full nonlinear dynamics: Topics by Science.gov

Sample records for full nonlinear dynamics

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.
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.
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.
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.
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.
Transient Negative Optical Nonlinearity of Indium Oxide Nanorod Arrays in the Full-Visible Range

DOE PAGES

Guo, Peijun; Chang, Robert P. H.; Schaller, Richard D.

2017-06-09

Dynamic control of the optical response of materials at visible wavelengths is key to future metamaterials and photonic integrated circuits. Here we demonstrate large amplitude, negative optical nonlinearity (Δ n from -0.05 to -0.09) of indium oxide nanorod arrays in the full-visible range. We experimentally quantify and theoretically calculate the optical nonlinearity, which arises from the modifications of interband optical transitions. Furthermore, the approach towards negative optical nonlinearity can be generalized to other transparent semiconductors and opens door to reconfigurable, sub-wavelength optical components.
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.
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 dynamic model of the human postural control system

NASA Technical Reports Server (NTRS)

Hill, J. C.

1972-01-01

A digital simulation of the pitch axis dynamics of a stick man of figures is described. Difficulties encountered in linearizing the equations of motion are discussed; the conclusion reached is that a completely linear simulation is of such restricted validity that only a nonlinear simulation is of any practical use. Typical simulation results obtained from the full nonlinear model are presented.
A dynamic model of the human postural control system.

NASA Technical Reports Server (NTRS)

Hill, J. C.

1971-01-01

Description of a digital simulation of the pitch axis dynamics of a stick man. The difficulties encountered in linearizing the equations of motion are discussed; the conclusion reached is that a completely linear simulation is of such restricted validity that only a nonlinear simulation is of any practical use. Typical simulation results obtained from the full nonlinear model are illustrated.
The design of nonlinear observers for wind turbine dynamic state and parameter estimation

NASA Astrophysics Data System (ADS)

Ritter, B.; Schild, A.; Feldt, M.; Konigorski, U.

2016-09-01

This contribution addresses the dynamic state and parameter estimation problem which arises with more advanced wind turbine controllers. These control devices need precise information about the system's current state to outperform conventional industrial controllers effectively. First, the necessity of a profound scientific treatment on nonlinear observers for wind turbine application is highlighted. Secondly, the full estimation problem is introduced and the variety of nonlinear filters is discussed. Finally, a tailored observer architecture is proposed and estimation results of an illustrative application example from a complex simulation set-up are presented.
A Nonlinear Dynamic Inversion Predictor-Based Model Reference Adaptive Controller for a Generic Transport Model

NASA Technical Reports Server (NTRS)

Campbell, Stefan F.; Kaneshige, John T.

2010-01-01

Presented here is a Predictor-Based Model Reference Adaptive Control (PMRAC) architecture for a generic transport aircraft. At its core, this architecture features a three-axis, non-linear, dynamic-inversion controller. Command inputs for this baseline controller are provided by pilot roll-rate, pitch-rate, and sideslip commands. This paper will first thoroughly present the baseline controller followed by a description of the PMRAC adaptive augmentation to this control system. Results are presented via a full-scale, nonlinear simulation of NASA s Generic Transport Model (GTM).
Verification of nonlinear dynamic structural test results by combined image processing and acoustic analysis

NASA Astrophysics Data System (ADS)

Tene, Yair; Tene, Noam; Tene, G.

1993-08-01

An interactive data fusion methodology of video, audio, and nonlinear structural dynamic analysis for potential application in forensic engineering is presented. The methodology was developed and successfully demonstrated in the analysis of heavy transportable bridge collapse during preparation for testing. Multiple bridge elements failures were identified after the collapse, including fracture, cracks and rupture of high performance structural materials. Videotape recording by hand held camcorder was the only source of information about the collapse sequence. The interactive data fusion methodology resulted in extracting relevant information form the videotape and from dynamic nonlinear structural analysis, leading to full account of the sequence of events during the bridge collapse.
Full analogue electronic realisation of the Hodgkin-Huxley neuronal dynamics in weak-inversion CMOS.

PubMed

Lazaridis, E; Drakakis, E M; Barahona, M

2007-01-01

This paper presents a non-linear analog synthesis path towards the modeling and full implementation of the Hodgkin-Huxley neuronal dynamics in silicon. The proposed circuits have been realized in weak-inversion CMOS technology and take advantage of both log-domain and translinear transistor-level techniques.
Large optical nonlinearity of ITO nanorods for sub-picosecond all-optical modulation of the full-visible spectrum

NASA Astrophysics Data System (ADS)

Guo, Peijun; Schaller, Richard D.; Ocola, Leonidas E.; Diroll, Benjamin T.; Ketterson, John B.; Chang, Robert P. H.

2016-09-01

Nonlinear optical responses of materials play a vital role for the development of active nanophotonic and plasmonic devices. Optical nonlinearity induced by intense optical excitation of mobile electrons in metallic nanostructures can provide large-amplitude, dynamic tuning of their electromagnetic response, which is potentially useful for all-optical processing of information and dynamic beam control. Here we report on the sub-picosecond optical nonlinearity of indium tin oxide nanorod arrays (ITO-NRAs) following intraband, on-plasmon-resonance optical pumping, which enables modulation of the full-visible spectrum with large absolute change of transmission, favourable spectral tunability and beam-steering capability. Furthermore, we observe a transient response in the microsecond regime associated with slow lattice cooling, which arises from the large aspect-ratio and low thermal conductivity of ITO-NRAs. Our results demonstrate that all-optical control of light can be achieved by using heavily doped wide-bandgap semiconductors in their transparent regime with speed faster than that of noble metals.
Sparsity enabled cluster reduced-order models for control

NASA Astrophysics Data System (ADS)

Kaiser, Eurika; Morzyński, Marek; Daviller, Guillaume; Kutz, J. Nathan; Brunton, Bingni W.; Brunton, Steven L.

2018-01-01

Characterizing and controlling nonlinear, multi-scale phenomena are central goals in science and engineering. Cluster-based reduced-order modeling (CROM) was introduced to exploit the underlying low-dimensional dynamics of complex systems. CROM builds a data-driven discretization of the Perron-Frobenius operator, resulting in a probabilistic model for ensembles of trajectories. A key advantage of CROM is that it embeds nonlinear dynamics in a linear framework, which enables the application of standard linear techniques to the nonlinear system. CROM is typically computed on high-dimensional data; however, access to and computations on this full-state data limit the online implementation of CROM for prediction and control. Here, we address this key challenge by identifying a small subset of critical measurements to learn an efficient CROM, referred to as sparsity-enabled CROM. In particular, we leverage compressive measurements to faithfully embed the cluster geometry and preserve the probabilistic dynamics. Further, we show how to identify fewer optimized sensor locations tailored to a specific problem that outperform random measurements. Both of these sparsity-enabled sensing strategies significantly reduce the burden of data acquisition and processing for low-latency in-time estimation and control. We illustrate this unsupervised learning approach on three different high-dimensional nonlinear dynamical systems from fluids with increasing complexity, with one application in flow control. Sparsity-enabled CROM is a critical facilitator for real-time implementation on high-dimensional systems where full-state information may be inaccessible.
Nonlinear saturation of the slab ITG instability and zonal flow generation with fully kinetic ions

NASA Astrophysics Data System (ADS)

Miecnikowski, Matthew T.; Sturdevant, Benjamin J.; Chen, Yang; Parker, Scott E.

2018-05-01

Fully kinetic turbulence models are of interest for their potential to validate or replace gyrokinetic models in plasma regimes where the gyrokinetic expansion parameters are marginal. Here, we demonstrate fully kinetic ion capability by simulating the growth and nonlinear saturation of the ion-temperature-gradient instability in shearless slab geometry assuming adiabatic electrons and including zonal flow dynamics. The ion trajectories are integrated using the Lorentz force, and the cyclotron motion is fully resolved. Linear growth and nonlinear saturation characteristics show excellent agreement with analogous gyrokinetic simulations across a wide range of parameters. The fully kinetic simulation accurately reproduces the nonlinearly generated zonal flow. This work demonstrates nonlinear capability, resolution of weak gradient drive, and zonal flow physics, which are critical aspects of modeling plasma turbulence with full ion dynamics.
Residual mode correction in calibrating nonlinear damper for vibration control of flexible structures

NASA Astrophysics Data System (ADS)

Sun, Limin; Chen, Lin

2017-10-01

Residual mode correction is found crucial in calibrating linear resonant absorbers for flexible structures. The classic modal representation augmented with stiffness and inertia correction terms accounting for non-resonant modes improves the calibration accuracy and meanwhile avoids complex modal analysis of the full system. This paper explores the augmented modal representation in calibrating control devices with nonlinearity, by studying a taut cable attached with a general viscous damper and its Equivalent Dynamic Systems (EDSs), i.e. the augmented modal representations connected to the same damper. As nonlinearity is concerned, Frequency Response Functions (FRFs) of the EDSs are investigated in detail for parameter calibration, using the harmonic balance method in combination with numerical continuation. The FRFs of the EDSs and corresponding calibration results are then compared with those of the full system documented in the literature for varied structural modes, damper locations and nonlinearity. General agreement is found and in particular the EDS with both stiffness and inertia corrections (quasi-dynamic correction) performs best among available approximate methods. This indicates that the augmented modal representation although derived from linear cases is applicable to a relatively wide range of damper nonlinearity. Calibration of nonlinear devices by this means still requires numerical analysis while the efficiency is largely improved owing to the system order reduction.
Jacobian projection reduced-order models for dynamic systems with contact nonlinearities

NASA Astrophysics Data System (ADS)

Gastaldi, Chiara; Zucca, Stefano; Epureanu, Bogdan I.

2018-02-01

In structural dynamics, the prediction of the response of systems with localized nonlinearities, such as friction dampers, is of particular interest. This task becomes especially cumbersome when high-resolution finite element models are used. While state-of-the-art techniques such as Craig-Bampton component mode synthesis are employed to generate reduced order models, the interface (nonlinear) degrees of freedom must still be solved in-full. For this reason, a new generation of specialized techniques capable of reducing linear and nonlinear degrees of freedom alike is emerging. This paper proposes a new technique that exploits spatial correlations in the dynamics to compute a reduction basis. The basis is composed of a set of vectors obtained using the Jacobian of partial derivatives of the contact forces with respect to nodal displacements. These basis vectors correspond to specifically chosen boundary conditions at the contacts over one cycle of vibration. The technique is shown to be effective in the reduction of several models studied using multiple harmonics with a coupled static solution. In addition, this paper addresses another challenge common to all reduction techniques: it presents and validates a novel a posteriori error estimate capable of evaluating the quality of the reduced-order solution without involving a comparison with the full-order solution.
A Nonlinear Physics-Based Optimal Control Method for Magnetostrictive Actuators

NASA Technical Reports Server (NTRS)

Smith, Ralph C.

1998-01-01

This paper addresses the development of a nonlinear optimal control methodology for magnetostrictive actuators. At moderate to high drive levels, the output from these actuators is highly nonlinear and contains significant magnetic and magnetomechanical hysteresis. These dynamics must be accommodated by models and control laws to utilize the full capabilities of the actuators. A characterization based upon ferromagnetic mean field theory provides a model which accurately quantifies both transient and steady state actuator dynamics under a variety of operating conditions. The control method consists of a linear perturbation feedback law used in combination with an optimal open loop nonlinear control. The nonlinear control incorporates the hysteresis and nonlinearities inherent to the transducer and can be computed offline. The feedback control is constructed through linearization of the perturbed system about the optimal system and is efficient for online implementation. As demonstrated through numerical examples, the combined hybrid control is robust and can be readily implemented in linear PDE-based structural models.

Robust Gain-Scheduled Fault Tolerant Control for a Transport Aircraft

NASA Technical Reports Server (NTRS)

Shin, Jong-Yeob; Gregory, Irene

2007-01-01

This paper presents an application of robust gain-scheduled control concepts using a linear parameter-varying (LPV) control synthesis method to design fault tolerant controllers for a civil transport aircraft. To apply the robust LPV control synthesis method, the nonlinear dynamics must be represented by an LPV model, which is developed using the function substitution method over the entire flight envelope. The developed LPV model associated with the aerodynamic coefficient uncertainties represents nonlinear dynamics including those outside the equilibrium manifold. Passive and active fault tolerant controllers (FTC) are designed for the longitudinal dynamics of the Boeing 747-100/200 aircraft in the presence of elevator failure. Both FTC laws are evaluated in the full nonlinear aircraft simulation in the presence of the elevator fault and the results are compared to show pros and cons of each control law.
Numerical modelling of nonlinear full-wave acoustic propagation

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

Velasco-Segura, Roberto, E-mail: roberto.velasco@ccadet.unam.mx; Rendón, Pablo L., E-mail: pablo.rendon@ccadet.unam.mx

2015-10-28

The various model equations of nonlinear acoustics are arrived at by making assumptions which permit the observation of the interaction with propagation of either single or joint effects. We present here a form of the conservation equations of fluid dynamics which are deduced using slightly less restrictive hypothesis than those necessary to obtain the well known Westervelt equation. This formulation accounts for full wave diffraction, nonlinearity, and thermoviscous dissipative effects. A two-dimensional, finite-volume method using Roe’s linearisation has been implemented to obtain numerically the solution of the proposed equations. This code, which has been written for parallel execution on amore » GPU, can be used to describe moderate nonlinear phenomena, at low Mach numbers, in domains as large as 100 wave lengths. Applications range from models of diagnostic and therapeutic HIFU, to parametric acoustic arrays and nonlinear propagation in acoustic waveguides. Examples related to these applications are shown and discussed.« less
Designing for aircraft structural crashworthiness

NASA Technical Reports Server (NTRS)

Thomson, R. G.; Caiafa, C.

1981-01-01

This report describes structural aviation crash dynamics research activities being conducted on general aviation aircraft and transport aircraft. The report includes experimental and analytical correlations of load-limiting subfloor and seat configurations tested dynamically in vertical drop tests and in a horizontal sled deceleration facility. Computer predictions using a finite-element nonlinear computer program, DYCAST, of the acceleration time-histories of these innovative seat and subfloor structures are presented. Proposed application of these computer techniques, and the nonlinear lumped mass computer program KRASH, to transport aircraft crash dynamics is discussed. A proposed FAA full-scale crash test of a fully instrumented radio controlled transport airplane is also described.
Scaling of F-actin network rheology to probe single filament elasticity and dynamics.

PubMed

Gardel, M L; Shin, J H; MacKintosh, F C; Mahadevan, L; Matsudaira, P A; Weitz, D A

2004-10-29

The linear and nonlinear viscoelastic response of networks of cross-linked and bundled cytoskeletal filaments demonstrates remarkable scaling with both frequency and applied prestress, which helps elucidate the origins of the viscoelasticity. The frequency dependence of the shear modulus reflects the underlying single-filament relaxation dynamics for 0.1-10 rad/sec. Moreover, the nonlinear strain stiffening of such networks exhibits a universal form as a function of prestress; this is quantitatively explained by the full force-extension relation of single semiflexible filaments.
Dynamic output feedback control of a flexible air-breathing hypersonic vehicle via T-S fuzzy approach

NASA Astrophysics Data System (ADS)

Hu, Xiaoxiang; Wu, Ligang; Hu, Changhua; Wang, Zhaoqiang; Gao, Huijun

2014-08-01

By utilising Takagi-Sugeno (T-S) fuzzy set approach, this paper addresses the robust H∞ dynamic output feedback control for the non-linear longitudinal model of flexible air-breathing hypersonic vehicles (FAHVs). The flight control of FAHVs is highly challenging due to the unique dynamic characteristics, and the intricate couplings between the engine and fight dynamics and external disturbance. Because of the dynamics' enormous complexity, currently, only the longitudinal dynamics models of FAHVs have been used for controller design. In this work, T-S fuzzy modelling technique is utilised to approach the non-linear dynamics of FAHVs, then a fuzzy model is developed for the output tracking problem of FAHVs. The fuzzy model contains parameter uncertainties and disturbance, which can approach the non-linear dynamics of FAHVs more exactly. The flexible models of FAHVs are difficult to measure because of the complex dynamics and the strong couplings, thus a full-order dynamic output feedback controller is designed for the fuzzy model. A robust H∞ controller is designed for the obtained closed-loop system. By utilising the Lyapunov functional approach, sufficient solvability conditions for such controllers are established in terms of linear matrix inequalities. Finally, the effectiveness of the proposed T-S fuzzy dynamic output feedback control method is demonstrated by numerical simulations.
A parallel algorithm for nonlinear convection-diffusion equations

NASA Technical Reports Server (NTRS)

Scroggs, Jeffrey S.

1990-01-01

A parallel algorithm for the efficient solution of nonlinear time-dependent convection-diffusion equations with small parameter on the diffusion term is presented. The method is based on a physically motivated domain decomposition that is dictated by singular perturbation analysis. The analysis is used to determine regions where certain reduced equations may be solved in place of the full equation. The method is suitable for the solution of problems arising in the simulation of fluid dynamics. Experimental results for a nonlinear equation in two-dimensions are presented.
A data driven nonlinear stochastic model for blood glucose dynamics.

PubMed

Zhang, Yan; Holt, Tim A; Khovanova, Natalia

2016-03-01

The development of adequate mathematical models for blood glucose dynamics may improve early diagnosis and control of diabetes mellitus (DM). We have developed a stochastic nonlinear second order differential equation to describe the response of blood glucose concentration to food intake using continuous glucose monitoring (CGM) data. A variational Bayesian learning scheme was applied to define the number and values of the system's parameters by iterative optimisation of free energy. The model has the minimal order and number of parameters to successfully describe blood glucose dynamics in people with and without DM. The model accounts for the nonlinearity and stochasticity of the underlying glucose-insulin dynamic process. Being data-driven, it takes full advantage of available CGM data and, at the same time, reflects the intrinsic characteristics of the glucose-insulin system without detailed knowledge of the physiological mechanisms. We have shown that the dynamics of some postprandial blood glucose excursions can be described by a reduced (linear) model, previously seen in the literature. A comprehensive analysis demonstrates that deterministic system parameters belong to different ranges for diabetes and controls. Implications for clinical practice are discussed. This is the first study introducing a continuous data-driven nonlinear stochastic model capable of describing both DM and non-DM profiles. Copyright © 2015 The Authors. Published by Elsevier Ireland Ltd.. All rights reserved.
Zero-sum two-player game theoretic formulation of affine nonlinear discrete-time systems using neural networks.

PubMed

Mehraeen, Shahab; Dierks, Travis; Jagannathan, S; Crow, Mariesa L

2013-12-01

In this paper, the nearly optimal solution for discrete-time (DT) affine nonlinear control systems in the presence of partially unknown internal system dynamics and disturbances is considered. The approach is based on successive approximate solution of the Hamilton-Jacobi-Isaacs (HJI) equation, which appears in optimal control. Successive approximation approach for updating control and disturbance inputs for DT nonlinear affine systems are proposed. Moreover, sufficient conditions for the convergence of the approximate HJI solution to the saddle point are derived, and an iterative approach to approximate the HJI equation using a neural network (NN) is presented. Then, the requirement of full knowledge of the internal dynamics of the nonlinear DT system is relaxed by using a second NN online approximator. The result is a closed-loop optimal NN controller via offline learning. A numerical example is provided illustrating the effectiveness of the approach.
Dynamic Modeling Accuracy Dependence on Errors in Sensor Measurements, Mass Properties, and Aircraft Geometry

NASA Technical Reports Server (NTRS)

Grauer, Jared A.; Morelli, Eugene A.

2013-01-01

A nonlinear simulation of the NASA Generic Transport Model was used to investigate the effects of errors in sensor measurements, mass properties, and aircraft geometry on the accuracy of dynamic models identified from flight data. Measurements from a typical system identification maneuver were systematically and progressively deteriorated and then used to estimate stability and control derivatives within a Monte Carlo analysis. Based on the results, recommendations were provided for maximum allowable errors in sensor measurements, mass properties, and aircraft geometry to achieve desired levels of dynamic modeling accuracy. Results using other flight conditions, parameter estimation methods, and a full-scale F-16 nonlinear aircraft simulation were compared with these recommendations.
Unraveling complex nonlinear elastic behaviors in rocks using dynamic acousto-elasticity

NASA Astrophysics Data System (ADS)

Riviere, J.; Guyer, R.; Renaud, G.; TenCate, J. A.; Johnson, P. A.

2012-12-01

In comparison with standard nonlinear ultrasonic methods like frequency mixing or resonance based measurements that allow one to extract average, bulk variations of modulus and attenuation versus strain level, dynamic acousto-elasticity (DAE) allows to obtain the elastic behavior over the entire dynamic cycle, detailing the full nonlinear behavior under tension and compression, including hysteresis and memory effects. This method consists of exciting a sample in Bulk-mode resonance at strains of 10-7 to 10-5 and simultaneously probing with a sequence of high frequency, low amplitude pulses. Time of flight and amplitudes of these pulses, respectively related to nonlinear elastic and dissipative parameters, can be plotted versus vibration strain level. Despite complex nonlinear signatures obtained for most rocks, it can be shown that for low strain amplitude (< 10-6), the nonlinear classical theory issued from a Taylor decomposition can explain the harmonic content. For higher strain, harmonic content becomes richer and the material exhibits more hysteretic behaviors, i.e. strain rate dependencies. Such observations have been made in the past (e.g., Pasqualini et al., JGR 2007), but not with the extreme detail of elasticity provided by DAE. Previous quasi-static measurements made in Berea sandstone (Claytor et al, GRL 2009), show that the hysteretic behavior disappears when the protocol is performed at a very low strain-rate (static limit). Therefore, future work will aim at linking quasi-static and dynamic observations, i.e. the frequency or strain-rate dependence, in order to understand underlying physical phenomena.
Situations, Interaction, Process and Affordances: An Ecological Psychology Perspective.

ERIC Educational Resources Information Center

Young, Michael F.; DePalma, Andrew; Garrett, Steven

2002-01-01

From an ecological psychology perspective, a full analysis of any learning context must acknowledge the complex nonlinear dynamics that unfold as an intentionally-driven learner interacts with a technology-based purposefully designed learning environment. A full situation model would need to incorporate constraints from the environment and also…
Complex Dynamical Networks Constructed with Fully Controllable Nonlinear Nanomechanical Oscillators.

PubMed

Fon, Warren; Matheny, Matthew H; Li, Jarvis; Krayzman, Lev; Cross, Michael C; D'Souza, Raissa M; Crutchfield, James P; Roukes, Michael L

2017-10-11

Control of the global parameters of complex networks has been explored experimentally in a variety of contexts. Yet, the more difficult prospect of realizing arbitrary network architectures, especially analog physical networks that provide dynamical control of individual nodes and edges, has remained elusive. Given the vast hierarchy of time scales involved, it also proves challenging to measure a complex network's full internal dynamics. These span from the fastest nodal dynamics to very slow epochs over which emergent global phenomena, including network synchronization and the manifestation of exotic steady states, eventually emerge. Here, we demonstrate an experimental system that satisfies these requirements. It is based upon modular, fully controllable, nonlinear radio frequency nanomechanical oscillators, designed to form the nodes of complex dynamical networks with edges of arbitrary topology. The dynamics of these oscillators and their surrounding network are analog and continuous-valued and can be fully interrogated in real time. They comprise a piezoelectric nanomechanical membrane resonator, which serves as the frequency-determining element within an electrical feedback circuit. This embodiment permits network interconnections entirely within the electrical domain and provides unprecedented node and edge control over a vast region of parameter space. Continuous measurement of the instantaneous amplitudes and phases of every constituent oscillator node are enabled, yielding full and detailed network data without reliance upon statistical quantities. We demonstrate the operation of this platform through the real-time capture of the dynamics of a three-node ring network as it evolves from the uncoupled state to full synchronization.
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
Nonlinear Dynamic Modeling of a Supersonic Commercial Transport Turbo-Machinery Propulsion System for Aero-Propulso-Servo-Elasticity Research

NASA Technical Reports Server (NTRS)

Connolly, Joseph W.; Kopasakis, George; Carlson, Jan-Renee; Woolwine, Kyle

2015-01-01

This paper covers the development of an integrated nonlinear dynamic model for a variable cycle turbofan engine, supersonic inlet, and convergent-divergent nozzle that can be integrated with an aeroelastic vehicle model to create an overall Aero-Propulso-Servo-Elastic (APSE) modeling tool. The primary focus of this study is to provide a means to capture relevant thrust dynamics of a full supersonic propulsion system by using relatively simple quasi-one dimensional computational fluid dynamics (CFD) methods that will allow for accurate control algorithm development and capture the key aspects of the thrust to feed into an APSE model. Previously, propulsion system component models have been developed and are used for this study of the fully integrated propulsion system. An overview of the methodology is presented for the modeling of each propulsion component, with a focus on its associated coupling for the overall model. To conduct APSE studies the de- scribed dynamic propulsion system model is integrated into a high fidelity CFD model of the full vehicle capable of conducting aero-elastic studies. Dynamic thrust analysis for the quasi-one dimensional dynamic propulsion system model is presented along with an initial three dimensional flow field model of the engine integrated into a supersonic commercial transport.
Nonlinear Dynamic Modeling of a Supersonic Commercial Transport Turbo-Machinery Propulsion System for Aero-Propulso-Servo-Elasticity Research

NASA Technical Reports Server (NTRS)

Connolly, Joe; Carlson, Jan-Renee; Kopasakis, George; Woolwine, Kyle

2015-01-01

This paper covers the development of an integrated nonlinear dynamic model for a variable cycle turbofan engine, supersonic inlet, and convergent-divergent nozzle that can be integrated with an aeroelastic vehicle model to create an overall Aero-Propulso-Servo-Elastic (APSE) modeling tool. The primary focus of this study is to provide a means to capture relevant thrust dynamics of a full supersonic propulsion system by using relatively simple quasi-one dimensional computational fluid dynamics (CFD) methods that will allow for accurate control algorithm development and capture the key aspects of the thrust to feed into an APSE model. Previously, propulsion system component models have been developed and are used for this study of the fully integrated propulsion system. An overview of the methodology is presented for the modeling of each propulsion component, with a focus on its associated coupling for the overall model. To conduct APSE studies the described dynamic propulsion system model is integrated into a high fidelity CFD model of the full vehicle capable of conducting aero-elastic studies. Dynamic thrust analysis for the quasi-one dimensional dynamic propulsion system model is presented along with an initial three dimensional flow field model of the engine integrated into a supersonic commercial transport.
NASA/FAA general aviation crash dynamics program - An update

NASA Technical Reports Server (NTRS)

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

1979-01-01

Work in progress in the NASA/FAA General Aviation Crash Dynamics Program for the development of technology for increased crash-worthiness and occupant survivability of general aviation aircraft is presented. Full-scale crash testing facilities and procedures are outlined, and a chronological summary of full-scale tests conducted and planned is presented. The Plastic and Large Deflection Analysis of Nonlinear Structures and Modified Seat Occupant Model for Light Aircraft computer programs which form part of the effort to predict nonlinear geometric and material behavior of sheet-stringer aircraft structures subjected to large deformations are described, and excellent agreement between simulations and experiments is noted. The development of structural concepts to attenuate the load transmitted to the passenger through the seats and subfloor structure is discussed, and an apparatus built to test emergency locator transmitters in a realistic environment is presented.
Application of the MNA design method to a nonlinear turbofan engine. [multivariable Nyquist array method

NASA Technical Reports Server (NTRS)

Leininger, G. G.

1981-01-01

Using nonlinear digital simulation as a representative model of the dynamic operation of the QCSEE turbofan engine, a feedback control system is designed by variable frequency design techniques. Transfer functions are generated for each of five power level settings covering the range of operation from approach power to full throttle (62.5% to 100% full power). These transfer functions are then used by an interactive control system design synthesis program to provide a closed loop feedback control using the multivariable Nyquist array and extensions to multivariable Bode diagrams and Nichols charts.
Observation of nonlinear dissipation in piezoresistive diamond nanomechanical resonators by heterodyne down-mixing.

PubMed

Imboden, Matthias; Williams, Oliver A; Mohanty, Pritiraj

2013-09-11

We report the observation of nonlinear dissipation in diamond nanomechanical resonators measured by an ultrasensitive heterodyne down-mixing piezoresistive detection technique. The combination of a hybrid structure as well as symmetry breaking clamps enables sensitive piezoresistive detection of multiple orthogonal modes in a diamond resonator over a wide frequency and temperature range. Using this detection method, we observe the transition from purely linear dissipation at room temperature to strongly nonlinear dissipation at cryogenic temperatures. At high drive powers and below liquid nitrogen temperatures, the resonant structure dynamics follows the Pol-Duffing equation of motion. Instead of using the broadening of the full width at half-maximum, we propose a nonlinear dissipation backbone curve as a method to characterize the strength of nonlinear dissipation in devices with a nonlinear spring constant.
E11, brane dynamics and duality symmetries

NASA Astrophysics Data System (ADS)

West, Peter

2018-05-01

Following arXiv:hep-th/0412336 we use the nonlinear realisation of the semi-direct product of E11 and its vector representation to construct brane dynamics. The brane moves through a space-time which arises in the nonlinear realisation from the vector representation and it contains the usual embedding coordinates as well as the worldvolume fields. The resulting equations of motion are first order in derivatives and can be thought of as duality relations. Each brane carries the full E11 symmetry and so the Cremmer-Julia duality symmetries. We apply this theory to find the dynamics of the IIA and IIB strings, the M2 and M5 branes, the IIB D3 brane as well as the one and two branes in seven dimensions.
The Development of Methodologies for Determining Non-Linear Effects in Infrasound Sensors

DTIC Science & Technology

2010-09-01

THE DEVELOPMENT OF METHODOLOGIES FOR DETERMINING NON-LINEAR EFFECTS IN INFRASOUND SENSORS Darren M. Hart, Harold V. Parks, and Randy K. Rembold...the past year, four new infrasound sensor designs were evaluated for common performance characteristics, i.e., power consumption, response (amplitude...and phase), noise, full-scale, and dynamic range. In the process of evaluating a fifth infrasound sensor, which is an update of an original design

A Simplified Model of ARIS for Optimal Controller Design

NASA Technical Reports Server (NTRS)

Beech, Geoffrey S.; Hampton, R. David; Kross, Denny (Technical Monitor)

2001-01-01

Many space-science experiments require active vibration isolation. Boeing's Active Rack Isolation System (ARIS) isolates experiments at the rack (vs. experiment or sub-experiment) level, with multi e experiments per rack. An ARIS-isolated rack typically employs eight actuators and thirteen umbilicals; the umbilicals provide services such as power, data transmission, and cooling. Hampton, et al., used "Kane's method" to develop an analytical, nonlinear, rigid-body model of ARIS that includes full actuator dynamics (inertias). This model, less the umbilicals, was first implemented for simulation by Beech and Hampton; they developed and tested their model using two commercial-off-the-shelf (COTS) software packages. Rupert, et al., added umbilical-transmitted disturbances to this nonlinear model. Because the nonlinear model, even for the untethered system, is both exceedingly complex and "encapsulated" inside these COTS tools, it is largely inaccessible to ARIS controller designers. This paper shows that ISPR rattle-space constraints and small ARIS actuator masses permit considerable model simplification, without significant loss of fidelity. First, for various loading conditions, comparisons are made between the dynamic responses of the nonlinear model (untethered) and a truth model. Then comparisons are made among nonlinear, linearized, and linearized reduced-mass models. It is concluded that these three models all capture the significant system rigid-body dynamics, with the third being preferred due to its relative simplicity.
Application of Probabilistic Analysis to Aircraft Impact Dynamics

NASA Technical Reports Server (NTRS)

Lyle, Karen H.; Padula, Sharon L.; Stockwell, Alan E.

2003-01-01

Full-scale aircraft crash simulations performed with nonlinear, transient dynamic, finite element codes can incorporate structural complexities such as: geometrically accurate models; human occupant models; and advanced material models to include nonlinear stressstrain behaviors, laminated composites, and material failure. Validation of these crash simulations is difficult due to a lack of sufficient information to adequately determine the uncertainty in the experimental data and the appropriateness of modeling assumptions. This paper evaluates probabilistic approaches to quantify the uncertainty in the simulated responses. Several criteria are used to determine that a response surface method is the most appropriate probabilistic approach. The work is extended to compare optimization results with and without probabilistic constraints.
Functional Wigner representation of quantum dynamics of Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Opanchuk, B.; Drummond, P. D.

2013-04-01

We develop a method of simulating the full quantum field dynamics of multi-mode multi-component Bose-Einstein condensates in a trap. We use the truncated Wigner representation to obtain a probabilistic theory that can be sampled. This method produces c-number stochastic equations which may be solved using conventional stochastic methods. The technique is valid for large mode occupation numbers. We give a detailed derivation of methods of functional Wigner representation appropriate for quantum fields. Our approach describes spatial evolution of spinor components and properly accounts for nonlinear losses. Such techniques are applicable to calculating the leading quantum corrections, including effects such as quantum squeezing, entanglement, EPR correlations, and interactions with engineered nonlinear reservoirs. By using a consistent expansion in the inverse density, we are able to explain an inconsistency in the nonlinear loss equations found by earlier authors.
DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Wonjung; Kovacic, Gregor; Cai, David

Using the (1+1)D Majda-McLaughlin-Tabak model as an example, we present an extension of the wave turbulence (WT) theory to systems with strong nonlinearities. We demonstrate that nonlinear wave interactions renormalize the dynamics, leading to (i) a possible destruction of scaling structures in the bare wave systems and a drastic deformation of the resonant manifold even at weak nonlinearities, and (ii) creation of nonlinear resonance quartets in wave systems for which there would be no resonances as predicted by the linear dispersion relation. Finally, we derive an effective WT kinetic equation and show that our prediction of the renormalized Rayleigh-Jeans distributionmore » is in excellent agreement with the simulation of the full wave system in equilibrium.« less
Application of the concept of dynamic trim control and nonlinear system inverses to automatic control of a vertical attitude takeoff and landing aircraft

NASA Technical Reports Server (NTRS)

Smith, G. A.; Meyer, G.

1981-01-01

A full envelope automatic flight control system based on nonlinear inverse systems concepts has been applied to a vertical attitude takeoff and landing (VATOL) fighter aircraft. A new method for using an airborne digital aircraft model to perform the inversion of a nonlinear aircraft model is presented together with the results of a simulation study of the nonlinear inverse system concept for the vertical-attitude hover mode. The system response to maneuver commands in the vertical attitude was found to be excellent; and recovery from large initial offsets and large disturbances was found to be very satisfactory.
DOE Office of Scientific and Technical Information (OSTI.GOV)

Nunes, R. P.; Rizzato, F. B.

This work analyzes the transversal dynamics of an inhomogeneous and mismatched charged particle beam. The beam is azimuthally symmetric, initially cold, and evolves in a linear channel permeated by an external constant magnetic field. Based on a Lagrangian approach, a low-dimensional model for the description of the beam dynamics has been obtained. The small set of nonlinear dynamical equations provided results that are in reasonable agreement with that ones observed in full self-consistent N-particle beam numerical simulations.
Nonlinear wave propagation in discrete and continuous systems

NASA Astrophysics Data System (ADS)

Rothos, V. M.

2016-09-01

In this review we try to capture some of the recent excitement induced by a large volume of theoretical and computational studies addressing nonlinear Schrödinger models (discrete and continuous) and the localized structures that they support. We focus on some prototypical structures, namely the breather solutions and solitary waves. In particular, we investigate the bifurcation of travelling wave solution in Discrete NLS system applying dynamical systems methods. Next, we examine the combined effects of cubic and quintic terms of the long range type in the dynamics of a double well potential. The relevant bifurcations, the stability of the branches and their dynamical implications are examined both in the reduced (ODE) and in the full (PDE) setting. We also offer an outlook on interesting possibilities for future work on this theme.
Nonlinear dynamic phase contrast microscopy for microfluidic and microbiological applications

NASA Astrophysics Data System (ADS)

Denz, C.; Holtmann, F.; Woerdemann, M.; Oevermann, M.

2008-08-01

In live sciences, the observation and analysis of moving living cells, molecular motors or motion of micro- and nano-objects is a current field of research. At the same time, microfluidic innovations are needed for biological and medical applications on a micro- and nano-scale. Conventional microscopy techniques are reaching considerable limits with respect to these issues. A promising approach for this challenge is nonlinear dynamic phase contrast microscopy. It is an alternative full field approach that allows to detect motion as well as phase changes of living unstained micro-objects in real-time, thereby being marker free, without contact and non destructive, i.e. fully biocompatible. The generality of this system allows it to be combined with several other microscope techniques such as conventional bright field or fluorescence microscopy. In this article we will present the dynamic phase contrast technique and its applications in analysis of micro organismic dynamics, micro flow velocimetry and micro-mixing analysis.
Vortex and half-vortex dynamics in a nonlinear spinor quantum fluid

PubMed Central

Dominici, Lorenzo; Dagvadorj, Galbadrakh; Fellows, Jonathan M.; Ballarini, Dario; De Giorgi, Milena; Marchetti, Francesca M.; Piccirillo, Bruno; Marrucci, Lorenzo; Bramati, Alberto; Gigli, Giuseppe; Szymańska, Marzena H.; Sanvitto, Daniele

2015-01-01

Vortices are archetypal objects that recur in the universe across the scale of complexity, from subatomic particles to galaxies and black holes. Their appearance is connected with spontaneous symmetry breaking and phase transitions. In Bose-Einstein condensates and superfluids, vortices are both point-like and quantized quasiparticles. We use a two-dimensional (2D) fluid of polaritons, bosonic particles constituted by hybrid photonic and electronic oscillations, to study quantum vortex dynamics. Polaritons benefit from easiness of wave function phase detection, a spinor nature sustaining half-integer vorticity, strong nonlinearity, and tuning of the background disorder. We can directly generate by resonant pulsed excitations a polariton condensate carrying either a full or half-integer vortex as initial condition and follow their coherent evolution using ultrafast imaging on the picosecond scale. The observations highlight a rich phenomenology, such as the spiraling of the half-vortex and the joint path of the twin charges of a full vortex, until the moment of their splitting. Furthermore, we observe the ordered branching into newly generated secondary couples, associated with the breaking of radial and azimuthal symmetries. This allows us to devise the interplay of nonlinearity and sample disorder in shaping the fluid and driving the vortex dynamics. In addition, our observations suggest that phase singularities may be seen as fundamental particles whose quantized events span from pair creation and recombination to 2D+t topological vortex strings. PMID:26665174
Vortex and half-vortex dynamics in a nonlinear spinor quantum fluid.

PubMed

Dominici, Lorenzo; Dagvadorj, Galbadrakh; Fellows, Jonathan M; Ballarini, Dario; De Giorgi, Milena; Marchetti, Francesca M; Piccirillo, Bruno; Marrucci, Lorenzo; Bramati, Alberto; Gigli, Giuseppe; Szymańska, Marzena H; Sanvitto, Daniele

2015-12-01

Vortices are archetypal objects that recur in the universe across the scale of complexity, from subatomic particles to galaxies and black holes. Their appearance is connected with spontaneous symmetry breaking and phase transitions. In Bose-Einstein condensates and superfluids, vortices are both point-like and quantized quasiparticles. We use a two-dimensional (2D) fluid of polaritons, bosonic particles constituted by hybrid photonic and electronic oscillations, to study quantum vortex dynamics. Polaritons benefit from easiness of wave function phase detection, a spinor nature sustaining half-integer vorticity, strong nonlinearity, and tuning of the background disorder. We can directly generate by resonant pulsed excitations a polariton condensate carrying either a full or half-integer vortex as initial condition and follow their coherent evolution using ultrafast imaging on the picosecond scale. The observations highlight a rich phenomenology, such as the spiraling of the half-vortex and the joint path of the twin charges of a full vortex, until the moment of their splitting. Furthermore, we observe the ordered branching into newly generated secondary couples, associated with the breaking of radial and azimuthal symmetries. This allows us to devise the interplay of nonlinearity and sample disorder in shaping the fluid and driving the vortex dynamics. In addition, our observations suggest that phase singularities may be seen as fundamental particles whose quantized events span from pair creation and recombination to 2D+t topological vortex strings.
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
Functional Wigner representation of quantum dynamics of Bose-Einstein condensate

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

Opanchuk, B.; Drummond, P. D.

2013-04-15

We develop a method of simulating the full quantum field dynamics of multi-mode multi-component Bose-Einstein condensates in a trap. We use the truncated Wigner representation to obtain a probabilistic theory that can be sampled. This method produces c-number stochastic equations which may be solved using conventional stochastic methods. The technique is valid for large mode occupation numbers. We give a detailed derivation of methods of functional Wigner representation appropriate for quantum fields. Our approach describes spatial evolution of spinor components and properly accounts for nonlinear losses. Such techniques are applicable to calculating the leading quantum corrections, including effects such asmore » quantum squeezing, entanglement, EPR correlations, and interactions with engineered nonlinear reservoirs. By using a consistent expansion in the inverse density, we are able to explain an inconsistency in the nonlinear loss equations found by earlier authors.« less
Chaos and Forecasting - Proceedings of the Royal Society Discussion Meeting

NASA Astrophysics Data System (ADS)

Tong, Howell

1995-04-01

The Table of Contents for the full book PDF is as follows: * Preface * Orthogonal Projection, Embedding Dimension and Sample Size in Chaotic Time Series from a Statistical Perspective * A Theory of Correlation Dimension for Stationary Time Series * On Prediction and Chaos in Stochastic Systems * Locally Optimized Prediction of Nonlinear Systems: Stochastic and Deterministic * A Poisson Distribution for the BDS Test Statistic for Independence in a Time Series * Chaos and Nonlinear Forecastability in Economics and Finance * Paradigm Change in Prediction * Predicting Nonuniform Chaotic Attractors in an Enzyme Reaction * Chaos in Geophysical Fluids * Chaotic Modulation of the Solar Cycle * Fractal Nature in Earthquake Phenomena and its Simple Models * Singular Vectors and the Predictability of Weather and Climate * Prediction as a Criterion for Classifying Natural Time Series * Measuring and Characterising Spatial Patterns, Dynamics and Chaos in Spatially-Extended Dynamical Systems and Ecologies * Non-Linear Forecasting and Chaos in Ecology and Epidemiology: Measles as a Case Study
Effective field theory of dissipative fluids

DOE PAGES

Crossley, Michael; Glorioso, Paolo; Liu, Hong

2017-09-20

We develop an effctive fi eld theory for dissipative fluids which governs the dynamics of long-lived gapless modes associated with conserved quantities. The resulting theory gives a path integral formulation of fluctuating hydrodynamics which systematically incorporates nonlinear interactions of noises. The dynamical variables are mappings between a "fluid spacetime" and the physical spacetime and an essential aspect of our formulation is to identify the appropriate symmetries in the fluid spacetime. The theory applies to nonlinear disturbances around a general density matrix. For a thermal density matrix, we require an additional Z2 symmetry, to which we refer as the local KMSmore » condition. This leads to the standard constraints of hydrodynamics, as well as a nonlinear generalization of the Onsager relations. It also leads to an emergent supersymmetry in the classical statistical regime, and a higher derivative deformation of supersymmetry in the full quantum regime.« less
Effective field theory of dissipative fluids

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

Crossley, Michael; Glorioso, Paolo; Liu, Hong

We develop an effctive fi eld theory for dissipative fluids which governs the dynamics of long-lived gapless modes associated with conserved quantities. The resulting theory gives a path integral formulation of fluctuating hydrodynamics which systematically incorporates nonlinear interactions of noises. The dynamical variables are mappings between a "fluid spacetime" and the physical spacetime and an essential aspect of our formulation is to identify the appropriate symmetries in the fluid spacetime. The theory applies to nonlinear disturbances around a general density matrix. For a thermal density matrix, we require an additional Z2 symmetry, to which we refer as the local KMSmore » condition. This leads to the standard constraints of hydrodynamics, as well as a nonlinear generalization of the Onsager relations. It also leads to an emergent supersymmetry in the classical statistical regime, and a higher derivative deformation of supersymmetry in the full quantum regime.« less
Rayleigh-type parametric chemical oscillation.

PubMed

Ghosh, Shyamolina; Ray, Deb Shankar

2015-09-28

We consider a nonlinear chemical dynamical system of two phase space variables in a stable steady state. When the system is driven by a time-dependent sinusoidal forcing of a suitable scaling parameter at a frequency twice the output frequency and the strength of perturbation exceeds a threshold, the system undergoes sustained Rayleigh-type periodic oscillation, wellknown for parametric oscillation in pipe organs and distinct from the usual forced quasiperiodic oscillation of a damped nonlinear system where the system is oscillatory even in absence of any external forcing. Our theoretical analysis of the parametric chemical oscillation is corroborated by full numerical simulation of two well known models of chemical dynamics, chlorite-iodine-malonic acid and iodine-clock reactions.
Parachute dynamics and stability analysis. [using nonlinear differential equations of motion

NASA Technical Reports Server (NTRS)

Ibrahim, S. K.; Engdahl, R. A.

1974-01-01

The nonlinear differential equations of motion for a general parachute-riser-payload system are developed. The resulting math model is then applied for analyzing the descent dynamics and stability characteristics of both the drogue stabilization phase and the main descent phase of the space shuttle solid rocket booster (SRB) recovery system. The formulation of the problem is characterized by a minimum number of simplifying assumptions and full application of state-of-the-art parachute technology. The parachute suspension lines and the parachute risers can be modeled as elastic elements, and the whole system may be subjected to specified wind and gust profiles in order to assess their effects on the stability of the recovery system.
Nonlinear aeroelastic analysis, flight dynamics, and control of a complete aircraft

NASA Astrophysics Data System (ADS)

Patil, Mayuresh Jayawant

The focus of this research was to analyze a high-aspect-ratio wing aircraft flying at low subsonic speeds. Such aircraft are designed for high-altitude, long-endurance missions. Due to the high flexibility and associated wing deformation, accurate prediction of aircraft response requires use of nonlinear theories. Also strong interactions between flight dynamics and aeroelasticity are expected. To analyze such aircraft one needs to have an analysis tool which includes the various couplings and interactions. A theoretical basis has been established for a consistent analysis which takes into account, (i) material anisotropy, (ii) geometrical nonlinearities of the structure, (iii) rigid-body motions, (iv) unsteady flow behavior, and (v) dynamic stall. The airplane structure is modeled as a set of rigidly attached beams. Each of the beams is modeled using the geometrically exact mixed variational formulation, thus taking into account geometrical nonlinearities arising due to large displacements and rotations. The cross-sectional stiffnesses are obtained using an asymptotically exact analysis, which can model arbitrary cross sections and material properties. An aerodynamic model, consisting of a unified lift model, a consistent combination of finite-state inflow model and a modified ONERA dynamic stall model, is coupled to the structural system to determine the equations of motion. The results obtained indicate the necessity of including nonlinear effects in aeroelastic analysis. Structural geometric nonlinearities result in drastic changes in aeroelastic characteristics, especially in case of high-aspect-ratio wings. The nonlinear stall effect is the dominant factor in limiting the amplitude of oscillation for most wings. The limit cycle oscillation (LCO) phenomenon is also investigated. Post-flutter and pre-flutter LCOs are possible depending on the disturbance mode and amplitude. Finally, static output feedback (SOF) controllers are designed for flutter suppression and gust alleviation. SOF controllers are very simple and thus easy to implement. For the case considered, SOF controllers with proper choice of sensors give results comparable to full state feedback (linear quadratic regulator) designs.

Persistent model order reduction for complex dynamical systems using smooth orthogonal decomposition

NASA Astrophysics Data System (ADS)

Ilbeigi, Shahab; Chelidze, David

2017-11-01

Full-scale complex dynamic models are not effective for parametric studies due to the inherent constraints on available computational power and storage resources. A persistent reduced order model (ROM) that is robust, stable, and provides high-fidelity simulations for a relatively wide range of parameters and operating conditions can provide a solution to this problem. The fidelity of a new framework for persistent model order reduction of large and complex dynamical systems is investigated. The framework is validated using several numerical examples including a large linear system and two complex nonlinear systems with material and geometrical nonlinearities. While the framework is used for identifying the robust subspaces obtained from both proper and smooth orthogonal decompositions (POD and SOD, respectively), the results show that SOD outperforms POD in terms of stability, accuracy, and robustness.
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.
Rigorous Model Reduction for a Damped-Forced Nonlinear Beam Model: An Infinite-Dimensional Analysis

NASA Astrophysics Data System (ADS)

Kogelbauer, Florian; Haller, George

2018-06-01

We use invariant manifold results on Banach spaces to conclude the existence of spectral submanifolds (SSMs) in a class of nonlinear, externally forced beam oscillations. SSMs are the smoothest nonlinear extensions of spectral subspaces of the linearized beam equation. Reduction in the governing PDE to SSMs provides an explicit low-dimensional model which captures the correct asymptotics of the full, infinite-dimensional dynamics. Our approach is general enough to admit extensions to other types of continuum vibrations. The model-reduction procedure we employ also gives guidelines for a mathematically self-consistent modeling of damping in PDEs describing structural vibrations.
Shocks near Jamming

NASA Astrophysics Data System (ADS)

Gómez, Leopoldo R.; Turner, Ari M.; van Hecke, Martin; Vitelli, Vincenzo

2012-02-01

Nonlinear sound is an extreme phenomenon typically observed in solids after violent explosions. But granular media are different. Right when they jam, these fragile and disordered solids exhibit a vanishing rigidity and sound speed, so that even tiny mechanical perturbations form supersonic shocks. Here, we perform simulations in which two-dimensional jammed granular packings are dynamically compressed and demonstrate that the elementary excitations are strongly nonlinear shocks, rather than ordinary phonons. We capture the full dependence of the shock speed on pressure and impact intensity by a surprisingly simple analytical model.
A Class of Exact Solutions of the Boussinesq Equation for Horizontal and Sloping Aquifers

NASA Astrophysics Data System (ADS)

Bartlett, M. S.; Porporato, A.

2018-02-01

The nonlinear equation of Boussinesq (1877) is a foundational approach for studying groundwater flow through an unconfined aquifer, but solving the full nonlinear version of the Boussinesq equation remains a challenge. Here, we present an exact solution to the full nonlinear Boussinesq equation that not only applies to sloping aquifers but also accounts for source and sink terms such as bedrock seepage, an often significant flux in headwater catchments. This new solution captures the hysteretic relationship (a loop rating curve) between the groundwater flow rate and the water table height, which may be used to provide a more realistic representation of streamflow and groundwater dynamics in hillslopes. In addition, the solution provides an expression where the flow recession varies based on hillslope parameters such as bedrock slope, bedrock seepage, aquifer recharge, plant transpiration, and other factors that vary across landscape types.
A Collection of Nonlinear Aircraft Simulations in MATLAB

NASA Technical Reports Server (NTRS)

Garza, Frederico R.; Morelli, Eugene A.

2003-01-01

Nonlinear six degree-of-freedom simulations for a variety of aircraft were created using MATLAB. Data for aircraft geometry, aerodynamic characteristics, mass / inertia properties, and engine characteristics were obtained from open literature publications documenting wind tunnel experiments and flight tests. Each nonlinear simulation was implemented within a common framework in MATLAB, and includes an interface with another commercially-available program to read pilot inputs and produce a three-dimensional (3-D) display of the simulated airplane motion. Aircraft simulations include the General Dynamics F-16 Fighting Falcon, Convair F-106B Delta Dart, Grumman F-14 Tomcat, McDonnell Douglas F-4 Phantom, NASA Langley Free-Flying Aircraft for Sub-scale Experimental Research (FASER), NASA HL-20 Lifting Body, NASA / DARPA X-31 Enhanced Fighter Maneuverability Demonstrator, and the Vought A-7 Corsair II. All nonlinear simulations and 3-D displays run in real time in response to pilot inputs, using contemporary desktop personal computer hardware. The simulations can also be run in batch mode. Each nonlinear simulation includes the full nonlinear dynamics of the bare airframe, with a scaled direct connection from pilot inputs to control surface deflections to provide adequate pilot control. Since all the nonlinear simulations are implemented entirely in MATLAB, user-defined control laws can be added in a straightforward fashion, and the simulations are portable across various computing platforms. Routines for trim, linearization, and numerical integration are included. The general nonlinear simulation framework and the specifics for each particular aircraft are documented.
Fixation, transient landscape, and diffusion dilemma in stochastic evolutionary game dynamics

NASA Astrophysics Data System (ADS)

Zhou, Da; Qian, Hong

2011-09-01

Agent-based stochastic models for finite populations have recently received much attention in the game theory of evolutionary dynamics. Both the ultimate fixation and the pre-fixation transient behavior are important to a full understanding of the dynamics. In this paper, we study the transient dynamics of the well-mixed Moran process through constructing a landscape function. It is shown that the landscape playing a central theoretical “device” that integrates several lines of inquiries: the stable behavior of the replicator dynamics, the long-time fixation, and continuous diffusion approximation associated with asymptotically large population. Several issues relating to the transient dynamics are discussed: (i) multiple time scales phenomenon associated with intra- and inter-attractoral dynamics; (ii) discontinuous transition in stochastically stationary process akin to Maxwell construction in equilibrium statistical physics; and (iii) the dilemma diffusion approximation facing as a continuous approximation of the discrete evolutionary dynamics. It is found that rare events with exponentially small probabilities, corresponding to the uphill movements and barrier crossing in the landscape with multiple wells that are made possible by strong nonlinear dynamics, plays an important role in understanding the origin of the complexity in evolutionary, nonlinear biological systems.
Nonlinear control of linear parameter varying systems with applications to hypersonic vehicles

NASA Astrophysics Data System (ADS)

Wilcox, Zachary Donald

The focus of this dissertation is to design a controller for linear parameter varying (LPV) systems, apply it specifically to air-breathing hypersonic vehicles, and examine the interplay between control performance and the structural dynamics design. Specifically a Lyapunov-based continuous robust controller is developed that yields exponential tracking of a reference model, despite the presence of bounded, nonvanishing disturbances. The hypersonic vehicle has time varying parameters, specifically temperature profiles, and its dynamics can be reduced to an LPV system with additive disturbances. Since the HSV can be modeled as an LPV system the proposed control design is directly applicable. The control performance is directly examined through simulations. A wide variety of applications exist that can be effectively modeled as LPV systems. In particular, flight systems have historically been modeled as LPV systems and associated control tools have been applied such as gain-scheduling, linear matrix inequalities (LMIs), linear fractional transformations (LFT), and mu-types. However, as the type of flight environments and trajectories become more demanding, the traditional LPV controllers may no longer be sufficient. In particular, hypersonic flight vehicles (HSVs) present an inherently difficult problem because of the nonlinear aerothermoelastic coupling effects in the dynamics. HSV flight conditions produce temperature variations that can alter both the structural dynamics and flight dynamics. Starting with the full nonlinear dynamics, the aerothermoelastic effects are modeled by a temperature dependent, parameter varying state-space representation with added disturbances. The model includes an uncertain parameter varying state matrix, an uncertain parameter varying non-square (column deficient) input matrix, and an additive bounded disturbance. In this dissertation, a robust dynamic controller is formulated for a uncertain and disturbed LPV system. The developed controller is then applied to a HSV model, and a Lyapunov analysis is used to prove global exponential reference model tracking in the presence of uncertainty in the state and input matrices and exogenous disturbances. Simulations with a spectrum of gains and temperature profiles on the full nonlinear dynamic model of the HSV is used to illustrate the performance and robustness of the developed controller. In addition, this work considers how the performance of the developed controller varies over a wide variety of control gains and temperature profiles and are optimized with respect to different performance metrics. Specifically, various temperature profile models and related nonlinear temperature dependent disturbances are used to characterize the relative control performance and effort for each model. Examining such metrics as a function of temperature provides a potential inroad to examine the interplay between structural/thermal protection design and control development and has application for future HSV design and control implementation.
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)
Generation of linear dynamic models from a digital nonlinear simulation

NASA Technical Reports Server (NTRS)

Daniele, C. J.; Krosel, S. M.

1979-01-01

The results and methodology used to derive linear models from a nonlinear simulation are presented. It is shown that averaged positive and negative perturbations in the state variables can reduce numerical errors in finite difference, partial derivative approximations and, in the control inputs, can better approximate the system response in both directions about the operating point. Both explicit and implicit formulations are addressed. Linear models are derived for the F 100 engine, and comparisons of transients are made with the nonlinear simulation. The problem of startup transients in the nonlinear simulation in making these comparisons is addressed. Also, reduction of the linear models is investigated using the modal and normal techniques. Reduced-order models of the F 100 are derived and compared with the full-state models.
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.
Numerical study of nonlinear full wave acoustic propagation

NASA Astrophysics Data System (ADS)

Velasco-Segura, Roberto; Rendon, Pablo L.

2013-11-01

With the aim of describing nonlinear acoustic phenomena, a form of the conservation equations for fluid dynamics is presented, deduced using slightly less restrictive hypothesis than those necessary to obtain the well known Westervelt equation. This formulation accounts for full wave diffraction, nonlinearity, and thermoviscous dissipative effects. A CLAWPACK based, 2D finite-volume method using Roe's linearization has been implemented to obtain numerically the solution of the proposed equations. In order to validate the code, two different tests have been performed: one against a special Taylor shock-like analytic solution, the other against published results on a HIFU system, both with satisfactory results. The code is written for parallel execution on a GPU and improves performance by a factor of over 50 when compared to the standard CLAWPACK Fortran code. This code can be used to describe moderate nonlinear phenomena, at low Mach numbers, in domains as large as 100 wave lengths. Applications range from modest models of diagnostic and therapeutic HIFU, parametric acoustic arrays, to acoustic wave guides. A couple of examples will be presented showing shock formation and oblique interaction. DGAPA PAPIIT IN110411, PAEP UNAM 2013.
Complex dynamics of a delayed discrete neural network of two nonidentical neurons

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

Chen, Yuanlong; Huang, Tingwen; Huang, Yu, E-mail: stshyu@mail.sysu.edu.cn

2014-03-15

In this paper, we discover that a delayed discrete Hopfield neural network of two nonidentical neurons with self-connections and no self-connections can demonstrate chaotic behaviors. To this end, we first transform the model, by a novel way, into an equivalent system which has some interesting properties. Then, we identify the chaotic invariant set for this system and show that the dynamics of this system within this set is topologically conjugate to the dynamics of the full shift map with two symbols. This confirms chaos in the sense of Devaney. Our main results generalize the relevant results of Huang and Zoumore » [J. Nonlinear Sci. 15, 291–303 (2005)], Kaslik and Balint [J. Nonlinear Sci. 18, 415–432 (2008)] and Chen et al. [Sci. China Math. 56(9), 1869–1878 (2013)]. We also give some numeric simulations to verify our theoretical results.« less
Complex dynamics of a delayed discrete neural network of two nonidentical neurons.

PubMed

Chen, Yuanlong; Huang, Tingwen; Huang, Yu

2014-03-01

In this paper, we discover that a delayed discrete Hopfield neural network of two nonidentical neurons with self-connections and no self-connections can demonstrate chaotic behaviors. To this end, we first transform the model, by a novel way, into an equivalent system which has some interesting properties. Then, we identify the chaotic invariant set for this system and show that the dynamics of this system within this set is topologically conjugate to the dynamics of the full shift map with two symbols. This confirms chaos in the sense of Devaney. Our main results generalize the relevant results of Huang and Zou [J. Nonlinear Sci. 15, 291-303 (2005)], Kaslik and Balint [J. Nonlinear Sci. 18, 415-432 (2008)] and Chen et al. [Sci. China Math. 56(9), 1869-1878 (2013)]. We also give some numeric simulations to verify our theoretical results.
Energetic and dynamical instability of spin-orbit coupled Bose-Einstein condensate in a deep optical lattice

NASA Astrophysics Data System (ADS)

Yu, Zi-Fa; Chai, Xu-Dan; Xue, Ju-Kui

2018-05-01

We investigate the energetic and dynamical instability of spin-orbit coupled Bose-Einstein condensate in a deep optical lattice via a tight-binding model. The stability phase diagram is completely revealed in full parameter space, while the dependence of superfluidity on the dispersion relation is illustrated explicitly. In the absence of spin-orbit coupling, the superfluidity only exists in the center of the Brillouin zone. However, the combination of spin-orbit coupling, Zeeman field, nonlinearity and optical lattice potential can modify the dispersion relation of the system, and change the position of Brillouin zone for generating the superfluidity. Thus, the superfluidity can appear in either the center or the other position of the Brillouin zone. Namely, in the center of the Brillouin zone, the system is either superfluid or Landau unstable, which depends on the momentum of the lowest energy. Therefore, the superfluidity can occur at optional position of the Brillouin zone by elaborating spin-orbit coupling, Zeeman splitting, nonlinearity and optical lattice potential. For the linear case, the system is always dynamically stable, however, the nonlinearity can induce the dynamical instability, and also expand the superfluid region. These predicted results can provide a theoretical evidence for exploring the superfluidity of the system experimentally.
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.
Nonlinear evolution dynamics of holographic superconductor model with scalar self-interaction

NASA Astrophysics Data System (ADS)

Li, Ran; Zi, Tieguang; Zhang, Hongbao

2018-04-01

We investigate the holographic superconductor model that is described by the Einstein-Maxwell theory with the self-interaction term λ |Ψ |4 of complex scalar field in asymptotic anti-de Sitter (AdS) spacetime. Below critical temperature Tc, the planar Reissner-Nordström-AdS black hole is unstable due to the near-horizon scalar condensation instability. We study the full nonlinear development of this instability by numerically solving the gravitational dynamics in the asymptotic AdS spacetime, and observe a dynamical process from the perturbed Reissner-Nordström-AdS black hole to a hairy black hole when the initial black hole temperature T
Bubble and Drop Nonlinear Dynamics (BDND)

NASA Technical Reports Server (NTRS)

Trinh, E. H.; Leal, L. Gary; Thomas, D. A.; Crouch, R. K.

1998-01-01

Free drops and bubbles are weakly nonlinear mechanical systems that are relatively simple to characterize experimentally in 1-G as well as in microgravity. The understanding of the details of their motion contributes to the fundamental study of nonlinear phenomena and to the measurement of the thermophysical properties of freely levitated melts. The goal of this Glovebox-based experimental investigation is the low-gravity assessment of the capabilities of a modular apparatus based on ultrasonic resonators and on the pseudo- extinction optical method. The required experimental task is the accurate measurements of the large-amplitude dynamics of free drops and bubbles in the absence of large biasing influences such as gravity and levitation fields. A single-axis levitator used for the positioning of drops in air, and an ultrasonic water-filled resonator for the trapping of air bubbles have been evaluated in low-gravity and in 1-G. The basic feasibility of drop positioning and shape oscillations measurements has been verified by using a laptop-interfaced automated data acquisition and the optical extinction technique. The major purpose of the investigation was to identify the salient technical issues associated with the development of a full-scale Microgravity experiment on single drop and bubble dynamics.
Renormalized dynamics of the Dean-Kawasaki model

NASA Astrophysics Data System (ADS)

Bidhoodi, Neeta; Das, Shankar P.

2015-07-01

We study the model of a supercooled liquid for which the equation of motion for the coarse-grained density ρ (x ,t ) is the nonlinear diffusion equation originally proposed by Dean and Kawasaki, respectively, for Brownian and Newtonian dynamics of fluid particles. Using a Martin-Siggia-Rose (MSR) field theory we study the renormalization of the dynamics in a self-consistent form in terms of the so-called self-energy matrix Σ . The appropriate model for the renormalized dynamics involves an extended set of field variables {ρ ,θ } , linked through a nonlinear constraint. The latter incorporates, in a nonperturbative manner, the effects of an infinite number of density nonlinearities in the dynamics. We show that the contributing element of Σ which renormalizes the bare diffusion constant D0 to DR is same as that proposed by Kawasaki and Miyazima [Z. Phys. B Condens. Matter 103, 423 (1997), 10.1007/s002570050396]. DR sharply decreases with increasing density. We consider the likelihood of a ergodic-nonergodic (ENE) transition in the model beyond a critical point. The transition is characterized by the long-time limit of the density correlation freezing at a nonzero value. From our analysis we identify an element of Σ which arises from the above-mentioned nonlinear constraint and is key to the viability of the ENE transition. If this self-energy would be zero, then the model supports a sharp ENE transition with DR=0 as predicted by Kawasaki and Miyazima. With the full model having nonzero value for this self-energy, the density autocorrelation function decays to zero in the long-time limit. Hence the ENE transition is not supported in the model.
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.

Dynamic model including piping acoustics of a centrifugal compression system

NASA Astrophysics Data System (ADS)

van Helvoirt, Jan; de Jager, Bram

2007-04-01

This paper deals with low-frequency pulsation phenomena in full-scale centrifugal compression systems associated with compressor surge. The Greitzer lumped parameter model is applied to describe the dynamic behavior of an industrial compressor test rig and experimental evidence is provided for the presence of acoustic pulsations in the compression system under study. It is argued that these acoustic phenomena are common for full-scale compression systems where pipe system dynamics have a significant influence on the overall system behavior. The main objective of this paper is to extend the basic compressor model in order to include the relevant pipe system dynamics. For this purpose a pipeline model is proposed, based on previous developments for fluid transmission lines. The connection of this model to the lumped parameter model is accomplished via the selection of appropriate boundary conditions. Validation results will be presented, showing a good agreement between simulation and measurement data. The results indicate that the damping of piping transients depends on the nominal, time-varying pressure and flow velocity. Therefore, model parameters are made dependent on the momentary pressure and a switching nonlinearity is introduced into the model to vary the acoustic damping as a function of flow velocity. These modifications have limited success and the results indicate that a more sophisticated model is required to fully describe all (nonlinear) acoustic effects. However, the very good qualitative results show that the model adequately combines compressor and pipe system dynamics. Therefore, the proposed model forms a step forward in the analysis and modeling of surge in full-scale centrifugal compression systems and opens the path for further developments in this field.
On discrete control of nonlinear systems with applications to robotics

NASA Technical Reports Server (NTRS)

Eslami, Mansour

1989-01-01

Much progress has been reported in the areas of modeling and control of nonlinear dynamic systems in a continuous-time framework. From implementation point of view, however, it is essential to study these nonlinear systems directly in a discrete setting that is amenable for interfacing with digital computers. But to develop discrete models and discrete controllers for a nonlinear system such as robot is a nontrivial task. Robot is also inherently a variable-inertia dynamic system involving additional complications. Not only the computer-oriented models of these systems must satisfy the usual requirements for such models, but these must also be compatible with the inherent capabilities of computers and must preserve the fundamental physical characteristics of continuous-time systems such as the conservation of energy and/or momentum. Preliminary issues regarding discrete systems in general and discrete models of a typical industrial robot that is developed with full consideration of the principle of conservation of energy are presented. Some research on the pertinent tactile information processing is reviewed. Finally, system control methods and how to integrate these issues in order to complete the task of discrete control of a robot manipulator are also reviewed.
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
Analysis of friction and instability by the centre manifold theory for a non-linear sprag-slip model

NASA Astrophysics Data System (ADS)

Sinou, J.-J.; Thouverez, F.; Jezequel, L.

2003-08-01

This paper presents the research devoted to the study of instability phenomena in non-linear model with a constant brake friction coefficient. Indeed, the impact of unstable oscillations can be catastrophic. It can cause vehicle control problems and component degradation. Accordingly, complex stability analysis is required. This paper outlines stability analysis and centre manifold approach for studying instability problems. To put it more precisely, one considers brake vibrations and more specifically heavy trucks judder where the dynamic characteristics of the whole front axle assembly is concerned, even if the source of judder is located in the brake system. The modelling introduces the sprag-slip mechanism based on dynamic coupling due to buttressing. The non-linearity is expressed as a polynomial with quadratic and cubic terms. This model does not require the use of brake negative coefficient, in order to predict the instability phenomena. Finally, the centre manifold approach is used to obtain equations for the limit cycle amplitudes. The centre manifold theory allows the reduction of the number of equations of the original system in order to obtain a simplified system, without loosing the dynamics of the original system as well as the contributions of non-linear terms. The goal is the study of the stability analysis and the validation of the centre manifold approach for a complex non-linear model by comparing results obtained by solving the full system and by using the centre manifold approach. The brake friction coefficient is used as an unfolding parameter of the fundamental Hopf bifurcation point.
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.
The Principle of Energetic Consistency

NASA Technical Reports Server (NTRS)

Cohn, Stephen E.

2009-01-01

A basic result in estimation theory is that the minimum variance estimate of the dynamical state, given the observations, is the conditional mean estimate. This result holds independently of the specifics of any dynamical or observation nonlinearity or stochasticity, requiring only that the probability density function of the state, conditioned on the observations, has two moments. For nonlinear dynamics that conserve a total energy, this general result implies the principle of energetic consistency: if the dynamical variables are taken to be the natural energy variables, then the sum of the total energy of the conditional mean and the trace of the conditional covariance matrix (the total variance) is constant between observations. Ensemble Kalman filtering methods are designed to approximate the evolution of the conditional mean and covariance matrix. For them the principle of energetic consistency holds independently of ensemble size, even with covariance localization. However, full Kalman filter experiments with advection dynamics have shown that a small amount of numerical dissipation can cause a large, state-dependent loss of total variance, to the detriment of filter performance. The principle of energetic consistency offers a simple way to test whether this spurious loss of variance limits ensemble filter performance in full-blown applications. The classical second-moment closure (third-moment discard) equations also satisfy the principle of energetic consistency, independently of the rank of the conditional covariance matrix. Low-rank approximation of these equations offers an energetically consistent, computationally viable alternative to ensemble filtering. Current formulations of long-window, weak-constraint, four-dimensional variational methods are designed to approximate the conditional mode rather than the conditional mean. Thus they neglect the nonlinear bias term in the second-moment closure equation for the conditional mean. The principle of energetic consistency implies that, to precisely the extent that growing modes are important in data assimilation, this term is also important.
Refraction of dispersive shock waves

NASA Astrophysics Data System (ADS)

El, G. A.; Khodorovskii, V. V.; Leszczyszyn, A. M.

2012-09-01

We study a dispersive counterpart of the classical gas dynamics problem of the interaction of a shock wave with a counter-propagating simple rarefaction wave, often referred to as the shock wave refraction. The refraction of a one-dimensional dispersive shock wave (DSW) due to its head-on collision with the centred rarefaction wave (RW) is considered in the framework of the defocusing nonlinear Schrödinger (NLS) equation. For the integrable cubic nonlinearity case we present a full asymptotic description of the DSW refraction by constructing appropriate exact solutions of the Whitham modulation equations in Riemann invariants. For the NLS equation with saturable nonlinearity, whose modulation system does not possess Riemann invariants, we take advantage of the recently developed method for the DSW description in non-integrable dispersive systems to obtain main physical parameters of the DSW refraction. The key features of the DSW-RW interaction predicted by our modulation theory analysis are confirmed by direct numerical solutions of the full dispersive problem.
Self-consistent projection operator theory in nonlinear quantum optical systems: A case study on degenerate optical parametric oscillators

NASA Astrophysics Data System (ADS)

Degenfeld-Schonburg, Peter; Navarrete-Benlloch, Carlos; Hartmann, Michael J.

2015-05-01

Nonlinear quantum optical systems are of paramount relevance for modern quantum technologies, as well as for the study of dissipative phase transitions. Their nonlinear nature makes their theoretical study very challenging and hence they have always served as great motivation to develop new techniques for the analysis of open quantum systems. We apply the recently developed self-consistent projection operator theory to the degenerate optical parametric oscillator to exemplify its general applicability to quantum optical systems. We show that this theory provides an efficient method to calculate the full quantum state of each mode with a high degree of accuracy, even at the critical point. It is equally successful in describing both the stationary limit and the dynamics, including regions of the parameter space where the numerical integration of the full problem is significantly less efficient. We further develop a Gaussian approach consistent with our theory, which yields sensibly better results than the previous Gaussian methods developed for this system, most notably standard linearization techniques.
Semiflexible polymer dynamics with a bead-spring model

NASA Astrophysics Data System (ADS)

Barkema, Gerard T.; Panja, Debabrata; van Leeuwen, J. M. J.

2014-11-01

We study the dynamical properties of semiflexible polymers with a recently introduced bead-spring model. We focus on double-stranded DNA (dsDNA). The two parameters of the model, T* and ν, are chosen to match its experimental force-extension curve. In comparison to its groundstate value, the bead-spring Hamiltonian is approximated in the first order by the Hessian that is quadratic in the bead positions. The eigenmodes of the Hessian provide the longitudinal (stretching) and transverse (bending) eigenmodes of the polymer, and the corresponding eigenvalues match well with the established phenomenology of semiflexible polymers. At the Hessian approximation of the Hamiltonian, the polymer dynamics is linear. Using the longitudinal and transverse eigenmodes, for the linearized problem, we obtain analytical expressions of (i) the autocorrelation function of the end-to-end vector, (ii) the autocorrelation function of a bond (i.e. a spring, or a tangent) vector at the middle of the chain, and (iii) the mean-square displacement of a tagged bead in the middle of the chain, as the sum over the contributions from the modes—the so-called ‘mode sums’. We also perform simulations with the full dynamics of the model. The simulations yield numerical values of the correlations functions (i-iii) that agree very well with the analytical expressions for the linearized dynamics. This does not however mean that the nonlinearities are not present. In fact, we also study the mean-square displacement of the longitudinal component of the end-to-end vector that showcases strong nonlinear effects in the polymer dynamics, and we identify at least an effective t7/8 power-law regime in its time-dependence. Nevertheless, in comparison to the full mean-square displacement of the end-to-end vector the nonlinear effects remain small at all times—it is in this sense we state that our results demonstrate that the linearized dynamics suffices for dsDNA fragments that are shorter than or comparable to the persistence length. Our results are consistent with those of the wormlike chain (WLC) model, the commonly used descriptive tool of semiflexible polymers.
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.
Algebraic and adaptive learning in neural control systems

NASA Astrophysics Data System (ADS)

Ferrari, Silvia

A systematic approach is developed for designing adaptive and reconfigurable nonlinear control systems that are applicable to plants modeled by ordinary differential equations. The nonlinear controller comprising a network of neural networks is taught using a two-phase learning procedure realized through novel techniques for initialization, on-line training, and adaptive critic design. A critical observation is that the gradients of the functions defined by the neural networks must equal corresponding linear gain matrices at chosen operating points. On-line training is based on a dual heuristic adaptive critic architecture that improves control for large, coupled motions by accounting for actual plant dynamics and nonlinear effects. An action network computes the optimal control law; a critic network predicts the derivative of the cost-to-go with respect to the state. Both networks are algebraically initialized based on prior knowledge of satisfactory pointwise linear controllers and continue to adapt on line during full-scale simulations of the plant. On-line training takes place sequentially over discrete periods of time and involves several numerical procedures. A backpropagating algorithm called Resilient Backpropagation is modified and successfully implemented to meet these objectives, without excessive computational expense. This adaptive controller is as conservative as the linear designs and as effective as a global nonlinear controller. The method is successfully implemented for the full-envelope control of a six-degree-of-freedom aircraft simulation. The results show that the on-line adaptation brings about improved performance with respect to the initialization phase during aircraft maneuvers that involve large-angle and coupled dynamics, and parameter variations.
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.
Optimal control of dissipative nonlinear dynamical systems with triggers of coupled singularities

NASA Astrophysics Data System (ADS)

Stevanović Hedrih, K.

2008-02-01

This paper analyses the controllability of motion of nonconservative nonlinear dynamical systems in which triggers of coupled singularities exist or appear. It is shown that the phase plane method is useful for the analysis of nonlinear dynamics of nonconservative systems with one degree of freedom of control strategies and also shows the way it can be used for controlling the relative motion in rheonomic systems having equivalent scleronomic conservative or nonconservative system For the system with one generalized coordinate described by nonlinear differential equation of nonlinear dynamics with trigger of coupled singularities, the functions of system potential energy and conservative force must satisfy some conditions defined by a Theorem on the existence of a trigger of coupled singularities and the separatrix in the form of "an open a spiral form" of number eight. Task of the defined dynamical nonconservative system optimal control is: by using controlling force acting to the system, transfer initial state of the nonlinear dynamics of the system into the final state of the nonlinear dynamics in the minimal time for that optimal control task
Lifespan differences in nonlinear dynamics during rest and auditory oddball performance.

PubMed

Müller, Viktor; Lindenberger, Ulman

2012-07-01

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 indicator of cortical reactivity. During rest, both nonlinear coupling and spectral alpha power decreased with age, whereas dimensional complexity increased. In contrast, when attending to the deviant stimulus, nonlinear coupling increased with age, and complexity decreased. Correlational analyses showed that nonlinear measures assessed during auditory oddball performance were reliably related to an independently assessed measure of perceptual speed. We conclude that cortical dynamics during rest and stimulus processing undergo substantial reorganization from childhood to old age, and propose that lifespan age differences in nonlinear dynamics during stimulus processing reflect lifespan changes in the functional organization of neuronal cell assemblies. © 2012 Blackwell Publishing Ltd.
Low-dimensional manifold of actin polymerization dynamics

NASA Astrophysics Data System (ADS)

Floyd, Carlos; Jarzynski, Christopher; Papoian, Garegin

2017-12-01

Actin filaments are critical components of the eukaryotic cytoskeleton, playing important roles in a number of cellular functions, such as cell migration, organelle transport, and mechanosensation. They are helical polymers with a well-defined polarity, composed of globular subunits that bind nucleotides in one of three hydrolysis states (ATP, ADP-Pi, or ADP). Mean-field models of the dynamics of actin polymerization have succeeded in, among other things, determining the nucleotide profile of an average filament and resolving the mechanisms of accessory proteins. However, these models require numerical solution of a high-dimensional system of nonlinear ordinary differential equations. By truncating a set of recursion equations, the Brooks-Carlsson (BC) model reduces dimensionality to 11, but it still remains nonlinear and does not admit an analytical solution, hence, significantly hindering understanding of its resulting dynamics. In this work, by taking advantage of the fast timescales of the hydrolysis states of the filament tips, we propose two model reduction schemes: the quasi steady-state approximation model is five-dimensional and nonlinear, whereas the constant tip (CT) model is five-dimensional and linear, resulting from the approximation that the tip states are not dynamic variables. We provide an exact solution of the CT model and use it to shed light on the dynamical behaviors of the full BC model, highlighting the relative ordering of the timescales of various collective processes, and explaining some unusual dependence of the steady-state behavior on initial conditions.
A full time-domain approach to spatio-temporal dynamics of semiconductor lasers. II. Spatio-temporal dynamics

NASA Astrophysics Data System (ADS)

Böhringer, Klaus; Hess, Ortwin

The spatio-temporal dynamics of novel semiconductor lasers is discussed on the basis of a space- and momentum-dependent full time-domain approach. To this means the space-, time-, and momentum-dependent Full-Time Domain Maxwell Semiconductor Bloch equations, derived and discussed in our preceding paper I [K. Böhringer, O. Hess, A full time-domain approach to spatio-temporal dynamics of semiconductor lasers. I. Theoretical formulation], are solved by direct numerical integration. Focussing on the device physics of novel semiconductor lasers that profit, in particular, from recent advances in nanoscience and nanotechnology, we discuss the examples of photonic band edge surface emitting lasers (PBE-SEL) and semiconductor disc lasers (SDLs). It is demonstrated that photonic crystal effects can be obtained for finite crystal structures, and leading to a significant improvement in laser performance such as reduced lasing thresholds. In SDLs, a modern device concept designed to increase the power output of surface-emitters in combination with near-diffraction-limited beam quality, we explore the complex interplay between the intracavity optical fields and the quantum well gain material in SDL structures. Our simulations reveal the dynamical balance between carrier generation due to pumping into high energy states, momentum relaxation of carriers, and stimulated recombination from states near the band edge. Our full time-domain approach is shown to also be an excellent framework for the modelling of the interaction of high-intensity femtosecond and picosecond pulses with semiconductor nanostructures. It is demonstrated that group velocity dispersion, dynamical gain saturation and fast self-phase modulation (SPM) are the main causes for the induced changes and asymmetries in the amplified pulse shape and spectrum of an ultrashort high-intensity pulse. We attest that the time constants of the intraband scattering processes are critical to gain recovery. Moreover, we present new insight into the physics of nonlinear coherent pulse propagation phenomena in active (semiconductor) gain media. Our numerical full time-domain simulations are shown to generally agree well with analytical predictions, while in the case of optical pulses with large pulse areas or few-cycle pulses they reveal the limits of analytic approaches. Finally, it is demonstrated that coherent ultrafast nonlinear propagation effects become less distinctive if we apply a realistic model of the quantum well semiconductor gain material, consider characteristic loss channels and take into account de-phasing processes and homogeneous broadening.
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.
Nonlinear Plasma Response to Resonant Magnetic Perturbation in Rutherford Regime

NASA Astrophysics Data System (ADS)

Zhu, Ping; Yan, Xingting; Huang, Wenlong

2017-10-01

Recently a common analytic relation for both the locked mode and the nonlinear plasma response in the Rutherford regime has been developed based on the steady-state solution to the coupled dynamic system of magnetic island evolution and torque balance equations. The analytic relation predicts the threshold and the island size for the full penetration of resonant magnetic perturbation (RMP). It also rigorously proves a screening effect of the equilibrium toroidal flow. In this work, we test the theory by solving for the nonlinear plasma response to a single-helicity RMP of a circular-shaped limiter tokamak equilibrium with a constant toroidal flow, using the initial-value, full MHD simulation code NIMROD. Time evolution of the parallel flow or ``slip frequency'' profile and its asymptotic approach to steady state obtained from the NIMROD simulations qualitatively agree with the theory predictions. Further comparisons are carried out for the saturated island size, the threshold for full mode penetration, as well as the screening effects of equilibrium toroidal flow in order to understand the physics of nonlinear plasma response in the Rutherford regime. Supported by National Magnetic Confinement Fusion Science Program of China Grants 2014GB124002 and 2015GB101004, the 100 Talent Program of the Chinese Academy of Sciences, and U.S. Department of Energy Grants DE-FG02-86ER53218 and DE-FC02-08ER54975.

Fluctuating Nonlinear Spring Model of Mechanical Deformation of Biological Particles

PubMed Central

Kononova, Olga; Snijder, Joost; Kholodov, Yaroslav; Marx, Kenneth A.; Wuite, Gijs J. L.; Roos, Wouter H.; Barsegov, Valeri

2016-01-01

The mechanical properties of virus capsids correlate with local conformational dynamics in the capsid structure. They also reflect the required stability needed to withstand high internal pressures generated upon genome loading and contribute to the success of important events in viral infectivity, such as capsid maturation, genome uncoating and receptor binding. The mechanical properties of biological nanoparticles are often determined from monitoring their dynamic deformations in Atomic Force Microscopy nanoindentation experiments; but a comprehensive theory describing the full range of observed deformation behaviors has not previously been described. We present a new theory for modeling dynamic deformations of biological nanoparticles, which considers the non-linear Hertzian deformation, resulting from an indenter-particle physical contact, and the bending of curved elements (beams) modeling the particle structure. The beams’ deformation beyond the critical point triggers a dynamic transition of the particle to the collapsed state. This extreme event is accompanied by a catastrophic force drop as observed in the experimental or simulated force (F)-deformation (X) spectra. The theory interprets fine features of the spectra, including the nonlinear components of the FX-curves, in terms of the Young’s moduli for Hertzian and bending deformations, and the structural damage dependent beams’ survival probability, in terms of the maximum strength and the cooperativity parameter. The theory is exemplified by successfully describing the deformation dynamics of natural nanoparticles through comparing theoretical curves with experimental force-deformation spectra for several virus particles. This approach provides a comprehensive description of the dynamic structural transitions in biological and artificial nanoparticles, which is essential for their optimal use in nanotechnology and nanomedicine applications. PMID:26821264
Nonlinear Characterization of Half and Full Wavelength Power Ultrasonic Devices

NASA Astrophysics Data System (ADS)

Mathieson, Andrew; Cerisola, Niccolò; Cardoni, Andrea

It is well known that power ultrasonic devices whilst driven under elevated excitation levels exhibit nonlinear behaviors. If no attempt is made to understand and subsequently control these behaviors, these devices can exhibit poor performance or even suffer premature failure. This paper presents an experimental method for the dynamic characterization of a commercial ultrasonic transducer for bone cutting applications (Piezosurgery® Device) operated together with a variety of rod horns that are tuned to operate in a longitudinal mode of vibration. Near resonance responses, excited via a burst sine sweep method were used to identify nonlinear responses exhibited by the devices, while experimental modal analysis was performed to identify the modal parameters of the longitudinal modes of vibration of the assemblies between 0-80 kHz. This study tries to provide an understanding of the effects that geometry and material choices may have on the nonlinear behavior of a tuned device.
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.
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.
Magnetic-sensor performance evaluated from magneto-conductance curve in magnetic tunnel junctions using in-plane or perpendicularly magnetized synthetic antiferromagnetic reference layers

NASA Astrophysics Data System (ADS)

Nakano, T.; Oogane, M.; Furuichi, T.; Ando, Y.

2018-04-01

The automotive industry requires magnetic sensors exhibiting highly linear output within a dynamic range as wide as ±1 kOe. A simple model predicts that the magneto-conductance (G-H) curve in a magnetic tunnel junction (MTJ) is perfectly linear, whereas the magneto-resistance (R-H) curve inevitably contains a finite nonlinearity. We prepared two kinds of MTJs using in-plane or perpendicularly magnetized synthetic antiferromagnetic (i-SAF or p-SAF) reference layers and investigated their sensor performance. In the MTJ with the i-SAF reference layer, the G-H curve did not necessarily show smaller nonlinearities than those of the R-H curve with different dynamic ranges. This is because the magnetizations of the i-SAF reference layer start to rotate at a magnetic field even smaller than the switching field (Hsw) measured by a magnetometer, which significantly affects the tunnel magnetoresistance (TMR) effect. In the MTJ with the p-SAF reference layer, the G-H curve showed much smaller nonlinearities than those of the R-H curve, thanks to a large Hsw value of the p-SAF reference layer. We achieved a nonlinearity of 0.08% FS (full scale) in the G-H curve with a dynamic range of ±1 kOe, satisfying our target for automotive applications. This demonstrated that a reference layer exhibiting a large Hsw value is indispensable in order to achieve a highly linear G-H curve.
Modelling, validation and analysis of a three-dimensional railway vehicle-track system model with linear and nonlinear track properties in the presence of wheel flats

NASA Astrophysics Data System (ADS)

Uzzal, R. U. A.; Ahmed, A. K. W.; Bhat, R. B.

2013-11-01

This paper presents dynamic contact loads at wheel-rail contact point in a three-dimensional railway vehicle-track model as well as dynamic response at vehicle-track component levels in the presence of wheel flats. The 17-degrees of freedom lumped mass vehicle is modelled as a full car body, two bogies and four wheelsets, whereas the railway track is modelled as two parallel Timoshenko beams periodically supported by lumped masses representing the sleepers. The rail beam is also supported by nonlinear spring and damper elements representing the railpad and ballast. In order to ensure the interactions between the railpads, a shear parameter beneath the rail beams has also been considered into the model. The wheel-rail contact is modelled using nonlinear Hertzian contact theory. In order to solve the coupled partial and ordinary differential equations of the vehicle-track system, modal analysis method is employed. Idealised Haversine wheel flats with the rounded corner are included in the wheel-rail contact model. The developed model is validated with the existing measured and analytical data available in the literature. The nonlinear model is then employed to investigate the wheel-rail impact forces that arise in the wheel-rail interface due to the presence of wheel flats. The validated model is further employed to investigate the dynamic responses of vehicle and track components in terms of displacement, velocity, and acceleration in the presence of single wheel flat.
Response of a 2-story test-bed structure for the seismic evaluation of nonstructural systems

NASA Astrophysics Data System (ADS)

Soroushian, Siavash; Maragakis, E. "Manos"; Zaghi, Arash E.; Rahmanishamsi, Esmaeel; Itani, Ahmad M.; Pekcan, Gokhan

2016-03-01

A full-scale, two-story, two-by-one bay, steel braced-frame was subjected to a number of unidirectional ground motions using three shake tables at the UNR-NEES site. The test-bed frame was designed to study the seismic performance of nonstructural systems including steel-framed gypsum partition walls, suspended ceilings and fire sprinkler systems. The frame can be configured to perform as an elastic or inelastic system to generate large floor accelerations or large inter story drift, respectively. In this study, the dynamic performance of the linear and nonlinear test-beds was comprehensively studied. The seismic performance of nonstructural systems installed in the linear and nonlinear test-beds were assessed during extreme excitations. In addition, the dynamic interactions of the test-bed and installed nonstructural systems are investigated.
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.
Exciton-polariton dynamics in a GaAs bulk microcavity

NASA Astrophysics Data System (ADS)

Ceccherini, S.; Gurioli, M.; Bogani, F.; Colocci, M.; Tredicucci, A.; Bassani, F.; Beltram, F.; Sorba, L.

1998-01-01

We present a full analysis of exciton dynamics in a GaAs λ/2 bulk microcavity following excitation by ultrafast laser pulses. Coherent dynamics was probed by means of an interferometric technique; beating and dephasing times were studied for various excitation intensities. At high incident power, population effects begin to show up reducing exciton oscillator strength and suppressing Rabi splitting. This feature produces marked non-linearities in the input-output characteristic of the optical functions, which were studied in view of reaching bistable operation. Theoretical calculations performed within the transfer-matrix framework show good agreement with experimental results.
Analysis of dynamic accumulative damage about the lining structure of high speed railway’s tunnel based on ultrasonic testing technology

NASA Astrophysics Data System (ADS)

Wang, Xiang-qiu; Zhang, Huojun; Xie, Wen-xi

2017-08-01

Based on the similar material model test of full tunnel, the theory of elastic wave propagation and the testing technology of intelligent ultrasonic wave had been used to research the dynamic accumulative damage characteristics of tunnel’s lining structure under the dynamic loads of high speed train. For the more, the dynamic damage variable of lining structure of high speed railway’s tunnel was obtained. The results shown that the dynamic cumulative damage of lining structure increases nonlinearly with the times of cumulative vibration, the weakest part of dynamic cumulative damage is the arch foot of tunnel. Much more attention should be paid to the design and operation management of high speed railway’s tunnel.
Bifurcation analysis of an automatic dynamic balancing mechanism for eccentric rotors

NASA Astrophysics Data System (ADS)

Green, K.; Champneys, A. R.; Lieven, N. J.

2006-04-01

We present a nonlinear bifurcation analysis of the dynamics of an automatic dynamic balancing mechanism for rotating machines. The principle of operation is to deploy two or more masses that are free to travel around a race at a fixed distance from the hub and, subsequently, balance any eccentricity in the rotor. Mathematically, we start from a Lagrangian description of the system. It is then shown how under isotropic conditions a change of coordinates into a rotating frame turns the problem into a regular autonomous dynamical system, amenable to a full nonlinear bifurcation analysis. Using numerical continuation techniques, curves are traced of steady states, limit cycles and their bifurcations as parameters are varied. These results are augmented by simulations of the system trajectories in phase space. Taking the case of a balancer with two free masses, broad trends are revealed on the existence of a stable, dynamically balanced steady-state solution for specific rotation speeds and eccentricities. However, the analysis also reveals other potentially attracting states—non-trivial steady states, limit cycles, and chaotic motion—which are not in balance. The transient effects which lead to these competing states, which in some cases coexist, are investigated.
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.
Experimental characterization of deployable trusses and joints

NASA Technical Reports Server (NTRS)

Ikegami, R.; Church, S. M.; Keinholz, D. A.; Fowler, B. L.

1987-01-01

The structural dynamic properties of trusses are strongly affected by the characteristics of joints connecting the individual beam elements. Joints are particularly significant in that they are often the source of nonlinearities and energy dissipation. While the joints themselves may be physically simple, direct measurement is often necessary to obtain a mathematical description suitable for inclusion in a system model. Force state mapping is a flexible, practical test method for obtaining such a description, particularly when significant nonlinear effects are present. It involves measurement of the relationship, nonlinear or linear, between force transmitted through a joint and the relative displacement and velocity across it. An apparatus and procedure for force state mapping are described. Results are presented from tests of joints used in a lightweight, composite, deployable truss built by the Boeing Aerospace Company. The results from the joint tests are used to develop a model of a full 4-bay truss segment. The truss segment was statically and dynamically tested. The results of the truss tests are presented and compared with the analytical predictions from the model.
Nonlinear Dynamic Inversion Baseline Control Law: Flight-Test Results for the Full-scale Advanced Systems Testbed F/A-18 Airplane

NASA Technical Reports Server (NTRS)

Miller, Christopher J.

2011-01-01

A model reference nonlinear dynamic inversion control law has been developed to provide a baseline controller for research into simple adaptive elements for advanced flight control laws. This controller has been implemented and tested in a hardware-in-the-loop simulation and in flight. The flight results agree well with the simulation predictions and show good handling qualities throughout the tested flight envelope with some noteworthy deficiencies highlighted both by handling qualities metrics and pilot comments. Many design choices and implementation details reflect the requirements placed on the system by the nonlinear flight environment and the desire to keep the system as simple as possible to easily allow the addition of the adaptive elements. The flight-test results and how they compare to the simulation predictions are discussed, along with a discussion about how each element affected pilot opinions. Additionally, aspects of the design that performed better than expected are presented, as well as some simple improvements that will be suggested for follow-on work.
On-line implementation of nonlinear parameter estimation for the Space Shuttle main engine

NASA Technical Reports Server (NTRS)

Buckland, Julia H.; Musgrave, Jeffrey L.; Walker, Bruce K.

1992-01-01

We investigate the performance of a nonlinear estimation scheme applied to the estimation of several parameters in a performance model of the Space Shuttle Main Engine. The nonlinear estimator is based upon the extended Kalman filter which has been augmented to provide estimates of several key performance variables. The estimated parameters are directly related to the efficiency of both the low pressure and high pressure fuel turbopumps. Decreases in the parameter estimates may be interpreted as degradations in turbine and/or pump efficiencies which can be useful measures for an online health monitoring algorithm. This paper extends previous work which has focused on off-line parameter estimation by investigating the filter's on-line potential from a computational standpoint. ln addition, we examine the robustness of the algorithm to unmodeled dynamics. The filter uses a reduced-order model of the engine that includes only fuel-side dynamics. The on-line results produced during this study are comparable to off-line results generated previously. The results show that the parameter estimates are sensitive to dynamics not included in the filter model. Off-line results using an extended Kalman filter with a full order engine model to address the robustness problems of the reduced-order model are also presented.
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.
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.
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 forecasting analysis of inflation-deflation patterns of an active caldera (Campi Flegrei, Italy)

USGS Publications Warehouse

Cortini, M.; Barton, C.C.

1993-01-01

The ground level in Pozzuoli, Italy, at the center of the Campi Flegrei caldera, has been monitored by tide gauges. Previous work suggests that the dynamics of the Campi Flegrei system, as reconstructed from the tide gauge record, is chaotic and low dimensional. According to this suggestion, in spite of the complexity of the system, at a time scale of days the ground motion is driven by a deterministic mechanism with few degrees of freedom; however, the interactions of the system may never be describable in full detail. New analysis of the tide gauge record using Nonlinear Forecasting, confirms low-dimensional chaos in the ground elevation record at Campi Flegrei and suggests that Nonlinear Forecasting could be a useful tool in volcanic surveillance. -from Authors
MURI: Adaptive Waveform Design for Full Spectral Dominance

DTIC Science & Technology

2011-03-11

a three- dimensional urban tracking model, based on the nonlinear measurement model (that uses the urban multipath geometry with different types of ... the time evolution of the scattering function with a high dimensional dynamic system; a multiple particle filter technique is used to sequentially...integration of space -time coding with a fixed set of beams. It complements the
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
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.
Transitions of stationary to pulsating solutions in the complex cubic-quintic Ginzburg-Landau equation under the influence of nonlinear gain and higher-order effects

NASA Astrophysics Data System (ADS)

Uzunov, Ivan M.; Georgiev, Zhivko D.; Arabadzhiev, Todor N.

2018-05-01

In this paper we study the transitions of stationary to pulsating solutions in the complex cubic-quintic Ginzburg-Landau equation (CCQGLE) under the influence of nonlinear gain, its saturation, and higher-order effects: self-steepening, third-order of dispersion, and intrapulse Raman scattering in the anomalous dispersion region. The variation method and the method of moments are applied in order to obtain the dynamic models with finite degrees of freedom for the description of stationary and pulsating solutions. Having applied the first model and its bifurcation analysis we have discovered the existence of families of subcritical Poincaré-Andronov-Hopf bifurcations due to the intrapulse Raman scattering, as well as some small nonlinear gain and the saturation of the nonlinear gain. A phenomenon of nonlinear stability has been studied and it has been shown that long living pulsating solutions with relatively small fluctuations of amplitude and frequencies exist at the bifurcation point. The numerical analysis of the second model has revealed the existence of Poincaré-Andronov-Hopf bifurcations of Raman dissipative soliton under the influence of the self-steepening effect and large nonlinear gain. All our theoretical predictions have been confirmed by the direct numerical solution of the full perturbed CCQGLE. The detailed comparison between the results obtained by both dynamic models and the direct numerical solution of the perturbed CCQGLE has proved the applicability of the proposed models in the investigation of the solutions of the perturbed CCQGLE.
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.
The numerical dynamic for highly nonlinear partial differential equations

NASA Technical Reports Server (NTRS)

Lafon, A.; Yee, H. C.

1992-01-01

Problems associated with the numerical computation of highly nonlinear equations in computational fluid dynamics are set forth and analyzed in terms of the potential ranges of spurious behaviors. A reaction-convection equation with a nonlinear source term is employed to evaluate the effects related to spatial and temporal discretizations. The discretization of the source term is described according to several methods, and the various techniques are shown to have a significant effect on the stability of the spurious solutions. Traditional linearized stability analyses cannot provide the level of confidence required for accurate fluid dynamics computations, and the incorporation of nonlinear analysis is proposed. Nonlinear analysis based on nonlinear dynamical systems complements the conventional linear approach and is valuable in the analysis of hypersonic aerodynamics and combustion phenomena.
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.
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.
Large optical nonlinearity of ITO nanorods for sub-picosecond all-optical modulation of the full-visible spectrum

DOE PAGES

Guo, Peijun; Schaller, Richard D.; Ocola, Leonidas E.; ...

2016-09-29

Optical nonlinearity induced by intense optical excitation of mobile electrons in metallic nanostructures can provide dynamic tuning of their electromagnetic response, which is potentially useful for all-optical information processing. Here we report on the sub-picosecond optical nonlinearity of indium tin oxide nanorod arrays (ITO-NRAs) following intraband, on-plasmon-resonance optical pumping, which enables modulation of the full-visible spectrum with large absolute change of transmission, favorable spectral tunability and beam-steering capability. We semi-quantitatively model the permittivity change, whose large amplitude stems from a significant electron redistribution under intraband pumping due to the low electron concentration. Further, we observe a transient response in themore » microsecond regime associated with the slow lattice cooling, which arises from the large aspect-ratio and low thermal conductivity of ITO-NRAs. Finally, our results demonstrate that all-optical control of the visible spectrum can be achieved by using heavily doped wide-bandgap semiconductors in their transparent regime with speed faster than that of noble metals.« less
Nonlinear software sensor for monitoring genetic regulation processes with noise and modeling errors

NASA Astrophysics Data System (ADS)

Ibarra-Junquera, V.; Torres, L. A.; Rosu, H. C.; Argüello, G.; Collado-Vides, J.

2005-07-01

Nonlinear control techniques by means of a software sensor that are commonly used in chemical engineering could be also applied to genetic regulation processes. We provide here a realistic formulation of this procedure by introducing an additive white Gaussian noise, which is usually found in experimental data. Besides, we include model errors, meaning that we assume we do not know the nonlinear regulation function of the process. In order to illustrate this procedure, we employ the Goodwin dynamics of the concentrations [B. C. Goodwin, Temporal Oscillations in Cells (Academic, New York, 1963)] in the simple form recently applied to single gene systems and some operon cases [H. De Jong, J. Comput. Biol. 9, 67 (2002)], which involves the dynamics of the mRNA, given protein and metabolite concentrations. Further, we present results for a three gene case in coregulated sets of transcription units as they occur in prokaryotes. However, instead of considering their full dynamics, we use only the data of the metabolites and a designed software sensor. We also show, more generally, that it is possible to rebuild the complete set of nonmeasured concentrations despite the uncertainties in the regulation function or, even more, in the case of not knowing the mRNA dynamics. In addition, the rebuilding of concentrations is not affected by the perturbation due to the additive white Gaussian noise and also we managed to filter the noisy output of the biological system.
Nonlinear optics of fibre event horizons.

PubMed

Webb, Karen E; Erkintalo, Miro; Xu, Yiqing; Broderick, Neil G R; Dudley, John M; Genty, Goëry; Murdoch, Stuart G

2014-09-17

The nonlinear interaction of light in an optical fibre can mimic the physics at an event horizon. This analogue arises when a weak probe wave is unable to pass through an intense soliton, despite propagating at a different velocity. To date, these dynamics have been described in the time domain in terms of a soliton-induced refractive index barrier that modifies the velocity of the probe. Here we complete the physical description of fibre-optic event horizons by presenting a full frequency-domain description in terms of cascaded four-wave mixing between discrete single-frequency fields, and experimentally demonstrate signature frequency shifts using continuous wave lasers. Our description is confirmed by the remarkable agreement with experiments performed in the continuum limit, reached using ultrafast lasers. We anticipate that clarifying the description of fibre event horizons will significantly impact on the description of horizon dynamics and soliton interactions in photonics and other systems.
The formation of blobs from a pure interchange process

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

Zhu, P., E-mail: pzhu@ustc.edu.cn; Department of Engineering Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706; Sovinec, C. R.

2015-02-15

In this work, we focus on examining a pure interchange process in a shear-less slab configuration as a prototype mechanism for blob formation. We employ full magnetohydrodynamic simulations to demonstrate that the blob-like structures can emerge through the nonlinear development of a pure interchange instability originating from a pedestal-like transition region. In the early nonlinear stage, filamentary structures develop and extend in the direction of the effective gravity. The blob-like structures appear when the radially extending filaments break off and disconnect from the core plasma. The morphology and the dynamics of these filaments and blobs vary dramatically with a sensitivemore » dependence on the dissipation mechanisms in the system and the initial perturbation. Despite the complexity in morphology and dynamics, the nature of the entire blob formation process in the shear-less slab configuration remains strictly interchange without involving any change in magnetic topology.« less
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.
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.
Assessment of linear and nonlinear/complex heartbeat dynamics in subclinical depression (dysphoria).

PubMed

Greco, Alberto; Messerotti Benvenuti, Simone; Gentili, Claudio; Palomba, Daniela; Scilingo, Enzo Pasquale; Valenza, Gaetano

2018-03-29

Depression is one of the leading causes of disability worldwide. Most previous studies have focused on major depression, and studies on subclinical depression, such as those on so-called dysphoria, have been overlooked. Indeed, dysphoria is associated with a high prevalence of somatic disorders, and a reduction of quality of life and life expectancy. In current clinical practice, dysphoria is assessed using psychometric questionnaires and structured interviews only, without taking into account objective pathophysiological indices. To address this problem, in this study we investigated heartbeat linear and nonlinear dynamics to derive objective autonomic nervous system biomarkers of dysphoria. Sixty undergraduate students participated in the study: according to clinical evaluation, 24 of them were dysphoric. Extensive group-wise statistics was performed to characterize the pathological and control groups. Moreover, a recursive feature elimination algorithm based on a K-NN classifier was carried out for the automatic recognition of dysphoria at a single-subject level. The results showed that the most significant group-wise differences referred to increased heartbeat complexity (particularly for fractal dimension, sample entropy and recurrence plot analysis) with regards to the healthy controls, confirming dysfunctional nonlinear sympatho-vagal dynamics in mood disorders. Furthermore, a balanced accuracy of 79.17% was achieved in automatically distinguishing dysphoric patients from controls, with the most informative power attributed to nonlinear, spectral and polyspectral quantifiers of cardiovascular variability. This study experimentally supports the assessment of dysphoria as a defined clinical condition with specific characteristics which are different both from healthy, fully euthymic controls and from full-blown major depression.
DOE Office of Scientific and Technical Information (OSTI.GOV)

Kuzmina, L.K.

The research deals with different aspects of mathematical modelling and the analysis of complex dynamic non-linear systems as a consequence of applied problems in mechanics (in particular those for gyrosystems, for stabilization and orientation systems, control systems of movable objects, including the aviation and aerospace systems) Non-linearity, multi-connectedness and high dimensionness of dynamical problems, that occur at the initial full statement lead to the need of the problem narrowing, and of the decomposition of the full model, but with safe-keeping of main properties and of qualitative equivalence. The elaboration of regular methods for modelling problems in dynamics, the generalization ofmore » reduction principle are the main aims of the investigations. Here, uniform methodology, based on Lyapunov`s methods, founded by N.G.Ohetayev, is developed. The objects of the investigations are considered with exclusive positions, as systems of singularly perturbed class, treated as ones with singular parametrical perturbations. It is the natural extension of the statements of N.G.Chetayev and P.A.Kuzmin for parametrical stability. In paper the systematical procedures for construction of correct simplified models (comparison ones) are developed, the validity conditions of the transition are determined the appraisals are received, the regular algorithms of engineering level are obtained. Applicabilitelly to the stabilization and orientation systems with the gyroscopic controlling subsystems, these methods enable to build the hierarchical sequence of admissible simplified models; to determine the conditions of their correctness.« less
Full-motion video analysis for improved gender classification

NASA Astrophysics Data System (ADS)

Flora, Jeffrey B.; Lochtefeld, Darrell F.; Iftekharuddin, Khan M.

2014-06-01

The ability of computer systems to perform gender classification using the dynamic motion of the human subject has important applications in medicine, human factors, and human-computer interface systems. Previous works in motion analysis have used data from sensors (including gyroscopes, accelerometers, and force plates), radar signatures, and video. However, full-motion video, motion capture, range data provides a higher resolution time and spatial dataset for the analysis of dynamic motion. Works using motion capture data have been limited by small datasets in a controlled environment. In this paper, we explore machine learning techniques to a new dataset that has a larger number of subjects. Additionally, these subjects move unrestricted through a capture volume, representing a more realistic, less controlled environment. We conclude that existing linear classification methods are insufficient for the gender classification for larger dataset captured in relatively uncontrolled environment. A method based on a nonlinear support vector machine classifier is proposed to obtain gender classification for the larger dataset. In experimental testing with a dataset consisting of 98 trials (49 subjects, 2 trials per subject), classification rates using leave-one-out cross-validation are improved from 73% using linear discriminant analysis to 88% using the nonlinear support vector machine classifier.
Review and evaluation of recent developments in melic inlet dynamic flow distortion prediction and computer program documentation and user's manual estimating maximum instantaneous inlet flow distortion from steady-state total pressure measurements with full, limited, or no dynamic data

NASA Technical Reports Server (NTRS)

Schweikhard, W. G.; Dennon, S. R.

1986-01-01

A review of the Melick method of inlet flow dynamic distortion prediction by statistical means is provided. These developments include the general Melick approach with full dynamic measurements, a limited dynamic measurement approach, and a turbulence modelling approach which requires no dynamic rms pressure fluctuation measurements. These modifications are evaluated by comparing predicted and measured peak instantaneous distortion levels from provisional inlet data sets. A nonlinear mean-line following vortex model is proposed and evaluated as a potential criterion for improving the peak instantaneous distortion map generated from the conventional linear vortex of the Melick method. The model is simplified to a series of linear vortex segments which lay along the mean line. Maps generated with this new approach are compared with conventionally generated maps, as well as measured peak instantaneous maps. Inlet data sets include subsonic, transonic, and supersonic inlets under various flight conditions.
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.
Distributed Coordinated Control of Large-Scale Nonlinear Networks

DOE PAGES

Kundu, Soumya; Anghel, Marian

2015-11-08

We provide a distributed coordinated approach to the stability analysis and control design of largescale nonlinear dynamical systems by using a vector Lyapunov functions approach. In this formulation the large-scale system is decomposed into a network of interacting subsystems and the stability of the system is analyzed through a comparison system. However finding such comparison system is not trivial. In this work, we propose a sum-of-squares based completely decentralized approach for computing the comparison systems for networks of nonlinear systems. Moreover, based on the comparison systems, we introduce a distributed optimal control strategy in which the individual subsystems (agents) coordinatemore » with their immediate neighbors to design local control policies that can exponentially stabilize the full system under initial disturbances.We illustrate the control algorithm on a network of interacting Van der Pol systems.« less
Discrete approach to stochastic parametrization and dimension reduction in nonlinear dynamics.

PubMed

Chorin, Alexandre J; Lu, Fei

2015-08-11

Many physical systems are described by nonlinear differential equations that are too complicated to solve in full. A natural way to proceed is to divide the variables into those that are of direct interest and those that are not, formulate solvable approximate equations for the variables of greater interest, and use data and statistical methods to account for the impact of the other variables. In the present paper we consider time-dependent problems and introduce a fully discrete solution method, which simplifies both the analysis of the data and the numerical algorithms. The resulting time series are identified by a NARMAX (nonlinear autoregression moving average with exogenous input) representation familiar from engineering practice. The connections with the Mori-Zwanzig formalism of statistical physics are discussed, as well as an application to the Lorenz 96 system.
A Nonlinear Interactions Approximation Model for Large-Eddy Simulation

NASA Astrophysics Data System (ADS)

Haliloglu, Mehmet U.; Akhavan, Rayhaneh

2003-11-01

A new approach to LES modelling is proposed based on direct approximation of the nonlinear terms \\overlineu_iuj in the filtered Navier-Stokes equations, instead of the subgrid-scale stress, τ_ij. The proposed model, which we call the Nonlinear Interactions Approximation (NIA) model, uses graded filters and deconvolution to parameterize the local interactions across the LES cutoff, and a Smagorinsky eddy viscosity term to parameterize the distant interactions. A dynamic procedure is used to determine the unknown eddy viscosity coefficient, rendering the model free of adjustable parameters. The proposed NIA model has been applied to LES of turbulent channel flows at Re_τ ≈ 210 and Re_τ ≈ 570. The results show good agreement with DNS not only for the mean and resolved second-order turbulence statistics but also for the full (resolved plus subgrid) Reynolds stress and turbulence intensities.
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.
Why the soliton wavelet transform is useful for nonlinear dynamic phenomena

NASA Astrophysics Data System (ADS)

Szu, Harold H.

1992-10-01

If signal analyses were perfect without noise and clutters, then any transform can be equally chosen to represent the signal without any loss of information. However, if the analysis using Fourier transform (FT) happens to be a nonlinear dynamic phenomenon, the effect of nonlinearity must be postponed until a later time when a complicated mode-mode coupling is attempted without the assurance of any convergence. Alternatively, there exists a new paradigm of linear transforms called wavelet transform (WT) developed for French oil explorations. Such a WT enjoys the linear superposition principle, the computational efficiency, and the signal/noise ratio enhancement for a nonsinusoidal and nonstationary signal. Our extensions to a dynamic WT and furthermore to an adaptive WT are possible due to the fact that there exists a large set of square-integrable functions that are special solutions of the nonlinear dynamic medium and could be adopted for the WT. In order to analyze nonlinear dynamics phenomena in ocean, we are naturally led to the construction of a soliton mother wavelet. This common sense of 'pay the nonlinear price now and enjoy the linearity later' is certainly useful to probe any nonlinear dynamics. Research directions in wavelets, such as adaptivity, and neural network implementations are indicated, e.g., tailoring an active sonar profile for explorations.
Geometrically induced nonlinear dynamics in one-dimensional lattices

NASA Astrophysics Data System (ADS)

Hamilton, Merle D.; de Alcantara Bonfim, O. F.

2006-03-01

We present a lattice model consisting of a single one-dimensional chain, where the masses are interconnected by linear springs and allowed to move in a horizontal direction only, as in a monorail. In the transverse direction each mass is also attached to two other linear springs, one on each side of the mass. The ends of these springs are kept at fixed positions. The nonlinearity in the model arises from the geometric constraints imposed on the motion of the masses, as well as from the configuration of the springs, where in the transverse direction the springs are either in the extended or compressed state depending on the position of the masses. Under these conditions we show that solitary waves are present in the system. In the long wavelength limit an analytic solution for these nonlinear waves is found. Numerical integrations of the equations of motion in the full system are also performed to analyze the conditions for the existence and stability of the nonlinear waves.

Material Model Evaluation of a Composite Honeycomb Energy Absorber

NASA Technical Reports Server (NTRS)

Jackson, Karen E.; Annett, Martin S.; Fasanella, Edwin L.; Polanco, Michael A.

2012-01-01

A study was conducted to evaluate four different material models in predicting the dynamic crushing response of solid-element-based models of a composite honeycomb energy absorber, designated the Deployable Energy Absorber (DEA). Dynamic crush tests of three DEA components were simulated using the nonlinear, explicit transient dynamic code, LS-DYNA . In addition, a full-scale crash test of an MD-500 helicopter, retrofitted with DEA blocks, was simulated. The four material models used to represent the DEA included: *MAT_CRUSHABLE_FOAM (Mat 63), *MAT_HONEYCOMB (Mat 26), *MAT_SIMPLIFIED_RUBBER/FOAM (Mat 181), and *MAT_TRANSVERSELY_ANISOTROPIC_CRUSHABLE_FOAM (Mat 142). Test-analysis calibration metrics included simple percentage error comparisons of initial peak acceleration, sustained crush stress, and peak compaction acceleration of the DEA components. In addition, the Roadside Safety Verification and Validation Program (RSVVP) was used to assess similarities and differences between the experimental and analytical curves for the full-scale crash test.
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.
Nonlinear modeling and dynamic analysis of a hydro-turbine governing system in the process of sudden load increase transient

NASA Astrophysics Data System (ADS)

Li, Huanhuan; Chen, Diyi; Zhang, Hao; Wang, Feifei; Ba, Duoduo

2016-12-01

In order to study the nonlinear dynamic behaviors of a hydro-turbine governing system in the process of sudden load increase transient, we establish a novel nonlinear dynamic model of the hydro-turbine governing system which considers the elastic water-hammer model of the penstock and the second-order model of the generator. The six nonlinear dynamic transfer coefficients of the hydro-turbine are innovatively proposed by utilizing internal characteristics and analyzing the change laws of the characteristic parameters of the hydro-turbine governing system. Moreover, from the point of view of engineering, the nonlinear dynamic behaviors of the above system are exhaustively investigated based on bifurcation diagrams and time waveforms. More importantly, all of the above analyses supply theoretical basis for allowing a hydropower station to maintain a stable operation in the process of sudden load increase transient.
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.
Roll and pitch independently tuned interconnected suspension: modelling and dynamic analysis

NASA Astrophysics Data System (ADS)

Xu, Guangzhong; Zhang, Nong; Roser, Holger M.

2015-12-01

In this paper, a roll and pitch independently tuned hydraulically interconnected passive suspension is presented. Due to decoupling of vibration modes and the improved lateral and longitudinal stability, the stiffness of individual suspension spring can be reduced for improving ride comfort and road grip. A generalised 14 degree-of-freedom nonlinear vehicle model with anti-roll bars is established to investigate the vehicle ride and handling dynamic responses. The nonlinear fluidic model of the hydraulically interconnected suspension is developed and integrated with the full vehicle model to investigate the anti-roll and anti-pitch characteristics. Time domain analysis of the vehicle model with the proposed suspension is conducted under different road excitations and steering/braking manoeuvres. The dynamic responses are compared with conventional suspensions to demonstrate the potential of enhanced ride and handling performance. The results illustrate the model-decoupling property of the hydraulically interconnected system. The anti-roll and anti-pitch performance could be tuned independently by the interconnected systems. With the improved anti-roll and anti-pitch characteristics, the bounce stiffness and ride damping can be optimised for better ride comfort and tyre grip.
Computation of a controlled store separation from a cavity

NASA Technical Reports Server (NTRS)

Atwood, Christopher A.

1993-01-01

Coupling of the Reynolds-averaged Navier-Stokes equations, rigid-body dynamics, and a pitch attitude control law is demonstrated in two- and three-dimensions. The application problem was the separation of a canard-controlled store from an open-flow rectangular cavity bay at a freestream Mach number of 1.2. The transient flowfield was computed using a diagonal scheme in an overset mesh framework, with the resultant aerodynamic loads used as the forcing functions in the nonlinear dynamics equations. The proportional and rate gyro sensitivities were computed a priori using pole placement techniques for the linearized dynamical equations. These fixed gain values were used in the controller for the nonlinear simulation. Reasonable comparison between the full and linearized equations for a perturbed two-dimensional missile was found. Also in two-dimensions, a controlled store was found to possess improved separation characteristics over a canard-fixed store. In three-dimensions, trajectory comparisons with wind-tunnel data for the canard-fixed case will be made. In addition, it will be determined if a canard-controlled store is an effective means of improving cavity store separation characteristics.
Localized solutions of Lugiato-Lefever equations with focused pump.

PubMed

Cardoso, Wesley B; Salasnich, Luca; Malomed, Boris A

2017-12-04

Lugiato-Lefever (LL) equations in one and two dimensions (1D and 2D) accurately describe the dynamics of optical fields in pumped lossy cavities with the intrinsic Kerr nonlinearity. The external pump is usually assumed to be uniform, but it can be made tightly focused too-in particular, for building small pixels. We obtain solutions of the LL equations, with both the focusing and defocusing intrinsic nonlinearity, for 1D and 2D confined modes supported by the localized pump. In the 1D setting, we first develop a simple perturbation theory, based in the sech ansatz, in the case of weak pump and loss. Then, a family of exact analytical solutions for spatially confined modes is produced for the pump focused in the form of a delta-function, with a nonlinear loss (two-photon absorption) added to the LL model. Numerical findings demonstrate that these exact solutions are stable, both dynamically and structurally (the latter means that stable numerical solutions close to the exact ones are found when a specific condition, necessary for the existence of the analytical solution, does not hold). In 2D, vast families of stable confined modes are produced by means of a variational approximation and full numerical simulations.
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
Complexity analyses show two distinct types of nonlinear dynamics in short heart period variability recordings

PubMed Central

Porta, Alberto; Bari, Vlasta; Marchi, Andrea; De Maria, Beatrice; Cysarz, Dirk; Van Leeuwen, Peter; Takahashi, Anielle C. M.; Catai, Aparecida M.; Gnecchi-Ruscone, Tomaso

2015-01-01

Two diverse complexity metrics quantifying time irreversibility and local prediction, in connection with a surrogate data approach, were utilized to detect nonlinear dynamics in short heart period (HP) variability series recorded in fetuses, as a function of the gestational period, and in healthy humans, as a function of the magnitude of the orthostatic challenge. The metrics indicated the presence of two distinct types of nonlinear HP dynamics characterized by diverse ranges of time scales. These findings stress the need to render more specific the analysis of nonlinear components of HP dynamics by accounting for different temporal scales. PMID:25806002
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.
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.
The role of model dynamics in ensemble Kalman filter performance for chaotic systems

USGS Publications Warehouse

Ng, G.-H.C.; McLaughlin, D.; Entekhabi, D.; Ahanin, A.

2011-01-01

The ensemble Kalman filter (EnKF) is susceptible to losing track of observations, or 'diverging', when applied to large chaotic systems such as atmospheric and ocean models. Past studies have demonstrated the adverse impact of sampling error during the filter's update step. We examine how system dynamics affect EnKF performance, and whether the absence of certain dynamic features in the ensemble may lead to divergence. The EnKF is applied to a simple chaotic model, and ensembles are checked against singular vectors of the tangent linear model, corresponding to short-term growth and Lyapunov vectors, corresponding to long-term growth. Results show that the ensemble strongly aligns itself with the subspace spanned by unstable Lyapunov vectors. Furthermore, the filter avoids divergence only if the full linearized long-term unstable subspace is spanned. However, short-term dynamics also become important as non-linearity in the system increases. Non-linear movement prevents errors in the long-term stable subspace from decaying indefinitely. If these errors then undergo linear intermittent growth, a small ensemble may fail to properly represent all important modes, causing filter divergence. A combination of long and short-term growth dynamics are thus critical to EnKF performance. These findings can help in developing practical robust filters based on model dynamics. ?? 2011 The Authors Tellus A ?? 2011 John Wiley & Sons A/S.
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.

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.
Multidirectional In Vivo Characterization of Skin Using Wiener Nonlinear Stochastic System Identification Techniques.

PubMed

Parker, Matthew D; Jones, Lynette A; Hunter, Ian W; Taberner, A J; Nash, M P; Nielsen, P M F

2017-01-01

A triaxial force-sensitive microrobot was developed to dynamically perturb skin in multiple deformation modes, in vivo. Wiener static nonlinear identification was used to extract the linear dynamics and static nonlinearity of the force-displacement behavior of skin. Stochastic input forces were applied to the volar forearm and thenar eminence of the hand, producing probe tip perturbations in indentation and tangential extension. Wiener static nonlinear approaches reproduced the resulting displacements with variances accounted for (VAF) ranging 94-97%, indicating a good fit to the data. These approaches provided VAF improvements of 0.1-3.4% over linear models. Thenar eminence stiffness measures were approximately twice those measured on the forearm. Damping was shown to be significantly higher on the palm, whereas the perturbed mass typically was lower. Coefficients of variation (CVs) for nonlinear parameters were assessed within and across individuals. Individual CVs ranged from 2% to 11% for indentation and from 2% to 19% for extension. Stochastic perturbations with incrementally increasing mean amplitudes were applied to the same test areas. Differences between full-scale and incremental reduced-scale perturbations were investigated. Different incremental preloading schemes were investigated. However, no significant difference in parameters was found between different incremental preloading schemes. Incremental schemes provided depth-dependent estimates of stiffness and damping, ranging from 300 N/m and 2 Ns/m, respectively, at the surface to 5 kN/m and 50 Ns/m at greater depths. The device and techniques used in this research have potential applications in areas, such as evaluating skincare products, assessing skin hydration, or analyzing wound healing.
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.
EKF-Based Enhanced Performance Controller Design for Nonlinear Stochastic Systems

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

Zhou, Yuyang; Zhang, Qichun; Wang, Hong

In this paper, a novel control algorithm is presented to enhance the performance of tracking property for a class of non-linear dynamic stochastic systems with unmeasurable variables. To minimize the entropy of tracking errors without changing the existing closed loop with PI controller, the enhanced performance loop is constructed based on the state estimation by extended Kalman Filter and the new controller is designed by full state feedback following this presented control algorithm. Besides, the conditions are obtained for the stability analysis in the mean square sense. In the end, the comparative simulation results are given to illustrate the effectivenessmore » of proposed control algorithm.« less
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.
Numerical solution of a non-linear conservation law applicable to the interior dynamics of partially molten planets

NASA Astrophysics Data System (ADS)

Bower, Dan J.; Sanan, Patrick; Wolf, Aaron S.

2018-01-01

The energy balance of a partially molten rocky planet can be expressed as a non-linear diffusion equation using mixing length theory to quantify heat transport by both convection and mixing of the melt and solid phases. Crucially, in this formulation the effective or eddy diffusivity depends on the entropy gradient, ∂S / ∂r , as well as entropy itself. First we present a simplified model with semi-analytical solutions that highlights the large dynamic range of ∂S / ∂r -around 12 orders of magnitude-for physically-relevant parameters. It also elucidates the thermal structure of a magma ocean during the earliest stage of crystal formation. This motivates the development of a simple yet stable numerical scheme able to capture the large dynamic range of ∂S / ∂r and hence provide a flexible and robust method for time-integrating the energy equation. Using insight gained from the simplified model, we consider a full model, which includes energy fluxes associated with convection, mixing, gravitational separation, and conduction that all depend on the thermophysical properties of the melt and solid phases. This model is discretised and evolved by applying the finite volume method (FVM), allowing for extended precision calculations and using ∂S / ∂r as the solution variable. The FVM is well-suited to this problem since it is naturally energy conserving, flexible, and intuitive to incorporate arbitrary non-linear fluxes that rely on lookup data. Special attention is given to the numerically challenging scenario in which crystals first form in the centre of a magma ocean. The computational framework we devise is immediately applicable to modelling high melt fraction phenomena in Earth and planetary science research. Furthermore, it provides a template for solving similar non-linear diffusion equations that arise in other science and engineering disciplines, particularly for non-linear functional forms of the diffusion coefficient.
Linear State-Space Representation of the Dynamics of Relative Motion, Based on Restricted Three Body Dynamics

NASA Technical Reports Server (NTRS)

Luquette,Richard J.; Sanner, Robert M.

2004-01-01

Precision Formation Flying is an enabling technology for a variety of proposed space-based observatories, including the Micro-Arcsecond X-ray Imaging Mission (MAXIM) , the associated MAXIM pathfinder mission, Stellar Imager (SI) and the Terrestrial Planet Finder (TPF). An essential element of the technology is the control algorithm, requiring a clear understanding of the dynamics of relative motion. This paper examines the dynamics of relative motion in the context of the Restricted Three Body Problem (RTBP). The natural dynamics of relative motion are presented in their full nonlinear form. Motivated by the desire to apply linear control methods, the dynamics equations are linearized and presented in state-space form. The stability properties are explored for regions in proximity to each of the libration points in the Earth/Moon - Sun rotating frame. The dynamics of relative motion are presented in both the inertial and rotating coordinate frames.
Assessment of current state of the art in modeling techniques and analysis methods for large space structures

NASA Technical Reports Server (NTRS)

Noor, A. K.

1983-01-01

Advances in continuum modeling, progress in reduction methods, and analysis and modeling needs for large space structures are covered with specific attention given to repetitive lattice trusses. As far as continuum modeling is concerned, an effective and verified analysis capability exists for linear thermoelastic stress, birfurcation buckling, and free vibration problems of repetitive lattices. However, application of continuum modeling to nonlinear analysis needs more development. Reduction methods are very effective for bifurcation buckling and static (steady-state) nonlinear analysis. However, more work is needed to realize their full potential for nonlinear dynamic and time-dependent problems. As far as analysis and modeling needs are concerned, three areas are identified: loads determination, modeling and nonclassical behavior characteristics, and computational algorithms. The impact of new advances in computer hardware, software, integrated analysis, CAD/CAM stems, and materials technology is also discussed.
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.
Cosmic bubble and domain wall instabilities II: fracturing of colliding walls

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

Braden, Jonathan; Bond, J. Richard; Mersini-Houghton, Laura, E-mail: j.braden@ucl.ac.uk, E-mail: bond@cita.utoronto.ca, E-mail: mersini@physics.unc.edu

2015-08-01

We study collisions between nearly planar domain walls including the effects of small initial nonplanar fluctuations. These perturbations represent the small fluctuations that must exist in a quantum treatment of the problem. In a previous paper, we demonstrated that at the linear level a subset of these fluctuations experience parametric amplification as a result of their coupling to the planar symmetric background. Here we study the full three-dimensional nonlinear dynamics using lattice simulations, including both the early time regime when the fluctuations are well described by linear perturbation theory as well as the subsequent stage of fully nonlinear evolution. Wemore » find that the nonplanar fluctuations have a dramatic effect on the overall evolution of the system. Specifically, once these fluctuations begin to interact nonlinearly the split into a planar symmetric part of the field and the nonplanar fluctuations loses its utility. At this point the colliding domain walls dissolve, with the endpoint of this being the creation of a population of oscillons in the collision region. The original (nearly) planar symmetry has been completely destroyed at this point and an accurate study of the system requires the full three-dimensional simulation.« less
Cosmic bubble and domain wall instabilities II: fracturing of colliding walls

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

Braden, Jonathan; Department of Physics, University of Toronto,60 St. George Street, Toronto, ON, M5S 3H8; Department of Physics and Astronomy, University College London,Gower Street, London, WC1E 6BT

2015-08-26

We study collisions between nearly planar domain walls including the effects of small initial nonplanar fluctuations. These perturbations represent the small fluctuations that must exist in a quantum treatment of the problem. In a previous paper, we demonstrated that at the linear level a subset of these fluctuations experience parametric amplification as a result of their coupling to the planar symmetric background. Here we study the full three-dimensional nonlinear dynamics using lattice simulations, including both the early time regime when the fluctuations are well described by linear perturbation theory as well as the subsequent stage of fully nonlinear evolution. Wemore » find that the nonplanar fluctuations have a dramatic effect on the overall evolution of the system. Specifically, once these fluctuations begin to interact nonlinearly the split into a planar symmetric part of the field and the nonplanar fluctuations loses its utility. At this point the colliding domain walls dissolve, with the endpoint of this being the creation of a population of oscillons in the collision region. The original (nearly) planar symmetry has been completely destroyed at this point and an accurate study of the system requires the full three-dimensional simulation.« less
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.
The analysis of non-linear dynamic behavior (including snap-through) of postbuckled plates by simple analytical solution

NASA Technical Reports Server (NTRS)

Ng, C. F.

1988-01-01

Static postbuckling and nonlinear dynamic analysis of plates are usually accomplished by multimode analyses, although the methods are complicated and do not give straightforward understanding of the nonlinear behavior. Assuming single-mode transverse displacement, a simple formula is derived for the transverse load displacement relationship of a plate under in-plane compression. The formula is used to derive a simple analytical expression for the static postbuckling displacement and nonlinear dynamic responses of postbuckled plates under sinusoidal or random excitation. Regions with softening and hardening spring behavior are identified. Also, the highly nonlinear motion of snap-through and its effects on the overall dynamic response can be easily interpreted using the single-mode formula. Theoretical results are compared with experimental results obtained using a buckled aluminum panel, using discrete frequency and broadband point excitation. Some important effects of the snap-through motion on the dynamic response of the postbuckled plates are found.
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
Chaos crisis and bistability of self-pulsing dynamics in a laser diode with phase-conjugate feedback

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

Virte, Martin; Karsaklian Dal Bosco, Andreas; Wolfersberger, Delphine

2011-10-15

A laser diode subject to a phase-conjugate optical feedback can exhibit rich nonlinear dynamics and chaos. We report here on two bifurcation mechanisms that appear when increasing the amount of light being fed back to the laser. First, we report on a full suppression of chaos from a crisis induced by a saddle-node bifurcation on self-pulsing, so-called external-cavity-mode solutions (ECMs). Second, the feedback-dependent torus and saddle-node bifurcations on ECMs may be responsible for large regions of bistability between ECMs of different and high (beyond gigahertz) frequencies.
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).
Auditory Power-Law Activation Avalanches Exhibit a Fundamental Computational Ground State

NASA Astrophysics Data System (ADS)

Stoop, Ruedi; Gomez, Florian

2016-07-01

The cochlea provides a biological information-processing paradigm that we are only beginning to understand in its full complexity. Our work reveals an interacting network of strongly nonlinear dynamical nodes, on which even a simple sound input triggers subnetworks of activated elements that follow power-law size statistics ("avalanches"). From dynamical systems theory, power-law size distributions relate to a fundamental ground state of biological information processing. Learning destroys these power laws. These results strongly modify the models of mammalian sound processing and provide a novel methodological perspective for understanding how the brain processes information.
Dispersive shock waves in Bose-Einstein condensates and nonlinear nano-oscillators in ferromagnetic thin films

NASA Astrophysics Data System (ADS)

Hoefer, Mark A.

This thesis examines nonlinear wave phenomena, in two physical systems: a Bose-Einstein condensate (BEC) and thin film ferromagnets where the magnetization dynamics are excited by the spin momentum transfer (SMT) effect. In the first system, shock waves generated by steep gradients in the BEC wavefunction are shown to be of the disperse type. Asymptotic and averaging methods are used to determine shock speeds and structure in one spatial dimension. These results are compared with multidimensional numerical simulations and experiment showing good, qualitative agreement. In the second system, a model of magnetization dynamics due to SMT is presented. Using this model, nonlinear oscillating modes---nano-oscillators---are found numerically and analytically using perturbative methods. These results compare well with experiment. A Bose-Einstein condensate (BEC) is a quantum fluid that gives rise to interesting shock wave nonlinear dynamics. Experiments depict a BEC that exhibits behavior similar to that of a shock wave in a compressible gas, e.g. traveling fronts with steep gradients. However, the governing Gross-Pitaevskii (GP) equation that describes the mean field of a BEC admits no dissipation hence classical dissipative shock solutions do not explain the phenomena. Instead, wave dynamics with small dispersion is considered and it is shown that this provides a mechanism for the generation of a dispersive shock wave (DSW). Computations with the GP equation are compared to experiment with excellent agreement. A comparison between a canonical 1D dissipative and dispersive shock problem shows significant differences in shock structure and shock front speed. Numerical results associated with laboratory experiments show that three and two-dimensional approximations are in excellent agreement and one dimensional approximations are in qualitative agreement. The interaction of two DSWs is investigated analytically and numerically. Using one dimensional DSW theory it is argued that the experimentally observed blast waves may be viewed as dispersive shock waves. A nonlinear mathematical model of spin-wave excitation using a point contact in a thin ferromagnetic film is introduced. This work incorporates a recently proposed spin-torque contribution to classical magnetodynamic theory with a variable coefficient terra in the magnetic torque equation. Large-amplitude magnetic solitary waves are computed, which help explain recent spin-torque experiments. Numerical simulations of the full nonlinear model predict excitation frequencies in excess of 0.2 THz for contact diameters smaller than 6 nm. Simulations also predict a saturation and red shift of the frequency at currents large enough to invert the magnetization tinder the point contact. In the weak nonlinear limit, the theory is approximated by a cubic complex Ginzburg-Landau type equation. The mode's nonlinear frequency shift is found by use of perturbation techniques, whose results agree with those of direct numerical simulations.
Nonlinear soil parameter effects on dynamic embedment of offshore pipeline on soft clay

NASA Astrophysics Data System (ADS)

Yu, Su Young; Choi, Han Suk; Lee, Seung Keon; Park, Kyu-Sik; Kim, Do Kyun

2015-06-01

In this paper, the effects of nonlinear soft clay on dynamic embedment of offshore pipeline were investigated. Seabed embedment by pipe-soil interactions has impacts on the structural boundary conditions for various subsea structures such as pipeline, riser, pile, and many other systems. A number of studies have been performed to estimate real soil behavior, but their estimation of seabed embedment has not been fully identified and there are still many uncertainties. In this regards, comparison of embedment between field survey and existing empirical models has been performed to identify uncertainties and investigate the effect of nonlinear soil parameter on dynamic embedment. From the comparison, it is found that the dynamic embedment with installation effects based on nonlinear soil model have an influence on seabed embedment. Therefore, the pipe embedment under dynamic condition by nonlinear parameters of soil models was investigated by Dynamic Embedment Factor (DEF) concept, which is defined as the ratio of the dynamic and static embedment of pipeline, in order to overcome the gap between field embedment and currently used empirical and numerical formula. Although DEF through various researches is suggested, its range is too wide and it does not consider dynamic laying effect. It is difficult to find critical parameters that are affecting to the embedment result. Therefore, the study on dynamic embedment factor by soft clay parameters of nonlinear soil model was conducted and the sensitivity analyses about parameters of nonlinear soil model were performed as well. The tendency on dynamic embedment factor was found by conducting numerical analyses using OrcaFlex software. It is found that DEF was influenced by shear strength gradient than other factors. The obtained results will be useful to understand the pipe embedment on soft clay seabed for applying offshore pipeline designs such as on-bottom stability and free span analyses.
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
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.
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.
Probing and exploiting the chaotic dynamics of a hydrodynamic photochemical oscillator to implement all the basic binary logic functions

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

Hayashi, Kenta; Department of Chemistry, Biology, and Biotechnology, University of Perugia, 06123 Perugia; Gotoda, Hiroshi

2016-05-15

The convective motions within a solution of a photochromic spiro-oxazine being irradiated by UV only on the bottom part of its volume, give rise to aperiodic spectrophotometric dynamics. In this paper, we study three nonlinear properties of the aperiodic time series: permutation entropy, short-term predictability and long-term unpredictability, and degree distribution of the visibility graph networks. After ascertaining the extracted chaotic features, we show how the aperiodic time series can be exploited to implement all the fundamental two-inputs binary logic functions (AND, OR, NAND, NOR, XOR, and XNOR) and some basic arithmetic operations (half-adder, full-adder, half-subtractor). This is possible duemore » to the wide range of states a nonlinear system accesses in the course of its evolution. Therefore, the solution of the convective photochemical oscillator results in hardware for chaos-computing alternative to conventional complementary metal-oxide semiconductor-based integrated circuits.« less
A Novel Interfacing Technique for Distributed Hybrid Simulations Combining EMT and Transient Stability Models

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

Shu, Dewu; Xie, Xiaorong; Jiang, Qirong

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

NASA Astrophysics Data System (ADS)

Herzallah, Randa

2010-02-01

Adaptive critic (AC) methods have common roots as generalisations of dynamic programming for neural reinforcement learning approaches. Since they approximate the dynamic programming solutions, they are potentially suitable for learning in noisy, non-linear and non-stationary environments. In this study, a novel probabilistic dual heuristic programming (DHP)-based AC controller is proposed. Distinct to current approaches, the proposed probabilistic (DHP) AC method takes uncertainties of forward model and inverse controller into consideration. Therefore, it is suitable for deterministic and stochastic control problems characterised by functional uncertainty. Theoretical development of the proposed method is validated by analytically evaluating the correct value of the cost function which satisfies the Bellman equation in a linear quadratic control problem. The target value of the probabilistic critic network is then calculated and shown to be equal to the analytically derived correct value. Full derivation of the Riccati solution for this non-standard stochastic linear quadratic control problem is also provided. Moreover, the performance of the proposed probabilistic controller is demonstrated on linear and non-linear control examples.
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 Dynamic Characteristics of Oil-in-Water Emulsions

NASA Astrophysics Data System (ADS)

Yin, Zhaoqi; Han, Yunfeng; Ren, Yingyu; Yang, Qiuyi; Jin, Ningde

2016-08-01

In this article, the nonlinear dynamic characteristics of oil-in-water emulsions under the addition of surfactant were experimentally investigated. Firstly, based on the vertical upward oil-water two-phase flow experiment in 20 mm inner diameter (ID) testing pipe, dynamic response signals of oil-in-water emulsions were recorded using vertical multiple electrode array (VMEA) sensor. Afterwards, the recurrence plot (RP) algorithm and multi-scale weighted complexity entropy causality plane (MS-WCECP) were employed to analyse the nonlinear characteristics of the signals. The results show that the certainty is decreasing and the randomness is increasing with the increment of surfactant concentration. This article provides a novel method for revealing the nonlinear dynamic characteristics, complexity, and randomness of oil-in-water emulsions with experimental measurement signals.
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.
Continuum kinetic methods for analyzing wave physics and distribution function dynamics in the turbulence dissipation challenge

NASA Astrophysics Data System (ADS)

Juno, J.; Hakim, A.; TenBarge, J.; Dorland, W.

2015-12-01

We present for the first time results for the turbulence dissipation challenge, with specific focus on the linear wave portion of the challenge, using a variety of continuum kinetic models: hybrid Vlasov-Maxwell, gyrokinetic, and full Vlasov-Maxwell. As one of the goals of the wave problem as it is outlined is to identify how well various models capture linear physics, we compare our results to linear Vlasov and gyrokinetic theory. Preliminary gyrokinetic results match linear theory extremely well due to the geometry of the problem, which eliminates the dominant nonlinearity. With the non-reduced models, we explore how the subdominant nonlinearities manifest and affect the evolution of the turbulence and the energy budget. We also take advantage of employing continuum methods to study the dynamics of the distribution function, with particular emphasis on the full Vlasov results where a basic collision operator has been implemented. As the community prepares for the next stage of the turbulence dissipation challenge, where we hope to do large 3D simulations to inform the next generation of observational missions such as THOR (Turbulence Heating ObserveR), we argue for the consideration of hybrid Vlasov and full Vlasov as candidate models for these critical simulations. With the use of modern numerical algorithms, we demonstrate the competitiveness of our code with traditional particle-in-cell algorithms, with a clear plan for continued improvements and optimizations to further strengthen the code's viability as an option for the next stage of the challenge.
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
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.
Firing-rate response of linear and nonlinear integrate-and-fire neurons to modulated current-based and conductance-based synaptic drive.

PubMed

Richardson, Magnus J E

2007-08-01

Integrate-and-fire models are mainstays of the study of single-neuron response properties and emergent states of recurrent networks of spiking neurons. They also provide an analytical base for perturbative approaches that treat important biological details, such as synaptic filtering, synaptic conductance increase, and voltage-activated currents. Steady-state firing rates of both linear and nonlinear integrate-and-fire models, receiving fluctuating synaptic drive, can be calculated from the time-independent Fokker-Planck equation. The dynamic firing-rate response is less easy to extract, even at the first-order level of a weak modulation of the model parameters, but is an important determinant of neuronal response and network stability. For the linear integrate-and-fire model the response to modulations of current-based synaptic drive can be written in terms of hypergeometric functions. For the nonlinear exponential and quadratic models no such analytical forms for the response are available. Here it is demonstrated that a rather simple numerical method can be used to obtain the steady-state and dynamic response for both linear and nonlinear models to parameter modulation in the presence of current-based or conductance-based synaptic fluctuations. To complement the full numerical solution, generalized analytical forms for the high-frequency response are provided. A special case is also identified--time-constant modulation--for which the response to an arbitrarily strong modulation can be calculated exactly.
Experimental investigation of alternative transmission functions: Quantitative evidence for the importance of nonlinear transmission dynamics in host-parasite systems.

PubMed

Orlofske, Sarah A; Flaxman, Samuel M; Joseph, Maxwell B; Fenton, Andy; Melbourne, Brett A; Johnson, Pieter T J

2018-05-01

Understanding pathogen transmission is crucial for predicting and managing disease. Nonetheless, experimental comparisons of alternative functional forms of transmission remain rare, and those experiments that are conducted are often not designed to test the full range of possible forms. To differentiate among 10 candidate transmission functions, we used a novel experimental design in which we independently varied four factors-duration of exposure, numbers of parasites, numbers of hosts and parasite density-in laboratory infection experiments. We used interactions between amphibian hosts and trematode parasites as a model system and all candidate models incorporated parasite depletion. An additional manipulation involving anaesthesia addressed the effects of host behaviour on transmission form. Across all experiments, nonlinear transmission forms involving either a power law or a negative binomial function were the best-fitting models and consistently outperformed the linear density-dependent and density-independent functions. By testing previously published data for two other host-macroparasite systems, we also found support for the same nonlinear transmission forms. Although manipulations of parasite density are common in transmission studies, the comprehensive set of variables tested in our experiments revealed that variation in density alone was least likely to differentiate among competing transmission functions. Across host-pathogen systems, nonlinear functions may often more accurately represent transmission dynamics and thus provide more realistic predictions for infection. © 2017 The Authors. Journal of Animal Ecology published by John Wiley & Sons Ltd on behalf of British Ecological Society.
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
The influence of surface roughness on the contact stiffness and the contact filter effect in nonlinear wheel-track interaction

NASA Astrophysics Data System (ADS)

Lundberg, Oskar E.; Nordborg, Anders; Lopez Arteaga, Ines

2016-03-01

A state-dependent contact model including nonlinear contact stiffness and nonlinear contact filtering is used to calculate contact forces and rail vibrations with a time-domain wheel-track interaction model. In the proposed method, the full three-dimensional contact geometry is reduced to a point contact in order to lower the computational cost and to reduce the amount of required input roughness-data. Green's functions including the linear dynamics of the wheel and the track are coupled with a point contact model, leading to a numerically efficient model for the wheel-track interaction. Nonlinear effects due to the shape and roughness of the wheel and the rail surfaces are included in the point contact model by pre-calculation of functions for the contact stiffness and contact filters. Numerical results are compared to field measurements of rail vibrations for passenger trains running at 200 kph on a ballast track. Moreover, the influence of vehicle pre-load and different degrees of roughness excitation on the resulting wheel-track interaction is studied by means of numerical predictions.

Linking structure and activity in nonlinear spiking networks

PubMed Central

Josić, Krešimir; Shea-Brown, Eric

2017-01-01

Recent experimental advances are producing an avalanche of data on both neural connectivity and neural activity. To take full advantage of these two emerging datasets we need a framework that links them, revealing how collective neural activity arises from the structure of neural connectivity and intrinsic neural dynamics. This problem of structure-driven activity has drawn major interest in computational neuroscience. Existing methods for relating activity and architecture in spiking networks rely on linearizing activity around a central operating point and thus fail to capture the nonlinear responses of individual neurons that are the hallmark of neural information processing. Here, we overcome this limitation and present a new relationship between connectivity and activity in networks of nonlinear spiking neurons by developing a diagrammatic fluctuation expansion based on statistical field theory. We explicitly show how recurrent network structure produces pairwise and higher-order correlated activity, and how nonlinearities impact the networks’ spiking activity. Our findings open new avenues to investigating how single-neuron nonlinearities—including those of different cell types—combine with connectivity to shape population activity and function. PMID:28644840
Nonlinear waves in repulsive media supported by spatially localized parity-time-symmetric potentials

NASA Astrophysics Data System (ADS)

Devassy, Lini; Jisha, Chandroth P.; Alberucci, Alessandro; Kuriakose, V. C.

2017-06-01

We study the existence, stability and dynamics of solitons in a PT-symmetric potential in the presence of a local defocusing nonlinearity. For the sake of concreteness, we refer to Bose-Einstein condensates, where defocusing nonlinearity stems from a repulsive inter-particle interaction. Two kinds of transverse profiles for the gain-loss mechanism, i.e., the imaginary part of the potential, are considered. Differently from the attractive inter-particle interaction, solitons exist only inside a narrow band of chemical potential and particle number. The existence region shrinks as the magnitude of the gain-loss is increased, with the soliton ceasing to exist above the linear exceptional point, that is, the point at which PT symmetry is broken. Using linear stability analysis together with full numerical simulations of the Gross-Pitaevskii equation, we show that solitons survive on temporal scales much longer than the diffusion time. For magnitude of gain-loss close to the exceptional point, stability depends on the transverse profile of the gain-loss mechanism and the magnitude of the nonlinear excitation.
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 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.
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.
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
Comparison of the Tangent Linear Properties of Tracer Transport Schemes Applied to Geophysical Problems.

NASA Technical Reports Server (NTRS)

Kent, James; Holdaway, Daniel

2015-01-01

A number of geophysical applications require the use of the linearized version of the full model. One such example is in numerical weather prediction, where the tangent linear and adjoint versions of the atmospheric model are required for the 4DVAR inverse problem. The part of the model that represents the resolved scale processes of the atmosphere is known as the dynamical core. Advection, or transport, is performed by the dynamical core. It is a central process in many geophysical applications and is a process that often has a quasi-linear underlying behavior. However, over the decades since the advent of numerical modelling, significant effort has gone into developing many flavors of high-order, shape preserving, nonoscillatory, positive definite advection schemes. These schemes are excellent in terms of transporting the quantities of interest in the dynamical core, but they introduce nonlinearity through the use of nonlinear limiters. The linearity of the transport schemes used in Goddard Earth Observing System version 5 (GEOS-5), as well as a number of other schemes, is analyzed using a simple 1D setup. The linearized version of GEOS-5 is then tested using a linear third order scheme in the tangent linear version.
Parametric resonance in the early Universe—a fitting analysis

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

Figueroa, Daniel G.; Torrentí, Francisco, E-mail: daniel.figueroa@cern.ch, E-mail: f.torrenti@csic.es

Particle production via parametric resonance in the early Universe, is a non-perturbative, non-linear and out-of-equilibrium phenomenon. Although it is a well studied topic, whenever a new scenario exhibits parametric resonance, a full re-analysis is normally required. To avoid this tedious task, many works present often only a simplified linear treatment of the problem. In order to surpass this circumstance in the future, we provide a fitting analysis of parametric resonance through all its relevant stages: initial linear growth, non-linear evolution, and relaxation towards equilibrium. Using lattice simulations in an expanding grid in 3+1 dimensions, we parametrize the dynamics' outcome scanningmore » over the relevant ingredients: role of the oscillatory field, particle coupling strength, initial conditions, and background expansion rate. We emphasize the inaccuracy of the linear calculation of the decay time of the oscillatory field, and propose a more appropriate definition of this scale based on the subsequent non-linear dynamics. We provide simple fits to the relevant time scales and particle energy fractions at each stage. Our fits can be applied to post-inflationary preheating scenarios, where the oscillatory field is the inflaton, or to spectator-field scenarios, where the oscillatory field can be e.g. a curvaton, or the Standard Model Higgs.« less
Time-periodic solutions of driven-damped trimer granular crystals

DOE PAGES

Charalampidis, E. G.; Li, F.; Chong, C.; ...

2015-01-01

In this work, we consider time-periodic structures of granular crystals consisting of alternate chrome steel (S) and tungsten carbide (W) spherical particles where each unit cell follows the pattern of a 2:1 trimer: S-W-S. The configuration at the left boundary is driven by a harmonic in-time actuation with given amplitude and frequency while the right one is a fixed wall. Similar to the case of a dimer chain, the combination of dissipation, driving of the boundary, and intrinsic nonlinearity leads to complex dynamics. For fixed driving frequencies in each of the spectral gaps, we find that the nonlinear surface modesmore » and the states dictated by the linear drive collide in a saddle-node bifurcation as the driving amplitude is increased, beyond which the dynamics of the system becomes chaotic. While the bifurcation structure is similar for solutions within the first and second gap, those in the first gap appear to be less robust. We also conduct a continuation in driving frequency, where it is apparent that the nonlinearity of the system results in a complex bifurcation diagram, involving an intricate set of loops of branches, especially within the spectral gap. The theoretical findings are qualitatively corroborated by the experimental full-field visualization of the time-periodic structures.« less
Theory of nonlinear, distortive phenomena in solids: Martensitic, crack, and multiscale structures-phenomenology and physics. Progress summary, 1991--1994

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

Sethna, J.P.; Krumhansl, J.A.

1994-08-01

We have identified tweed precursors to martensitic phase transformations as a spin glass phase due to composition variations, and used simulations and exact replica theory predictions to predict diffraction peaks and model phase diagrams, and provide real space data for comparison to transmission electron micrograph images. We have used symmetry principles to derive the crack growth laws for mixed-mode brittle fracture, explaining the results for two-dimensional fracture and deriving the growth laws in three dimensions. We have used recent advances in dynamical critical phenomena to study hysteresis in disordered systems, explaining the return-point-memory effect, predicting distributions for Barkhausen noise, andmore » elucidating the transition from athermal to burst behavior in martensites. From a nonlinear lattice-dynamical model of a first-order transition using simulations, finite-size scaling, and transfer matrix methods, it is shown that heterophase transformation precursors cannot occur in a pure homogeneous system, thus emphasizing the role of disorder in real materials. Full integration of nonlinear Landau-Ginzburg continuum theory with experimental neutron-scattering data and first-principles calculations has been carried out to compute semi-quantitative values of the energy and thickness of twin boundaries in InTl and FePd martensites.« less
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.
Living on the edge of chaos: minimally nonlinear models of genetic regulatory dynamics.

PubMed

Hanel, Rudolf; Pöchacker, Manfred; Thurner, Stefan

2010-12-28

Linearized catalytic reaction equations (modelling, for example, the dynamics of genetic regulatory networks), under the constraint that expression levels, i.e. molecular concentrations of nucleic material, are positive, exhibit non-trivial dynamical properties, which depend on the average connectivity of the reaction network. In these systems, an inflation of the edge of chaos and multi-stability have been demonstrated to exist. The positivity constraint introduces a nonlinearity, which makes chaotic dynamics possible. Despite the simplicity of such minimally nonlinear systems, their basic properties allow us to understand the fundamental dynamical properties of complex biological reaction networks. We analyse the Lyapunov spectrum, determine the probability of finding stationary oscillating solutions, demonstrate the effect of the nonlinearity on the effective in- and out-degree of the active interaction network, and study how the frequency distributions of oscillatory modes of such a system depend on the average connectivity.

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.
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.
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.
Non-linear dynamics of compound sawteeth in tokamaks

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

Ahn, J.-H., E-mail: jae-heon.ahn@polytechnique.edu; Garbet, X.; Sabot, R.

2016-05-15

Compound sawteeth is studied with the XTOR-2F code. Non-linear full 3D magnetohydrodynamic simulations show that the plasma hot core is radially displaced and rotates during the partial crash, but is not fully expelled out of the q = 1 surface. Partial crashes occur when the radius of the q = 1 surface exceeds a critical value, at fixed poloidal beta. This critical value depends on the plasma elongation. The partial crash time is larger than the collapse time of an ordinary sawtooth, likely due to a weaker diamagnetic stabilization. This suggests that partial crashes result from a competition between destabilizing effects such as themore » q = 1 radius and diamagnetic stabilization.« less
Application of Probability Methods to Assess Crash Modeling Uncertainty

NASA Technical Reports Server (NTRS)

Lyle, Karen H.; Stockwell, Alan E.; Hardy, Robin C.

2003-01-01

Full-scale aircraft crash simulations performed with nonlinear, transient dynamic, finite element codes can incorporate structural complexities such as: geometrically accurate models; human occupant models; and advanced material models to include nonlinear stress-strain behaviors, and material failure. Validation of these crash simulations is difficult due to a lack of sufficient information to adequately determine the uncertainty in the experimental data and the appropriateness of modeling assumptions. This paper evaluates probabilistic approaches to quantify the effects of finite element modeling assumptions on the predicted responses. The vertical drop test of a Fokker F28 fuselage section will be the focus of this paper. The results of a probabilistic analysis using finite element simulations will be compared with experimental data.
Application of Probability Methods to Assess Crash Modeling Uncertainty

NASA Technical Reports Server (NTRS)

Lyle, Karen H.; Stockwell, Alan E.; Hardy, Robin C.

2007-01-01

Full-scale aircraft crash simulations performed with nonlinear, transient dynamic, finite element codes can incorporate structural complexities such as: geometrically accurate models; human occupant models; and advanced material models to include nonlinear stress-strain behaviors, and material failure. Validation of these crash simulations is difficult due to a lack of sufficient information to adequately determine the uncertainty in the experimental data and the appropriateness of modeling assumptions. This paper evaluates probabilistic approaches to quantify the effects of finite element modeling assumptions on the predicted responses. The vertical drop test of a Fokker F28 fuselage section will be the focus of this paper. The results of a probabilistic analysis using finite element simulations will be compared with experimental data.
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.
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.
Operation and tests of a DDC101 A/D

NASA Astrophysics Data System (ADS)

Nguyen, H.

1994-11-01

For the KTeV PMT laser monitoring system, one needs a high resolution device with a large dynamic range to be used for digitizing PIN photodiodes. The dynamic range should be wider than or comparable to the KTeV digitizer (17-bits). The Burr-Brown DDC101 is a precision, wide dynamic range, charge digitizing A/D converter with 20-bit resolution, packaged in a 28-pin plastic, double-wide DP. Low level current output devices such as photosensors can be directly connected to its input. The digital output can be clocked-out serially from the pins. For typical operations, a relatively wide gate of 1 msec should be used. The full scale charge is 500 pC for unipolar mode. The bipolar mode scale is +/- 250 pC. The advertised integral nonlinearity is 0.003% of FSR. This document describes only the basic DDC101 operations since full detail can be found in the DDC101 manual. Tests results are given in section 3.
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.
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.
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.
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.
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.
Simplified method for numerical modeling of fiber lasers.

PubMed

Shtyrina, O V; Yarutkina, I A; Fedoruk, M P

2014-12-29

A simplified numerical approach to modeling of dissipative dispersion-managed fiber lasers is examined. We present a new numerical iteration algorithm for finding the periodic solutions of the system of nonlinear ordinary differential equations describing the intra-cavity dynamics of the dissipative soliton characteristics in dispersion-managed fiber lasers. We demonstrate that results obtained using simplified model are in good agreement with full numerical modeling based on the corresponding partial differential equations.

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:…
Past and present cosmic structure in the SDSS DR7 main sample

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

Jasche, J.; Leclercq, F.; Wandelt, B.D., E-mail: jasche@iap.fr, E-mail: florent.leclercq@polytechnique.org, E-mail: wandelt@iap.fr

2015-01-01

We present a chrono-cosmography project, aiming at the inference of the four dimensional formation history of the observed large scale structure from its origin to the present epoch. To do so, we perform a full-scale Bayesian analysis of the northern galactic cap of the Sloan Digital Sky Survey (SDSS) Data Release 7 main galaxy sample, relying on a fully probabilistic, physical model of the non-linearly evolved density field. Besides inferring initial conditions from observations, our methodology naturally and accurately reconstructs non-linear features at the present epoch, such as walls and filaments, corresponding to high-order correlation functions generated by late-time structuremore » formation. Our inference framework self-consistently accounts for typical observational systematic and statistical uncertainties such as noise, survey geometry and selection effects. We further account for luminosity dependent galaxy biases and automatic noise calibration within a fully Bayesian approach. As a result, this analysis provides highly-detailed and accurate reconstructions of the present density field on scales larger than ∼ 3 Mpc/h, constrained by SDSS observations. This approach also leads to the first quantitative inference of plausible formation histories of the dynamic large scale structure underlying the observed galaxy distribution. The results described in this work constitute the first full Bayesian non-linear analysis of the cosmic large scale structure with the demonstrated capability of uncertainty quantification. Some of these results will be made publicly available along with this work. The level of detail of inferred results and the high degree of control on observational uncertainties pave the path towards high precision chrono-cosmography, the subject of simultaneously studying the dynamics and the morphology of the inhomogeneous Universe.« less
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.
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.
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…

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.
Quality of motion considerations in numerical analysis of motion restoring implants of the spine.

PubMed

Bowden, Anton E; Guerin, Heather L; Villarraga, Marta L; Patwardhan, Avinash G; Ochoa, Jorge A

2008-06-01

Motion restoring implants function in a dynamic environment that encompasses the full range of spinal kinematics. Accurate assessment of the in situ performance of these devices using numerical techniques requires model verification and validation against the well-established nonlinear quality of motion of the spine, as opposed to the previous norm of matching kinematic endpoint metrics such as range of motion and intervertebral disc pressure measurements at a single kinematic reference point. Experimental data was obtained during cadaveric testing of nine three-functional spinal unit (L3-S1) lumbar spine segments. Each specimen was tested from 8 Nm of applied flexion moment to 6 Nm of applied extension moment with an applied 400 N compressive follower preload. A nonlinear kinematic curve representing the spinal quality of motion (applied moment versus angular rotation) for the index finite element model was constructed and compared to the kinematic responses of the experimental specimens. The effect of spinal soft tissue structure mechanical behaviors on the fidelity of the model's quality of motion to experimental data was assessed by iteratively modifying the material representations of annulus fibrosus, nucleus pulposus, and ligaments. The present work demonstrated that for this model, the annulus fibrosus played a small role in the nonlinear quality of motion of the model, whereas changes in ligament representations had a large effect, as validated against the full kinematic range of motion. An anisotropic continuum representation of the annulus fibrosus was used, along with nonlinear fabric representations of the ligaments and a hyperelastic representation of the nucleus pulposus. Our results suggest that improvements in current methodologies broadly used in numerical simulations of the lumbar spine are needed to fully describe the highly nonlinear motion of the spine.
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.
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.
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.
Mechanism of nonlinear flow pattern selection in moderately non-Boussinesq mixed convection.

PubMed

Suslov, Sergey A

2010-02-01

Nonlinear (non-Boussinesq) variations in fluid's density, viscosity, and thermal conductivity caused by a large temperature gradient in a flow domain lead to a wide variety of instability phenomena in mixed convection channel flow of a simple gas such as air. It is known that in strongly nonisothermal flows, the instabilities and the resulting flow patterns are caused by competing buoyancy and shear effects [see S. A. Suslov and S. Paolucci, J. Fluid Mech. 302, 91 (1995)]. However, as is the case in the Boussinesq limit of small temperature gradients, in moderately non-Boussinesq regimes, only a shear instability mechanism is active. Yet in contrast to Boussinesq flows, multiple instability modes are still detected. By reducing the system of full governing Navier-Stokes equations to a dynamical system of coupled Landau-type disturbance amplitude equations we compute a comprehensive parametric map of various shear-driven instabilities observed in a representative moderately non-Boussinesq regime. Subsequently, we analyze nonlinear interaction of unstable modes and reveal physical reasons for their appearance.
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.
A wind turbine hybrid simulation framework considering aeroelastic effects

NASA Astrophysics Data System (ADS)

Song, Wei; Su, Weihua

2015-04-01

In performing an effective structural analysis for wind turbine, the simulation of turbine aerodynamic loads is of great importance. The interaction between the wake flow and the blades may impact turbine blades loading condition, energy yield and operational behavior. Direct experimental measurement of wind flow field and wind profiles around wind turbines is very helpful to support the wind turbine design. However, with the growth of the size of wind turbines for higher energy output, it is not convenient to obtain all the desired data in wind-tunnel and field tests. In this paper, firstly the modeling of dynamic responses of large-span wind turbine blades will consider nonlinear aeroelastic effects. A strain-based geometrically nonlinear beam formulation will be used for the basic structural dynamic modeling, which will be coupled with unsteady aerodynamic equations and rigid-body rotations of the rotor. Full wind turbines can be modeled by using the multi-connected beams. Then, a hybrid simulation experimental framework is proposed to potentially address this issue. The aerodynamic-dominant components, such as the turbine blades and rotor, are simulated as numerical components using the nonlinear aeroelastic model; while the turbine tower, where the collapse of failure may occur under high level of wind load, is simulated separately as the physical component. With the proposed framework, dynamic behavior of NREL's 5MW wind turbine blades will be studied and correlated with available numerical data. The current work will be the basis of the authors' further studies on flow control and hazard mitigation on wind turbine blades and towers.
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.
Modulational instability of beat waves in a transversely magnetized plasma: Ion effects

NASA Astrophysics Data System (ADS)

Ferdous, T.; Amin, M. R.; Salimullah, M.

1996-05-01

The effect of ion dynamics on the modulational instability of the electrostatic beat wave at the difference frequency of two incident laser beams in a hot, collisionless, and transversely magnetized plasma has been studied theoretically. The full Vlasov equation in terms of gyrokinetic variables is employed to obtain the nonlinear response of ions and electrons. It is found that the growth rate of modulational instability is about two orders higher when ion motions are included.
Adaptive Nonlinear Tracking Control of Kinematically Redundant Robot Manipulators with Sub-Task Extensions

DTIC Science & Technology

2005-01-01

C. Hughes, Spacecraft Attitude Dynamics, New York, NY: Wiley, 1994. [8] H. K. Khalil, “Adaptive Output Feedback Control of Non- linear Systems...Closed-Loop Manipulator Control Using Quaternion Feedback ”, IEEE Trans. Robotics and Automation, Vol. 4, No. 4, pp. 434-440, (1988). [23] E...full-state feedback quaternion based controller de- veloped in [5] and focuses on the design of a general sub-task controller. This sub-task controller

Rotational elasticity

NASA Astrophysics Data System (ADS)

Vassiliev, Dmitri

2017-04-01

We consider an infinite three-dimensional elastic continuum whose material points experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of material points are described mathematically by attaching to each geometric point an orthonormal basis that gives a field of orthonormal bases called the coframe. As the dynamical variables (unknowns) of our theory, we choose the coframe and a density. We write down the general dynamic variational functional for our rotational theory of elasticity, assuming our material to be physically linear but the kinematic model geometrically nonlinear. Allowing geometric nonlinearity is natural when dealing with rotations because rotations in dimension three are inherently nonlinear (rotations about different axes do not commute) and because there is no reason to exclude from our study large rotations such as full turns. The main result of the talk is an explicit construction of a class of time-dependent solutions that we call plane wave solutions; these are travelling waves of rotations. The existence of such explicit closed-form solutions is a non-trivial fact given that our system of Euler-Lagrange equations is highly nonlinear. We also consider a special case of our rotational theory of elasticity which in the stationary setting (harmonic time dependence and arbitrary dependence on spatial coordinates) turns out to be equivalent to a pair of massless Dirac equations. The talk is based on the paper [1]. [1] C.G.Boehmer, R.J.Downes and D.Vassiliev, Rotational elasticity, Quarterly Journal of Mechanics and Applied Mathematics, 2011, vol. 64, p. 415-439. The paper is a heavily revised version of preprint https://arxiv.org/abs/1008.3833
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.
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.
Infectious diseases in space and time: noise and nonlinearity in epidemiological dynamics

NASA Astrophysics Data System (ADS)

Grenfell, Bryan

2005-03-01

I illustrate the impact of noise and nonlinearity on the spatio-temporal dynamics and evolution of epidemics using mathematical models and analyses of detailed epidemiological data from childhood infections, such as measles.
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.
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.
Nonlinear earthquake analysis of reinforced concrete frames with fiber and Bernoulli-Euler beam-column element.

PubMed

Karaton, Muhammet

2014-01-01

A beam-column element based on the Euler-Bernoulli beam theory is researched for nonlinear dynamic analysis of reinforced concrete (RC) structural element. Stiffness matrix of this element is obtained by using rigidity method. A solution technique that included nonlinear dynamic substructure procedure is developed for dynamic analyses of RC frames. A predicted-corrected form of the Bossak-α method is applied for dynamic integration scheme. A comparison of experimental data of a RC column element with numerical results, obtained from proposed solution technique, is studied for verification the numerical solutions. Furthermore, nonlinear cyclic analysis results of a portal reinforced concrete frame are achieved for comparing the proposed solution technique with Fibre element, based on flexibility method. However, seismic damage analyses of an 8-story RC frame structure with soft-story are investigated for cases of lumped/distributed mass and load. Damage region, propagation, and intensities according to both approaches are researched.
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
Time series analyses of breathing patterns of lung cancer patients using nonlinear dynamical system theory.

PubMed

Tewatia, D K; Tolakanahalli, R P; Paliwal, B R; Tomé, W A

2011-04-07

The underlying requirements for successful implementation of any efficient tumour motion management strategy are regularity and reproducibility of a patient's breathing pattern. The physiological act of breathing is controlled by multiple nonlinear feedback and feed-forward couplings. It would therefore be appropriate to analyse the breathing pattern of lung cancer patients in the light of nonlinear dynamical system theory. The purpose of this paper is to analyse the one-dimensional respiratory time series of lung cancer patients based on nonlinear dynamics and delay coordinate state space embedding. It is very important to select a suitable pair of embedding dimension 'm' and time delay 'τ' when performing a state space reconstruction. Appropriate time delay and embedding dimension were obtained using well-established methods, namely mutual information and the false nearest neighbour method, respectively. Establishing stationarity and determinism in a given scalar time series is a prerequisite to demonstrating that the nonlinear dynamical system that gave rise to the scalar time series exhibits a sensitive dependence on initial conditions, i.e. is chaotic. Hence, once an appropriate state space embedding of the dynamical system has been reconstructed, we show that the time series of the nonlinear dynamical systems under study are both stationary and deterministic in nature. Once both criteria are established, we proceed to calculate the largest Lyapunov exponent (LLE), which is an invariant quantity under time delay embedding. The LLE for all 16 patients is positive, which along with stationarity and determinism establishes the fact that the time series of a lung cancer patient's breathing pattern is not random or irregular, but rather it is deterministic in nature albeit chaotic. These results indicate that chaotic characteristics exist in the respiratory waveform and techniques based on state space dynamics should be employed for tumour motion management.
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.
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.
Numerical Simulations of Light Bullets, Using The Full Vector, Time Dependent, Nonlinear Maxwell Equations

NASA Technical Reports Server (NTRS)

Goorjian, Peter M.; Silberberg, Yaron; Kwak, Dochan (Technical Monitor)

1994-01-01

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that are currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Kerr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations.
Numerical Simulations of Light Bullets, Using The Full Vector, Time Dependent, Nonlinear Maxwell Equations

NASA Technical Reports Server (NTRS)

Goorjian, Peter M.; Silberberg, Yaron; Kwak, Dochan (Technical Monitor)

1995-01-01

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that we currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Karr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations.

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 model for thermal effects in free-electron lasers

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

Peter, E., E-mail: peterpeter@uol.com.br; Endler, A., E-mail: aendler@if.ufrgs.br; Rizzato, F. B., E-mail: rizzato@if.ufrgs.br

2014-11-15

In the present work, we extend results of a previous paper [Peter et al., Phys. Plasmas 20, 12 3104 (2013)] and develop a semi-analytical model to account for thermal effects on the nonlinear dynamics of the electron beam in free-electron lasers. We relax the condition of a cold electron beam but still use the concept of compressibility, now associated with a warm beam model, to evaluate the time scale for saturation and the peak laser intensity in high-gain regimes. Although vanishing compressibilites and the associated divergent densities are absent in warm models, a series of discontinuities in the electron density precedemore » the saturation process. We show that full wave-particle simulations agree well with the predictions of the model.« less
State of charge estimation in Ni-MH rechargeable batteries

NASA Astrophysics Data System (ADS)

Milocco, R. H.; Castro, B. E.

In this work we estimate the state of charge (SOC) of Ni-MH rechargeable batteries using the Kalman filter based on a simplified electrochemical model. First, we derive the complete electrochemical model of the battery which includes diffusional processes and kinetic reactions in both Ni and MH electrodes. The full model is further reduced in a cascade of two parts, a linear time invariant dynamical sub-model followed by a static nonlinearity. Both parts are identified using the current and potential measured at the terminals of the battery with a simple 1-D minimization procedure. The inverse of the static nonlinearity together with a Kalman filter provide the SOC estimation as a linear estimation problem. Experimental results with commercial batteries are provided to illustrate the estimation procedure and to show the performance.
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.
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.
Perceptual suppression revealed by adaptive multi-scale entropy analysis of local field potential in monkey visual cortex.

PubMed

Hu, Meng; Liang, Hualou

2013-04-01

Generalized flash suppression (GFS), in which a salient visual stimulus can be rendered invisible despite continuous retinal input, provides a rare opportunity to directly study the neural mechanism of visual perception. Previous work based on linear methods, such as spectral analysis, on local field potential (LFP) during GFS has shown that the LFP power at distinctive frequency bands are differentially modulated by perceptual suppression. Yet, the linear method alone may be insufficient for the full assessment of neural dynamic due to the fundamentally nonlinear nature of neural signals. In this study, we set forth to analyze the LFP data collected from multiple visual areas in V1, V2 and V4 of macaque monkeys while performing the GFS task using a nonlinear method - adaptive multi-scale entropy (AME) - to reveal the neural dynamic of perceptual suppression. In addition, we propose a new cross-entropy measure at multiple scales, namely adaptive multi-scale cross-entropy (AMCE), to assess the nonlinear functional connectivity between two cortical areas. We show that: (1) multi-scale entropy exhibits percept-related changes in all three areas, with higher entropy observed during perceptual suppression; (2) the magnitude of the perception-related entropy changes increases systematically over successive hierarchical stages (i.e. from lower areas V1 to V2, up to higher area V4); and (3) cross-entropy between any two cortical areas reveals higher degree of asynchrony or dissimilarity during perceptual suppression, indicating a decreased functional connectivity between cortical areas. These results, taken together, suggest that perceptual suppression is related to a reduced functional connectivity and increased uncertainty of neural responses, and the modulation of perceptual suppression is more effective at higher visual cortical areas. AME is demonstrated to be a useful technique in revealing the underlying dynamic of nonlinear/nonstationary neural signal.
Efficient loads analyses of Shuttle-payloads using dynamic models with linear or nonlinear interfaces

NASA Technical Reports Server (NTRS)

Spanos, P. D.; Cao, T. T.; Hamilton, D. A.; Nelson, D. A. R.

1989-01-01

An efficient method for the load analysis of Shuttle-payload systems with linear or nonlinear attachment interfaces is presented which allows the kinematics of the interface degrees of freedom at a given time to be evaluated without calculating the combined system modal representation of the Space Shuttle and its payload. For the case of a nonlinear dynamic model, an iterative procedure is employed to converge the nonlinear terms of the equations of motion to reliable values. Results are presented for a Shuttle abort landing event.
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.
Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents.

PubMed

Kundu, Anjan; Mukherjee, Abhik; Naskar, Tapan

2014-04-08

Rogue waves are extraordinarily high and steep isolated waves, which appear suddenly in a calm sea and disappear equally fast. However, though the rogue waves are localized surface waves, their theoretical models and experimental observations are available mostly in one dimension, with the majority of them admitting only limited and fixed amplitude and modular inclination of the wave. We propose two dimensions, exactly solvable nonlinear Schrödinger (NLS) equation derivable from the basic hydrodynamic equations and endowed with integrable structures. The proposed two-dimensional equation exhibits modulation instability and frequency correction induced by the nonlinear effect, with a directional preference, all of which can be determined through precise analytic result. The two-dimensional NLS equation allows also an exact lump soliton which can model a full-grown surface rogue wave with adjustable height and modular inclination. The lump soliton under the influence of an ocean current appears and disappears preceded by a hole state, with its dynamics controlled by the current term. These desirable properties make our exact model promising for describing ocean rogue waves.

Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents

PubMed Central

Kundu, Anjan; Mukherjee, Abhik; Naskar, Tapan

2014-01-01

Rogue waves are extraordinarily high and steep isolated waves, which appear suddenly in a calm sea and disappear equally fast. However, though the rogue waves are localized surface waves, their theoretical models and experimental observations are available mostly in one dimension, with the majority of them admitting only limited and fixed amplitude and modular inclination of the wave. We propose two dimensions, exactly solvable nonlinear Schrödinger (NLS) equation derivable from the basic hydrodynamic equations and endowed with integrable structures. The proposed two-dimensional equation exhibits modulation instability and frequency correction induced by the nonlinear effect, with a directional preference, all of which can be determined through precise analytic result. The two-dimensional NLS equation allows also an exact lump soliton which can model a full-grown surface rogue wave with adjustable height and modular inclination. The lump soliton under the influence of an ocean current appears and disappears preceded by a hole state, with its dynamics controlled by the current term. These desirable properties make our exact model promising for describing ocean rogue waves. PMID:24711719
Reduced-Order Modeling for Flutter/LCO Using Recurrent Artificial Neural Network

NASA Technical Reports Server (NTRS)

Yao, Weigang; Liou, Meng-Sing

2012-01-01

The present study demonstrates the efficacy of a recurrent artificial neural network to provide a high fidelity time-dependent nonlinear reduced-order model (ROM) for flutter/limit-cycle oscillation (LCO) modeling. An artificial neural network is a relatively straightforward nonlinear method for modeling an input-output relationship from a set of known data, for which we use the radial basis function (RBF) with its parameters determined through a training process. The resulting RBF neural network, however, is only static and is not yet adequate for an application to problems of dynamic nature. The recurrent neural network method [1] is applied to construct a reduced order model resulting from a series of high-fidelity time-dependent data of aero-elastic simulations. Once the RBF neural network ROM is constructed properly, an accurate approximate solution can be obtained at a fraction of the cost of a full-order computation. The method derived during the study has been validated for predicting nonlinear aerodynamic forces in transonic flow and is capable of accurate flutter/LCO simulations. The obtained results indicate that the present recurrent RBF neural network is accurate and efficient for nonlinear aero-elastic system analysis
Nonlinear transient analysis by energy minimization: A theoretical basis for the ACTION computer code. [predicting the response of a lightweight aircraft during a crash

NASA Technical Reports Server (NTRS)

Kamat, M. P.

1980-01-01

The formulation basis for establishing the static or dynamic equilibrium configurations of finite element models of structures which may behave in the nonlinear range are provided. With both geometric and time independent material nonlinearities included, the development is restricted to simple one and two dimensional finite elements which are regarded as being the basic elements for modeling full aircraft-like structures under crash conditions. Representations of a rigid link and an impenetrable contact plane are added to the deformation model so that any number of nodes of the finite element model may be connected by a rigid link or may contact the plane. Equilibrium configurations are derived as the stationary conditions of a potential function of the generalized nodal variables of the model. Minimization of the nonlinear potential function is achieved by using the best current variable metric update formula for use in unconstrained minimization. Powell's conjugate gradient algorithm, which offers very low storage requirements at some slight increase in the total number of calculations, is the other alternative algorithm to be used for extremely large scale problems.
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.
Identifying Complex Dynamics in Social Systems: A New Methodological Approach Applied to Study School Segregation

ERIC Educational Resources Information Center

Spaiser, Viktoria; Hedström, Peter; Ranganathan, Shyam; Jansson, Kim; Nordvik, Monica K.; Sumpter, David J. T.

2018-01-01

It is widely recognized that segregation processes are often the result of complex nonlinear dynamics. Empirical analyses of complex dynamics are however rare, because there is a lack of appropriate empirical modeling techniques that are capable of capturing complex patterns and nonlinearities. At the same time, we know that many social phenomena…
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.
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.
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
Tangent map intermittency as an approximate analysis of intermittency in a high dimensional fully stochastic dynamical system: The Tangled Nature model.

PubMed

Diaz-Ruelas, Alvaro; Jeldtoft Jensen, Henrik; Piovani, Duccio; Robledo, Alberto

2016-12-01

It is well known that low-dimensional nonlinear deterministic maps close to a tangent bifurcation exhibit intermittency and this circumstance has been exploited, e.g., by Procaccia and Schuster [Phys. Rev. A 28, 1210 (1983)], to develop a general theory of 1/f spectra. This suggests it is interesting to study the extent to which the behavior of a high-dimensional stochastic system can be described by such tangent maps. The Tangled Nature (TaNa) Model of evolutionary ecology is an ideal candidate for such a study, a significant model as it is capable of reproducing a broad range of the phenomenology of macroevolution and ecosystems. The TaNa model exhibits strong intermittency reminiscent of punctuated equilibrium and, like the fossil record of mass extinction, the intermittency in the model is found to be non-stationary, a feature typical of many complex systems. We derive a mean-field version for the evolution of the likelihood function controlling the reproduction of species and find a local map close to tangency. This mean-field map, by our own local approximation, is able to describe qualitatively only one episode of the intermittent dynamics of the full TaNa model. To complement this result, we construct a complete nonlinear dynamical system model consisting of successive tangent bifurcations that generates time evolution patterns resembling those of the full TaNa model in macroscopic scales. The switch from one tangent bifurcation to the next in the sequences produced in this model is stochastic in nature, based on criteria obtained from the local mean-field approximation, and capable of imitating the changing set of types of species and total population in the TaNa model. The model combines full deterministic dynamics with instantaneous parameter random jumps at stochastically drawn times. In spite of the limitations of our approach, which entails a drastic collapse of degrees of freedom, the description of a high-dimensional model system in terms of a low-dimensional one appears to be illuminating.
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.

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.
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
Robust dynamic inversion controller design and analysis (using the X-38 vehicle as a case study)

NASA Astrophysics Data System (ADS)

Ito, Daigoro

A new way to approach robust Dynamic Inversion controller synthesis is addressed in this paper. A Linear Quadratic Gaussian outer-loop controller improves the robustness of a Dynamic Inversion inner-loop controller in the presence of uncertainties. Desired dynamics are given by the dynamic compensator, which shapes the loop. The selected dynamics are based on both performance and stability robustness requirements. These requirements are straightforwardly formulated as frequency-dependent singular value bounds during synthesis of the controller. Performance and robustness of the designed controller is tested using a worst case time domain quadratic index, which is a simple but effective way to measure robustness due to parameter variation. Using this approach, a lateral-directional controller for the X-38 vehicle is designed and its robustness to parameter variations and disturbances is analyzed. It is found that if full state measurements are available, the performance of the designed lateral-directional control system, measured by the chosen cost function, improves by approximately a factor of four. Also, it is found that the designed system is stable up to a parametric variation of 1.65 standard deviation with the set of uncertainty considered. The system robustness is determined to be highly sensitive to the dihedral derivative and the roll damping coefficients. The controller analysis is extended to the nonlinear system where both control input displacements and rates are bounded. In this case, the considered nonlinear system is stable up to 48.1° in bank angle and 1.59° in sideslip angle variations, indicating it is more sensitive to variations in sideslip angle than in bank angle. This nonlinear approach is further extended for the actuator failure mode analysis. The results suggest that the designed system maintains a high level of stability in the event of aileron failure. However, only 35% or less of the original stability range is maintained for the rudder failure case. Overall, this combination of controller synthesis and robustness criteria compares well with the mu-synthesis technique. It also is readily accessible to the practicing engineer, in terms of understanding and use.
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 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.
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.
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.
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.
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.
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.
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.
Modeling of testosterone regulation by pulse-modulated feedback: An experimental data study

NASA Astrophysics Data System (ADS)

Mattsson, Per; Medvedev, Alexander

2013-10-01

The continuous part of a hybrid (pulse-modulated) model of testosterone feedback regulation is extended with infinite-dimensional and nonlinear dynamics, to better explain the testosterone concentration profiles observed in clinical data. A linear least-squares based optimization algorithm is developed for the purpose of detecting impulses of gonadotropin-realsing hormone from measured concentration of luteinizing hormone. The parameters in the model are estimated from hormone concentration measured in human males, and simulation results from the full closed-loop system are provided.

Dynamics behaviour of an elastic non-ideal (NIS) portal frame, including fractional nonlinearities

NASA Astrophysics Data System (ADS)

Balthazar, J. M.; Brasil, R. M. L. F.; Felix, J. L. P.; Tusset, A. M.; Picirillo, V.; Iluik, I.; Rocha, R. T.; Nabarrete, A.; Oliveira, C.

2016-05-01

This paper overviews recent developments on some problems related to elastic structures, such as portal frames, taking into account the full interactions of the vibrating systems, with an energy source of limited power supply (small motors, electro-mechanical shakers). We include a discussion on fractional (rational) damping and stiffness effects on the adopted modelling. This was a plenary lecture, delivered in the event titled: Mechanics of Slender Structures, organized in Northampton, England from 21-22, September 2015.
Status of the KTH-NASA Wind-Tunnel Test for Acquisition of Transonic Nonlinear Aeroelastic Data

NASA Technical Reports Server (NTRS)

Silva, Walter A.; Ringertz, Ulf; Stenfelt, Gloria; Eller, David; Keller, Donald F.; Chwalowski, Pawel

2016-01-01

This paper presents a status report on the collaboration between the Royal Institute of Technology (KTH) in Sweden and the NASA Langley Research Center regarding the design, fabrication, modeling, and testing of a full-span lighter configuration in the Transonic Dynamics Tunnel (TDT). The goal of the test is to acquire transonic limit-cycle- oscillation (LCO) data, including accelerations, strains, and unsteady pressures. Finite element models (FEMs) and aerodynamic models are presented and discussed along with results obtained to date.
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.
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.
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.
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.
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.
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.

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.
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.
Nonlinear Earthquake Analysis of Reinforced Concrete Frames with Fiber and Bernoulli-Euler Beam-Column Element

PubMed Central

Karaton, Muhammet

2014-01-01

A beam-column element based on the Euler-Bernoulli beam theory is researched for nonlinear dynamic analysis of reinforced concrete (RC) structural element. Stiffness matrix of this element is obtained by using rigidity method. A solution technique that included nonlinear dynamic substructure procedure is developed for dynamic analyses of RC frames. A predicted-corrected form of the Bossak-α method is applied for dynamic integration scheme. A comparison of experimental data of a RC column element with numerical results, obtained from proposed solution technique, is studied for verification the numerical solutions. Furthermore, nonlinear cyclic analysis results of a portal reinforced concrete frame are achieved for comparing the proposed solution technique with Fibre element, based on flexibility method. However, seismic damage analyses of an 8-story RC frame structure with soft-story are investigated for cases of lumped/distributed mass and load. Damage region, propagation, and intensities according to both approaches are researched. PMID:24578667
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.
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.
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
Measurement of nonlinear normal modes using multi-harmonic stepped force appropriation and free decay

NASA Astrophysics Data System (ADS)

Ehrhardt, David A.; Allen, Matthew S.

2016-08-01

Nonlinear Normal Modes (NNMs) offer tremendous insight into the dynamic behavior of a nonlinear system, extending many concepts that are familiar in linear modal analysis. Hence there is interest in developing methods to experimentally and numerically determine a system's NNMs for model updating or simply to characterize its dynamic response. Previous experimental work has shown that a mono-harmonic excitation can be used to isolate a system's dynamic response in the neighborhood of a NNM along the main backbones of a system. This work shows that a multi-harmonic excitation is needed to isolate a NNM when well separated linear modes of a structure couple to produce an internal resonance. It is shown that one can tune the multiple harmonics of the input excitation using a plot of the input force versus the response velocity until the area enclosed by the force-velocity curve is minimized. Once an appropriated NNM is measured, one can increase the force level and retune the frequency to obtain a NNM at a higher amplitude or remove the excitation and measure the structure's decay down a NNM backbone. This work explores both methods using simulations and measurements of a nominally-flat clamped-clamped beam excited at a single point with a magnetic force. Numerical simulations are used to validate the method in a well defined environment and to provide comparison with the experimentally measured NNMs. The experimental results seem to produce a good estimate of two NNMs along their backbone and part of an internal resonance branch. Full-field measurements are then used to further explore the couplings between the underlying linear modes along the identified NNMs.
A unifying view of synchronization for data assimilation in complex nonlinear networks

NASA Astrophysics Data System (ADS)

Abarbanel, Henry D. I.; Shirman, Sasha; Breen, Daniel; Kadakia, Nirag; Rey, Daniel; Armstrong, Eve; Margoliash, Daniel

2017-12-01

Networks of nonlinear systems contain unknown parameters and dynamical degrees of freedom that may not be observable with existing instruments. From observable state variables, we want to estimate the connectivity of a model of such a network and determine the full state of the model at the termination of a temporal observation window during which measurements transfer information to a model of the network. The model state at the termination of a measurement window acts as an initial condition for predicting the future behavior of the network. This allows the validation (or invalidation) of the model as a representation of the dynamical processes producing the observations. Once the model has been tested against new data, it may be utilized as a predictor of responses to innovative stimuli or forcing. We describe a general framework for the tasks involved in the "inverse" problem of determining properties of a model built to represent measured output from physical, biological, or other processes when the measurements are noisy, the model has errors, and the state of the model is unknown when measurements begin. This framework is called statistical data assimilation and is the best one can do in estimating model properties through the use of the conditional probability distributions of the model state variables, conditioned on observations. There is a very broad arena of applications of the methods described. These include numerical weather prediction, properties of nonlinear electrical circuitry, and determining the biophysical properties of functional networks of neurons. Illustrative examples will be given of (1) estimating the connectivity among neurons with known dynamics in a network of unknown connectivity, and (2) estimating the biophysical properties of individual neurons in vitro taken from a functional network underlying vocalization in songbirds.
Application of an Ensemble Smoother to Precipitation Assimilation

NASA Technical Reports Server (NTRS)

Zhang, Sara; Zupanski, Dusanka; Hou, Arthur; Zupanski, Milija

2008-01-01

Assimilation of precipitation in a global modeling system poses a special challenge in that the observation operators for precipitation processes are highly nonlinear. In the variational approach, substantial development work and model simplifications are required to include precipitation-related physical processes in the tangent linear model and its adjoint. An ensemble based data assimilation algorithm "Maximum Likelihood Ensemble Smoother (MLES)" has been developed to explore the ensemble representation of the precipitation observation operator with nonlinear convection and large-scale moist physics. An ensemble assimilation system based on the NASA GEOS-5 GCM has been constructed to assimilate satellite precipitation data within the MLES framework. The configuration of the smoother takes the time dimension into account for the relationship between state variables and observable rainfall. The full nonlinear forward model ensembles are used to represent components involving the observation operator and its transpose. Several assimilation experiments using satellite precipitation observations have been carried out to investigate the effectiveness of the ensemble representation of the nonlinear observation operator and the data impact of assimilating rain retrievals from the TMI and SSM/I sensors. Preliminary results show that this ensemble assimilation approach is capable of extracting information from nonlinear observations to improve the analysis and forecast if ensemble size is adequate, and a suitable localization scheme is applied. In addition to a dynamically consistent precipitation analysis, the assimilation system produces a statistical estimate of the analysis uncertainty.
A new adaptive control strategy for a class of nonlinear system using RBF neuro-sliding-mode technique: application to SEIG wind turbine control system

NASA Astrophysics Data System (ADS)

Kenné, Godpromesse; Fotso, Armel Simo; Lamnabhi-Lagarrigue, Françoise

2017-04-01

In this paper, a new hybrid method which combines radial basis function (RBF) neural network with a sliding-mode technique to take advantage of their common features is used to control a class of nonlinear systems. A real-time dynamic nonlinear learning law of the weight vector is synthesized and the closed-loop stability has been demonstrated using Lyapunov theory. The solution presented in this work does not need the knowledge of the perturbation bounds, neither the knowledge of the full state of the nonlinear system. In addition, the bounds of the nonlinear functions are assumed to be unknown and the proposed RBF structure uses reduced number of hidden units. This hybrid control strategy is applied to extract the maximum available energy from a stand-alone self-excited variable low-wind speed energy conversion system and design the dc-voltage and rotor flux controllers as well as the load-side frequency and voltage regulators assuming that the measured outputs are the rotor speed, stator currents, load-side currents and voltages despite large variation of the rotor resistance and uncertainties on the inductances. Finally, simulation results compared with those obtained using the well-known second-order sliding-mode controller are given to show the effectiveness and feasibility of the proposed approach.
Real-time full-field characterization of transient dissipative soliton dynamics in a mode-locked laser

NASA Astrophysics Data System (ADS)

Ryczkowski, P.; Närhi, M.; Billet, C.; Merolla, J.-M.; Genty, G.; Dudley, J. M.

2018-04-01

Dissipative solitons are remarkably localized states of a physical system that arise from the dynamical balance between nonlinearity, dispersion and environmental energy exchange. They are the most universal form of soliton that can exist, and are seen in far-from-equilibrium systems in many fields, including chemistry, biology and physics. There has been particular interest in studying their properties in mode-locked lasers, but experiments have been limited by the inability to track the dynamical soliton evolution in real time. Here, we use simultaneous dispersive Fourier transform and time-lens measurements to completely characterize the spectral and temporal evolution of ultrashort dissipative solitons as their dynamics pass through a transient unstable regime with complex break-up and collisions before stabilization. Further insight is obtained from reconstruction of the soliton amplitude and phase and calculation of the corresponding complex-valued eigenvalue spectrum. These findings show how real-time measurements provide new insights into ultrafast transient dynamics in optics.
Nonlinear evolution and final fate of (charged) superradiant instability

NASA Astrophysics Data System (ADS)

Green, Stephen; Bosch, Pablo; Lehner, Luis

2016-03-01

We describe the full nonlinear development of the superradiant instability for a charged massless scalar field, coupled to general relativity and electromagnetism, in the vicinity of a Reissner-Nordstrom-AdS black hole. The presence of the negative cosmological constant provides a natural context for considering perfectly reflecting boundary conditions and studying the dynamics as the scalar field interacts repeateadly with the black hole. At early times, small superradiant perturbations grow as expected from linearized studies. Backreaction then causes the black hole to lose charge and mass until the perturbation becomes nonsuperradiant, with the final state described by a stable hairy black hole. For large gauge coupling, the instability extracts a large amount of charge per unit mass, resulting in greater entropy increase. We discuss the implications of the observed behavior for the general problem of superradiance in black hole spacetimes.
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

Caustic Skeleton & Cosmic Web

NASA Astrophysics Data System (ADS)

Feldbrugge, Job; van de Weygaert, Rien; Hidding, Johan; Feldbrugge, Joost

2018-05-01

We present a general formalism for identifying the caustic structure of a dynamically evolving mass distribution, in an arbitrary dimensional space. The identification of caustics in fluids with Hamiltonian dynamics, viewed in Lagrangian space, corresponds to the classification of singularities in Lagrangian catastrophe theory. On the basis of this formalism we develop a theoretical framework for the dynamics of the formation of the cosmic web, and specifically those aspects that characterize its unique nature: its complex topological connectivity and multiscale spinal structure of sheetlike membranes, elongated filaments and compact cluster nodes. Given the collisionless nature of the gravitationally dominant dark matter component in the universe, the presented formalism entails an accurate description of the spatial organization of matter resulting from the gravitationally driven formation of cosmic structure. The present work represents a significant extension of the work by Arnol'd et al. [1], who classified the caustics that develop in one- and two-dimensional systems that evolve according to the Zel'dovich approximation. His seminal work established the defining role of emerging singularities in the formation of nonlinear structures in the universe. At the transition from the linear to nonlinear structure evolution, the first complex features emerge at locations where different fluid elements cross to establish multistream regions. Involving a complex folding of the 6-D sheetlike phase-space distribution, it manifests itself in the appearance of infinite density caustic features. The classification and characterization of these mass element foldings can be encapsulated in caustic conditions on the eigenvalue and eigenvector fields of the deformation tensor field. In this study we introduce an alternative and transparent proof for Lagrangian catastrophe theory. This facilitates the derivation of the caustic conditions for general Lagrangian fluids, with arbitrary dynamics. Most important in the present context is that it allows us to follow and describe the full three-dimensional geometric and topological complexity of the purely gravitationally evolving nonlinear cosmic matter field. While generic and statistical results can be based on the eigenvalue characteristics, one of our key findings is that of the significance of the eigenvector field of the deformation field for outlining the entire spatial structure of the caustic skeleton emerging from a primordial density field. In this paper we explicitly consider the caustic conditions for the three-dimensional Zel'dovich approximation, extending earlier work on those for one- and two-dimensional fluids towards the full spatial richness of the cosmic web. In an accompanying publication, we apply this towards a full three-dimensional study of caustics in the formation of the cosmic web and evaluate in how far it manages to outline and identify the intricate skeletal features in the corresponding N-body simulations.
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.
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
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.
Study on the After Cavity Interaction in a 140 GHz Gyrotron Using 3D CFDTD PIC Simulations

NASA Astrophysics Data System (ADS)

Lin, M. C.; Illy, S.; Avramidis, K.; Thumm, M.; Jelonnek, J.

2016-10-01

A computational study on after cavity interaction (ACI) in a 140 GHz gryotron for fusion research has been performed using a 3-D conformal finite-difference time-domain (CFDTD) particle-in-cell (PIC) method. The ACI, i.e. beam wave interaction in the non-linear uptaper after the cavity has attracted a lot of attention and been widely investigated in recent years. In a dynamic ACI, a TE mode is excited by the electron beam at the same frequency as in the cavity, and the same mode is also interacting with the spent electron beam at a different frequency in the non-linear uptaper after the cavity while in a static ACI, a mode interacts with the beam both at the cavity and at the uptaper, but at the same frequency. A previous study on the dynamic ACI on a 140 GHz gyrotron has concluded that more advanced numerical simulations such as particle-in-cell (PIC) modeling should be employed to study or confirm the dynamic ACI in addition to using trajectory codes. In this work, we use a 3-D full wave time domain simulation based on the CFDTD PIC method to include the rippled-wall launcher of the quasi-optical output coupler into the simulations which breaks the axial symmetry of the original model employing a symmetric one. A preliminary simulation result has confirmed the dynamic ACI effect in this 140 GHz gyrotron in good agreement with the former study. A realistic launcher will be included in the model for studying the dynamic ACI and compared with the homogenous one.
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.
Resonance and Chaotic Trajectories in Magnetic Field Reversed Configuration

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

A.S. Landsman; S.A. Cohen; M. Edelman

The nonlinear dynamics of a single ion in a field-reversed configuration (FRC) were investigated. FRC is a toroidal fusion device which uses a specific type of magnetic field to confine ions. As a result of angular invariance, the full three-dimensional Hamiltonian system can be expressed as two coupled, highly nonlinear oscillators. Due to the high nonlinearity in the equations of motion, the behavior of the system is extremely complex, showing different regimes, depending on the values of the conserved canonical angular momentum and the geometry of the fusion vessel. Perturbation theory and averaging were used to derive the unperturbed Hamiltonianmore » and frequencies of the two degrees of freedom. The derived equations were then used to find resonances and compare to Poincar{copyright} surface-of-section plots. A regime was found where the nonlinear resonances were clearly separated by KAM [Kolmogorov-Arnold-Mosher] curves. The structure of the observed island chains was explained. The condition for the destruction of KAM curves and the onset of strong chaos was derived, using Chirikov island overlap criterion, and shown qualitatively to depend both on the canonical angular momentum and geometry of the device. After a brief discussion of the adiabatic regime the paper goes on to explore the degenerate regime that sets in at higher values of angular momenta. In this regime, the unperturbed Hamiltonian can be approximated as two uncoupled linear oscillators. In this case, the system is near-integrable, except in cases of a universal resonance, which results in large island structures, due to the smallness of nonlinear terms, which bound the resonance. The linear force constants, dominant in this regime, were derived and the geometry for a large one-to-one resonance identified. The above analysis showed good agreement with numerical simulations and was able to explain characteristic features of the dynamics.« less
Fuzzy Model-based Pitch Stabilization and Wing Vibration Suppression of Flexible Wing Aircraft.

NASA Technical Reports Server (NTRS)

Ayoubi, Mohammad A.; Swei, Sean Shan-Min; Nguyen, Nhan T.

2014-01-01

This paper presents a fuzzy nonlinear controller to regulate the longitudinal dynamics of an aircraft and suppress the bending and torsional vibrations of its flexible wings. The fuzzy controller utilizes full-state feedback with input constraint. First, the Takagi-Sugeno fuzzy linear model is developed which approximates the coupled aeroelastic aircraft model. Then, based on the fuzzy linear model, a fuzzy controller is developed to utilize a full-state feedback and stabilize the system while it satisfies the control input constraint. Linear matrix inequality (LMI) techniques are employed to solve the fuzzy control problem. Finally, the performance of the proposed controller is demonstrated on the NASA Generic Transport Model (GTM).
First full dynamic range calibration of the JUNGFRAU photon detector

NASA Astrophysics Data System (ADS)

Redford, S.; Andrä, M.; Barten, R.; Bergamaschi, A.; Brückner, M.; Dinapoli, R.; Fröjdh, E.; Greiffenberg, D.; Lopez-Cuenca, C.; Mezza, D.; Mozzanica, A.; Ramilli, M.; Ruat, M.; Ruder, C.; Schmitt, B.; Shi, X.; Thattil, D.; Tinti, G.; Vetter, S.; Zhang, J.

2018-01-01

The JUNGFRAU detector is a charge integrating hybrid silicon pixel detector developed at the Paul Scherrer Institut for photon science applications, in particular for the upcoming free electron laser SwissFEL. With a high dynamic range, analogue readout, low noise and three automatically switching gains, JUNGFRAU promises excellent performance not only at XFELs but also at synchrotrons in areas such as protein crystallography, ptychography, pump-probe and time resolved measurements. To achieve its full potential, the detector must be calibrated on a pixel-by-pixel basis. This contribution presents the current status of the JUNGFRAU calibration project, in which a variety of input charge sources are used to parametrise the energy response of the detector across four orders of magnitude of dynamic range. Building on preliminary studies, the first full calibration procedure of a JUNGFRAU 0.5 Mpixel module is described. The calibration is validated using alternative sources of charge deposition, including laboratory experiments and measurements at ESRF and LCLS. The findings from these measurements are presented. Calibrated modules have already been used in proof-of-principle style protein crystallography experiments at the SLS. A first look at selected results is shown. Aspects such as the conversion of charge to number of photons, treatment of multi-size pixels and the origin of non-linear response are also discussed.
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
Proceedings of the 2nd Experimental Chaos Conference

NASA Astrophysics Data System (ADS)

Ditto, William; Pecora, Lou; Shlesinger, Michael; Spano, Mark; Vohra, Sandeep

1995-02-01

The Table of Contents for the full book PDF is as follows: * Introduction * Spatiotemporal Phenomena * Experimental Studies of Chaotic Mixing * Using Random Maps in the Analysis of Experimental Fluid Flows * Transition to Spatiotemporal Chaos in a Reaction-Diffusion System * Ion-Dynamical Chaos in Plasmas * Optics * Chaos in a Synchronously Driven Optical Resonator * Chaos, Patterns and Defects in Stimulated Scattering Phenomena * Test of the Normal Form for a Subcritical Bifurcation * Observation of Bifurcations and Chaos in a Driven Fiber Optic Coil * Applications -- Communications * Robustness and Signal Recovery in a Synchronized Chaotic System * Synchronizing Nonautonomous Chaotic Circuits * Synchronization of Pulse-Coupled Chaotic Oscillators * Ocean Transmission Effects on Chaotic Signals * Controlling Symbolic Dynamics for Communication * Applications -- Control * Analysis of Nonlinear Actuators Using Chaotic Waveforms * Controlling Chaos in a Quasiperiodic Electronic System * Control of Chaos in a CO2 Laser * General Research * Video-Based Analysis of Bifurcation Phenomena in Radio-Frequency-Excited Inert Gas Plasmas * Transition from Soliton to Chaotic Motion During the Impact of a Nonlinear Structure * Sonoluminescence in a Single Bubble: Periodic, Quasiperiodic and Chaotic Light Source * Quantum Chaos Experiments Using Microwave Cavities * Experiments on Quantum Chaos With and Without Time Reversibility * When Small Noise Imposed on Deterministic Dynamics Becomes Important * Biology * Chaos Control for Cardiac Arrhythmias * Irregularities in Spike Trains of Cat Retinal Ganglion Cells * Broad-Band Synchronization in Monkey Neocortex * Applicability of Correlation Dimension Calculations to Blood Pressure Signal in Rats * Tests for Deterministic Chaos in Noisy Time Series * The Crayfish Mechanoreceptor Cell: A Biological Example of Stochastic Resonance * Chemistry * Chaos During Heterogeneous Chemical Reactions * Stabilizing and Tracking Unstable Periodic Orbits and Stationary States in Chemical Systems * Recursive Proportional-Feedback and Its Use to Control Chaos in an Electrochemical System * Temperature Patterns on Catalytic Surfaces * Meteorology/Oceanography * Nonlinear Evolution of Water Waves: Hilbert's View * Fractal Properties of Isoconcentration Surfaces in a Smoke Plume * Fractal Dimensions of Remotely Sensed Atmospheric Signals * Are Ocean Surface Waves Chaotic? * Dynamical Attractor Reconstruction for a Marine Stratocumulus Cloud

Dynamics of Nuclear Regions of Galaxies

NASA Technical Reports Server (NTRS)

Miller, Richard H.

1996-01-01

Current research carried out with the help of the ASEE-NASA Summer Faculty Program, at NASA-Ames, is concentrated on the dynamics of nuclear regions of galaxies. From a dynamical point of view a galaxy is a collection of around 10(sup 11) stars like our Sun, each of which moves in the summed gravitational field of all the remaining stars. Thus galaxy dynamics becomes a self-consistent n-body problem with forces given by Newtonian gravitation. Strong nonlinearity in the gravitational force and the inherent nonlinearity of self-consistent problems both argue for a numerical approach. The technique of numerical experiments consis of constructing an environment in the computer that is as close as possible to the physical conditions in a real galaxy and then carrying out experiments much like laboratory experiments in physics or engineering, in this environment. Computationally, an experiment is an initial value problem, and a good deal of thought and effort goes into the design of the starting conditions that serve as initial values. Experiments are run at Ames because all the 'equipment' is in place-the programs, the necessary computational power, and good facilities for post-run analysis. Our goal for this research program is to study the nuclear regions in detail and this means replacing most of the galaxy by a suitable boundary condition to allow the full capability of numerical experiments to be brought to bear on a small region perhaps 1/1000 of the linear dimensions of an entire galaxy. This is an extremely delicate numerical problem, one in which some small feature overlook, can easily lead to a collapse or blow-up of the entire system. All particles attract each other in gravitational problems, and the 1/r(sup 2) force is: (1) nonlinear; (2) strong at short range; (3) long-range, and (4) unscreened at any distance.
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.
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.
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.
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 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...
Modelling of the nonlinear soliton dynamics in the ring fibre cavity

NASA Astrophysics Data System (ADS)

Razukov, Vadim A.; Melnikov, Leonid A.

2018-04-01

Using the cabaret method numerical realization, long-time spatio-temporal dynamics of the electromagnetic field in a nonlinear ring fibre cavity with dispersion is investigated during the hundreds of round trips. Formation of both the temporal cavity solitons and irregular pulse trains is demonstrated and discussed.
Dynamics and control for Constrained Multibody Systems modeled with Maggi's equation: Application to Differential Mobile Robots Partll

NASA Astrophysics Data System (ADS)

Amengonu, Yawo H.; Kakad, Yogendra P.

2014-07-01

Quasivelocity techniques were applied to derive the dynamics of a Differential Wheeled Mobile Robot (DWMR) in the companion paper. The present paper formulates a control system design for trajectory tracking of this class of robots. The method develops a feedback linearization technique for the nonlinear system using dynamic extension algorithm. The effectiveness of the nonlinear controller is illustrated with simulation example.
A simultaneous all-optical half/full-subtraction strategy using cascaded highly nonlinear fibers

NASA Astrophysics Data System (ADS)

Singh, Karamdeep; Kaur, Gurmeet; Singh, Maninder Lal

2018-02-01

Using non-linear effects such as cross-gain modulation (XGM) and cross-phase modulation (XPM) inside two highly non-linear fibres (HNLF) arranged in cascaded configuration, a simultaneous half/full-subtracter is proposed. The proposed simultaneous half/full-subtracter design is attractive due to several features such as input data pattern independence and usage of minimal number of non-linear elements i.e. HNLFs. Proof of concept simulations have been conducted at 100 Gbps rate, indicating fine performance, as extinction ratio (dB) > 6.28 dB and eye opening factors (EO) > 77.1072% are recorded for each implemented output. The proposed simultaneous half/full-subtracter can be used as a key component in all-optical information processing circuits.
Non-autonomous multi-rogue waves for spin-1 coupled nonlinear Gross-Pitaevskii equation and management by external potentials.

PubMed

Li, Li; Yu, Fajun

2017-09-06

We investigate non-autonomous multi-rogue wave solutions in a three-component(spin-1) coupled nonlinear Gross-Pitaevskii(GP) equation with varying dispersions, higher nonlinearities, gain/loss and external potentials. The similarity transformation allows us to relate certain class of multi-rogue wave solutions of the spin-1 coupled nonlinear GP equation to the solutions of integrable coupled nonlinear Schrödinger(CNLS) equation. We study the effect of time-dependent quadratic potential on the profile and dynamic of non-autonomous rogue waves. With certain requirement on the backgrounds, some non-autonomous multi-rogue wave solutions exhibit the different shapes with two peaks and dip in bright-dark rogue waves. Then, the managements with external potential and dynamic behaviors of these solutions are investigated analytically. The results could be of interest in such diverse fields as Bose-Einstein condensates, nonlinear fibers and super-fluids.
Ultra-fast dynamics in the nonlinear optical response of silver nanoprism ordered arrays.

PubMed

Sánchez-Esquivel, Héctor; Raygoza-Sanchez, Karen Y; Rangel-Rojo, Raúl; Kalinic, Boris; Michieli, Niccolò; Cesca, Tiziana; Mattei, Giovanni

2018-03-15

In this work we present the study of the ultra-fast dynamics of the nonlinear optical response of a honeycomb array of silver triangular nanoprisms, performed using a femtosecond pulsed laser tuned with the dipolar surface plasmon resonance of the nanoarray. Nonlinear absorption and refraction, and their time-dependence, were explored using the z-scan and time-resolved excite-probe techniques. Nonlinear absorption is shown to change sign with the input irradiance and the behavior was explained on the basis of a three-level model. The response time was determined to be in the picosecond regime. A technique based on a variable frequency chopper was also used in order to discriminate the thermal and electronic contributions to the nonlinearity, which were found to have opposite signs. All these findings propel the investigated nanoprism arrays as good candidates for applications in advanced ultra-fast nonlinear nanophotonic devices.
A novel method for predicting the power outputs of wave energy converters

NASA Astrophysics Data System (ADS)

Wang, Yingguang

2018-03-01

This paper focuses on realistically predicting the power outputs of wave energy converters operating in shallow water nonlinear waves. A heaving two-body point absorber is utilized as a specific calculation example, and the generated power of the point absorber has been predicted by using a novel method (a nonlinear simulation method) that incorporates a second order random wave model into a nonlinear dynamic filter. It is demonstrated that the second order random wave model in this article can be utilized to generate irregular waves with realistic crest-trough asymmetries, and consequently, more accurate generated power can be predicted by subsequently solving the nonlinear dynamic filter equation with the nonlinearly simulated second order waves as inputs. The research findings demonstrate that the novel nonlinear simulation method in this article can be utilized as a robust tool for ocean engineers in their design, analysis and optimization of wave energy converters.
Correlation techniques to determine model form in robust nonlinear system realization/identification

NASA Technical Reports Server (NTRS)

Stry, Greselda I.; Mook, D. Joseph

1991-01-01

The fundamental challenge in identification of nonlinear dynamic systems is determining the appropriate form of the model. A robust technique is presented which essentially eliminates this problem for many applications. The technique is based on the Minimum Model Error (MME) 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 is the ability to identify nonlinear dynamic systems without prior assumption regarding the form of the nonlinearities, in contrast to existing nonlinear identification approaches which usually require detailed assumptions of the nonlinearities. Model form is determined via statistical correlation of the MME optimal state estimates with the MME optimal model error estimates. 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.
Nonlinear dynamics induced anomalous Hall effect in topological insulators

PubMed Central

Wang, Guanglei; Xu, Hongya; Lai, Ying-Cheng

2016-01-01

We uncover an alternative mechanism for anomalous Hall effect. In particular, we investigate the magnetisation dynamics of an insulating ferromagnet (FM) deposited on the surface of a three-dimensional topological insulator (TI), subject to an external voltage. The spin-polarised current on the TI surface induces a spin-transfer torque on the magnetisation of the top FM while its dynamics can change the transmission probability of the surface electrons through the exchange coupling and hence the current. We find a host of nonlinear dynamical behaviors including multistability, chaos, and phase synchronisation. Strikingly, a dynamics mediated Hall-like current can arise, which exhibits a nontrivial dependence on the channel conductance. We develop a physical understanding of the mechanism that leads to the anomalous Hall effect. The nonlinear dynamical origin of the effect stipulates that a rich variety of final states exist, implying that the associated Hall current can be controlled to yield desirable behaviors. The phenomenon can find applications in Dirac-material based spintronics. PMID:26819223
Nonlinear dynamics induced anomalous Hall effect in topological insulators.

PubMed

Wang, Guanglei; Xu, Hongya; Lai, Ying-Cheng

2016-01-28

We uncover an alternative mechanism for anomalous Hall effect. In particular, we investigate the magnetisation dynamics of an insulating ferromagnet (FM) deposited on the surface of a three-dimensional topological insulator (TI), subject to an external voltage. The spin-polarised current on the TI surface induces a spin-transfer torque on the magnetisation of the top FM while its dynamics can change the transmission probability of the surface electrons through the exchange coupling and hence the current. We find a host of nonlinear dynamical behaviors including multistability, chaos, and phase synchronisation. Strikingly, a dynamics mediated Hall-like current can arise, which exhibits a nontrivial dependence on the channel conductance. We develop a physical understanding of the mechanism that leads to the anomalous Hall effect. The nonlinear dynamical origin of the effect stipulates that a rich variety of final states exist, implying that the associated Hall current can be controlled to yield desirable behaviors. The phenomenon can find applications in Dirac-material based spintronics.
Uncovering Droop Control Laws Embedded Within the Nonlinear Dynamics of Van der Pol Oscillators

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

Sinha, Mohit; Dorfler, Florian; Johnson, Brian B.

This paper examines the dynamics of power-electronic inverters in islanded microgrids that are controlled to emulate the dynamics of Van der Pol oscillators. The general strategy of controlling inverters to emulate the behavior of nonlinear oscillators presents a compelling time-domain alternative to ubiquitous droop control methods which presume the existence of a quasistationary sinusoidal steady state and operate on phasor quantities. We present two main results in this paper. First, by leveraging the method of periodic averaging, we demonstrate that droop laws are intrinsically embedded within a slower time scale in the nonlinear dynamics of Van der Pol oscillators. Second,more » we establish the global convergence of amplitude and phase dynamics in a resistive network interconnecting inverters controlled as Van der Pol oscillators. Furthermore, under a set of nonrestrictive decoupling approximations, we derive sufficient conditions for local exponential stability of desirable equilibria of the linearized amplitude and phase dynamics.« less
Adaptive Actor-Critic Design-Based Integral Sliding-Mode Control for Partially Unknown Nonlinear Systems With Input Disturbances.

PubMed

Fan, Quan-Yong; Yang, Guang-Hong

2016-01-01

This paper is concerned with the problem of integral sliding-mode control for a class of nonlinear systems with input disturbances and unknown nonlinear terms through the adaptive actor-critic (AC) control method. The main objective is to design a sliding-mode control methodology based on the adaptive dynamic programming (ADP) method, so that the closed-loop system with time-varying disturbances is stable and the nearly optimal performance of the sliding-mode dynamics can be guaranteed. In the first step, a neural network (NN)-based observer and a disturbance observer are designed to approximate the unknown nonlinear terms and estimate the input disturbances, respectively. Based on the NN approximations and disturbance estimations, the discontinuous part of the sliding-mode control is constructed to eliminate the effect of the disturbances and attain the expected equivalent sliding-mode dynamics. Then, the ADP method with AC structure is presented to learn the optimal control for the sliding-mode dynamics online. Reconstructed tuning laws are developed to guarantee the stability of the sliding-mode dynamics and the convergence of the weights of critic and actor NNs. Finally, the simulation results are presented to illustrate the effectiveness of the proposed method.
Nonlinear modeling of chaotic time series: Theory and applications

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

Casdagli, M.; Eubank, S.; Farmer, J.D.

1990-01-01

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 identifyingmore » 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. 162 refs., 13 figs.« less
A Modal Model to Simulate Typical Structural Dynamic Nonlinearity [PowerPoint

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

Mayes, Randall L.; Pacini, Benjamin Robert; Roettgen, Dan

2016-01-01

Some initial investigations have been published which simulate nonlinear response with almost traditional modal models: instead of connecting the modal mass to ground through the traditional spring and damper, a nonlinear Iwan element was added. This assumes that the mode shapes do not change with amplitude and there are no interactions between modal degrees of freedom. This work expands on these previous studies. An impact experiment is performed on a structure which exhibits typical structural dynamic nonlinear response, i.e. weak frequency dependence and strong damping dependence on the amplitude of vibration. Use of low level modal test results in combinationmore » with high level impacts are processed using various combinations of modal filtering, the Hilbert Transform and band-pass filtering to develop response data that are then fit with various nonlinear elements to create a nonlinear pseudo-modal model. Simulations of forced response are compared with high level experimental data for various nonlinear element assumptions.« less
A Modal Model to Simulate Typical Structural Dynamic Nonlinearity

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

Pacini, Benjamin Robert; Mayes, Randall L.; Roettgen, Daniel R

2015-10-01

Some initial investigations have been published which simulate nonlinear response with almost traditional modal models: instead of connecting the modal mass to ground through the traditional spring and damper, a nonlinear Iwan element was added. This assumes that the mode shapes do not change with amplitude and there are no interactions between modal degrees of freedom. This work expands on these previous studies. An impact experiment is performed on a structure which exhibits typical structural dynamic nonlinear response, i.e. weak frequency dependence and strong damping dependence on the amplitude of vibration. Use of low level modal test results in combinationmore » with high level impacts are processed using various combinations of modal filtering, the Hilbert Transform and band-pass filtering to develop response data that are then fit with various nonlinear elements to create a nonlinear pseudo-modal model. Simulations of forced response are compared with high level experimental data for various nonlinear element assumptions.« less
FRF decoupling of nonlinear systems

NASA Astrophysics Data System (ADS)

Kalaycıoğlu, Taner; Özgüven, H. Nevzat

2018-03-01

Structural decoupling problem, i.e. predicting dynamic behavior of a particular substructure from the knowledge of the dynamics of the coupled structure and the other substructure, has been well investigated for three decades and led to several decoupling methods. In spite of the inherent nonlinearities in a structural system in various forms such as clearances, friction and nonlinear stiffness, all decoupling studies are for linear systems. In this study, decoupling problem for nonlinear systems is addressed for the first time. A method, named as FRF Decoupling Method for Nonlinear Systems (FDM-NS), is proposed for calculating FRFs of a substructure decoupled from a coupled nonlinear structure where nonlinearity can be modeled as a single nonlinear element. Depending on where nonlinear element is, i.e., either in the known or unknown subsystem, or at the connection point, the formulation differs. The method requires relative displacement information between two end points of the nonlinear element, in addition to point and transfer FRFs at some points of the known subsystem. However, it is not necessary to excite the system from the unknown subsystem even when the nonlinear element is in that subsystem. The validation of FDM-NS is demonstrated with two different case studies using nonlinear lumped parameter systems. Finally, a nonlinear experimental test structure is used in order to show the real-life application and accuracy of FDM-NS.
Bifurcation Analysis of an Electrostatically Actuated Nano-Beam Based on Modified Couple Stress Theory

NASA Astrophysics Data System (ADS)

Rezaei Kivi, Araz; Azizi, Saber; Norouzi, Peyman

2017-12-01

In this paper, the nonlinear size-dependent static and dynamic behavior of an electrostatically actuated nano-beam is investigated. A fully clamped nano-beam is considered for the modeling of the deformable electrode of the NEMS. The governing differential equation of the motion is derived using Hamiltonian principle based on couple stress theory; a non-classical theory for considering length scale effects. The nonlinear partial differential equation of the motion is discretized to a nonlinear Duffing type ODE's using Galerkin method. Static and dynamic pull-in instabilities obtained by both classical theory and MCST are compared. At the second stage of analysis, shooting technique is utilized to obtain the frequency response curve, and to capture the periodic solutions of the motion; the stability of the periodic solutions are gained by Floquet theory. The nonlinear dynamic behavior of the deformable electrode due to the AC harmonic accompanied with size dependency is investigated.
Stochastic Resonance and Safe Basin of Single-Walled Carbon Nanotubes with Strongly Nonlinear Stiffness under Random Magnetic Field.

PubMed

Xu, Jia; Li, Chao; Li, Yiran; Lim, Chee Wah; Zhu, Zhiwen

2018-05-04

In this paper, a kind of single-walled carbon nanotube nonlinear model is developed and the strongly nonlinear dynamic characteristics of such carbon nanotubes subjected to random magnetic field are studied. The nonlocal effect of the microstructure is considered based on Eringen’s differential constitutive model. The natural frequency of the strongly nonlinear dynamic system is obtained by the energy function method, the drift coefficient and the diffusion coefficient are verified. The stationary probability density function of the system dynamic response is given and the fractal boundary of the safe basin is provided. Theoretical analysis and numerical simulation show that stochastic resonance occurs when varying the random magnetic field intensity. The boundary of safe basin has fractal characteristics and the area of safe basin decreases when the intensity of the magnetic field permeability increases.
Substrate clamping effects on irreversible domain wall dynamics in lead zirconate titanate thin films.

PubMed

Griggio, F; Jesse, S; Kumar, A; Ovchinnikov, O; Kim, H; Jackson, T N; Damjanovic, D; Kalinin, S V; Trolier-McKinstry, S

2012-04-13

The role of long-range strain interactions on domain wall dynamics is explored through macroscopic and local measurements of nonlinear behavior in mechanically clamped and released polycrystalline lead zirconate-titanate (PZT) films. Released films show a dramatic change in the global dielectric nonlinearity and its frequency dependence as a function of mechanical clamping. Furthermore, we observe a transition from strong clustering of the nonlinear response for the clamped case to almost uniform nonlinearity for the released film. This behavior is ascribed to increased mobility of domain walls. These results suggest the dominant role of collective strain interactions mediated by the local and global mechanical boundary conditions on the domain wall dynamics. The work presented in this Letter demonstrates that measurements on clamped films may considerably underestimate the piezoelectric coefficients and coupling constants of released structures used in microelectromechanical systems, energy harvesting systems, and microrobots.

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