-performance polymer materials used in the fabrication of high-altitude scientific balloons. Predictions based upon a linear test and analysis approach are shown to deteriorate for moderate to high stress levels expected for extended applications. Tests verify that nonlinear viscoelastic response is induced by large stresses. Hence, an approach is developed in which the stress-dependent behavior is examined in a manner analogous to modeling temperature-dependent behavior with time-temperature correspondence and superposition principles. The development leads to time-stress correspondence and superposition of measurements obtained through dynamic mechanical tests. Predictions of material behavior using measurements based upon linear and nonlinear approaches are compared with experimental results obtained from traditional creep tests. Excellent agreement is shown for the nonlinear model.

Decoupling nonclassical nonlinear behavior of elastic wave types

DOE PAGES

Remillieux, Marcel C.; Guyer, Robert A.; Payan, Cedric; ...

2016-03-01

In this Letter, the tensorial nature of the nonequilibrium dynamics in nonlinear mesoscopic elastic materials is evidenced via multimode resonance experiments. In these experiments the dynamic response, including the spatial variations of velocities and strains, is carefully monitored while the sample is vibrated in a purely longitudinal or a purely torsional mode. By analogy with the fact that such experiments can decouple the elements of the linear elastic tensor, we demonstrate that the parameters quantifying the nonequilibrium dynamics of the material differ substantially for a compressional wave and for a shear wave. As a result, this could lead to furthermore » understanding of the nonlinear mechanical phenomena that arise in natural systems as well as to the design and engineering of nonlinear acoustic metamaterials.« less

Using waveform information in nonlinear data assimilation

NASA Astrophysics Data System (ADS)

Rey, Daniel; Eldridge, Michael; Morone, Uriel; Abarbanel, Henry D. I.; Parlitz, Ulrich; Schumann-Bischoff, Jan

2014-12-01

Information in measurements of a nonlinear dynamical system can be transferred to a quantitative model of the observed system to establish its fixed parameters and unobserved state variables. After this learning period is complete, one may predict the model response to new forces and, when successful, these predictions will match additional observations. This adjustment process encounters problems when the model is nonlinear and chaotic because dynamical instability impedes the transfer of information from the data to the model when the number of measurements at each observation time is insufficient. We discuss the use of information in the waveform of the data, realized through a time delayed collection of measurements, to provide additional stability and accuracy to this search procedure. Several examples are explored, including a few familiar nonlinear dynamical systems and small networks of Colpitts oscillators.

Mirror Instability: Quasi-linear Effects

NASA Astrophysics Data System (ADS)

Hellinger, P.; Travnicek, P. M.; Passot, T.; Sulem, P.; Kuznetsov, E. A.

2008-12-01

Nonlinear properties of the mirror instability are investigated by direct integration of the quasi-linear diffusion equation [Shapiro and Shevchenko, 1964] near threshold. The simulation results are compared to the results of standard hybrid simulations [Califano et al., 2008] and discussed in the context of the nonlinear dynamical model by Kuznetsov et al. [2007]. References: Califano, F., P. Hellinger, E. Kuznetsov, T. Passot, P. L. Sulem, and P. M. Travnicek (2008), Nonlinear mirror mode dynamics: Simulations and modeling, J. Geophys. Res., 113, A08219, doi:10.1029/2007JA012898. Kuznetsov, E., T. Passot and P. L. Sulem (2007), Dynamical model for nonlinear mirror modes near threshold, Phys. Rev. Lett., 98, 235003 . Shapiro, V. D., and V. I. Shevchenko (1964), Quasilinear theory of instability of a plasma with an anisotropic ion velocity distribution, Sov. JETP, 18, 1109.

A computational algorithm for spacecraft control and momentum management

NASA Technical Reports Server (NTRS)

Dzielski, John; Bergmann, Edward; Paradiso, Joseph

1990-01-01

Developments in the area of nonlinear control theory have shown how coordinate changes in the state and input spaces of a dynamical system can be used to transform certain nonlinear differential equations into equivalent linear equations. These techniques are applied to the control of a spacecraft equipped with momentum exchange devices. An optimal control problem is formulated that incorporates a nonlinear spacecraft model. An algorithm is developed for solving the optimization problem using feedback linearization to transform to an equivalent problem involving a linear dynamical constraint and a functional approximation technique to solve for the linear dynamics in terms of the control. The original problem is transformed into an unconstrained nonlinear quadratic program that yields an approximate solution to the original problem. Two examples are presented to illustrate the results.

Nonlinear Dynamics and Quantum Transport in Small Systems

DTIC Science & Technology

2012-02-22

2.3 Nonlinear wave and chaos in optical metamaterials 2.3.1 Transient chaos in optical metamaterials We investigated the dynamics of light rays in two...equations can be modeled by a set of ordinary differential equations for light rays . We found that transient chaotic dynamics, hyperbolic or nonhyperbolic...are common in optical metamaterial systems. Due to the analogy between light- ray dynamics in metamaterials and the motion of light and matter as

The topology of non-linear global carbon dynamics: from tipping points to planetary boundaries

NASA Astrophysics Data System (ADS)

Anderies, J. M.; Carpenter, S. R.; Steffen, Will; Rockström, Johan

2013-12-01

We present a minimal model of land use and carbon cycle dynamics and use it to explore the relationship between non-linear dynamics and planetary boundaries. Only the most basic interactions between land cover and terrestrial, atmospheric, and marine carbon stocks are considered in the model. Our goal is not to predict global carbon dynamics as it occurs in the actual Earth System. Rather, we construct a conceptually reasonable heuristic model of a feedback system between different carbon stocks that captures the qualitative features of the actual Earth System and use it to explore the topology of the boundaries of what can be called a ‘safe operating space’ for humans. The model analysis illustrates the existence of dynamic, non-linear tipping points in carbon cycle dynamics and the potential complexity of planetary boundaries. Finally, we use the model to illustrate some challenges associated with navigating planetary boundaries.

A Novel Nonlinear Piezoelectric Energy Harvesting System Based on Linear-Element Coupling: Design, Modeling and Dynamic Analysis.

PubMed

Zhou, Shengxi; Yan, Bo; Inman, Daniel J

2018-05-09

This paper presents a novel nonlinear piezoelectric energy harvesting system which consists of linear piezoelectric energy harvesters connected by linear springs. In principle, the presented nonlinear system can improve broadband energy harvesting efficiency where magnets are forbidden. The linear spring inevitably produces the nonlinear spring force on the connected harvesters, because of the geometrical relationship and the time-varying relative displacement between two adjacent harvesters. Therefore, the presented nonlinear system has strong nonlinear characteristics. A theoretical model of the presented nonlinear system is deduced, based on Euler-Bernoulli beam theory, Kirchhoff’s law, piezoelectric theory and the relevant geometrical relationship. The energy harvesting enhancement of the presented nonlinear system (when n = 2, 3) is numerically verified by comparing with its linear counterparts. In the case study, the output power area of the presented nonlinear system with two and three energy harvesters is 268.8% and 339.8% of their linear counterparts, respectively. In addition, the nonlinear dynamic response characteristics are analyzed via bifurcation diagrams, Poincare maps of the phase trajectory, and the spectrum of the output voltage.

Nonlinear dynamics of an elliptic vortex embedded in an oscillatory shear flow.

PubMed

Ryzhov, Eugene A

2017-11-01

The nonlinear dynamics of an elliptic vortex subjected to a time-periodic linear external shear flow is studied numerically. Making use of the ideas from the theory of nonlinear resonance overlaps, the study focuses on the appearance of chaotic regimes in the ellipse dynamics. When the superimposed flow is stationary, two general types of the steady-state phase portrait are considered: one that features a homoclinic separatrix delineating bounded and unbounded phase trajectories and one without a separatrix (all the phase trajectories are bounded in a periodic domain). When the external flow is time-periodic, the ensuing nonlinear dynamics differs significantly in both cases. For the case with a separatrix and two distinct types of phase trajectories: bounded and unbounded, the effect of the most influential nonlinear resonance with the winding number of 1:1 is analyzed in detail. Namely, the process of occupying the central stability region associated with the steady-state elliptic critical point by the stability region associated with the nonlinear resonance of 1:1 as the perturbation frequency gradually varies is investigated. A stark increase in the persistence of the central regular dynamics region against perturbation when the resonance of 1:1 associated stability region occupies the region associated with the steady-state elliptic critical point is observed. An analogous persistence of the regular motion occurs for higher perturbation frequencies when the corresponding stability islands reach the central stability region associated with the steady-state elliptic point. An analysis for the case with the resonance of 1:2 is presented. For the second case with only bounded phase trajectories and, therefore, no separatrix, the appearance of much bigger stability islands associated with nonlinear resonances compared with the case with a separatrix is reported.

Singularity perturbed zero dynamics of nonlinear systems

NASA Technical Reports Server (NTRS)

Isidori, A.; Sastry, S. S.; Kokotovic, P. V.; Byrnes, C. I.

1992-01-01

Stability properties of zero dynamics are among the crucial input-output properties of both linear and nonlinear systems. Unstable, or 'nonminimum phase', zero dynamics are a major obstacle to input-output linearization and high-gain designs. An analysis of the effects of regular perturbations in system equations on zero dynamics shows that whenever a perturbation decreases the system's relative degree, it manifests itself as a singular perturbation of zero dynamics. Conditions are given under which the zero dynamics evolve in two timescales characteristic of a standard singular perturbation form that allows a separate analysis of slow and fast parts of the zero dynamics.

Roles of dispersal, stochasticity, and nonlinear dynamics in the spatial structuring of seasonal natural enemy-victim populations

Treesearch

Patrick C. Tobin; Ottar N. Bjornstad

2005-01-01

Natural enemy-victim systems may exhibit a range of dynamic space-time patterns. We used a theoretical framework to study spatiotemporal structuring in a transient natural enemy-victim system subject to differential rates of dispersal, stochastic forcing, and nonlinear dynamics. Highly mobile natural enemies that attacked less mobile victims were locally spatially...

Efficient computational nonlinear dynamic analysis using modal modification response technique

NASA Astrophysics Data System (ADS)

Marinone, Timothy; Avitabile, Peter; Foley, Jason; Wolfson, Janet

2012-08-01

Generally, structural systems contain nonlinear characteristics in many cases. These nonlinear systems require significant computational resources for solution of the equations of motion. Much of the model, however, is linear where the nonlinearity results from discrete local elements connecting different components together. Using a component mode synthesis approach, a nonlinear model can be developed by interconnecting these linear components with highly nonlinear connection elements. The approach presented in this paper, the Modal Modification Response Technique (MMRT), is a very efficient technique that has been created to address this specific class of nonlinear problem. By utilizing a Structural Dynamics Modification (SDM) approach in conjunction with mode superposition, a significantly smaller set of matrices are required for use in the direct integration of the equations of motion. The approach will be compared to traditional analytical approaches to make evident the usefulness of the technique for a variety of test cases.

Nonlinear modeling of chaotic time series: Theory and applications

NASA Astrophysics Data System (ADS)

Casdagli, M.; Eubank, S.; Farmer, J. D.; Gibson, J.; Desjardins, D.; Hunter, N.; Theiler, J.

We review recent developments in the modeling and prediction of nonlinear time series. In some cases, apparent randomness in time series may be due to chaotic behavior of a nonlinear but deterministic system. In such cases, it is possible to exploit the determinism to make short term forecasts that are much more accurate than one could make from a linear stochastic model. This is done by first reconstructing a state space, and then using nonlinear function approximation methods to create a dynamical model. Nonlinear models are valuable not only as short term forecasters, but also as diagnostic tools for identifying and quantifying low-dimensional chaotic behavior. During the past few years, methods for nonlinear modeling have developed rapidly, and have already led to several applications where nonlinear models motivated by chaotic dynamics provide superior predictions to linear models. These applications include prediction of fluid flows, sunspots, mechanical vibrations, ice ages, measles epidemics, and human speech.

Counteracting structural errors in ensemble forecast of influenza outbreaks.

PubMed

Pei, Sen; Shaman, Jeffrey

2017-10-13

For influenza forecasts generated using dynamical models, forecast inaccuracy is partly attributable to the nonlinear growth of error. As a consequence, quantification of the nonlinear error structure in current forecast models is needed so that this growth can be corrected and forecast skill improved. Here, we inspect the error growth of a compartmental influenza model and find that a robust error structure arises naturally from the nonlinear model dynamics. By counteracting these structural errors, diagnosed using error breeding, we develop a new forecast approach that combines dynamical error correction and statistical filtering techniques. In retrospective forecasts of historical influenza outbreaks for 95 US cities from 2003 to 2014, overall forecast accuracy for outbreak peak timing, peak intensity and attack rate, are substantially improved for predicted lead times up to 10 weeks. This error growth correction method can be generalized to improve the forecast accuracy of other infectious disease dynamical models.Inaccuracy of influenza forecasts based on dynamical models is partly due to nonlinear error growth. Here the authors address the error structure of a compartmental influenza model, and develop a new improved forecast approach combining dynamical error correction and statistical filtering techniques.

Dynamics of metastable breathers in nonlinear chains in acoustic vacuum

NASA Astrophysics Data System (ADS)

Sen, Surajit; Mohan, T. R. Krishna

2009-03-01

The study of the dynamics of one-dimensional chains with both harmonic and nonlinear interactions, as in the Fermi-Pasta-Ulam and related problems, has played a central role in efforts to identify the broad consequences of nonlinearity in these systems. Nevertheless, little is known about the dynamical behavior of purely nonlinear chains where there is a complete absence of the harmonic term, and hence sound propagation is not admissible, i.e., under conditions of “acoustic vacuum.” Here we study the dynamics of highly localized excitations, or breathers, which are known to be initiated by the quasistatic stretching of the bonds between adjacent particles. We show via detailed particle-dynamics-based studies that many low-energy pulses also form in the vicinity of the perturbation, and the breathers that form are “fragile” in the sense that they can be easily delocalized by scattering events in the system. We show that the localized excitations eventually disperse, allowing the system to attain an equilibrium-like state that is realizable in acoustic vacuum. We conclude with a discussion of how the dynamics is affected by the presence of acoustic oscillations.

Growing complex network of citations of scientific papers: Modeling and measurements

NASA Astrophysics Data System (ADS)

Golosovsky, Michael; Solomon, Sorin

2017-01-01

We consider the network of citations of scientific papers and use a combination of the theoretical and experimental tools to uncover microscopic details of this network growth. Namely, we develop a stochastic model of citation dynamics based on the copying-redirection-triadic closure mechanism. In a complementary and coherent way, the model accounts both for statistics of references of scientific papers and for their citation dynamics. Originating in empirical measurements, the model is cast in such a way that it can be verified quantitatively in every aspect. Such validation is performed by measuring citation dynamics of physics papers. The measurements revealed nonlinear citation dynamics, the nonlinearity being intricately related to network topology. The nonlinearity has far-reaching consequences including nonstationary citation distributions, diverging citation trajectories of similar papers, runaways or "immortal papers" with infinite citation lifetime, etc. Thus nonlinearity in complex network growth is our most important finding. In a more specific context, our results can be a basis for quantitative probabilistic prediction of citation dynamics of individual papers and of the journal impact factor.

Finite elements and fluid dynamics. [instability effects on solution of nonlinear equations

NASA Technical Reports Server (NTRS)

Fix, G.

1975-01-01

Difficulties concerning a use of the finite element method in the solution of the nonlinear equations of fluid dynamics are partly related to various 'hidden' instabilities which often arise in fluid calculations. The instabilities are typically due to boundary effects or nonlinearities. It is shown that in certain cases these instabilities can be avoided if certain conservation laws are satisfied, and that the latter are often intimately related to finite elements.

Nonlinear maneuver autopilot for the F-15 aircraft

NASA Technical Reports Server (NTRS)

Menon, P. K. A.; Badgett, M. E.; Walker, R. A.

1989-01-01

A methodology is described for the development of flight test trajectory control laws based on singular perturbation methodology and nonlinear dynamic modeling. The control design methodology is applied to a detailed nonlinear six degree-of-freedom simulation of the F-15 and results for a level accelerations, pushover/pullup maneuver, zoom and pushover maneuver, excess thrust windup turn, constant thrust windup turn, and a constant dynamic pressure/constant load factor trajectory are presented.

Test-electron analysis of the magnetic reconnection topology

NASA Astrophysics Data System (ADS)

Borgogno, D.; Perona, A.; Grasso, D.

2017-12-01

Three-dimensional (3D) investigations of the magnetic reconnection field topology in space and laboratory plasmas have identified the abidance of magnetic coherent structures in the stochastic region, which develop during the nonlinear stage of the reconnection process. Further analytical and numerical analyses highlighted the efficacy of some of these structures in limiting the magnetic transport. The question then arises as to what is the possible role played by these patterns in the dynamics of the plasma particles populating the chaotic region. In order to explore this aspect, we provide a detailed description of the nonlinear 3D magnetic field topology in a collisionless magnetic reconnection event with a strong guide field. In parallel, we study the evolution of a population of test electrons in the guiding-center approximation all along the reconnection process. In particular, we focus on the nonlinear spatial redistribution of the initially thermal electrons and show how the electron dynamics in the stochastic region depends on the sign and on the value of their velocities. While the particles with the highest positive speed populate the coherent current structures that survive in the chaotic sea, the presence of the manifolds calculated in the stochastic region defines the confinement area for the electrons with the largest negative velocity. These results stress the link between the magnetic topology and the electron motion and contribute to the overall picture of a non-stationary fluid magnetic reconnection description in a geometry proper to physical systems where the effects of the curvature can be neglected.

Nonlinear dynamics of magnetically coupled beams for multi-modal vibration energy harvesting

NASA Astrophysics Data System (ADS)

Abed, I.; Kacem, N.; Bouhaddi, N.; Bouazizi, M. L.

2016-04-01

We investigate the nonlinear dynamics of magnetically coupled beams for multi-modal vibration energy harvesting. A multi-physics model for the proposed device is developed taking into account geometric and magnetic nonlinearities. The coupled nonlinear equations of motion are solved using the Galerkin discretization coupled with the harmonic balance method and the asymptotic numerical method. Several numerical simulations have been performed showing that the expected performances of the proposed vibration energy harvester are significantly promising with up to 130 % in term of bandwidth and up to 60 μWcm-3g-2 in term of normalized harvested power.

A 1-D model of the nonlinear dynamics of the human lumbar intervertebral disc

NASA Astrophysics Data System (ADS)

Marini, Giacomo; Huber, Gerd; Püschel, Klaus; Ferguson, Stephen J.

2017-01-01

Lumped parameter models of the spine have been developed to investigate its response to whole body vibration. However, these models assume the behaviour of the intervertebral disc to be linear-elastic. Recently, the authors have reported on the nonlinear dynamic behaviour of the human lumbar intervertebral disc. This response was shown to be dependent on the applied preload and amplitude of the stimuli. However, the mechanical properties of a standard linear elastic model are not dependent on the current deformation state of the system. The aim of this study was therefore to develop a model that is able to describe the axial, nonlinear quasi-static response and to predict the nonlinear dynamic characteristics of the disc. The ability to adapt the model to an individual disc's response was a specific focus of the study, with model validation performed against prior experimental data. The influence of the numerical parameters used in the simulations was investigated. The developed model exhibited an axial quasi-static and dynamic response, which agreed well with the corresponding experiments. However, the model needs further improvement to capture additional peculiar characteristics of the system dynamics, such as the change of mean point of oscillation exhibited by the specimens when oscillating in the region of nonlinear resonance. Reference time steps were identified for specific integration scheme. The study has demonstrated that taking into account the nonlinear-elastic behaviour typical of the intervertebral disc results in a predicted system oscillation much closer to the physiological response than that provided by linear-elastic models. For dynamic analysis, the use of standard linear-elastic models should be avoided, or restricted to study cases where the amplitude of the stimuli is relatively small.

Dynamics of a network-based SIS epidemic model with nonmonotone incidence rate

NASA Astrophysics Data System (ADS)

Li, Chun-Hsien

2015-06-01

This paper studies the dynamics of a network-based SIS epidemic model with nonmonotone incidence rate. This type of nonlinear incidence can be used to describe the psychological effect of certain diseases spread in a contact network at high infective levels. We first find a threshold value for the transmission rate. This value completely determines the dynamics of the model and interestingly, the threshold is not dependent on the functional form of the nonlinear incidence rate. Furthermore, if the transmission rate is less than or equal to the threshold value, the disease will die out. Otherwise, it will be permanent. Numerical experiments are given to illustrate the theoretical results. We also consider the effect of the nonlinear incidence on the epidemic dynamics.

Nonlinear modelling in time domain numerical analysis of stringed instrument dynamics

NASA Astrophysics Data System (ADS)

Bielski, Paweł; Kujawa, Marcin

2017-03-01

Musical instruments are very various in terms of sound quality with their timbre shaped by materials and geometry. Materials' impact is commonly treated as dominant one by musicians, while it is unclear whether it is true or not. The research proposed in the study focuses on determining influence of both these factors on sound quality based on their impact on harmonic composition. Numerical approach has been chosen to allowed independent manipulation of geometrical and material parameters as opposed to experimental study subjected to natural randomness of instrument construction. Distinctive element of this research is precise modelling of whole instrument and treating it as one big vibrating system instead of performing modal analysis on an isolated part. Finite elements model of a stringed instrument has been built and a series of nonlinear time-domain dynamic analyses were executed to obtain displacement signals and perform subsequent spectral analysis. Precision of computations seems sufficient to determine the influence of instrument's macroscopic mechanical parameters on timbre. Further research should focus on implementation of acoustic medium in attempt to include dissipation and synchronization mechanisms. Outside the musical field this kind of research could be potentially useful in noise reduction problems.

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control

PubMed Central

Brunton, Steven L.; Brunton, Bingni W.; Proctor, Joshua L.; Kutz, J. Nathan

2016-01-01

In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control. PMID:26919740

Is there evidence for the existence of nonlinear behavior within the interplanetary solar sector structure?

NASA Astrophysics Data System (ADS)

Brown, A. G.; Francis, N. M.; Broomhead, D. S.; Cannon, P. S.; Akram, A.

1999-06-01

Using data from the Sweden and Britain Radar Experiment (SABRE) VHF coherent radar, Yeoman et al. [1990] found evidence for two and four sector structures during the declining phase of solar cycle (SC) 21. No such obvious harmonic features were present during the ascending phase of SC 22. It was suggested that the structure of the heliospheric current sheet might exhibit nonlinear behavior during the latter period. A direct test of this suggestion, using established nonlinear methods, would require the computation of the fractal dimension of the data, for example. However, the quality of the SABRE data is insufficient for this purpose. Therefore we have tried to answer a simpler question: Is there any evidence that the SABRE data was generated by a (low-dimensional) nonlinear process? If this were the case, it would be a powerful indicator of nonlinear behavior in the solar current sheet. Our approach has been to use a system of orthogonal linear filters to separate the data into linearly uncorrelated time series. We then look for nonlinear dynamical relationships between these time series, using radial basis function models (which can be thought of as a class of neural networks). The presence of such a relationship, indicated by the ability to model one filter output given another, would equate to the presence of nonlinear properties within the data. Using this technique, evidence is found for the presence of low-level nonlinear behavior during both phases of the solar cycle investigated in this study. The evidence for nonlinear behavior is stronger during the descending phase of SC 21. However, it is not possible to distinguish between nonlinear dynamics and a nonlinearly transformed colored Gaussian noise process in either instance, using the available data. Therefore, in conclusion, we find insufficient evidence within the SABRE data set to support the suggestion of increased nonlinear dynamical behavior during the ascending phase of SC 22. In fact, nonlinear dynamics would seem to exert very little influence within the measurement time series at all, given the observed data. Therefore it is likely that stochastic or unresolved high-dimensional nonlinear mechanisms are responsible for the observed spectrum complexity during the ascending phase of SC 22.

Three-dimensional earthquake analysis of roller-compacted concrete dams

NASA Astrophysics Data System (ADS)

Kartal, M. E.

2012-07-01

Ground motion effect on a roller-compacted concrete (RCC) dams in the earthquake zone should be taken into account for the most critical conditions. This study presents three-dimensional earthquake response of a RCC dam considering geometrical non-linearity. Besides, material and connection non-linearity are also taken into consideration in the time-history analyses. Bilinear and multilinear kinematic hardening material models are utilized in the materially non-linear analyses for concrete and foundation rock respectively. The contraction joints inside the dam blocks and dam-foundation-reservoir interaction are modeled by the contact elements. The hydrostatic and hydrodynamic pressures of the reservoir water are modeled with the fluid finite elements based on the Lagrangian approach. The gravity and hydrostatic pressure effects are employed as initial condition before the strong ground motion. In the earthquake analyses, viscous dampers are defined in the finite element model to represent infinite boundary conditions. According to numerical solutions, horizontal displacements increase under hydrodynamic pressure. Besides, those also increase in the materially non-linear analyses of the dam. In addition, while the principle stress components by the hydrodynamic pressure effect the reservoir water, those decrease in the materially non-linear time-history analyses.

From point process observations to collective neural dynamics: Nonlinear Hawkes process GLMs, low-dimensional dynamics and coarse graining

PubMed Central

Truccolo, Wilson

2017-01-01

This review presents a perspective on capturing collective dynamics in recorded neuronal ensembles based on multivariate point process models, inference of low-dimensional dynamics and coarse graining of spatiotemporal measurements. A general probabilistic framework for continuous time point processes reviewed, with an emphasis on multivariate nonlinear Hawkes processes with exogenous inputs. A point process generalized linear model (PP-GLM) framework for the estimation of discrete time multivariate nonlinear Hawkes processes is described. The approach is illustrated with the modeling of collective dynamics in neocortical neuronal ensembles recorded in human and non-human primates, and prediction of single-neuron spiking. A complementary approach to capture collective dynamics based on low-dimensional dynamics (“order parameters”) inferred via latent state-space models with point process observations is presented. The approach is illustrated by inferring and decoding low-dimensional dynamics in primate motor cortex during naturalistic reach and grasp movements. Finally, we briefly review hypothesis tests based on conditional inference and spatiotemporal coarse graining for assessing collective dynamics in recorded neuronal ensembles. PMID:28336305

From point process observations to collective neural dynamics: Nonlinear Hawkes process GLMs, low-dimensional dynamics and coarse graining.

PubMed

Truccolo, Wilson

2016-11-01

This review presents a perspective on capturing collective dynamics in recorded neuronal ensembles based on multivariate point process models, inference of low-dimensional dynamics and coarse graining of spatiotemporal measurements. A general probabilistic framework for continuous time point processes reviewed, with an emphasis on multivariate nonlinear Hawkes processes with exogenous inputs. A point process generalized linear model (PP-GLM) framework for the estimation of discrete time multivariate nonlinear Hawkes processes is described. The approach is illustrated with the modeling of collective dynamics in neocortical neuronal ensembles recorded in human and non-human primates, and prediction of single-neuron spiking. A complementary approach to capture collective dynamics based on low-dimensional dynamics ("order parameters") inferred via latent state-space models with point process observations is presented. The approach is illustrated by inferring and decoding low-dimensional dynamics in primate motor cortex during naturalistic reach and grasp movements. Finally, we briefly review hypothesis tests based on conditional inference and spatiotemporal coarse graining for assessing collective dynamics in recorded neuronal ensembles. Published by Elsevier Ltd.

Optimisation of the vibrational response of ultrasonic cutting systems

NASA Astrophysics Data System (ADS)

Cartmell, M. P.; Lim, F. C. N.; Cardoni, A.; Lucas, M.

2005-10-01

This paper provides an account of an investigation into possible dynamic interactions between two coupled non-linear sub-systems, each possessing opposing non-linear overhang characteristics in the frequency domain in terms of positive and negative cubic stiffnesses. This system is a two-degree-of-freedom Duffing oscillator in which certain non-linear effects can be advantageously neutralised under specific conditions. This theoretical vehicle has been used as a preliminary methodology for understanding the interactive behaviour within typical industrial ultrasonic cutting components. Ultrasonic energy is generated within a piezoelectric exciter, which is inherently non-linear, and which is coupled to a bar- or block-horn, and to one or more material cutting blades, for example. The horn/blade configurations are also non-linear, and within the whole system there are response features which are strongly reminiscent of positive and negative cubic stiffness effects. The two-degree-of-freedom model is analysed and it is shown that a practically useful mitigating effect on the overall non-linear response of the system can be created under certain conditions when one of the cubic stiffnesses is varied. It has also been shown experimentally that coupling of ultrasonic components with different non-linear characteristics can strongly influence the performance of the system and that the general behaviour of the hypothetical theoretical model is indeed borne out in practice. Further experiments have shown that a multiple horn/blade configuration can, under certain circumstances, display autoparametric responses based on the forced response of the desired longitudinal mode parametrically exciting an undesired lateral mode. Typical autoparametric response phenomena have been observed and are presented at the end of the paper.

Non-linear models for the detection of impaired cerebral blood flow autoregulation.

PubMed

Chacón, Max; Jara, José Luis; Miranda, Rodrigo; Katsogridakis, Emmanuel; Panerai, Ronney B

2018-01-01

The ability to discriminate between normal and impaired dynamic cerebral autoregulation (CA), based on measurements of spontaneous fluctuations in arterial blood pressure (BP) and cerebral blood flow (CBF), has considerable clinical relevance. We studied 45 normal subjects at rest and under hypercapnia induced by breathing a mixture of carbon dioxide and air. Non-linear models with BP as input and CBF velocity (CBFV) as output, were implemented with support vector machines (SVM) using separate recordings for learning and validation. Dynamic SVM implementations used either moving average or autoregressive structures. The efficiency of dynamic CA was estimated from the model's derived CBFV response to a step change in BP as an autoregulation index for both linear and non-linear models. Non-linear models with recurrences (autoregressive) showed the best results, with CA indexes of 5.9 ± 1.5 in normocapnia, and 2.5 ± 1.2 for hypercapnia with an area under the receiver-operator curve of 0.955. The high performance achieved by non-linear SVM models to detect deterioration of dynamic CA should encourage further assessment of its applicability to clinical conditions where CA might be impaired.

Non-linear models for the detection of impaired cerebral blood flow autoregulation

PubMed Central

Miranda, Rodrigo; Katsogridakis, Emmanuel

2018-01-01

The ability to discriminate between normal and impaired dynamic cerebral autoregulation (CA), based on measurements of spontaneous fluctuations in arterial blood pressure (BP) and cerebral blood flow (CBF), has considerable clinical relevance. We studied 45 normal subjects at rest and under hypercapnia induced by breathing a mixture of carbon dioxide and air. Non-linear models with BP as input and CBF velocity (CBFV) as output, were implemented with support vector machines (SVM) using separate recordings for learning and validation. Dynamic SVM implementations used either moving average or autoregressive structures. The efficiency of dynamic CA was estimated from the model’s derived CBFV response to a step change in BP as an autoregulation index for both linear and non-linear models. Non-linear models with recurrences (autoregressive) showed the best results, with CA indexes of 5.9 ± 1.5 in normocapnia, and 2.5 ± 1.2 for hypercapnia with an area under the receiver-operator curve of 0.955. The high performance achieved by non-linear SVM models to detect deterioration of dynamic CA should encourage further assessment of its applicability to clinical conditions where CA might be impaired. PMID:29381724

Robust model predictive control of nonlinear systems with unmodeled dynamics and bounded uncertainties based on neural networks.

PubMed

Yan, Zheng; Wang, Jun

2014-03-01

This paper presents a neural network approach to robust model predictive control (MPC) for constrained discrete-time nonlinear systems with unmodeled dynamics affected by bounded uncertainties. The exact nonlinear model of underlying process is not precisely known, but a partially known nominal model is available. This partially known nonlinear model is first decomposed to an affine term plus an unknown high-order term via Jacobian linearization. The linearization residue combined with unmodeled dynamics is then modeled using an extreme learning machine via supervised learning. The minimax methodology is exploited to deal with bounded uncertainties. The minimax optimization problem is reformulated as a convex minimization problem and is iteratively solved by a two-layer recurrent neural network. The proposed neurodynamic approach to nonlinear MPC improves the computational efficiency and sheds a light for real-time implementability of MPC technology. Simulation results are provided to substantiate the effectiveness and characteristics of the proposed approach.

Non-Linearity in Wide Dynamic Range CMOS Image Sensors Utilizing a Partial Charge Transfer Technique.

PubMed

Shafie, Suhaidi; Kawahito, Shoji; Halin, Izhal Abdul; Hasan, Wan Zuha Wan

2009-01-01

The partial charge transfer technique can expand the dynamic range of a CMOS image sensor by synthesizing two types of signal, namely the long and short accumulation time signals. However the short accumulation time signal obtained from partial transfer operation suffers of non-linearity with respect to the incident light. In this paper, an analysis of the non-linearity in partial charge transfer technique has been carried, and the relationship between dynamic range and the non-linearity is studied. The results show that the non-linearity is caused by two factors, namely the current diffusion, which has an exponential relation with the potential barrier, and the initial condition of photodiodes in which it shows that the error in the high illumination region increases as the ratio of the long to the short accumulation time raises. Moreover, the increment of the saturation level of photodiodes also increases the error in the high illumination region.

Robust ADP Design for Continuous-Time Nonlinear Systems With Output Constraints.

PubMed

Fan, Bo; Yang, Qinmin; Tang, Xiaoyu; Sun, Youxian

2018-06-01

In this paper, a novel robust adaptive dynamic programming (RADP)-based control strategy is presented for the optimal control of a class of output-constrained continuous-time unknown nonlinear systems. Our contribution includes a step forward beyond the usual optimal control result to show that the output of the plant is always within user-defined bounds. To achieve the new results, an error transformation technique is first established to generate an equivalent nonlinear system, whose asymptotic stability guarantees both the asymptotic stability and the satisfaction of the output restriction of the original system. Furthermore, RADP algorithms are developed to solve the transformed nonlinear optimal control problem with completely unknown dynamics as well as a robust design to guarantee the stability of the closed-loop systems in the presence of unavailable internal dynamic state. Via small-gain theorem, asymptotic stability of the original and transformed nonlinear system is theoretically guaranteed. Finally, comparison results demonstrate the merits of the proposed control policy.

A Stewart isolator with high-static-low-dynamic stiffness struts based on negative stiffness magnetic springs

NASA Astrophysics Data System (ADS)

Zheng, Yisheng; Li, Qingpin; Yan, Bo; Luo, Yajun; Zhang, Xinong

2018-05-01

In order to improve the isolation performance of passive Stewart platforms, the negative stiffness magnetic spring (NSMS) is employed to construct high static low dynamic stiffness (HSLDS) struts. With the NSMS, the resonance frequencies of the platform can be reduced effectively without deteriorating its load bearing capacity. The model of the Stewart isolation platform with HSLDS struts is presented and the stiffness characteristic of its struts is studied firstly. Then the nonlinear dynamic model of the platform including both geometry nonlinearity and stiffness nonlinearity is established; and its simplified dynamic model is derived under the condition of small vibration. The effect of nonlinearity on the isolation performance is also evaluated. Finally, a prototype is built and the isolation performance is tested. Both simulated and experimental results demonstrate that, by using the NSMS, the resonance frequencies of the Stewart isolator are reduced and the isolation performance in all six directions is improved: the isolation frequency band is increased and extended to a lower-frequency level.

Formation Learning Control of Multiple Autonomous Underwater Vehicles With Heterogeneous Nonlinear Uncertain Dynamics.

PubMed

Yuan, Chengzhi; Licht, Stephen; He, Haibo

2017-09-26

In this paper, a new concept of formation learning control is introduced to the field of formation control of multiple autonomous underwater vehicles (AUVs), which specifies a joint objective of distributed formation tracking control and learning/identification of nonlinear uncertain AUV dynamics. A novel two-layer distributed formation learning control scheme is proposed, which consists of an upper-layer distributed adaptive observer and a lower-layer decentralized deterministic learning controller. This new formation learning control scheme advances existing techniques in three important ways: 1) the multi-AUV system under consideration has heterogeneous nonlinear uncertain dynamics; 2) the formation learning control protocol can be designed and implemented by each local AUV agent in a fully distributed fashion without using any global information; and 3) in addition to the formation control performance, the distributed control protocol is also capable of accurately identifying the AUVs' heterogeneous nonlinear uncertain dynamics and utilizing experiences to improve formation control performance. Extensive simulations have been conducted to demonstrate the effectiveness of the proposed results.

Modelling the influence of sensory dynamics on linear and nonlinear driver steering control

NASA Astrophysics Data System (ADS)

Nash, C. J.; Cole, D. J.

2018-05-01

A recent review of the literature has indicated that sensory dynamics play an important role in the driver-vehicle steering task, motivating the design of a new driver model incorporating human sensory systems. This paper presents a full derivation of the linear driver model developed in previous work, and extends the model to control a vehicle with nonlinear tyres. Various nonlinear controllers and state estimators are compared with different approximations of the true system dynamics. The model simulation time is found to increase significantly with the complexity of the controller and state estimator. In general the more complex controllers perform best, although with certain vehicle and tyre models linearised controllers perform as well as a full nonlinear optimisation. Various extended Kalman filters give similar results, although the driver's sensory dynamics reduce control performance compared with full state feedback. The new model could be used to design vehicle systems which interact more naturally and safely with a human driver.

Reflections on the nature of non-linear responses of the climate to forcing

NASA Astrophysics Data System (ADS)

Ditlevsen, Peter

2017-04-01

On centennial to multi-millennial time scales the paleoclimatic record shows that climate responds in a very non-linear way to the external forcing. Perhaps most puzzling is the change in glacial period duration at the Middle Pleistocene Transition. From a dynamical systems perspective, this could be a change in frequency locking between the orbital forcing and the climatic response or it could be a non-linear resonance phenomenon. In both cases the climate system shows a non-trivial oscillatory behaviour. From the records it seems that this behaviour can be described by an effective dynamics on a low-dimensional slow manifold. These different possible dynamical behaviours will be discussed. References: Arianna Marchionne, Peter Ditlevsen, and Sebastian Wieczorek, "Three types of nonlinear resonances", arXiv:1605.00858 Peter Ashwin and Peter Ditlevsen, "The middle Pleistocene transition as a generic bifurcation on a slow manifold", Climate Dynamics, 45, 2683, 2015. Peter D. Ditlevsen, "The bifurcation structure and noise assisted transitions in the Pleistocene glacial cycles", Paleoceanography, 24, PA3204, 2009

Nonlinear elasticity in rocks: A comprehensive three-dimensional description

DOE PAGES

Lott, Martin; Remillieux, Marcel; Garnier, Vincent; ...

2017-07-17

Here we study theoretically and experimentally the mechanisms of nonlinear and nonequilibrium dynamics in geomaterials through dynamic acoustoelasticity testing. In the proposed theoretical formulation, the classical theory of nonlinear elasticity is extended to include the effects of conditioning. This formulation is adapted to the context of dynamic acoustoelasticity testing in which a low-frequency “pump” wave induces a strain field in the sample and modulates the propagation of a high-frequency “probe” wave. Experiments are conducted to validate the formulation in a long thin bar of Berea sandstone. Several configurations of the pump and probe are examined: the pump successively consists ofmore » the first longitudinal and first torsional mode of vibration of the sample while the probe is successively based on (pressure) $P$ and (shear) $S$ waves. The theoretical predictions reproduce many features of the elastic response observed experimentally, in particular, the coupling between nonlinear and nonequilibrium dynamics and the three-dimensional effects resulting from the tensorial nature of elasticity.« less

Nonlinear dynamics and predictability in the atmospheric sciences

NASA Technical Reports Server (NTRS)

Ghil, M.; Kimoto, M.; Neelin, J. D.

1991-01-01

Systematic applications of nonlinear dynamics to studies of the atmosphere and climate are reviewed for the period 1987-1990. Problems discussed include paleoclimatic applications, low-frequency atmospheric variability, and interannual variability of the ocean-atmosphere system. Emphasis is placed on applications of the successive bifurcation approach and the ergodic theory of dynamical systems to understanding and prediction of intraseasonal, interannual, and Quaternary climate changes.

Toward Control of Universal Scaling in Critical Dynamics

DTIC Science & Technology

2016-01-27

program that aims to synergistically combine two powerful and very successful theories for non-linear stochastic dynamics of cooperative multi...RESPONSIBLE PERSON 19b. TELEPHONE NUMBER Uwe Tauber Uwe C. T? uber , Michel Pleimling, Daniel J. Stilwell 611102 c. THIS PAGE The public reporting burden...to synergistically combine two powerful and very successful theories for non-linear stochastic dynamics of cooperative multi-component systems, namely

Veering and nonlinear interactions of a clamped beam in bending and torsion

NASA Astrophysics Data System (ADS)

Ehrhardt, David A.; Hill, Thomas L.; Neild, Simon A.; Cooper, Jonathan E.

2018-03-01

Understanding the linear and nonlinear dynamic behaviour of beams is critical for the design of many engineering structures such as spacecraft antennae, aircraft wings, and turbine blades. When the eigenvalues of such structures are closely-spaced, nonlinearity may lead to interactions between the underlying linear normal modes (LNMs). This work considers a clamped-clamped beam which exhibits nonlinear behaviour due to axial tension from large amplitudes of deformation. An additional cross-beam, mounted transversely and with a movable mass at each tip, allows tuning of the primary torsion LNM such that it is close to the primary bending LNM. Perturbing the location of one mass relative to that of the other leads to veering between the eigenvalues of the bending and torsion LNMs. For a number of selected geometries in the region of veering, a nonlinear reduced order model (NLROM) is created and the nonlinear normal modes (NNMs) are used to describe the underlying nonlinear behaviour of the structure. The relationship between the 'closeness' of the eigenvalues and the nonlinear dynamic behaviour is demonstrated in the NNM backbone curves, and veering-like behaviour is observed. Finally, the forced and damped dynamics of the structure are predicted using several analytical and numerical tools and are compared to experimental measurements. As well as showing a good agreement between the predicted and measured responses, phenomena such as a 1:1 internal resonance and quasi-periodic behaviour are identified.

Effects of guided breath exercise on complex behaviour of heart rate dynamics.

PubMed

Tavares, Bruna S; de Paula Vidigal, Giovanna; Garner, David M; Raimundo, Rodrigo D; de Abreu, Luiz Carlos; Valenti, Vitor E

2017-11-01

Cardiac autonomic regulation is influenced by changes in respiratory rate, which has been demonstrated by linear analysis of heart rate variability (HRV). Conversely, the complex behaviour is not well defined for HRV during this physiological state. In this sense, Higuchi Fractal Dimension is applied directly to the time series. It analyses the fractal dimension of discrete time sequences and is simpler and faster than correlation dimension and many other classical measures derived from chaos theory. We investigated chaotic behaviour of heart rate dynamics during guided breath exercises. We investigated 21 healthy male volunteers aged between 18 and 30 years. HRV was analysed 10 min before and 10 min during guided breath exercises. HRV was analysed in the time and frequency domain for linear analysis and through HFD for non-linear analysis. Linear analysis indicated that SDNN, pNN50, RMSSD, LF, HF and LF/HF increased during guided breath exercises. HFD analysis illustrated that between K max 20 to K max 120 intervals, was enhanced during guided breath exercises. Guided breath exercises acutely increased chaotic behaviour of HRV measured by HFD. © 2016 Scandinavian Society of Clinical Physiology and Nuclear Medicine. Published by John Wiley & Sons Ltd.

A method for reducing the order of nonlinear dynamic systems

NASA Astrophysics Data System (ADS)

Masri, S. F.; Miller, R. K.; Sassi, H.; Caughey, T. K.

1984-06-01

An approximate method that uses conventional condensation techniques for linear systems together with the nonparametric identification of the reduced-order model generalized nonlinear restoring forces is presented for reducing the order of discrete multidegree-of-freedom dynamic systems that possess arbitrary nonlinear characteristics. The utility of the proposed method is demonstrated by considering a redundant three-dimensional finite-element model half of whose elements incorporate hysteretic properties. A nonlinear reduced-order model, of one-third the order of the original model, is developed on the basis of wideband stationary random excitation and the validity of the reduced-order model is subsequently demonstrated by its ability to predict with adequate accuracy the transient response of the original nonlinear model under a different nonstationary random excitation.

Quasi-Linear Parameter Varying Representation of General Aircraft Dynamics Over Non-Trim Region

NASA Technical Reports Server (NTRS)

Shin, Jong-Yeob

2007-01-01

For applying linear parameter varying (LPV) control synthesis and analysis to a nonlinear system, it is required that a nonlinear system be represented in the form of an LPV model. In this paper, a new representation method is developed to construct an LPV model from a nonlinear mathematical model without the restriction that an operating point must be in the neighborhood of equilibrium points. An LPV model constructed by the new method preserves local stabilities of the original nonlinear system at "frozen" scheduling parameters and also represents the original nonlinear dynamics of a system over a non-trim region. An LPV model of the motion of FASER (Free-flying Aircraft for Subscale Experimental Research) is constructed by the new method.

Observability of nonlinear dynamics: normalized results and a time-series approach.

PubMed

Aguirre, Luis A; Bastos, Saulo B; Alves, Marcela A; Letellier, Christophe

2008-03-01

This paper investigates the observability of nonlinear dynamical systems. Two difficulties associated with previous studies are dealt with. First, a normalized degree observability is defined. This permits the comparison of different systems, which was not generally possible before. Second, a time-series approach is proposed based on omnidirectional nonlinear correlation functions to rank a set of time series of a system in terms of their potential use to reconstruct the original dynamics without requiring the knowledge of the system equations. The two approaches proposed in this paper and a former method were applied to five benchmark systems and an overall agreement of over 92% was found.

Wavepacket dynamics in a family of nonlinear Fibonacci lattices

NASA Astrophysics Data System (ADS)

Pandey, Mohit; Campbell, David

We examine the dynamics of a quantum particle in a variety of one-dimensional Fibonacci lattices (which are shifted from each other) in the presence of interaction. To describe the nonlinear interactions we employ the discrete nonlinear Schrödinger (DNLS) equation. Using a single-site localized state in the lattice as our initial condition, we evolve the wavepacket numerically using DNLS equation. We compute the root-mean-square width of the wavepacket as it evolves in time and show how the ``global location'' of initial wavepacket affects the dynamics. We compare and contrast our results with earlier studies of related but distinct models.

Fitting Nonlinear Ordinary Differential Equation Models with Random Effects and Unknown Initial Conditions Using the Stochastic Approximation Expectation-Maximization (SAEM) Algorithm.

PubMed

Chow, Sy-Miin; Lu, Zhaohua; Sherwood, Andrew; Zhu, Hongtu

2016-03-01

The past decade has evidenced the increased prevalence of irregularly spaced longitudinal data in social sciences. Clearly lacking, however, are modeling tools that allow researchers to fit dynamic models to irregularly spaced data, particularly data that show nonlinearity and heterogeneity in dynamical structures. We consider the issue of fitting multivariate nonlinear differential equation models with random effects and unknown initial conditions to irregularly spaced data. A stochastic approximation expectation-maximization algorithm is proposed and its performance is evaluated using a benchmark nonlinear dynamical systems model, namely, the Van der Pol oscillator equations. The empirical utility of the proposed technique is illustrated using a set of 24-h ambulatory cardiovascular data from 168 men and women. Pertinent methodological challenges and unresolved issues are discussed.

Experimental feedback linearisation of a vibrating system with a non-smooth nonlinearity

NASA Astrophysics Data System (ADS)

Lisitano, D.; Jiffri, S.; Bonisoli, E.; Mottershead, J. E.

2018-03-01

Input-output partial feedback linearisation is demonstrated experimentally for the first time on a system with non-smooth nonlinearity, a laboratory three degrees of freedom lumped mass system with a piecewise-linear spring. The output degree of freedom is located away from the nonlinearity so that the partial feedback linearisation possesses nonlinear internal dynamics. The dynamic behaviour of the linearised part is specified by eigenvalue assignment and an investigation of the zero dynamics is carried out to confirm stability of the overall system. A tuned numerical model is developed for use in the controller and to produce numerical outputs for comparison with experimental closed-loop results. A new limitation of the feedback linearisation method is discovered in the case of lumped mass systems - that the input and output must share the same degrees of freedom.

FITTING NONLINEAR ORDINARY DIFFERENTIAL EQUATION MODELS WITH RANDOM EFFECTS AND UNKNOWN INITIAL CONDITIONS USING THE STOCHASTIC APPROXIMATION EXPECTATION–MAXIMIZATION (SAEM) ALGORITHM

PubMed Central

Chow, Sy- Miin; Lu, Zhaohua; Zhu, Hongtu; Sherwood, Andrew

2014-01-01

The past decade has evidenced the increased prevalence of irregularly spaced longitudinal data in social sciences. Clearly lacking, however, are modeling tools that allow researchers to fit dynamic models to irregularly spaced data, particularly data that show nonlinearity and heterogeneity in dynamical structures. We consider the issue of fitting multivariate nonlinear differential equation models with random effects and unknown initial conditions to irregularly spaced data. A stochastic approximation expectation–maximization algorithm is proposed and its performance is evaluated using a benchmark nonlinear dynamical systems model, namely, the Van der Pol oscillator equations. The empirical utility of the proposed technique is illustrated using a set of 24-h ambulatory cardiovascular data from 168 men and women. Pertinent methodological challenges and unresolved issues are discussed. PMID:25416456

A nonlinear control method based on ANFIS and multiple models for a class of SISO nonlinear systems and its application.

PubMed

Zhang, Yajun; Chai, Tianyou; Wang, Hong

2011-11-01

This paper presents a novel nonlinear control strategy for a class of uncertain single-input and single-output discrete-time nonlinear systems with unstable zero-dynamics. The proposed method combines adaptive-network-based fuzzy inference system (ANFIS) with multiple models, where a linear robust controller, an ANFIS-based nonlinear controller and a switching mechanism are integrated using multiple models technique. It has been shown that the linear controller can ensure the boundedness of the input and output signals and the nonlinear controller can improve the dynamic performance of the closed loop system. Moreover, it has also been shown that the use of the switching mechanism can simultaneously guarantee the closed loop stability and improve its performance. As a result, the controller has the following three outstanding features compared with existing control strategies. First, this method relaxes the assumption of commonly-used uniform boundedness on the unmodeled dynamics and thus enhances its applicability. Second, since ANFIS is used to estimate and compensate the effect caused by the unmodeled dynamics, the convergence rate of neural network learning has been increased. Third, a "one-to-one mapping" technique is adapted to guarantee the universal approximation property of ANFIS. The proposed controller is applied to a numerical example and a pulverizing process of an alumina sintering system, respectively, where its effectiveness has been justified.

Nonlinear stochastic exclusion financial dynamics modeling and time-dependent intrinsic detrended cross-correlation

NASA Astrophysics Data System (ADS)

Zhang, Wei; Wang, Jun

2017-09-01

In attempt to reproduce price dynamics of financial markets, a stochastic agent-based financial price model is proposed and investigated by stochastic exclusion process. The exclusion process, one of interacting particle systems, is usually thought of as modeling particle motion (with the conserved number of particles) in a continuous time Markov process. In this work, the process is utilized to imitate the trading interactions among the investing agents, in order to explain some stylized facts found in financial time series dynamics. To better understand the correlation behaviors of the proposed model, a new time-dependent intrinsic detrended cross-correlation (TDI-DCC) is introduced and performed, also, the autocorrelation analyses are applied in the empirical research. Furthermore, to verify the rationality of the financial price model, the actual return series are also considered to be comparatively studied with the simulation ones. The comparison results of return behaviors reveal that this financial price dynamics model can reproduce some correlation features of actual stock markets.

Perturbation and Nonlinear Dynamic Analysis of Different Singing Styles

PubMed Central

Butte, Caitlin J.; Zhang, Yu; Song, Huangqiang; Jiang, Jack J.

2012-01-01

Summary Previous research has used perturbation analysis methods to study the singing voice. Using perturbation and nonlinear dynamic analysis (NDA) methods in conjunction may provide more accurate information on the singing voice and may distinguish vocal usage in different styles. Acoustic samples from different styles of singing were compared using nonlinear dynamic and perturbation measures. Twenty-six songs from different musical styles were obtained from an online music database (Rhapsody, RealNetworks, Inc., Seattle, WA). One-second samples were selected from each song for analysis. Perturbation analyses of jitter, shimmer, and signal-to-noise ratio and NDA of correlation dimension (D2) were performed on samples from each singing style. Percent jitter and shimmer median values were low normal for country (0.32% and 3.82%), musical theater (MT) (0.280% and 2.80%), jazz (0.440% and 2.34%), and soul (0.430% and 6.42%). The popular style had slightly higher median jitter and shimmer values (1.13% and 6.78%) than other singing styles, although this was not statistically significant. The opera singing style had median jitter of 0.520%, and yielded significantly high shimmer (P = 0.001) of 7.72%. All six singing styles were measured reliably using NDA, indicating that operatic singing is notably more chaotic than other singing styles. Median correlation dimension values were low to normal, compared to healthy voices, in country (median D2 = 2.14), jazz (median D2 = 2.24), pop (median D2 = 2.60), MT (median D2 = 2.73), and soul (mean D2 = 3.26). Correlation dimension was significantly higher in opera (P < 0.001) with median D2 = 6.19. In this study, acoustic analysis in opera singing gave significantly high values for shimmer and D2, suggesting that it is more irregular than other singing styles; a previously unknown quality of opera singing. Perturbation analysis also suggested significant differences in vocal output in different singing styles. This preliminary study using acoustic analysis with nonlinear dynamic measures and perturbation measures may represent a valuable procedure in quantitatively describing the properties of the singing voice. Further research with human test subjects may allow us to characterize singing styles and diagnose vocal dysfunction in the singing voice. PMID:18504114

Application of Contraction Mappings to the Control of Nonlinear Systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Killingsworth, W. R., Jr.

1972-01-01

The theoretical and applied aspects of successive approximation techniques are considered for the determination of controls for nonlinear dynamical systems. Particular emphasis is placed upon the methods of contraction mappings and modified contraction mappings. It is shown that application of the Pontryagin principle to the optimal nonlinear regulator problem results in necessary conditions for optimality in the form of a two point boundary value problem (TPBVP). The TPBVP is represented by an operator equation and functional analytic results on the iterative solution of operator equations are applied. The general convergence theorems are translated and applied to those operators arising from the optimal regulation of nonlinear systems. It is shown that simply structured matrices and similarity transformations may be used to facilitate the calculation of the matrix Green functions and the evaluation of the convergence criteria. A controllability theory based on the integral representation of TPBVP's, the implicit function theorem, and contraction mappings is developed for nonlinear dynamical systems. Contraction mappings are theoretically and practically applied to a nonlinear control problem with bounded input control and the Lipschitz norm is used to prove convergence for the nondifferentiable operator. A dynamic model representing community drug usage is developed and the contraction mappings method is used to study the optimal regulation of the nonlinear system.

Propagation of a finite-amplitude elastic pulse in a bar of Berea sandstone: A detailed look at the mechanisms of classical nonlinearity, hysteresis, and nonequilibrium dynamics: Nonlinear propagation of elastic pulse

DOE Office of Scientific and Technical Information (OSTI.GOV)

Remillieux, Marcel C.; Ulrich, T. J.; Goodman, Harvey E.

Here, we study the propagation of a finite-amplitude elastic pulse in a long thin bar of Berea sandstone. In previous work, this type of experiment has been conducted to quantify classical nonlinearity, based on the amplitude growth of the second harmonic as a function of propagation distance. To greatly expand on that early work, a non-contact scanning 3D laser Doppler vibrometer was used to track the evolution of the axial component of the particle velocity over the entire surface of the bar as functions of the propagation distance and source amplitude. With these new measurements, the combined effects of classicalmore » nonlinearity, hysteresis, and nonequilibrium dynamics have all been measured simultaneously. We then show that the numerical resolution of the 1D wave equation with terms for classical nonlinearity and attenuation accurately captures the spectral features of the waves up to the second harmonic. But, for higher harmonics the spectral content is shown to be strongly influenced by hysteresis. This work also shows data which not only quantifies classical nonlinearity but also the nonequilibrium dynamics based on the relative change in the arrival time of the elastic pulse as a function of strain and distance from the source. Finally, a comparison is made to a resonant bar measurement, a reference experiment used to quantify nonequilibrium dynamics, based on the relative shift of the resonance frequencies as a function of the maximum dynamic strain in the sample.« less

Propagation of a finite-amplitude elastic pulse in a bar of Berea sandstone: A detailed look at the mechanisms of classical nonlinearity, hysteresis, and nonequilibrium dynamics: Nonlinear propagation of elastic pulse

DOE PAGES

Remillieux, Marcel C.; Ulrich, T. J.; Goodman, Harvey E.; ...

2017-10-18

Here, we study the propagation of a finite-amplitude elastic pulse in a long thin bar of Berea sandstone. In previous work, this type of experiment has been conducted to quantify classical nonlinearity, based on the amplitude growth of the second harmonic as a function of propagation distance. To greatly expand on that early work, a non-contact scanning 3D laser Doppler vibrometer was used to track the evolution of the axial component of the particle velocity over the entire surface of the bar as functions of the propagation distance and source amplitude. With these new measurements, the combined effects of classicalmore » nonlinearity, hysteresis, and nonequilibrium dynamics have all been measured simultaneously. We then show that the numerical resolution of the 1D wave equation with terms for classical nonlinearity and attenuation accurately captures the spectral features of the waves up to the second harmonic. But, for higher harmonics the spectral content is shown to be strongly influenced by hysteresis. This work also shows data which not only quantifies classical nonlinearity but also the nonequilibrium dynamics based on the relative change in the arrival time of the elastic pulse as a function of strain and distance from the source. Finally, a comparison is made to a resonant bar measurement, a reference experiment used to quantify nonequilibrium dynamics, based on the relative shift of the resonance frequencies as a function of the maximum dynamic strain in the sample.« less

Nonlinear Dynamics and the Growth of Literature.

ERIC Educational Resources Information Center

Tabah, Albert N.

1992-01-01

Discussion of nonlinear dynamic mechanisms focuses on whether information production and dissemination can be described by similar mechanisms. The exponential versus linear growth of literature is discussed, the time factor is considered, an example using literature from the field of superconductivity is given, and implications for information…

Molecular dynamics simulation of nonlinear spectroscopies of intermolecular motions in liquid water.

PubMed

Yagasaki, Takuma; Saito, Shinji

2009-09-15

Water is the most extensively studied of liquids because of both its ubiquity and its anomalous thermodynamic and dynamic properties. The properties of water are dominated by hydrogen bonds and hydrogen bond network rearrangements. Fundamental information on the dynamics of liquid water has been provided by linear infrared (IR), Raman, and neutron-scattering experiments; molecular dynamics simulations have also provided insights. Recently developed higher-order nonlinear spectroscopies open new windows into the study of the hydrogen bond dynamics of liquid water. For example, the vibrational lifetimes of stretches and a bend, intramolecular features of water dynamics, can be accurately measured and are found to be on the femtosecond time scale at room temperature. Higher-order nonlinear spectroscopy is expressed by a multitime correlation function, whereas traditional linear spectroscopy is given by a one-time correlation function. Thus, nonlinear spectroscopy yields more detailed information on the dynamics of condensed media than linear spectroscopy. In this Account, we describe the theoretical background and methods for calculating higher order nonlinear spectroscopy; equilibrium and nonequilibrium molecular dynamics simulations, and a combination of both, are used. We also present the intermolecular dynamics of liquid water revealed by fifth-order two-dimensional (2D) Raman spectroscopy and third-order IR spectroscopy. 2D Raman spectroscopy is sensitive to couplings between modes; the calculated 2D Raman signal of liquid water shows large anharmonicity in the translational motion and strong coupling between the translational and librational motions. Third-order IR spectroscopy makes it possible to examine the time-dependent couplings. The 2D IR spectra and three-pulse photon echo peak shift show the fast frequency modulation of the librational motion. A significant effect of the translational motion on the fast frequency modulation of the librational motion is elucidated by introducing the "translation-free" molecular dynamics simulation. The isotropic pump-probe signal and the polarization anisotropy decay show fast transfer of the librational energy to the surrounding water molecules, followed by relaxation to the hot ground state. These theoretical methods do not require frequently used assumptions and can thus be called ab initio methods; together with multidimensional nonlinear spectroscopies, they provide powerful methods for examining the inter- and intramolecular details of water dynamics.

Ontology of Earth's nonlinear dynamic complex systems

NASA Astrophysics Data System (ADS)

Babaie, Hassan; Davarpanah, Armita

2017-04-01

As a complex system, Earth and its major integrated and dynamically interacting subsystems (e.g., hydrosphere, atmosphere) display nonlinear behavior in response to internal and external influences. The Earth Nonlinear Dynamic Complex Systems (ENDCS) ontology formally represents the semantics of the knowledge about the nonlinear system element (agent) behavior, function, and structure, inter-agent and agent-environment feedback loops, and the emergent collective properties of the whole complex system as the result of interaction of the agents with other agents and their environment. It also models nonlinear concepts such as aperiodic, random chaotic behavior, sensitivity to initial conditions, bifurcation of dynamic processes, levels of organization, self-organization, aggregated and isolated functionality, and emergence of collective complex behavior at the system level. By incorporating several existing ontologies, the ENDCS ontology represents the dynamic system variables and the rules of transformation of their state, emergent state, and other features of complex systems such as the trajectories in state (phase) space (attractor and strange attractor), basins of attractions, basin divide (separatrix), fractal dimension, and system's interface to its environment. The ontology also defines different object properties that change the system behavior, function, and structure and trigger instability. ENDCS will help to integrate the data and knowledge related to the five complex subsystems of Earth by annotating common data types, unifying the semantics of shared terminology, and facilitating interoperability among different fields of Earth science.

A quantum-classical theory with nonlinear and stochastic dynamics

NASA Astrophysics Data System (ADS)

Burić, N.; Popović, D. B.; Radonjić, M.; Prvanović, S.

2014-12-01

The method of constrained dynamical systems on the quantum-classical phase space is utilized to develop a theory of quantum-classical hybrid systems. Effects of the classical degrees of freedom on the quantum part are modeled using an appropriate constraint, and the interaction also includes the effects of neglected degrees of freedom. Dynamical law of the theory is given in terms of nonlinear stochastic differential equations with Hamiltonian and gradient terms. The theory provides a successful dynamical description of the collapse during quantum measurement.

Internal transport barrier triggered by non-linear lower hybrid wave deposition under condition of beam-driven toroidal rotation

NASA Astrophysics Data System (ADS)

Gao, Q. D.; Budny, R. V.

2015-03-01

By using gyro-Landau fluid transport model (GLF23), time-dependent integrated modeling is carried out using TRANSP to explore the dynamic process of internal transport barrier (ITB) formation in the neutral beam heating discharges. When the current profile is controlled by LHCD (lower hybrid current drive), with appropriate neutral beam injection, the nonlinear interplay between the transport determined gradients in the plasma temperature (Ti,e) and toroidal velocity (Vϕ) and the E×B flow shear (including q-profile) produces transport bifurcations, generating spontaneously a stepwise growing ITB. In the discharge, the constraints imposed by the wave propagation condition causes interplay of the LH driven current distribution with the plasma configuration modification, which constitutes non-linearity in the LH wave deposition. The non-linear effects cause bifurcation in LHCD, generating two distinct quasi-stationary reversed magnetic shear configurations. The change of current profile during the transition period between the two quasi-stationary states results in increase of the E×B shearing flow arising from toroidal rotation. The turbulence transport suppression by sheared E×B flow during the ITB development is analysed, and the temporal evolution of some parameters characterized the plasma confinement is examined. Ample evidence shows that onset of the ITB development is correlated with the enhancement of E×B shearing rate caused by the bifurcation in LHCD. It is suggested that the ITB triggering is associated with the non-linear effects of the LH power deposition.

Dynamic trapping of a polarization rotation vector soliton in a fiber laser.

PubMed

Liu, Meng; Luo, Ai-Ping; Luo, Zhi-Chao; Xu, Wen-Cheng

2017-01-15

Ultrafast fiber laser, as a dissipative nonlinear optical system, plays an important role in investigating various nonlinear phenomena and soliton dynamics. Vector features of solitons, including polarization locked and polarization rotation vector solitons (PRVSs), are interesting nonlinear dynamics in ultrafast fiber lasers. Herein, we experimentally reveal the trapping characteristics of PRVSs for the first time, to the best of our best knowledge. We show that, for the conventional soliton trapping in the ultrafast fiber laser, the soliton central wavelengths of the two polarization components are constant at the laser output port. However, it is found that the dynamic trapping can be observed for the PRVS. That is, the peak frequencies along the two orthogonal polarization directions are dynamically alternating, depending on the relative intensities of the two polarization components. The obtained results would further unveil the physical mechanism of PRVSs.

The cultural implications of growth: Modeling nonlinear interaction of trait selection and population dynamics

NASA Astrophysics Data System (ADS)

Antoci, Angelo; Galeotti, Marcello; Russu, Paolo; Luigi Sacco, Pier

2018-05-01

In this paper, we study a nonlinear model of the interaction between trait selection and population dynamics, building on previous work of Ghirlanda et al. [Theor. Popul. Biol. 77, 181-188 (2010)] and Antoci et al. [Commun. Nonlinear Sci. Numer. Simul. 58, 92-106 (2018)]. We establish some basic properties of the model dynamics and present some simulations of the fine-grained structure of alternative dynamic regimes for chosen combinations of parameters. The role of the parameters that govern the reinforcement/corruption of maladaptive vs. adaptive traits is of special importance in determining the model's dynamic evolution. The main implication of this result is the need to pay special attention to the structural forces that may favor the emergence and consolidation of maladaptive traits in contemporary socio-economies, as it is the case, for example, for the stimulation of dysfunctional consumption habits and lifestyles in the pursuit of short-term profits.

The cultural implications of growth: Modeling nonlinear interaction of trait selection and population dynamics.

PubMed

Antoci, Angelo; Galeotti, Marcello; Russu, Paolo; Luigi Sacco, Pier

2018-05-01

In this paper, we study a nonlinear model of the interaction between trait selection and population dynamics, building on previous work of Ghirlanda et al. [Theor. Popul. Biol. 77, 181-188 (2010)] and Antoci et al. [Commun. Nonlinear Sci. Numer. Simul. 58, 92-106 (2018)]. We establish some basic properties of the model dynamics and present some simulations of the fine-grained structure of alternative dynamic regimes for chosen combinations of parameters. The role of the parameters that govern the reinforcement/corruption of maladaptive vs. adaptive traits is of special importance in determining the model's dynamic evolution. The main implication of this result is the need to pay special attention to the structural forces that may favor the emergence and consolidation of maladaptive traits in contemporary socio-economies, as it is the case, for example, for the stimulation of dysfunctional consumption habits and lifestyles in the pursuit of short-term profits.

Detecting and disentangling nonlinear structure from solar flux time series

NASA Technical Reports Server (NTRS)

Ashrafi, S.; Roszman, L.

1992-01-01

Interest in solar activity has grown in the past two decades for many reasons. Most importantly for flight dynamics, solar activity changes the atmospheric density, which has important implications for spacecraft trajectory and lifetime prediction. Building upon the previously developed Rayleigh-Benard nonlinear dynamic solar model, which exhibits many dynamic behaviors observed in the Sun, this work introduces new chaotic solar forecasting techniques. Our attempt to use recently developed nonlinear chaotic techniques to model and forecast solar activity has uncovered highly entangled dynamics. Numerical techniques for decoupling additive and multiplicative white noise from deterministic dynamics and examines falloff of the power spectra at high frequencies as a possible means of distinguishing deterministic chaos from noise than spectrally white or colored are presented. The power spectral techniques presented are less cumbersome than current methods for identifying deterministic chaos, which require more computationally intensive calculations, such as those involving Lyapunov exponents and attractor dimension.

Dynamics of a linear system coupled to a chain of light nonlinear oscillators analyzed through a continuous approximation

NASA Astrophysics Data System (ADS)

Charlemagne, S.; Ture Savadkoohi, A.; Lamarque, C.-H.

2018-07-01

The continuous approximation is used in this work to describe the dynamics of a nonlinear chain of light oscillators coupled to a linear main system. A general methodology is applied to an example where the chain has local nonlinear restoring forces. The slow invariant manifold is detected at fast time scale. At slow time scale, equilibrium and singular points are sought around this manifold in order to predict periodic regimes and strongly modulated responses of the system. Analytical predictions are in good accordance with numerical results and represent a potent tool for designing nonlinear chains for passive control purposes.

Nonlinear Model Predictive Control with Constraint Satisfactions for a Quadcopter

NASA Astrophysics Data System (ADS)

Wang, Ye; Ramirez-Jaime, Andres; Xu, Feng; Puig, Vicenç

2017-01-01

This paper presents a nonlinear model predictive control (NMPC) strategy combined with constraint satisfactions for a quadcopter. The full dynamics of the quadcopter describing the attitude and position are nonlinear, which are quite sensitive to changes of inputs and disturbances. By means of constraint satisfactions, partial nonlinearities and modeling errors of the control-oriented model of full dynamics can be transformed into the inequality constraints. Subsequently, the quadcopter can be controlled by an NMPC controller with the updated constraints generated by constraint satisfactions. Finally, the simulation results applied to a quadcopter simulator are provided to show the effectiveness of the proposed strategy.

Nonlinear tapping dynamics of multi-walled carbon nanotube tipped atomic force microcantilevers

NASA Astrophysics Data System (ADS)

Lee, S. I.; Howell, S. W.; Raman, A.; Reifenberger, R.; Nguyen, C. V.; Meyyappan, M.

2004-05-01

The nonlinear dynamics of an atomic force microcantilever (AFM) with an attached multi-walled carbon nanotube (MWCNT) tip is investigated experimentally and theoretically. We present the experimental nonlinear frequency response of a MWCNT tipped microcantilever in the tapping mode. Several unusual features in the response distinguish it from those traditionally observed for conventional tips. The MWCNT tipped AFM probe is apparently immune to conventional imaging instabilities related to the coexistence of attractive and repulsive tapping regimes. A theoretical interaction model for the system using an Euler elastica MWCNT model is developed and found to predict several unusual features of the measured nonlinear response.

Cooperativity and Heterogeneity in Plastic Crystals Studied by Nonlinear Dielectric Spectroscopy

NASA Astrophysics Data System (ADS)

Michl, M.; Bauer, Th.; Lunkenheimer, P.; Loidl, A.

2015-02-01

The glassy dynamics of plastic-crystalline cyclo-octanol and ortho-carborane, where only the molecular reorientational degrees of freedom freeze without long-range order, is investigated by nonlinear dielectric spectroscopy. Marked differences to canonical glass formers show up: While molecular cooperativity governs the glassy freezing, it leads to a much weaker slowing down of molecular dynamics than in supercooled liquids. Moreover, the observed nonlinear effects cannot be explained with the same heterogeneity scenario recently applied to canonical glass formers. This supports ideas that molecular relaxation in plastic crystals may be intrinsically nonexponential. Finally, no nonlinear effects were detected for the secondary processes in cyclo-octanol.

Design of robust iterative learning control schemes for systems with polytopic uncertainties and sector-bounded nonlinearities

NASA Astrophysics Data System (ADS)

Boski, Marcin; Paszke, Wojciech

2017-01-01

This paper deals with designing of iterative learning control schemes for uncertain systems with static nonlinearities. More specifically, the nonlinear part is supposed to be sector bounded and system matrices are assumed to range in the polytope of matrices. For systems with such nonlinearities and uncertainties the repetitive process setting is exploited to develop a linear matrix inequality based conditions for computing the feedback and feedforward (learning) controllers. These controllers guarantee acceptable dynamics along the trials and ensure convergence of the trial-to-trial error dynamics, respectively. Numerical examples illustrate the theoretical results and confirm effectiveness of the designed control scheme.

Nonlinear amplitude dynamics in flagellar beating

NASA Astrophysics Data System (ADS)

Oriola, David; Gadêlha, Hermes; Casademunt, Jaume

2017-03-01

The physical basis of flagellar and ciliary beating is a major problem in biology which is still far from completely understood. The fundamental cytoskeleton structure of cilia and flagella is the axoneme, a cylindrical array of microtubule doublets connected by passive cross-linkers and dynein motor proteins. The complex interplay of these elements leads to the generation of self-organized bending waves. Although many mathematical models have been proposed to understand this process, few attempts have been made to assess the role of dyneins on the nonlinear nature of the axoneme. Here, we investigate the nonlinear dynamics of flagella by considering an axonemal sliding control mechanism for dynein activity. This approach unveils the nonlinear selection of the oscillation amplitudes, which are typically either missed or prescribed in mathematical models. The explicit set of nonlinear equations are derived and solved numerically. Our analysis reveals the spatio-temporal dynamics of dynein populations and flagellum shape for different regimes of motor activity, medium viscosity and flagellum elasticity. Unstable modes saturate via the coupling of dynein kinetics and flagellum shape without the need of invoking a nonlinear axonemal response. Hence, our work reveals a novel mechanism for the saturation of unstable modes in axonemal beating.

A nonlinear Kalman filtering approach to embedded control of turbocharged diesel engines

NASA Astrophysics Data System (ADS)

Rigatos, Gerasimos; Siano, Pierluigi; Arsie, Ivan

2014-10-01

The development of efficient embedded control for turbocharged Diesel engines, requires the programming of elaborated nonlinear control and filtering methods. To this end, in this paper nonlinear control for turbocharged Diesel engines is developed with the use of Differential flatness theory and the Derivative-free nonlinear Kalman Filter. It is shown that the dynamic model of the turbocharged Diesel engine is differentially flat and admits dynamic feedback linearization. It is also shown that the dynamic model can be written in the linear Brunovsky canonical form for which a state feedback controller can be easily designed. To compensate for modeling errors and external disturbances the Derivative-free nonlinear Kalman Filter is used and redesigned as a disturbance observer. The filter consists of the Kalman Filter recursion on the linearized equivalent of the Diesel engine model and of an inverse transformation based on differential flatness theory which enables to obtain estimates for the state variables of the initial nonlinear model. Once the disturbances variables are identified it is possible to compensate them by including an additional control term in the feedback loop. The efficiency of the proposed control method is tested through simulation experiments.

Nonlinear amplitude dynamics in flagellar beating.

PubMed

Oriola, David; Gadêlha, Hermes; Casademunt, Jaume

2017-03-01

The physical basis of flagellar and ciliary beating is a major problem in biology which is still far from completely understood. The fundamental cytoskeleton structure of cilia and flagella is the axoneme, a cylindrical array of microtubule doublets connected by passive cross-linkers and dynein motor proteins. The complex interplay of these elements leads to the generation of self-organized bending waves. Although many mathematical models have been proposed to understand this process, few attempts have been made to assess the role of dyneins on the nonlinear nature of the axoneme. Here, we investigate the nonlinear dynamics of flagella by considering an axonemal sliding control mechanism for dynein activity. This approach unveils the nonlinear selection of the oscillation amplitudes, which are typically either missed or prescribed in mathematical models. The explicit set of nonlinear equations are derived and solved numerically. Our analysis reveals the spatio-temporal dynamics of dynein populations and flagellum shape for different regimes of motor activity, medium viscosity and flagellum elasticity. Unstable modes saturate via the coupling of dynein kinetics and flagellum shape without the need of invoking a nonlinear axonemal response. Hence, our work reveals a novel mechanism for the saturation of unstable modes in axonemal beating.

Nonlinear amplitude dynamics in flagellar beating

PubMed Central

Casademunt, Jaume

2017-01-01

The physical basis of flagellar and ciliary beating is a major problem in biology which is still far from completely understood. The fundamental cytoskeleton structure of cilia and flagella is the axoneme, a cylindrical array of microtubule doublets connected by passive cross-linkers and dynein motor proteins. The complex interplay of these elements leads to the generation of self-organized bending waves. Although many mathematical models have been proposed to understand this process, few attempts have been made to assess the role of dyneins on the nonlinear nature of the axoneme. Here, we investigate the nonlinear dynamics of flagella by considering an axonemal sliding control mechanism for dynein activity. This approach unveils the nonlinear selection of the oscillation amplitudes, which are typically either missed or prescribed in mathematical models. The explicit set of nonlinear equations are derived and solved numerically. Our analysis reveals the spatio-temporal dynamics of dynein populations and flagellum shape for different regimes of motor activity, medium viscosity and flagellum elasticity. Unstable modes saturate via the coupling of dynein kinetics and flagellum shape without the need of invoking a nonlinear axonemal response. Hence, our work reveals a novel mechanism for the saturation of unstable modes in axonemal beating. PMID:28405357

Nonlinear Viscoelastic Characterization of the Porcine Spinal Cord

PubMed Central

Shetye, Snehal; Troyer, Kevin; Streijger, Femke; Lee, Jae H. T.; Kwon, Brian K.; Cripton, Peter; Puttlitz, Christian M.

2014-01-01

Although quasi-static and quasi-linear viscoelastic properties of the spinal cord have been reported previously, there are no published studies that have investigated the fully (strain-dependent) nonlinear viscoelastic properties of the spinal cord. In this study, stress relaxation experiments and dynamic cycling were performed on six fresh porcine lumbar cord specimens to examine their viscoelastic mechanical properties. The stress relaxation data were fitted to a modified superposition formulation and a novel finite ramp time correction technique was applied. The parameters obtained from this fitting methodology were used to predict the average dynamic cyclic viscoelastic behavior of the porcine cord. The data indicate that the porcine spinal cord exhibited fully nonlinear viscoelastic behavior. The average weighted RMSE for a Heaviside ramp fit was 2.8kPa, which was significantly greater (p < 0.001) than that of the nonlinear (comprehensive viscoelastic characterization (CVC) method) fit (0.365kPa). Further, the nonlinear mechanical parameters obtained were able to accurately predict the dynamic behavior, thus exemplifying the reliability of the obtained nonlinear parameters. These parameters will be important for future studies investigating various damage mechanisms of the spinal cord and studies developing high resolution finite elements models of the spine. PMID:24211612

Chaos Theory: Implications for Nonlinear Dynamics in Counseling.

ERIC Educational Resources Information Center

Stickel, Sue A.

The purpose of this paper is to explore the implications of chaos theory for counseling. The scientific notion of chaos refers to the tendency of dynamical, nonlinear systems toward irregular, sometimes unpredictable, yet deterministic behavior. Therapists, especially those working from a brief approach, have noted the importance of the client's…

An Examination of the Utility of Non-Linear Dynamics Techniques for Analyzing Human Information Behaviors.

ERIC Educational Resources Information Center

Snyder, Herbert; Kurtze, Douglas

1992-01-01

Discusses the use of chaos, or nonlinear dynamics, for investigating computer-mediated communication. A comparison between real, human-generated data from a computer network and similarly constructed random-generated data is made, and mathematical procedures for determining chaos are described. (seven references) (LRW)

Chaos and insect ecology

Treesearch

Jesse A. Logan; Fred P. Hain

1990-01-01

Recent advances in applied mathematical analysis have uncovered a fascinating and unexpected dynamical richness that underlies behavior of even the simplest non-linear mathematical models. Due to the complexity of solutions to these non-linear equations, a new mathematical term, chaos, has been coined to describe the resulting dynamics. This term captures the notion...