A data driven nonlinear stochastic model for blood glucose dynamics.

Science.gov (United States)

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.

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

Science.gov (United States)

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.

Nonlinear dynamics and modelling of various wooden toys with impact and friction

NARCIS (Netherlands)

Leine, R.I.; Campen, van D.H.; Glocker, C.

2003-01-01

In this paper, we study bifurcations in systems with impact and friction, modeled with a rigid multibody approach. Knowledge from the field of nonlinear dynamics is therefore combined with theory from the field of non-smooth mechanics. We study the nonlinear dynamics of three commercial wooden toys.

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

Science.gov (United States)

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.

Dynamics of nonlinear feedback control.

Science.gov (United States)

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 electromechanical modelling and dynamical behavior analysis of a satellite reaction wheel

Science.gov (United States)

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.

An Efficient Reduced-Order Model for the Nonlinear Dynamics of Carbon Nanotubes

KAUST Repository

Xu, Tiantian

2014-08-17

Because of the inherent nonlinearities involving the behavior of CNTs when excited by electrostatic forces, modeling and simulating their behavior is challenging. The complicated form of the electrostatic force describing the interaction of their cylindrical shape, forming upper electrodes, to lower electrodes poises serious computational challenges. This presents an obstacle against applying and using several nonlinear dynamics tools that typically used to analyze the behavior of complicated nonlinear systems, such as shooting, continuation, and integrity analysis techniques. This works presents an attempt to resolve this issue. We present an investigation of the nonlinear dynamics of carbon nanotubes when actuated by large electrostatic forces. We study expanding the complicated form of the electrostatic force into enough number of terms of the Taylor series. We plot and compare the expanded form of the electrostatic force to the exact form and found that at least twenty terms are needed to capture accurately the strong nonlinear form of the force over the full range of motion. Then, we utilize this form along with an Euler–Bernoulli beam model to study the static and dynamic behavior of CNTs. The geometric nonlinearity and the nonlinear electrostatic force are considered. An efficient reduced-order model (ROM) based on the Galerkin method is developed and utilized to simulate the static and dynamic responses of the CNTs. We found that the use of the new expanded form of the electrostatic force enables avoiding the cumbersome evaluation of the spatial integrals involving the electrostatic force during the modal projection procedure in the Galerkin method, which needs to be done at every time step. Hence, the new method proves to be much more efficient computationally.

Modelling the influence of sensory dynamics on linear and nonlinear driver steering control

Science.gov (United States)

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.

A new modified resource budget model for nonlinear dynamics in citrus production

International Nuclear Information System (INIS)

Ye, Xujun; Sakai, Kenshi

2016-01-01

Highlights: • A theoretical modeling and simulation study of the nonlinear dynamics in citrus is conducted. • New leaf growth is incorporated into the model as a major factor responsible for the yield oscillations. • A Ricker-type equation for the relationship between costs for flowering and fruiting is proposed. • A generic form of the resource budget model for the nonlinear dynamics in citrus is obtained. • The new model is tested with experimental data for two citrus trees. - Abstract : Alternate bearing or masting is a general yield variability phenomenon in perennial tree crops. This paper first presents a theoretical modeling and simulation study of the mechanism for this dynamics in citrus, and then provides a test of the proposed models using data from a previous 16-year experiment in a citrus orchard. Our previous studies suggest that the mutual effects between vegetative and reproductive growths caused by resource allocation and budgeting in plant body might be considered as a major factor responsible for the yield oscillations in citrus. Based on the resource budget model proposed by Isagi et al. (J Theor Biol. 1997;187:231-9), we first introduce the new leaf growth as a major energy consumption component into the model. Further, we introduce a nonlinear Ricker-type equation to replace the linear relationship between costs for flowering and fruiting used in Isagi's model. Model simulations demonstrate that the proposed new models can successfully simulate the reproductive behaviors of citrus trees with different fruiting dynamics. These results may enrich the mechanical dynamics in tree crop reproductive models and help us to better understand the dynamics of vegetative-reproductive growth interactions in a real environment.

Null Controllability of a Nonlinear Dissipative System and Application to the Detection of the Incomplete Parameter for a Nonlinear Population Dynamics Model

Directory of Open Access Journals (Sweden)

Yacouba Simporé

2016-01-01

Full Text Available We first prove a null controllability result for a nonlinear system derived from a nonlinear population dynamics model. In order to tackle the controllability problem we use an adapted Carleman inequality. Next we consider the nonlinear population dynamics model with a source term called the pollution term. In order to obtain information on the pollution term we use the method of sentinel.

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

Science.gov (United States)

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 economic dynamics and financial modelling: essays in honour of Carl Chiarella

NARCIS (Netherlands)

Dieci, R.; He, X.Z.; Hommes, C.

2014-01-01

This book reflects the state of the art on nonlinear economic dynamics, financial market modelling and quantitative finance. It contains eighteen papers with topics ranging from disequilibrium macroeconomics, monetary dynamics, monopoly, financial market and limit order market models with boundedly

Identification of Nonlinear Dynamic Systems Possessing Some Non-linearities

Directory of Open Access Journals (Sweden)

Y. N. Pavlov

2015-01-01

Full Text Available The subject of this work is the problem of identification of nonlinear dynamic systems based on the experimental data obtained by applying test signals to the system. The goal is to determinate coefficients of differential equations of systems by experimental frequency hodographs and separate similar, but different, in essence, forces: dissipative forces with the square of the first derivative in the motion equations and dissipative force from the action of dry friction. There was a proposal to use the harmonic linearization method to approximate each of the nonlinearity of "quadratic friction" and "dry friction" by linear friction with the appropriate harmonic linearization coefficient.Assume that a frequency transfer function of the identified system has a known form. Assume as well that there are disturbances while obtaining frequency characteristics of the realworld system. As a result, the points of experimentally obtained hodograph move randomly. Searching for solution of the identification problem was in the hodograph class, specified by the system model, which has the form of the frequency transfer function the same as the form of the frequency transfer function of the system identified. Minimizing a proximity criterion (measure of the experimentally obtained system hodograph and the system hodograph model for all the experimental points described and previously published by one of the authors allowed searching for the unknown coefficients of the frequenc ransfer function of the system model. The paper shows the possibility to identify a nonlinear dynamic system with multiple nonlinearities, obtained on the experimental samples of the frequency system hodograph. The proposed algorithm allows to select the nonlinearity of the type "quadratic friction" and "dry friction", i.e. also in the case where the nonlinearity is dependent on the same dynamic parameter, in particular, on the derivative of the system output value. For the dynamic

Nonlinear Dynamic Model of PMBLDC Motor Considering Core Losses

DEFF Research Database (Denmark)

Fasil, Muhammed; Mijatovic, Nenad; Jensen, Bogi Bech

2017-01-01

The phase variable model is used commonly when simulating a motor drive system with a three-phase permanent magnet brushless DC (PMBLDC) motor. The phase variable model neglects core losses and this affects its accuracy when modelling fractional-slot machines. The inaccuracy of phase variable mod...... on the detailed analysis of the flux path and the variation of flux in different components of the machine. A prototype of fractional slot axial flux PMBLDC in-wheel motor is used to assess the proposed nonlinear dynamic model....... of fractional-slot machines can be attributed to considerable armature flux harmonics, which causes an increased core loss. This study proposes a nonlinear phase variable model of PMBLDC motor that considers the core losses induced in the stator and the rotor. The core loss model is developed based...

Advanced models of neural networks nonlinear dynamics and stochasticity in biological neurons

CERN Document Server

Rigatos, Gerasimos G

2015-01-01

This book provides a complete study on neural structures exhibiting nonlinear and stochastic dynamics, elaborating on neural dynamics by introducing advanced models of neural networks. It overviews the main findings in the modelling of neural dynamics in terms of electrical circuits and examines their stability properties with the use of dynamical systems theory. It is suitable for researchers and postgraduate students engaged with neural networks and dynamical systems theory.

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

Science.gov (United States)

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.

Dynamics of nonlinear feedback control

OpenAIRE

Snippe, H.P.; Hateren, J.H. van

2007-01-01

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 step...

Dynamics modeling for a rigid-flexible coupling system with nonlinear deformation field

International Nuclear Information System (INIS)

Deng Fengyan; He Xingsuo; Li Liang; Zhang Juan

2007-01-01

In this paper, a moving flexible beam, which incorporates the effect of the geometrically nonlinear kinematics of deformation, is investigated. Considering the second-order coupling terms of deformation in the longitudinal and transverse deflections, the exact nonlinear strain-displacement relations for a beam element are described. The shear strains formulated by the present modeling method in this paper are zero, so it is reasonable to use geometrically nonlinear deformation fields to demonstrate and simplify a flexible beam undergoing large overall motions. Then, considering the coupling terms of deformation in two dimensions, finite element shape functions of a beam element and Lagrange's equations are employed for deriving the coupling dynamical formulations. The complete expression of the stiffness matrix and all coupling terms are included in the formulations. A model consisting of a rotating planar flexible beam is presented. Then the frequency and dynamical response are studied, and the differences among the zero-order model, first-order coupling model and the new present model are discussed. Numerical examples demonstrate that a 'stiffening beam' can be obtained, when more coupling terms of deformation are added to the longitudinal and transverse deformation field. It is shown that the traditional zero-order and first-order coupling models may not provide an exact dynamic model in some cases

Quantitative theory of driven nonlinear brain dynamics.

Science.gov (United States)

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 dynamics new directions models and applications

CERN Document Server

Ugalde, Edgardo

2015-01-01

This book, along with its companion volume, Nonlinear Dynamics New Directions: Theoretical Aspects, covers topics ranging from fractal analysis to very specific applications of the theory of dynamical systems to biology. This second volume contains mostly new applications of the theory of dynamical systems to both engineering and biology. The first volume is devoted to fundamental aspects and includes a number of important new contributions as well as some review articles that emphasize new development prospects. The topics addressed in the two volumes include a rigorous treatment of fluctuations in dynamical systems, topics in fractal analysis, studies of the transient dynamics in biological networks, synchronization in lasers, and control of chaotic systems, among others. This book also: ·         Develops applications of nonlinear dynamics on a diversity of topics such as patterns of synchrony in neuronal networks, laser synchronization, control of chaotic systems, and the study of transient dynam...

Nonlinear and stochastic dynamics of coherent structures

DEFF Research Database (Denmark)

Rasmussen, Kim

1997-01-01

This Thesis deals with nonlinear and stochastic dynamics in systems which can be described by nonlinear Schrödinger models. Basically three different models are investigated. The first is the continuum nonlinear Schröndinger model in one and two dimensions generalized by a tunable degree of nonli......This Thesis deals with nonlinear and stochastic dynamics in systems which can be described by nonlinear Schrödinger models. Basically three different models are investigated. The first is the continuum nonlinear Schröndinger model in one and two dimensions generalized by a tunable degree...... introduces the nonlinear Schrödinger model in one and two dimensions, discussing the soliton solutions in one dimension and the collapse phenomenon in two dimensions. Also various analytical methods are described. Then a derivation of the nonlinear Schrödinger equation is given, based on a Davydov like...... system described by a tight-binding Hamiltonian and a harmonic lattice coupled b y a deformation-type potential. This derivation results in a two-dimensional nonline ar Schrödinger model, and considering the harmonic lattice to be in thermal contact with a heat bath w e show that the nonlinear...

Measurement Model Nonlinearity in Estimation of Dynamical Systems

Science.gov (United States)

Majji, Manoranjan; Junkins, J. L.; Turner, J. D.

2012-06-01

The role of nonlinearity of the measurement model and its interactions with the uncertainty of measurements and geometry of the problem is studied in this paper. An examination of the transformations of the probability density function in various coordinate systems is presented for several astrodynamics applications. Smooth and analytic nonlinear functions are considered for the studies on the exact transformation of uncertainty. Special emphasis is given to understanding the role of change of variables in the calculus of random variables. The transformation of probability density functions through mappings is shown to provide insight in to understanding the evolution of uncertainty in nonlinear systems. Examples are presented to highlight salient aspects of the discussion. A sequential orbit determination problem is analyzed, where the transformation formula provides useful insights for making the choice of coordinates for estimation of dynamic systems.

Structural stability of nonlinear population dynamics.

Science.gov (United States)

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

Science.gov (United States)

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.

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

Science.gov (United States)

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.

Magnetically nonlinear dynamic model of synchronous motor with permanent magnets

International Nuclear Information System (INIS)

Hadziselimovic, Miralem; Stumberger, Gorazd; Stumberger, Bojan; Zagradisnik, Ivan

2007-01-01

This paper deals with a magnetically nonlinear two-axis dynamic model of a permanent magnet synchronous motor (PMSM). The geometrical and material properties of iron core and permanent magnets, the effects of winding distribution, saturation, cross-saturation and slotting effects are, for the first time, simultaneously accounted for in a single two-axis dynamic model of a three-phase PMSM. They are accounted for by current- and position-dependent characteristics of flux linkages. These characteristics can be determined either experimentally or by the finite element (FE) computations. The results obtained by the proposed dynamic model show a very good agreement with the measured ones and those obtained by the FE computation

Nonlinear modeling and dynamic analysis of hydro-turbine governing system in the process of load rejection transient

International Nuclear Information System (INIS)

Zhang, Hao; Chen, Diyi; Xu, Beibei; Wang, Feifei

2015-01-01

Graphical abstract: Nonlinear dynamic transfer coefficients are introduced to the hydro-turbine governing system. In the process of load reject ion transient, the nonlinear dynamical behaviors of the system are studied in detail. - Highlights: • A novel mathematical model of a hydro-turbine governing system is established. • The process of load rejection transient is considered. • Nonlinear dynamic transfer coefficients are introduced to the system. • The bifurcation diagram with the variable t has better engineering significance. • The nonlinear dynamical behaviors of the system are studied in detail. - Abstract: This article pays attention to the mathematical modeling of a hydro-turbine governing system in the process of load rejection transient. As a pioneer work, the nonlinear dynamic transfer coefficients are introduced in a penstock system. Considering a generator system, a turbine system and a governor system, we present a novel nonlinear dynamical model of a hydro-turbine governing system. Fortunately, for the unchanged of PID parameters, we acquire the stable regions of the governing system in the process of load rejection transient by numerical simulations. Moreover, the nonlinear dynamic behaviors of the governing system are illustrated by bifurcation diagrams, Poincare maps, time waveforms and phase orbits. More importantly, these methods and analytic results will present theoretical groundwork for allowing a hydropower station in the process of load rejection transient

Nonlinear Dynamic Modeling of a Fixed-Wing Unmanned Aerial Vehicle: a Case Study of Wulung

Directory of Open Access Journals (Sweden)

Fadjar Rahino Triputra

2015-07-01

Full Text Available Developing a nonlinear adaptive control system for a fixed-wing unmanned aerial vehicle (UAV requires a mathematical representation of the system dynamics analytically as a set of differential equations in the form of a strict-feedback systems. This paper presents a method for modeling a nonlinear flight dynamics of the fixed-wing UAV of BPPT Wulung in any conditions of the flight altitude and airspeed for the first step into designing a nonlinear adaptive controller. The model was formed into 10-DOF differential equations in the form of strict-feedback systems which separates the terms of elevator, aileron, rudder and throttle from the model. The model simulation results show the behavior of the flight dynamics of the Wulung UAV and also prove the compliance with the actual flight test results.

Dynamics in a nonlinear Keynesian good market model

International Nuclear Information System (INIS)

Naimzada, Ahmad; Pireddu, Marina

2014-01-01

In this paper, we show how a rich variety of dynamical behaviors can emerge in the standard Keynesian income-expenditure model when a nonlinearity is introduced, both in the cases with and without endogenous government spending. A specific sigmoidal functional form is used for the adjustment mechanism of income with respect to the excess demand, in order to bound the income variation. With the aid of analytical and numerical tools, we investigate the stability conditions, bifurcations, as well as periodic and chaotic dynamics. Globally, we study multistability phenomena, i.e., the coexistence of different kinds of attractors

Nonlinear dynamics mathematical models for rigid bodies with a liquid

CERN Document Server

Lukovsky, Ivan A

2015-01-01

This book is devoted to analytically approximate methods in the nonlinear dynamics of a rigid body with cavities partly filled by liquid. It combines several methods and compares the results with experimental data. It is useful for experienced and early-stage readers interested in analytical approaches to fluid-structure interaction problems, the fundamental mathematical background and modeling the dynamics of such complex mechanical systems.

Nonlinear dynamical modeling and prediction of the terrestrial magnetospheric activity

International Nuclear Information System (INIS)

Vassiliadis, D.

1992-01-01

The irregular activity of the magnetosphere results from its complex internal dynamics as well as the external influence of the solar wind. The dominating self-organization of the magnetospheric plasma gives rise to repetitive, large-scale coherent behavior manifested in phenomena such as the magnetic substorm. Based on the nonlinearity of the global dynamics this dissertation examines the magnetosphere as a nonlinear dynamical system using time series analysis techniques. Initially the magnetospheric activity is modeled in terms of an autonomous system. A dimension study shows that its observed time series is self-similar, but the correlation dimension is high. The implication of a large number of degrees of freedom is confirmed by other state space techniques such as Poincare sections and search for unstable periodic orbits. At the same time a stability study of the time series in terms of Lyapunov exponents suggests that the series is not chaotic. The absence of deterministic chaos is supported by the low predictive capability of the autonomous model. Rather than chaos, it is an external input which is largely responsible for the irregularity of the magnetospheric activity. In fact, the external driving is so strong that the above state space techniques give results for magnetospheric and solar wind time series that are at least qualitatively similar. Therefore the solar wind input has to be included in a low-dimensional nonautonomous model. Indeed it is shown that such a model can reproduce the observed magnetospheric behavior up to 80-90 percent. The characteristic coefficients of the model show little variation depending on the external disturbance. The impulse response is consistent with earlier results of linear prediction filters. The model can be easily extended to contain nonlinear features of the magnetospheric activity and in particular the loading-unloading behavior of substorms

MEMS linear and nonlinear statics and dynamics

CERN Document Server

Younis, Mohammad I

2011-01-01

MEMS Linear and Nonlinear Statics and Dynamics presents the necessary analytical and computational tools for MEMS designers to model and simulate most known MEMS devices, structures, and phenomena. This book also provides an in-depth analysis and treatment of the most common static and dynamic phenomena in MEMS that are encountered by engineers. Coverage also includes nonlinear modeling approaches to modeling various MEMS phenomena of a nonlinear nature, such as those due to electrostatic forces, squeeze-film damping, and large deflection of structures. The book also: Includes examples of nume

Comparison of a nonlinear dynamic model of a piping system to test data

International Nuclear Information System (INIS)

Blakely, K.D.; Howard, G.E.; Walton, W.B.; Johnson, B.A.; Chitty, D.E.

1983-01-01

Response of a nonlinear finite element model of the Heissdampfreaktor recirculation piping loop (URL) was compared to measured data, representing the physical benchmarking of a nonlinear model. Analysis-test comparisons of piping response are presented for snapback tests that induced extreme nonlinear behavior of the URL system. Nonlinearities in the system are due to twelve swaybraces (pipe supports) that possessed nonlinear force-deflection characteristics. These nonlinearities distorted system damping estimates made by using the half-power bandwidth method on Fourier transforms of measured accelerations, with the severity of distortion increasing with increasing degree of nonlinearity. Time domain methods, which are not so severely affected by the presence of nonlinearities, were used to compute system damping ratios. Nonlinear dynamic analyses were accurately and efficiently performed using the pseudo-force technique and the finite element program MSC/NASTRAN. Measured damping was incorporated into the model for snapback simulations. Acceleration time histories, acceleration Fourier transforms, and swaybrace force time histories of the nonlinear model, plus several linear models, were compared to test measurements. The nonlinear model predicted three-fourths of the measured peak accelerations to within 50%, half of the accelerations to within 25%, and one-fifth of the accelerations to within 10%. This nonlinear model predicted accelerations (in the time and frequency domains) and swaybrace forces much better than did any of the linear models, demonstrating the increased accuracy resulting from properly simulating nonlinear support behavior. In addition, earthquake response comparisons were made between the experimentally validated nonlinear model and a linear model. Significantly lower element stresses were predicted for the nonlinear model, indicating the potential usefulness of nonlinear simulations in piping design assessments. (orig.)

Nonlinear dynamics and complexity

CERN Document Server

Luo, Albert; Fu, Xilin

2014-01-01

This important collection presents recent advances in nonlinear dynamics including analytical solutions, chaos in Hamiltonian systems, time-delay, uncertainty, and bio-network dynamics. Nonlinear Dynamics and Complexity equips readers to appreciate this increasingly main-stream approach to understanding complex phenomena in nonlinear systems as they are examined in a broad array of disciplines. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering.

Nonlinear Dynamic Model of Power Plants with Single-Phase Coolant Reactors

International Nuclear Information System (INIS)

Vollmer, H.

1968-12-01

The traditional way of developing dynamic models for a specific nuclear power plant and for specific purpose seems rather uneconomical, as much of the information often can not be utilized if the plant design or the required accuracy of the calculation is desired to be changed. It is therefore suggested that the model development may be made more systematic, general and flexible by - applying the 'box of bricks' system, where the main components of a nuclear power plant are treated separately and combined afterwards according to a given flow scheme, - a dynamic determination of the components which is as general as possible without taking into account those details which have a minor influence on the overall dynamics, - providing approximations of the more rigorous solution sufficient to meet the user s requirements on accuracy, - proper use of computers. A dynamic model for single-phase coolant reactor plants is established along these lines. By separation of the nonlinear and linear parts of the system, application of Laplace transformation and proper approximations, and the use of a hybrid computer it seems possible to determine the (nonlinear) dynamic behaviour of such a plant for perturbations which are not so large that phase changes of physical parameters occur, e. g. fuel does not melt. The model is applied to a steam cooled fast reactor power plant

Nonlinear Dynamic Model of Power Plants with Single-Phase Coolant Reactors

Energy Technology Data Exchange (ETDEWEB)

Vollmer, H

1968-12-15

The traditional way of developing dynamic models for a specific nuclear power plant and for specific purpose seems rather uneconomical, as much of the information often can not be utilized if the plant design or the required accuracy of the calculation is desired to be changed. It is therefore suggested that the model development may be made more systematic, general and flexible by - applying the 'box of bricks' system, where the main components of a nuclear power plant are treated separately and combined afterwards according to a given flow scheme, - a dynamic determination of the components which is as general as possible without taking into account those details which have a minor influence on the overall dynamics, - providing approximations of the more rigorous solution sufficient to meet the user s requirements on accuracy, - proper use of computers. A dynamic model for single-phase coolant reactor plants is established along these lines. By separation of the nonlinear and linear parts of the system, application of Laplace transformation and proper approximations, and the use of a hybrid computer it seems possible to determine the (nonlinear) dynamic behaviour of such a plant for perturbations which are not so large that phase changes of physical parameters occur, e. g. fuel does not melt. The model is applied to a steam cooled fast reactor power plant.

Dynamics of nonlinear feedback control

NARCIS (Netherlands)

Snippe, H.P.; Hateren, J.H. van

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

Nonlinear dynamics in biological systems

CERN Document Server

Carballido-Landeira, Jorge

2016-01-01

This book presents recent research results relating to applications of nonlinear dynamics, focusing specifically on four topics of wide interest: heart dynamics, DNA/RNA, cell mobility, and proteins. The book derives from the First BCAM Workshop on Nonlinear Dynamics in Biological Systems, held in June 2014 at the Basque Center of Applied Mathematics (BCAM). At this international meeting, researchers from different but complementary backgrounds, including molecular dynamics, physical chemistry, bio-informatics and biophysics, presented their most recent results and discussed the future direction of their studies using theoretical, mathematical modeling and experimental approaches. Such was the level of interest stimulated that the decision was taken to produce this publication, with the organizers of the event acting as editors. All of the contributing authors are researchers working on diverse biological problems that can be approached using nonlinear dynamics. The book will appeal especially to applied math...

Change detection in the dynamics of an intracellular protein synthesis model using nonlinear Kalman filtering.

Science.gov (United States)

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).

Teaching nonlinear dynamics through elastic cords

International Nuclear Information System (INIS)

Chacon, R; Galan, C A; Sanchez-Bajo, F

2011-01-01

We experimentally studied the restoring force of a length of stretched elastic cord. A simple analytical expression for the restoring force was found to fit all the experimental results for different elastic materials. Remarkably, this analytical expression depends upon an elastic-cord characteristic parameter which exhibits two limiting values corresponding to two nonlinear springs with different Hooke's elastic constants. Additionally, the simplest model of elastic cord dynamics is capable of exhibiting a great diversity of nonlinear phenomena, including bifurcations and chaos, thus providing a suitable alternative model system for discussing the basic essentials of nonlinear dynamics in the context of intermediate physics courses at university level.

Study on non-linear bistable dynamics model based EEG signal discrimination analysis method.

Science.gov (United States)

Ying, Xiaoguo; Lin, Han; Hui, Guohua

2015-01-01

Electroencephalogram (EEG) is the recording of electrical activity along the scalp. EEG measures voltage fluctuations generating from ionic current flows within the neurons of the brain. EEG signal is looked as one of the most important factors that will be focused in the next 20 years. In this paper, EEG signal discrimination based on non-linear bistable dynamical model was proposed. EEG signals were processed by non-linear bistable dynamical model, and features of EEG signals were characterized by coherence index. Experimental results showed that the proposed method could properly extract the features of different EEG signals.

Observing and modeling nonlinear dynamics in an internal combustion engine

International Nuclear Information System (INIS)

Daw, C.S.; Kennel, M.B.; Finney, C.E.; Connolly, F.T.

1998-01-01

We propose a low-dimensional, physically motivated, nonlinear map as a model for cyclic combustion variation in spark-ignited internal combustion engines. A key feature is the interaction between stochastic, small-scale fluctuations in engine parameters and nonlinear deterministic coupling between successive engine cycles. Residual cylinder gas from each cycle alters the in-cylinder fuel-air ratio and thus the combustion efficiency in succeeding cycles. The model close-quote s simplicity allows rapid simulation of thousands of engine cycles, permitting statistical studies of cyclic-variation patterns and providing physical insight into this technologically important phenomenon. Using symbol statistics to characterize the noisy dynamics, we find good quantitative matches between our model and experimental time-series measurements. copyright 1998 The American Physical Society

A new nonlinear magnetic circuit model for dynamic analysis of interior permanent magnet synchronous motor

International Nuclear Information System (INIS)

Nakamura, Kenji; Saito, Kenichi; Watanabe, Tadaaki; Ichinokura, Osamu

2005-01-01

Interior permanent magnet synchronous motors (IPMSMs) have high efficiency and torque, since the motors can utilize reluctance torque in addition to magnet torque. The IPMSMs are widely used for electric household appliances and electric bicycles and vehicles. A quantitative analysis method of dynamic characteristics of the IPMSMs, however, has not been clarified fully. For optimum design, investigation of dynamic characteristics considering magnetic nonlinearity is needed. This paper presents a new nonlinear magnetic circuit model of an IPMSM, and suggests a dynamic analysis method using the proposed magnetic circuit model

Parameter and Structure Inference for Nonlinear Dynamical Systems

Science.gov (United States)

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 model and attitude dynamics of flexible spacecraft with large amplitude slosh

Science.gov (United States)

Deng, Mingle; Yue, Baozeng

2017-04-01

This paper is focused on the nonlinearly modelling and attitude dynamics of spacecraft coupled with large amplitude liquid sloshing dynamics and flexible appendage vibration. The large amplitude fuel slosh dynamics is included by using an improved moving pulsating ball model. The moving pulsating ball model is an equivalent mechanical model that is capable of imitating the whole liquid reorientation process. A modification is introduced in the capillary force computation in order to more precisely estimate the settling location of liquid in microgravity or zero-g environment. The flexible appendage is modelled as a three dimensional Bernoulli-Euler beam and the assumed modal method is employed to derive the nonlinear mechanical model for the overall coupled system of liquid filled spacecraft with appendage. The attitude maneuver is implemented by the momentum transfer technique, and a feedback controller is designed. The simulation results show that the liquid sloshing can always result in nutation behavior, but the effect of flexible deformation of appendage depends on the amplitude and direction of attitude maneuver performed by spacecraft. Moreover, it is found that the liquid sloshing and the vibration of flexible appendage are coupled with each other, and the coupling becomes more significant with more rapid motion of spacecraft. This study reveals that the appendage's flexibility has influence on the liquid's location and settling time in microgravity. The presented nonlinear system model can provide an important reference for the overall design of the modern spacecraft composed of rigid platform, liquid filled tank and flexible appendage.

Nanopore Current Oscillations: Nonlinear Dynamics on the Nanoscale.

Science.gov (United States)

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.

Nonlinear dynamics modeling and simulation of two-wheeled self-balancing vehicle

Directory of Open Access Journals (Sweden)

Yunping Liu

2016-11-01

Full Text Available Two-wheeled self-balancing vehicle system is a kind of naturally unstable underactuated system with high-rank unstable multivariable strongly coupling complicated dynamic nonlinear property. Nonlinear dynamics modeling and simulation, as a basis of two-wheeled self-balancing vehicle dynamics research, has the guiding effect for system design of the project demonstration and design phase. Dynamics model of the two-wheeled self-balancing vehicle is established by importing a TSi ProPac package to the Mathematica software (version 8.0, which analyzes the stability and calculates the Lyapunov exponents of the system. The relationship between external force and stability of the system is analyzed by the phase trajectory. Proportional–integral–derivative control is added to the system in order to improve the stability of the two-wheeled self-balancing vehicle. From the research, Lyapunov exponent can be used to research the stability of hyperchaos system. The stability of the two-wheeled self-balancing vehicle is better by inputting the proportional–integral–derivative control. The Lyapunov exponent and phase trajectory can help us analyze the stability of a system better and lay the foundation for the analysis and control of the two-wheeled self-balancing vehicle system.

Qualitative and quantitative combined nonlinear dynamics model and its application in analysis of price, supply–demand ratio and selling rate

International Nuclear Information System (INIS)

Zhu, Dingju

2016-01-01

The qualitative and quantitative combined nonlinear dynamics model proposed in this paper fill the gap in nonlinear dynamics model in terms of qualitative and quantitative combined methods, allowing the qualitative model and quantitative model to perfectly combine and overcome their weaknesses by learning from each other. These two types of models use their strengths to make up for the other’s deficiencies. The qualitative and quantitative combined models can surmount the weakness that the qualitative model cannot be applied and verified in a quantitative manner, and the high costs and long time of multiple construction as well as verification of the quantitative model. The combined model is more practical and efficient, which is of great significance for nonlinear dynamics. The qualitative and quantitative combined modeling and model analytical method raised in this paper is not only applied to nonlinear dynamics, but can be adopted and drawn on in the modeling and model analysis of other fields. Additionally, the analytical method of qualitative and quantitative combined nonlinear dynamics model proposed in this paper can satisfactorily resolve the problems with the price system’s existing nonlinear dynamics model analytical method. The three-dimensional dynamics model of price, supply–demand ratio and selling rate established in this paper make estimates about the best commodity prices using the model results, thereby providing a theoretical basis for the government’s macro-control of price. Meanwhile, this model also offer theoretical guidance to how to enhance people’s purchasing power and consumption levels through price regulation and hence to improve people’s living standards.

Jacobian projection reduced-order models for dynamic systems with contact nonlinearities

Science.gov (United States)

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.

Nonlinear PDEs a dynamical systems approach

CERN Document Server

Schneider, Guido

2017-01-01

This is an introductory textbook about nonlinear dynamics of PDEs, with a focus on problems over unbounded domains and modulation equations. The presentation is example-oriented, and new mathematical tools are developed step by step, giving insight into some important classes of nonlinear PDEs and nonlinear dynamics phenomena which may occur in PDEs. The book consists of four parts. Parts I and II are introductions to finite- and infinite-dimensional dynamics defined by ODEs and by PDEs over bounded domains, respectively, including the basics of bifurcation and attractor theory. Part III introduces PDEs on the real line, including the Korteweg-de Vries equation, the Nonlinear Schrödinger equation and the Ginzburg-Landau equation. These examples often occur as simplest possible models, namely as amplitude or modulation equations, for some real world phenomena such as nonlinear waves and pattern formation. Part IV explores in more detail the connections between such complicated physical systems and the reduced...

A Nonlinear Dynamic Inversion Predictor-Based Model Reference Adaptive Controller for a Generic Transport Model

Science.gov (United States)

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).

Pseudorandom numbers: evolutionary models in image processing, biology, and nonlinear dynamic systems

Science.gov (United States)

Yaroslavsky, Leonid P.

1996-11-01

We show that one can treat pseudo-random generators, evolutionary models of texture images, iterative local adaptive filters for image restoration and enhancement and growth models in biology and material sciences in a unified way as special cases of dynamic systems with a nonlinear feedback.

Perspectives of nonlinear dynamics

International Nuclear Information System (INIS)

Jackson, E.A.

1985-03-01

Four lectures were given weekly in October and November, 1984, and some of the ideas presented here will be of use in the future. First, a brief survey of the historical development of nonlinear dynamics since about 1890 was given, and then, a few topics were discussed in detail. The objective was to introduce some of many concepts and methods which are presently used for describing nonlinear dynamics. The symbiotic relationship between sciences of all types and mathematics, two main categories of the models describing nature, the method for describing the dynamics of a system, the idea of control parameters and topological dimension, the asymptotic properties of dynamics, abstract dynamics, the concept of embedding, singular perturbation theory, strange attractor, Fermi-Pasta-Ulam phenomena, an example of computer heuristics, the idea of elementary catastrophe theory and so on were explained. The logistic map is the simplest introduction to complex dynamics. The complicated dynamics is referred to as strange attractors. Two-dimensional maps are the highest dimensional maps commonly studied. These were discussed in detail. (Kako, I.)

A Disentangled Recognition and Nonlinear Dynamics Model for Unsupervised Learning

DEFF Research Database (Denmark)

Fraccaro, Marco; Kamronn, Simon Due; Paquet, Ulrich

2017-01-01

This paper takes a step towards temporal reasoning in a dynamically changing video, not in the pixel space that constitutes its frames, but in a latent space that describes the non-linear dynamics of the objects in its world. We introduce the Kalman variational auto-encoder, a framework...... for unsupervised learning of sequential data that disentangles two latent representations: an object’s representation, coming from a recognition model, and a latent state describing its dynamics. As a result, the evolution of the world can be imagined and missing data imputed, both without the need to generate...

The cultural implications of growth: Modeling nonlinear interaction of trait selection and population dynamics.

Science.gov (United States)

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

Science.gov (United States)

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.

4th International Conference on Structural Nonlinear Dynamics and Diagnosis

CERN Document Server

2018-01-01

This book presents contributions on the most active lines of recent advanced research in the field of nonlinear mechanics and physics selected from the 4th International Conference on Structural Nonlinear Dynamics and Diagnosis. It includes fifteen chapters by outstanding scientists, covering various aspects of applications, including road tanker dynamics and stability, simulation of abrasive wear, energy harvesting, modeling and analysis of flexoelectric nanoactuator, periodic Fermi–Pasta–Ulam problems, nonlinear stability in Hamiltonian systems, nonlinear dynamics of rotating composites, nonlinear vibrations of a shallow arch, extreme pulse dynamics in mode-locked lasers, localized structures in a photonic crystal fiber resonator, nonlinear stochastic dynamics, linearization of nonlinear resonances, treatment of a linear delay differential equation, and fractional nonlinear damping. It appeals to a wide range of experts in the field of structural nonlinear dynamics and offers researchers and engineers a...

Nonlinear analysis of pupillary dynamics.

Science.gov (United States)

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 (pnonlinear 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.

Nonlinear flight dynamics and stability of hovering model insects

Science.gov (United States)

Liang, Bin; Sun, Mao

2013-01-01

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

Dynamics and vibrations progress in nonlinear analysis

CERN Document Server

Kachapi, Seyed Habibollah Hashemi

2014-01-01

Dynamical and vibratory systems are basically an application of mathematics and applied sciences to the solution of real world problems. Before being able to solve real world problems, it is necessary to carefully study dynamical and vibratory systems and solve all available problems in case of linear and nonlinear equations using analytical and numerical methods. It is of great importance to study nonlinearity in dynamics and vibration; because almost all applied processes act nonlinearly, and on the other hand, nonlinear analysis of complex systems is one of the most important and complicated tasks, especially in engineering and applied sciences problems. There are probably a handful of books on nonlinear dynamics and vibrations analysis. Some of these books are written at a fundamental level that may not meet ambitious engineering program requirements. Others are specialized in certain fields of oscillatory systems, including modeling and simulations. In this book, we attempt to strike a balance between th...

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

Science.gov (United States)

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

A Cumulant-based Analysis of Nonlinear Magnetospheric Dynamics

International Nuclear Information System (INIS)

Johnson, Jay R.; Wing, Simon

2004-01-01

Understanding magnetospheric dynamics and predicting future behavior of the magnetosphere is of great practical interest because it could potentially help to avert catastrophic loss of power and communications. In order to build good predictive models it is necessary to understand the most critical nonlinear dependencies among observed plasma and electromagnetic field variables in the coupled solar wind/magnetosphere system. In this work, we apply a cumulant-based information dynamical measure to characterize the nonlinear dynamics underlying the time evolution of the Dst and Kp geomagnetic indices, given solar wind magnetic field and plasma input. We examine the underlying dynamics of the system, the temporal statistical dependencies, the degree of nonlinearity, and the rate of information loss. We find a significant solar cycle dependence in the underlying dynamics of the system with greater nonlinearity for solar minimum. The cumulant-based approach also has the advantage that it is reliable even in the case of small data sets and therefore it is possible to avoid the assumption of stationarity, which allows for a measure of predictability even when the underlying system dynamics may change character. Evaluations of several leading Kp prediction models indicate that their performances are sub-optimal during active times. We discuss possible improvements of these models based on this nonparametric approach

Global Analysis of Nonlinear Dynamics

CERN Document Server

Luo, Albert

2012-01-01

Global Analysis of Nonlinear Dynamics collects chapters on recent developments in global analysis of non-linear dynamical systems with a particular emphasis on cell mapping methods developed by Professor C.S. Hsu of the University of California, Berkeley. This collection of contributions prepared by a diverse group of internationally recognized researchers is intended to stimulate interests in global analysis of complex and high-dimensional nonlinear dynamical systems, whose global properties are largely unexplored at this time. This book also: Presents recent developments in global analysis of non-linear dynamical systems Provides in-depth considerations and extensions of cell mapping methods Adopts an inclusive style accessible to non-specialists and graduate students Global Analysis of Nonlinear Dynamics is an ideal reference for the community of nonlinear dynamics in different disciplines including engineering, applied mathematics, meteorology, life science, computational science, and medicine.  

Nonlinear dynamics between linear and impact limits

CERN Document Server

Pilipchuk, Valery N; Wriggers, Peter

2010-01-01

This book examines nonlinear dynamic analyses based on the existence of strongly nonlinear but simple counterparts to the linear models and tools. Discusses possible application to periodic elastic structures with non-smooth or discontinuous characteristics.

FEM-based neural-network approach to nonlinear modeling with application to longitudinal vehicle dynamics control.

Science.gov (United States)

Kalkkuhl, J; Hunt, K J; Fritz, H

1999-01-01

An finite-element methods (FEM)-based neural-network approach to Nonlinear AutoRegressive with eXogenous input (NARX) modeling is presented. The method uses multilinear interpolation functions on C0 rectangular elements. The local and global structure of the resulting model is analyzed. It is shown that the model can be interpreted both as a local model network and a single layer feedforward neural network. The main aim is to use the model for nonlinear control design. The proposed FEM NARX description is easily accessible to feedback linearizing control techniques. Its use with a two-degrees of freedom nonlinear internal model controller is discussed. The approach is applied to modeling of the nonlinear longitudinal dynamics of an experimental lorry, using measured data. The modeling results are compared with local model network and multilayer perceptron approaches. A nonlinear speed controller was designed based on the identified FEM model. The controller was implemented in a test vehicle, and several experimental results are presented.

Nonlinear Dynamics of Nanomechanical Resonators

Science.gov (United States)

Ramakrishnan, Subramanian; Gulak, Yuiry; Sundaram, Bala; Benaroya, Haym

2007-03-01

Nanoelectromechanical systems (NEMS) offer great promise for many applications including motion and mass sensing. Recent experimental results suggest the importance of nonlinear effects in NEMS, an issue which has not been addressed fully in theory. We report on a nonlinear extension of a recent analytical model by Armour et al [1] for the dynamics of a single-electron transistor (SET) coupled to a nanomechanical resonator. We consider the nonlinear resonator motion in both (a) the Duffing and (b) nonlinear pendulum regimes. The corresponding master equations are derived and solved numerically and we consider moment approximations as well. In the Duffing case with hardening stiffness, we observe that the resonator is damped by the SET at a significantly higher rate. In the cases of softening stiffness and the pendulum, there exist regimes where the SET adds energy to the resonator. To our knowledge, this is the first instance of a single model displaying both negative and positive resonator damping in different dynamical regimes. The implications of the results for SET sensitivity as well as for, as yet unexplained, experimental results will be discussed. 1. Armour et al. Phys.Rev.B (69) 125313 (2004).

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

Science.gov (United States)

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.

Model reduction tools for nonlinear structural dynamics

NARCIS (Netherlands)

Slaats, P.M.A.; Jongh, de J.; Sauren, A.A.H.J.

1995-01-01

Three mode types are proposed for reducing nonlinear dynamical system equations, resulting from finite element discretizations: tangent modes, modal derivatives, and newly added static modes. Tangent modes are obtained from an eigenvalue problem with a momentary tangent stiffness matrix. Their

Nonlinear Modeling and Simulation of Thermal Effects in Microcantilever Resonators Dynamic

International Nuclear Information System (INIS)

Tadayon, M A; Sayyaadi, H; Jazar, G Nakhaie

2006-01-01

Thermal dependency of material characteristics in micro electromechanical systems strongly affects their performance, design, and control. Hence, it is essential to understand and model that in MEMS devices to optimize their designs. A thermal phenomenon introduces two main effects: damping due to internal friction, and softening due to Young modulus temperature relation. Based on some reported theoretical and experimental results, we model the thermal phenomena and use two Lorentzian functions to describe the restoring and damping forces caused by thermal phenomena. In order to emphasize the thermal effects, a nonlinear model of the MEMS, by considering capacitor nonlinearity, have been used. The response of the system is developed by employing multiple time scales perturbation method on nondimensionalized form of equations. Frequency response, resonant frequency and peak amplitude are examined for variation of dynamic parameters involved

Structure Learning in Stochastic Non-linear Dynamical Systems

Science.gov (United States)

Morris, R. D.; Smelyanskiy, V. N.; Luchinsky, D. G.

2005-12-01

A great many systems can be modeled in the non-linear dynamical systems framework, as x˙ = f(x) + ξ(t), where f(x) is the potential function for the system, and ξ(t) is the driving 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, for example in predator-prey systems, where the very structure of the coupling between predator-prey pairs can have great ecological significance.

General relativistic chaos and nonlinear dynamics

Energy Technology Data Exchange (ETDEWEB)

Barrow, J D [California Univ., Berkeley (USA). Dept. of Physics

1982-06-01

How new ideas in dynamical systems theory find application in the description of general relativistic systems is described. The concept of dynamical entropy is explained and the associated invariant evaluated for the Mixmaster cosmological model. The description of cosmological models as measure preserving dynamical systems leads to a number of interconnections with new ideas in non-linear dynamics. This may provide a new avenue of approach to ascertaining the nature of the general solution to Einstein's equations.

General relativistic chaos and nonlinear dynamics

International Nuclear Information System (INIS)

Barrow, J.D.

1982-01-01

How new ideas in dynamical systems theory find application in the description of general relativistic systems is described. The concept of dynamical entropy is explained and the associated invariant evaluated for the Mixmaster cosmological model. The description of cosmological models as measure preserving dynamical systems leads to a number of interconnections with new ideas in non-linear dynamics. This may provide a new avenue of approach to ascertaining the nature of the general solution to Einstein's equations. (author)

On the dynamical mass generation in gauge-invariant non-linear σ-models

International Nuclear Information System (INIS)

Diaz, A.; Helayel-Neto, J.A.; Smith, A.W.

1987-12-01

We argue that external gauge fields coupled in a gauge-invariant way to both the bosonic and supersymmetric two-dimensional non-linear σ-models acquire a dynamical mass term whenever the target space is restricted to be a group manifold. (author). 11 refs

Estimation of Nonlinear Dynamic Panel Data Models with Individual Effects

Directory of Open Access Journals (Sweden)

Yi Hu

2014-01-01

Full Text Available This paper suggests a generalized method of moments (GMM based estimation for dynamic panel data models with individual specific fixed effects and threshold effects simultaneously. We extend Hansen’s (Hansen, 1999 original setup to models including endogenous regressors, specifically, lagged dependent variables. To address the problem of endogeneity of these nonlinear dynamic panel data models, we prove that the orthogonality conditions proposed by Arellano and Bond (1991 are valid. The threshold and slope parameters are estimated by GMM, and asymptotic distribution of the slope parameters is derived. Finite sample performance of the estimation is investigated through Monte Carlo simulations. It shows that the threshold and slope parameter can be estimated accurately and also the finite sample distribution of slope parameters is well approximated by the asymptotic distribution.

Robust model predictive control of nonlinear systems with unmodeled dynamics and bounded uncertainties based on neural networks.

Science.gov (United States)

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.

Nonlinear dynamics aspects of particle accelerators

International Nuclear Information System (INIS)

Jowett, J.M.; Turner, S.; Month, M.

1986-01-01

These proceedings contain the lectures presented at the named winter school. They deal with the application of dynamical systems to accelerator theory. Especially considered are the statistical description of charged-beam plasmas, integrable and nonintegrable Hamiltonian systems, single particle dynamics and nonlinear resonances in circular accelerators, nonlinear dynamics aspects of modern storage rings, nonlinear beam-beam resonances, synchro-betatron resonances, observations of the beam-beam interactions, the dynamics of the beam-beam interactions, beam-beam simulations, the perturbation method in nonlinear dynamics, theories of statistical equilibrium in electron-positron storage rings, nonlinear dissipative phenomena in electron storage rings, the dynamical aperture, the transition to chaos for area-preserving maps, special processors for particle tracking, algorithms for tracking of charged particles in circular accelerators, the breakdown of stability, and a personal perspective of nonlinear dynamics. (HSI)

Nonlinear dynamics of the magnetosphere and space weather

Science.gov (United States)

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.

Dynamic modeling of geometrically nonlinear electrostatically actuated microbeams (Corotational Finite Element formulation and analysis)

Energy Technology Data Exchange (ETDEWEB)

Borhan, H; Ahmadian, M T [Sharif University of Technology, Center of Excellence for Design, Robotics and Automation, School of Mechanical Engineering, PO Box 11365-9567, Tehran (Iran, Islamic Republic of)

2006-04-01

In this paper, a complete nonlinear finite element model for coupled-domain MEMS devices with electrostatic actuation and squeeze film effect is developed. For this purpose, a corotational finite element formulation for the dynamic analysis of planer Euler beams is employed. In this method, the internal nodal forces due to deformation and intrinsic residual stresses, the inertial nodal forces, and the damping effect of squeezed air film are systematically derived by consistent linearization of the fully geometrically nonlinear beam theory using d'Alamber and virtual work principles. An incremental-iterative method based on the Newmark direct integration procedure and the Newton-Raphson algorithm is used to solve the nonlinear dynamic equilibrium equations. Numerical examples are presented and compared with experimental findings which indicate properly good agreement.

The Mathematics of Psychotherapy: A Nonlinear Model of Change Dynamics.

Science.gov (United States)

Schiepek, Gunter; Aas, Benjamin; Viol, Kathrin

2016-07-01

Psychotherapy is a dynamic process produced by a complex system of interacting variables. Even though there are qualitative models of such systems the link between structure and function, between network and network dynamics is still missing. The aim of this study is to realize these links. The proposed model is composed of five state variables (P: problem severity, S: success and therapeutic progress, M: motivation to change, E: emotions, I: insight and new perspectives) interconnected by 16 functions. The shape of each function is modified by four parameters (a: capability to form a trustful working alliance, c: mentalization and emotion regulation, r: behavioral resources and skills, m: self-efficacy and reward expectation). Psychologically, the parameters play the role of competencies or traits, which translate into the concept of control parameters in synergetics. The qualitative model was transferred into five coupled, deterministic, nonlinear difference equations generating the dynamics of each variable as a function of other variables. The mathematical model is able to reproduce important features of psychotherapy processes. Examples of parameter-dependent bifurcation diagrams are given. Beyond the illustrated similarities between simulated and empirical dynamics, the model has to be further developed, systematically tested by simulated experiments, and compared to empirical data.

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

Science.gov (United States)

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.

Nonlinear amplitude dynamics in flagellar beating.

Science.gov (United States)

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 dynamics of structures

CERN Document Server

Oller, Sergio

2014-01-01

This book lays the foundation of knowledge that will allow a better understanding of nonlinear phenomena that occur in structural dynamics.   This work is intended for graduate engineering students who want to expand their knowledge on the dynamic behavior of structures, specifically in the nonlinear field, by presenting the basis of dynamic balance in non‐linear behavior structures due to the material and kinematics mechanical effects.   Particularly, this publication shows the solution of the equation of dynamic equilibrium for structure with nonlinear time‐independent materials (plasticity, damage and frequencies evolution), as well as those time dependent non‐linear behavior materials (viscoelasticity and viscoplasticity). The convergence conditions for the non‐linear dynamic structure solution  are studied, and the theoretical concepts and its programming algorithms are presented.  

Nonlinear dynamics of quadratically cubic systems

International Nuclear Information System (INIS)

Rudenko, O V

2013-01-01

We propose a modified form of the well-known nonlinear dynamic equations with quadratic relations used to model a cubic nonlinearity. We show that such quadratically cubic equations sometimes allow exact solutions and sometimes make the original problem easier to analyze qualitatively. Occasionally, exact solutions provide a useful tool for studying new phenomena. Examples considered include nonlinear ordinary differential equations and Hopf, Burgers, Korteweg–de Vries, and nonlinear Schrödinger partial differential equations. Some problems are solved exactly in the space–time and spectral representations. Unsolved problems potentially solvable by the proposed approach are listed. (methodological notes)

Dynamic nonlinear interaction of elastic plates on discrete supports

International Nuclear Information System (INIS)

Coutinho, A.L.G.A.; Landau, L.; Lima, E.C.P. de; Ebecken, N.F.F.

1984-01-01

A study on the dynamic nonlinear interaction of elastic plates using the finite element method is presented. The elastic plate is discretized by 4-node isoparametric Mindlin elements. The constitutive relation of the discrete supports can be any nonlinear curve given by pairs of force-displacement points. The nonlinear behaviour is represented by the overlay approach. This model also allows the simulation of a progressive decrease on the supports stiffnesses during load cycles. The dynamic nonlinear incremental movement equations are integrated by the Newmark implicit operator. Two alternatives for the incremental-iterative formulation are compared. The paper ends with a discussion of the advantages and limitations of the presented numerical models. (Author) [pt

Nonlinear dynamical system approaches towards neural prosthesis

International Nuclear Information System (INIS)

Torikai, Hiroyuki; Hashimoto, Sho

2011-01-01

An asynchronous discrete-state spiking neurons is a wired system of shift registers that can mimic nonlinear dynamics of an ODE-based neuron model. The control parameter of the neuron is the wiring pattern among the registers and thus they are suitable for on-chip learning. In this paper an asynchronous discrete-state spiking neuron is introduced and its typical nonlinear phenomena are demonstrated. Also, a learning algorithm for a set of neurons is presented and it is demonstrated that the algorithm enables the set of neurons to reconstruct nonlinear dynamics of another set of neurons with unknown parameter values. The learning function is validated by FPGA experiments.

Nonlinear dynamics and astrophysics

International Nuclear Information System (INIS)

Vallejo, J. C.; Sanjuan, M. A. F.

2000-01-01

Concepts and techniques from Nonlinear Dynamics, also known as Chaos Theory, have been applied successfully to several astrophysical fields such as orbital motion, time series analysis or galactic dynamics, providing answers to old questions but also opening a few new ones. Some of these topics are described in this review article, showing the basis of Nonlinear Dynamics, and how it is applied in Astrophysics. (Author)

Nonlinear dynamics of zigzag molecular chains (in Russian)

DEFF Research Database (Denmark)

Savin, A. V.; Manevitsch, L. I.; Christiansen, Peter Leth

1999-01-01

models (two-dimensional alpha-spiral, polyethylene transzigzag backbone, and the zigzag chain of hydrogen bonds) shows that the zigzag structure essentially limits the soliton dynamics to finite, relatively narrow, supersonic soliton velocity intervals and may also result in that several acoustic soliton......Nonlinear, collective, soliton type excitations in zigzag molecular chains are analyzed. It is shown that the nonlinear dynamics of a chain dramatically changes in passing from the one-dimensional linear chain to the more realistic planar zigzag model-due, in particular, to the geometry...

Predictable nonlinear dynamics: Advances and limitations

International Nuclear Information System (INIS)

Anosov, L.A.; Butkovskii, O.Y.; Kravtsov, Y.A.; Surovyatkina, E.D.

1996-01-01

Methods for reconstruction chaotic dynamical system structure directly from experimental time series are described. Effectiveness of general methods is illustrated with the results of numerical simulation. It is of common interest that from the single time series it is possible to reconstruct a set of interconnected variables. Predictive power of dynamical models, provided by the nonlinear dynamics inverse problem solution, is limited firstly by the noise level in the system under study and is characterized by the horizon of predictability. New physical results are presented, concerning nonstationary and bifurcation nonlinear systems: (1) algorithms for revealing of nonstationarity in random-like chaotic time-series are suggested based on discriminant analysis with nonlinear discriminant function; (2) an opportunity is established to predict the final state in bifurcation system with quickly varying control parameters; (3) hysteresis is founded out in bifurcation system with quickly varying parameters; (4) delayed correlation left-angle noise-prediction error right-angle in chaotic systems is revealed. copyright 1996 American Institute of Physics

NONLINEAR DYNAMICS OF CARBON NANOTUBES UNDER LARGE ELECTROSTATIC FORCE

KAUST Repository

Xu, Tiantian

2015-06-01

Because of the inherent nonlinearities involving the behavior of CNTs when excited by electrostatic forces, modeling and simulating their behavior is challenging. The complicated form of the electrostatic force describing the interaction of their cylindrical shape, forming upper electrodes, to lower electrodes poises serious computational challenges. This presents an obstacle against applying and using several nonlinear dynamics tools typically used to analyze the behavior of complicated nonlinear systems undergoing large motion, such as shooting, continuation, and integrity analysis techniques. This works presents an attempt to resolve this issue. We present an investigation of the nonlinear dynamics of carbon nanotubes when actuated by large electrostatic forces. We study expanding the complicated form of the electrostatic force into enough number of terms of the Taylor series. Then, we utilize this form along with an Euler-Bernoulli beam model to study for the first time the dynamic behavior of CNTs when excited by large electrostatic force. The geometric nonlinearity and the nonlinear electrostatic force are considered. An efficient reduced-order model (ROM) based on the Galerkin method is developed and utilized to simulate the static and dynamic responses of the CNTs. Several results are generated demonstrating softening and hardening behavior of the CNTs near their primary and secondary resonances. The effects of the DC and AC voltage loads on the behavior have been studied. The impacts of the initial slack level and CNT diameter are also demonstrated.

Nonlinear Dynamics of Carbon Nanotubes Under Large Electrostatic Force

KAUST Repository

Xu, Tiantian

2015-06-01

Because of the inherent nonlinearities involving the behavior of CNTs when excited by electrostatic forces, modeling and simulating their behavior is challenging. The complicated form of the electrostatic force describing the interaction of their cylindrical shape, forming upper electrodes, to lower electrodes poises serious computational challenges. This presents an obstacle against applying and using several nonlinear dynamics tools typically used to analyze the behavior of complicated nonlinear systems undergoing large motion, such as shooting, continuation, and integrity analysis techniques. This works presents an attempt to resolve this issue. We present an investigation of the nonlinear dynamics of carbon nanotubes when actuated by large electrostatic forces. We study expanding the complicated form of the electrostatic force into enough number of terms of the Taylor series. Then, we utilize this form along with an Euler-Bernoulli beam model to study for the first time the dynamic behavior of CNTs when excited by large electrostatic force. The geometric nonlinearity and the nonlinear electrostatic force are considered. An efficient reduced-order model (ROM) based on the Galerkin method is developed and utilized to simulate the static and dynamic responses of the CNTs. Several results are generated demonstrating softening and hardening behavior of the CNTs near their primary and secondary resonances. The effects of the DC and AC voltage loads on the behavior have been studied. The impacts of the initial slack level and CNT diameter are also demonstrated.

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

Science.gov (United States)

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.

International Conference on Structural Nonlinear Dynamics and Diagnosis

CERN Document Server

CSNDD 2012; CSNDD 2014

2015-01-01

This book, which presents the peer-reviewed post-proceedings of CSNDD 2012 and CSNDD 2014, addresses the important role that relevant concepts and tools from nonlinear and complex dynamics could play in present and future engineering applications. It includes 22 chapters contributed by outstanding researchers and covering various aspects of applications, including: structural health monitoring, diagnosis and damage detection, experimental methodologies, active vibration control and smart structures, passive control of structures using nonlinear energy sinks, vibro-impact dynamic MEMS/NEMS/AFM, energy-harvesting materials and structures, and time-delayed feedback control, as well as aspects of deterministic versus stochastic dynamics and control of nonlinear phenomena in physics.  Researchers and engineers interested in the challenges posed and opportunities offered by nonlinearities in the development of passive and active control strategies, energy harvesting, novel design criteria, modeling and characteriz...

Nonlinear dynamics aspects of particle accelerators. Proceedings

Energy Technology Data Exchange (ETDEWEB)

Jowett, J M; Turner, S; Month, M

1986-01-01

These proceedings contain the lectures presented at the named winter school. They deal with the application of dynamical systems to accelerator theory. Especially considered are the statistical description of charged-beam plasmas, integrable and nonintegrable Hamiltonian systems, single particle dynamics and nonlinear resonances in circular accelerators, nonlinear dynamics aspects of modern storage rings, nonlinear beam-beam resonances, synchro-betatron resonances, observations of the beam-beam interactions, the dynamics of the beam-beam interactions, beam-beam simulations, the perturbation method in nonlinear dynamics, theories of statistical equilibrium in electron-positron storage rings, nonlinear dissipative phenomena in electron storage rings, the dynamical aperture, the transition to chaos for area-preserving maps, special processors for particle tracking, algorithms for tracking of charged particles in circular accelerators, the breakdown of stability, and a personal perspective of nonlinear dynamics. (HSI).

NUMERICAL MODELING AND DYNAMIC SIMULATIONS OF NONLINEAR AEROTHERMOELASTIC OF A DOUBLE-WEDGE LIFTING SURFACE

Directory of Open Access Journals (Sweden)

ARIF A. EBRAHEEM AL-QASSAR

2008-12-01

Full Text Available The design of the re-entry space vehicles and high-speed aircrafts requires special attention to the nonlinear thermoelastic and aerodynamic instabilities of their structural components. The thermal effects are important since temperature environment influences significantly the static and dynamic behaviors of flight structures in supersonic/hypersonic regimes. To contribute to the understanding of dynamic behavior of these “hot” structures, a double-wedge lifting surface with combined freeplay and cubic stiffening structural nonlinearities in both plunging and pitching degrees-of-freedom operating in supersonic/hypersonic flight speed regimes has been analyzed. A third order Piston Theory Aerodynamics is used to evaluate the applied nonlinear unsteady aerodynamic loads. The loss of torsional stiffness that may be incurred by lifting surfaces subjected to axial stresses induced by aerodynamic heating is also considered. The aerodynamic heating effect is estimated based on the adiabatic wall temperature due to high speed airstreams. Modelling issues as well as simulation results have been presented and pertinent conclusions outlined. It is highlighted that a serious loss of torsional stiffness may induce the dynamic instability of the lifting surfaces. The influence of various parameters such as flight condition, thickness ratio, freeplays and pitching stiffness nonlinearity are also discussed.

Nonlinear dynamics in Nuclotron

International Nuclear Information System (INIS)

Dinev, D.

1997-01-01

The paper represents an extensive study of the nonlinear beam dynamics in the Nuclotron. Chromatic effects, including the dependence of the betatron tunes on the amplitude, and chromatic perturbations have been investigated taking into account the measured field imperfections. Beam distortion, smear, dynamic aperture and nonlinear acceptance have been calculated for different particle energies and betatron tunes

Efficient Estimation of Non-Linear Dynamic Panel Data Models with Application to Smooth Transition Models

DEFF Research Database (Denmark)

Gørgens, Tue; Skeels, Christopher L.; Wurtz, Allan

This paper explores estimation of a class of non-linear dynamic panel data models with additive unobserved individual-specific effects. The models are specified by moment restrictions. The class includes the panel data AR(p) model and panel smooth transition models. We derive an efficient set...... of moment restrictions for estimation and apply the results to estimation of panel smooth transition models with fixed effects, where the transition may be determined endogenously. The performance of the GMM estimator, both in terms of estimation precision and forecasting performance, is examined in a Monte...

Robust variable selection method for nonparametric differential equation models with application to nonlinear dynamic gene regulatory network analysis.

Science.gov (United States)

Lu, Tao

2016-01-01

The gene regulation network (GRN) evaluates the interactions between genes and look for models to describe the gene expression behavior. These models have many applications; for instance, by characterizing the gene expression mechanisms that cause certain disorders, it would be possible to target those genes to block the progress of the disease. Many biological processes are driven by nonlinear dynamic GRN. In this article, we propose a nonparametric differential equation (ODE) to model the nonlinear dynamic GRN. Specially, we address following questions simultaneously: (i) extract information from noisy time course gene expression data; (ii) model the nonlinear ODE through a nonparametric smoothing function; (iii) identify the important regulatory gene(s) through a group smoothly clipped absolute deviation (SCAD) approach; (iv) test the robustness of the model against possible shortening of experimental duration. We illustrate the usefulness of the model and associated statistical methods through a simulation and a real application examples.

Nonlinear Dynamic Phenomena in Mechanics

CERN Document Server

Warminski, Jerzy; Cartmell, Matthew P

2012-01-01

Nonlinear phenomena should play a crucial role in the design and control of engineering systems and structures as they can drastically change the prevailing dynamical responses. This book covers theoretical and applications-based problems of nonlinear dynamics concerned with both discrete and continuous systems of interest in civil and mechanical engineering. They include pendulum-like systems, slender footbridges, shape memory alloys, sagged elastic cables and non-smooth problems. Pendulums can be used as a dynamic absorber mounted in high buildings, bridges or chimneys. Geometrical nonlinear

Nonlinear dynamic model of a gear-rotor-bearing system considering the flash temperature

Science.gov (United States)

Gou, Xiangfeng; Zhu, Lingyun; Qi, Changjun

2017-12-01

The instantaneous flash temperature is an important factor for gears in service. To investigate the effect of the flash temperature of a tooth surface on the dynamics of the spur gear system, a modified nonlinear dynamic model of a gear-rotor-bearing system is established. The factors such as the contact temperature of the tooth surface, time-varying stiffness, tooth surface friction, backlash, the comprehensive transmission error and so on are considered. The flash temperature of a tooth surface of pinion and gear is formulated according to Blok's flash temperature theory. The mathematical expression of the contact temperature of the tooth surface varied with time is derived and the tooth profile deformation caused by the change of the flash temperature of the tooth surface is calculated. The expression of the mesh stiffness varied with the flash temperature of the tooth surface is derived based on Hertz contact theory. The temperature stiffness is proposed and added to the nonlinear dynamic model of the system. The influence of load on the flash temperature of the tooth surface is analyzed in the parameters plane. The variation of the flash temperature of the tooth surface is studied. The numerical results indicate that the calculated method of the flash temperature of the gear tooth surface is effective and it can reflect the rules for the change of gear meshing temperature and sliding of the gear tooth surface. The effects of frequency, backlash, bearing clearance, comprehensive transmission error and time-varying stiffness on the nonlinear dynamics of the system are analyzed according to the bifurcation diagrams, Top Lyapunov Exponent (TLE) spectrums, phase portraits and Poincaré maps. Some nonlinear phenomena such as periodic bifurcation, grazing bifurcation, quasi-periodic bifurcation, chaos and its routes to chaos are investigated and the critical parameters are identified. The results provide an understanding of the system and serve as a useful reference

Finite element calculations illustrating a method of model reduction for the dynamics of structures with localized nonlinearities.

Energy Technology Data Exchange (ETDEWEB)

Griffith, Daniel Todd; Segalman, Daniel Joseph

2006-10-01

A technique published in SAND Report 2006-1789 ''Model Reduction of Systems with Localized Nonlinearities'' is illustrated in two problems of finite element structural dynamics. That technique, called here the Method of Locally Discontinuous Basis Vectors (LDBV), was devised to address the peculiar difficulties of model reduction of systems having spatially localized nonlinearities. It's illustration here is on two problems of different geometric and dynamic complexity, but each containing localized interface nonlinearities represented by constitutive models for bolted joint behavior. As illustrated on simple problems in the earlier SAND report, the LDBV Method not only affords reduction in size of the nonlinear systems of equations that must be solved, but it also facilitates the use of much larger time steps on problems of joint macro-slip than would be possible otherwise. These benefits are more dramatic for the larger problems illustrated here. The work of both the original SAND report and this one were funded by the LDRD program at Sandia National Laboratories.

Nonlinear Dynamic Analysis and Optimization of Closed-Form Planetary Gear System

Directory of Open Access Journals (Sweden)

Qilin Huang

2013-01-01

Full Text Available A nonlinear purely rotational dynamic model of a multistage closed-form planetary gear set formed by two simple planetary stages is proposed in this study. The model includes time-varying mesh stiffness, excitation fluctuation and gear backlash nonlinearities. The nonlinear differential equations of motion are solved numerically using variable step-size Runge-Kutta. In order to obtain function expression of optimization objective, the nonlinear differential equations of motion are solved analytically using harmonic balance method (HBM. Based on the analytical solution of dynamic equations, the optimization mathematical model which aims at minimizing the vibration displacement of the low-speed carrier and the total mass of the gear transmission system is established. The optimization toolbox in MATLAB program is adopted to obtain the optimal solution. A case is studied to demonstrate the effectiveness of the dynamic model and the optimization method. The results show that the dynamic properties of the closed-form planetary gear transmission system have been improved and the total mass of the gear set has been decreased significantly.

Nonlinear dynamics aspects of particle accelerators

International Nuclear Information System (INIS)

Araki, H.; Ehlers, J.; Hepp, K.; Kippenhahn, R.; Weidenmuller, A.; Zittartz, J.

1986-01-01

This book contains 18 selections. Some of the titles are: Integrable and Nonintegrable Hamiltonian Systems; Nonlinear Dynamics Aspects of Modern Storage Rings; Nonlinear Beam-Beam Resonances; Synchro-Betatron Resonances; Review of Beam-Beam Simulations; and Perturbation Method in Nonlinear Dynamics

Nonlinear transport of dynamic system phase space

International Nuclear Information System (INIS)

Xie Xi; Xia Jiawen

1993-01-01

The inverse transform of any order solution of the differential equation of general nonlinear dynamic systems is derived, realizing theoretically the nonlinear transport for the phase space of nonlinear dynamic systems. The result is applicable to general nonlinear dynamic systems, with the transport of accelerator beam phase space as a typical example

Nonlinear dynamic analysis of hydrodynamically-coupled stainless steel structures

International Nuclear Information System (INIS)

Zhao, Y.

1996-01-01

Spent nuclear fuel is usually stored temporarily on the site of nuclear power plants. The spent fuel storage racks are nuclear-safety-related stainless steel structures required to be analyzed for seismic loads. When the storage pool is subjected to three-dimensional (3-D) floor seismic excitations, rack modules, stored fuel bundles, adjacent racks and pool walls, and surrounding water are hydrodynamically coupled. Hydrodynamic coupling (HC) significantly affects the dynamic responses of the racks that are free-standing and submerged in water within the pool. A nonlinear time-history dynamic analysis is usually needed to describe the motion behavior of the racks that are both geometrically nonlinear and material nonlinear in nature. The nonlinearities include the friction resistance between the rack supporting legs and the pool floor, and various potential impacts of fuel-rack, rack-rack, and rack-pool wall. The HC induced should be included in the nonlinear dynamic analysis using the added-hydrodynamic-mass concept based on potential theory per the US Nuclear Regulatory Commission (USNRC) acceptance criteria. To this end, a finite element analysis constitutes a feasible and effective tool. However, most people perform somewhat simplified 1-D, or 2-D, or 3-D single rack and 2-D multiple rack analyses. These analyses are incomplete because a 3-D single rack model behaves quite differently from a 2-D mode. Furthermore, a 3-D whole pool multi-rack model behaves differently than a 3-D single rack model, especially when the strong HC effects are unsymmetrical. In this paper 3-D nonlinear dynamic time-history analyses were performed in a more quantitative manner using sophisticated finite element models developed for a single rack as well as all twelve racks in the whole-pool. Typical response results due to different HC effects are determined and discussed

Complex fluid network optimization and control integrative design based on nonlinear dynamic model

International Nuclear Information System (INIS)

Sui, Jinxue; Yang, Li; Hu, Yunan

2016-01-01

In view of distribution according to complex fluid network’s needs, this paper proposed one optimization computation method of the nonlinear programming mathematical model based on genetic algorithm. The simulation result shows that the overall energy consumption of the optimized fluid network has a decrease obviously. The control model of the fluid network is established based on nonlinear dynamics. We design the control law based on feedback linearization, take the optimal value by genetic algorithm as the simulation data, can also solve the branch resistance under the optimal value. These resistances can provide technical support and reference for fluid network design and construction, so can realize complex fluid network optimization and control integration design.

A novel condition for stable nonlinear sampled-data models using higher-order discretized approximations with zero dynamics.

Science.gov (United States)

Zeng, Cheng; Liang, Shan; Xiang, Shuwen

2017-05-01

Continuous-time systems are usually modelled by the form of ordinary differential equations arising from physical laws. However, the use of these models in practice and utilizing, analyzing or transmitting these data from such systems must first invariably be discretized. More importantly, for digital control of a continuous-time nonlinear system, a good sampled-data model is required. This paper investigates the new consistency condition which is weaker than the previous similar results presented. Moreover, given the stability of the high-order approximate model with stable zero dynamics, the novel condition presented stabilizes the exact sampled-data model of the nonlinear system for sufficiently small sampling periods. An insightful interpretation of the obtained results can be made in terms of the stable sampling zero dynamics, and the new consistency condition is surprisingly associated with the relative degree of the nonlinear continuous-time system. Our controller design, based on the higher-order approximate discretized model, extends the existing methods which mainly deal with the Euler approximation. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Hopf bifurcation in love dynamical models with nonlinear couples and time delays

International Nuclear Information System (INIS)

Liao Xiaofeng; Ran Jiouhong

2007-01-01

A love dynamical models with nonlinear couples and two delays is considered. Local stability of this model is studied by analyzing the associated characteristic transcendental equation. We find that the Hopf bifurcation occurs when the sum of the two delays varies and passes a sequence of critical values. The stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Numerical example is given to illustrate our results

Nonlinear dynamics of regenerative cutting processes-Comparison of two models

International Nuclear Information System (INIS)

Wang, X.S.; Hu, J.; Gao, J.B.

2006-01-01

Understanding the nonlinear dynamics of cutting processes is essential for the improvement of machining technology. We study machine cutting processes by two different models, one has been recently introduced by Litak [Litak G. Chaotic vibrations in a regenerative cutting process. Chaos, Solitons and Fractals 2002;13:1531-5] and the other is the classic delay differential equation model. Although chaotic solutions have been found in both models, well known routes to chaos, such as period-doubling or quasi-periodic motion to chaos are not observed in either model. Careful analysis shows that the chaotic motion from the Litak's model has sharper spectral peaks, a smaller correlation dimension and a smaller value for the largest positive Lyapunov exponent. Implications to the control of chaos in cutting processes are discussed

Nonlinear Spatio-Temporal Dynamics and Chaos in Semiconductors

Science.gov (United States)

Schöll, Eckehard

2005-08-01

Nonlinear transport phenomena are an increasingly important aspect of modern semiconductor research. This volume deals with complex nonlinear dynamics, pattern formation, and chaotic behavior in such systems. It bridges the gap between two well-established fields: the theory of dynamic systems and nonlinear charge transport in semiconductors. This unified approach helps reveal important electronic transport instabilities. The initial chapters lay a general framework for the theoretical description of nonlinear self-organized spatio-temporal patterns, such as current filaments, field domains, fronts, and analysis of their stability. Later chapters consider important model systems in detail: impact ionization induced impurity breakdown, Hall instabilities, superlattices, and low-dimensional structures. State-of-the-art results include chaos control, spatio-temporal chaos, multistability, pattern selection, activator-inhibitor kinetics, and global coupling, linking fundamental issues to electronic device applications. This book will be of great value to semiconductor physicists and nonlinear scientists alike.

Dynamic Flight Simulation Utilizing High Fidelity CFD-Based Nonlinear Reduced Order Model, Phase II

Data.gov (United States)

National Aeronautics and Space Administration — The Nonlinear Dynamic Flight Simulation (NL-DFS) system will be developed in the Phase II project by combining the classical nonlinear rigid-body flight dynamics...

SHOCK, Nonlinear Dynamic Structure Analysis, Spring and Mass Model, Runge-Kutta-Gill Method

International Nuclear Information System (INIS)

Gabrielson, V. K.

1981-01-01

1 - Description of problem or function: SHOCK calculates the dynamic response of a structure modeled as a spring-mass system having one or two degrees of freedom for each mass when subjected to specified environments. The code determines the behavior of each lumped mass (displacement, velocity, and acceleration for each degree of freedom) and the behavior of each spring or coupling (force, shear, moment, and displacement) as a function of time. Two types of models, axial, having one degree of freedom, and lateral, having two degrees of freedom at each mass can be processed. Damping can be included in all models and shock spectrums of responses can be obtained. 2 - Method of solution: Two methods of numerical integration of the second-order dynamic equations are provided: the Runge-Kutta-Gill method with variable step-size is recommended for highly nonlinear problems, and a variation of the Newmark-Beta method is available for use with large linear problems. 3 - Restrictions on the complexity of the problem: Maxima of: 100 masses, 200 springs or couplings. Complex arrangements of nonlinear options must be carefully checked by the user

Nonlinear Dynamics of the Woodpecker Toy

NARCIS (Netherlands)

Leine, R.I.; Glocker, C.; Campen, van D.H.

2001-01-01

This paper studies bifurcations in systems with impact andfriction, modeled with a rigid multibody approach. Knowledgefrom the field of Nonlinear Dynamics is therefore combined withtheory from the field of Nonsmooth Mechanics. The nonlineardynamics is studied of a commercial wooden toy. The toyshows

The coupled nonlinear dynamics of a lift system

Energy Technology Data Exchange (ETDEWEB)

Crespo, Rafael Sánchez, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Kaczmarczyk, Stefan, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Picton, Phil, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Su, Huijuan, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk [The University of Northampton, School of Science and Technology, Avenue Campus, St George' s Avenue, Northampton (United Kingdom)

2014-12-10

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

Nonlinear dynamic modeling of a V-shaped metal based thermally driven MEMS actuator for RF switches

Science.gov (United States)

Bakri-Kassem, Maher; Dhaouadi, Rached; Arabi, Mohamed; Estahbanati, Shahabeddin V.; Abdel-Rahman, Eihab

2018-05-01

In this paper, we propose a new dynamic model to describe the nonlinear characteristics of a V-shaped (chevron) metallic-based thermally driven MEMS actuator. We developed two models for the thermal actuator with two configurations. The first MEMS configuration has a small tip connected to the shuttle, while the second configuration has a folded spring and a wide beam attached to the shuttle. A detailed finite element model (FEM) and a lumped element model (LEM) are proposed for each configuration to completely characterize the electro-thermal and thermo-mechanical behaviors. The nonlinear resistivity of the polysilicon layer is extracted from the measured current-voltage (I-V) characteristics of the actuator and the simulated corresponding temperatures in the FEM model, knowing the resistivity of the polysilicon at room temperature from the manufacture’s handbook. Both developed models include the nonlinear temperature-dependent material properties. Numerical simulations in comparison with experimental data using a dedicated MEMS test apparatus verify the accuracy of the proposed LEM model to represent the complex dynamics of the thermal MEMS actuator. The LEM and FEM simulation results show an accuracy ranging from a maximum of 13% error down to a minimum of 1.4% error. The actuator with the lower thermal load to air that includes a folded spring (FS), also known as high surface area actuator is compared to the actuator without FS, also known as low surface area actuator, in terms of the I-V characteristics, power consumption, and experimental static and dynamic responses of the tip displacement.

Smooth Adaptive Internal Model Control Based on U Model for Nonlinear Systems with Dynamic Uncertainties

Directory of Open Access Journals (Sweden)

Li Zhao

2016-01-01

Full Text Available An improved smooth adaptive internal model control based on U model control method is presented to simplify modeling structure and parameter identification for a class of uncertain dynamic systems with unknown model parameters and bounded external disturbances. Differing from traditional adaptive methods, the proposed controller can simplify the identification of time-varying parameters in presence of bounded external disturbances. Combining the small gain theorem and the virtual equivalent system theory, learning rate of smooth adaptive internal model controller has been analyzed and the closed-loop virtual equivalent system based on discrete U model has been constructed as well. The convergence of this virtual equivalent system is proved, which further shows the convergence of the complex closed-loop discrete U model system. Finally, simulation and experimental results on a typical nonlinear dynamic system verified the feasibility of the proposed algorithm. The proposed method is shown to have lighter identification burden and higher control accuracy than the traditional adaptive controller.

Parameter and state estimation in nonlinear dynamical systems

Science.gov (United States)

Creveling, Daniel R.

This thesis is concerned with the problem of state and parameter estimation in nonlinear systems. The need to evaluate unknown parameters in models of nonlinear physical, biophysical and engineering systems occurs throughout the development of phenomenological or reduced models of dynamics. When verifying and validating these models, it is important to incorporate information from observations in an efficient manner. Using the idea of synchronization of nonlinear dynamical systems, this thesis develops a framework for presenting data to a candidate model of a physical process in a way that makes efficient use of the measured data while allowing for estimation of the unknown parameters in the model. The approach presented here builds on existing work that uses synchronization as a tool for parameter estimation. Some critical issues of stability in that work are addressed and a practical framework is developed for overcoming these difficulties. The central issue is the choice of coupling strength between the model and data. If the coupling is too strong, the model will reproduce the measured data regardless of the adequacy of the model or correctness of the parameters. If the coupling is too weak, nonlinearities in the dynamics could lead to complex dynamics rendering any cost function comparing the model to the data inadequate for the determination of model parameters. Two methods are introduced which seek to balance the need for coupling with the desire to allow the model to evolve in its natural manner without coupling. One method, 'balanced' synchronization, adds to the synchronization cost function a requirement that the conditional Lyapunov exponents of the model system, conditioned on being driven by the data, remain negative but small in magnitude. Another method allows the coupling between the data and the model to vary in time according to a specific form of differential equation. The coupling dynamics is damped to allow for a tendency toward zero coupling

Hybrid Cubature Kalman filtering for identifying nonlinear models from sampled recording: Estimation of neuronal dynamics.

Science.gov (United States)

Madi, Mahmoud K; Karameh, Fadi N

2017-01-01

Kalman filtering methods have long been regarded as efficient adaptive Bayesian techniques for estimating hidden states in models of linear dynamical systems under Gaussian uncertainty. Recent advents of the Cubature Kalman filter (CKF) have extended this efficient estimation property to nonlinear systems, and also to hybrid nonlinear problems where by the processes are continuous and the observations are discrete (continuous-discrete CD-CKF). Employing CKF techniques, therefore, carries high promise for modeling many biological phenomena where the underlying processes exhibit inherently nonlinear, continuous, and noisy dynamics and the associated measurements are uncertain and time-sampled. This paper investigates the performance of cubature filtering (CKF and CD-CKF) in two flagship problems arising in the field of neuroscience upon relating brain functionality to aggregate neurophysiological recordings: (i) estimation of the firing dynamics and the neural circuit model parameters from electric potentials (EP) observations, and (ii) estimation of the hemodynamic model parameters and the underlying neural drive from BOLD (fMRI) signals. First, in simulated neural circuit models, estimation accuracy was investigated under varying levels of observation noise (SNR), process noise structures, and observation sampling intervals (dt). When compared to the CKF, the CD-CKF consistently exhibited better accuracy for a given SNR, sharp accuracy increase with higher SNR, and persistent error reduction with smaller dt. Remarkably, CD-CKF accuracy shows only a mild deterioration for non-Gaussian process noise, specifically with Poisson noise, a commonly assumed form of background fluctuations in neuronal systems. Second, in simulated hemodynamic models, parametric estimates were consistently improved under CD-CKF. Critically, time-localization of the underlying neural drive, a determinant factor in fMRI-based functional connectivity studies, was significantly more accurate

Hybrid Cubature Kalman filtering for identifying nonlinear models from sampled recording: Estimation of neuronal dynamics

Science.gov (United States)

2017-01-01

Kalman filtering methods have long been regarded as efficient adaptive Bayesian techniques for estimating hidden states in models of linear dynamical systems under Gaussian uncertainty. Recent advents of the Cubature Kalman filter (CKF) have extended this efficient estimation property to nonlinear systems, and also to hybrid nonlinear problems where by the processes are continuous and the observations are discrete (continuous-discrete CD-CKF). Employing CKF techniques, therefore, carries high promise for modeling many biological phenomena where the underlying processes exhibit inherently nonlinear, continuous, and noisy dynamics and the associated measurements are uncertain and time-sampled. This paper investigates the performance of cubature filtering (CKF and CD-CKF) in two flagship problems arising in the field of neuroscience upon relating brain functionality to aggregate neurophysiological recordings: (i) estimation of the firing dynamics and the neural circuit model parameters from electric potentials (EP) observations, and (ii) estimation of the hemodynamic model parameters and the underlying neural drive from BOLD (fMRI) signals. First, in simulated neural circuit models, estimation accuracy was investigated under varying levels of observation noise (SNR), process noise structures, and observation sampling intervals (dt). When compared to the CKF, the CD-CKF consistently exhibited better accuracy for a given SNR, sharp accuracy increase with higher SNR, and persistent error reduction with smaller dt. Remarkably, CD-CKF accuracy shows only a mild deterioration for non-Gaussian process noise, specifically with Poisson noise, a commonly assumed form of background fluctuations in neuronal systems. Second, in simulated hemodynamic models, parametric estimates were consistently improved under CD-CKF. Critically, time-localization of the underlying neural drive, a determinant factor in fMRI-based functional connectivity studies, was significantly more accurate

Inferring Instantaneous, Multivariate and Nonlinear Sensitivities for the Analysis of Feedback Processes in a Dynamical System: Lorenz Model Case Study

Science.gov (United States)

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.

Nonlinear dynamics of biomimetic micro air vehicles

Energy Technology Data Exchange (ETDEWEB)

Hou, Y; Kong, J [College of Mechanical Automation, Wuhan University of Science and Technology, Wuhan, 430081 (China)], E-mail: fly_houyu@163.com.cn

2008-02-15

Flapping-wing micro air vehicles (FMAV) are new conceptual air vehicles that mimic the flying modes of birds and insects. They surpass the research fields of traditional airplane design and aerodynamics on application technologies, and initiate the applications of MEMS technologies on aviation fields. This paper studies a micro flapping mechanism that based upon insect thorax and actuated by electrostatic force. Because there are strong nonlinear coupling between the two physical domains, electrical and mechanical, the static and dynamic characteristics of this system are very complicated. Firstly, the nonlinear dynamic model of the electromechanical coupling system is set up according to the physical model of the flapping mechanism. The dynamic response of the system in constant voltage is studied by numerical method. Then the effect of damping and initial condition on dynamic characteristics of the system is analyzed in phase space. In addition, the dynamic responses of the system in sine voltage excitation are discussed. The results of research are helpful to the design, fabrication and application of the micro flapping mechanism of FMAV, and also to other micro electromechanical system that actuated by electrostatic force.

Nonlinear soil parameter effects on dynamic embedment of offshore pipeline on soft clay

Directory of Open Access Journals (Sweden)

Su Young Yu

2015-03-01

Full Text Available 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 para- meters 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.

International Conference on Applications in Nonlinear Dynamics

CERN Document Server

Longhini, Patrick; Palacios, Antonio

2017-01-01

This book presents collaborative research works carried out by experimentalists and theorists around the world in the field of nonlinear dynamical systems. It provides a forum for applications of nonlinear systems while solving practical problems in science and engineering. Topics include: Applied Nonlinear Optics, Sensor, Radar & Communication Signal Processing, Nano Devices, Nonlinear Biomedical Applications, Circuits & Systems, Coupled Nonlinear Oscillator, Precision Timing Devices, Networks, and other contemporary topics in the general field of Nonlinear Science. This book provides a comprehensive report of the various research projects presented at the International Conference on Applications in Nonlinear Dynamics (ICAND 2016) held in Denver, Colorado, 2016. It can be a valuable tool for scientists and engineering interested in connecting ideas and methods in nonlinear dynamics with actual design, fabrication and implementation of engineering applications or devices.

Fluid mechanics and heat transfer advances in nonlinear dynamics modeling

CERN Document Server

Asli, Kaveh Hariri

2015-01-01

This valuable new book focuses on new methods and techniques in fluid mechanics and heat transfer in mechanical engineering. The book includes the research of the authors on the development of optimal mathematical models and also uses modern computer technology and mathematical methods for the analysis of nonlinear dynamic processes. It covers technologies applicable to both fluid mechanics and heat transfer problems, which include a combination of physical, mechanical, and thermal techniques. The authors develop a new method for the calculation of mathematical models by computer technology, using parametric modeling techniques and multiple analyses for mechanical system. The information in this book is intended to help reduce the risk of system damage or failure. Included are sidebar discussions, which contain information and facts about each subject area that help to emphasize important points to remember.

An efficient nonlinear finite-difference approach in the computational modeling of the dynamics of a nonlinear diffusion-reaction equation in microbial ecology.

Science.gov (United States)

Macías-Díaz, J E; Macías, Siegfried; Medina-Ramírez, I E

2013-12-01

In this manuscript, we present a computational model to approximate the solutions of a partial differential equation which describes the growth dynamics of microbial films. The numerical technique reported in this work is an explicit, nonlinear finite-difference methodology which is computationally implemented using Newton's method. Our scheme is compared numerically against an implicit, linear finite-difference discretization of the same partial differential equation, whose computer coding requires an implementation of the stabilized bi-conjugate gradient method. Our numerical results evince that the nonlinear approach results in a more efficient approximation to the solutions of the biofilm model considered, and demands less computer memory. Moreover, the positivity of initial profiles is preserved in the practice by the nonlinear scheme proposed. Copyright © 2013 Elsevier Ltd. All rights reserved.

Nonlinear dynamic analysis and state space representation of a manipulator under viscoelastic material conditions

Directory of Open Access Journals (Sweden)

Esfandiar, H.

2013-05-01

Full Text Available In this paper, based on the VoigtKelvin constitutive model, nonlinear dynamic modelling and state space representation of a viscoelastic beam acting as a flexible robotic manipulator is investigated. Complete nonlinear dynamic modelling of a viscoelastic beam without premature linearisation of dynamic equations is developed. The adopted method is capable of reproducing nonlinear dynamic effects, such as beam stiffening due to centrifugal and Coriolis forces induced by rotation of the joints. Structural damping effects on the models dynamic behaviour are also shown. A reliable model for a viscoelastic beam is subsequently presented. The governing equations of motion are derived using Hamiltons principle, and using the finite difference method, nonlinear partial differential equations are reduced to ordinary differential equations. For the purpose of flexible manipulator control, the standard form of state space equations for the viscoelastic link and the actuator is obtained. Simulation results indicate substantial improvements in dynamic behaviour, and a parameter sensitivity study is carried out to investigate the effect of structural damping on the vibration amplitude.

Beam Stability and Nonlinear Dynamics. Proceedings

International Nuclear Information System (INIS)

Parsa, Z.

1997-01-01

These proceedings represent papers presented at the Beam Stability and Nonlinear Dynamics symposium held in Santa Barbara in December 1996. The symposium was sponsored by the National Science Foundation as part of the United States long term accelerator research. The focus of this symposium was on nonlinear dynamics and beam stability. The topics included single-particle and many-particle dynamics, and stability in large circular accelerators such as the Large Hadron Collider(LHC). Other subjects covered were spin dynamics, nonlinear aberration correction, collective effects in the LHC, sawtooth instability and Landau damping in the presence of strong nonlinearity. There were presentations concerning plasma physics including the effect of beam echo. There are 17 papers altogether in these proceedings and 8 of them have been abstracted for the Energy Science and Technology database

Nonlinear dynamics experiment in the Tevatron

International Nuclear Information System (INIS)

Merminga, N.; Edwards, D.; Finley, D.

1989-01-01

Results of the continuing analysis of the nonlinear dynamics experiment E778 are presented. Sixteen special sextupoles introduced nonlinearities in the Tevatron. 'Smear,' which is one of the parameters used to quantify the degree of nonlinearity, was extracted from the data and compared with calculation. Injection efficiency in the presence of nonlinearities was studied. Measurements of the dynamic aperture were performed. The final results in one degree of freedom of the smear, the injection efficiency and the dynamic aperture are presented. Particles captured on nonlinear resonance islands were directly observed and measurements were performed. The capture efficiency was extracted from the data and compared with prediction. The influence of tune modulation on the stability of these islands was investigated. Plans for future measurements are discussed. 4 refs., 6 figs

Nonlinear dynamics of two-phase flow

International Nuclear Information System (INIS)

Rizwan-uddin

1986-01-01

Unstable flow conditions can occur in a wide variety of laboratory and industry equipment that involve two-phase flow. Instabilities in industrial equipment, which include boiling water reactor (BWR) cores, steam generators, heated channels, cryogenic fluid heaters, heat exchangers, etc., are related to their nonlinear dynamics. These instabilities can be of static (Ledinegg instability) or dynamic (density wave oscillations) type. Determination of regions in parameters space where these instabilities can occur and knowledge of system dynamics in or near these regions is essential for the safe operation of such equipment. Many two-phase flow engineering components can be modeled as heated channels. The set of partial differential equations that describes the dynamics of single- and two-phase flow, for the special case of uniform heat flux along the length of the channel, can be reduced to a set of two coupled ordinary differential equations [in inlet velocity v/sub i/(t) and two-phase residence time tau(t)] involving history integrals: a nonlinear ordinary functional differential equation and an integral equation. Hence, to solve these equations, the dependent variables must be specified for -(nu + tau) ≤ t ≤ 0, where nu is the single-phase residence time. This system of nonlinear equations has been solved analytically using asymptotic expansion series for finite but small perturbations and numerically using finite difference techniques

Designing a Robust Nonlinear Dynamic Inversion Controller for Spacecraft Formation Flying

Directory of Open Access Journals (Sweden)

Inseok Yang

2014-01-01

Full Text Available The robust nonlinear dynamic inversion (RNDI control technique is proposed to keep the relative position of spacecrafts while formation flying. The proposed RNDI control method is based on nonlinear dynamic inversion (NDI. NDI is nonlinear control method that replaces the original dynamics into the user-selected desired dynamics. Because NDI removes nonlinearities in the model by inverting the original dynamics directly, it also eliminates the need of designing suitable controllers for each equilibrium point; that is, NDI works as self-scheduled controller. Removing the original model also provides advantages of ease to satisfy the specific requirements by simply handling desired dynamics. Therefore, NDI is simple and has many similarities to classical control. In real applications, however, it is difficult to achieve perfect cancellation of the original dynamics due to uncertainties that lead to performance degradation and even make the system unstable. This paper proposes robustness assurance method for NDI. The proposed RNDI is designed by combining NDI and sliding mode control (SMC. SMC is inherently robust using high-speed switching inputs. This paper verifies similarities of NDI and SMC, firstly. And then RNDI control method is proposed. The performance of the proposed method is evaluated by simulations applied to spacecraft formation flying problem.

Multi-Body Ski Jumper Model with Nonlinear Dynamic Inversion Muscle Control for Trajectory Optimization

Directory of Open Access Journals (Sweden)

Patrick Piprek

2018-02-01

Full Text Available This paper presents an approach to model a ski jumper as a multi-body system for an optimal control application. The modeling is based on the constrained Newton-Euler-Equations. Within this paper the complete multi-body modeling methodology as well as the musculoskeletal modeling is considered. For the musculoskeletal modeling and its incorporation in the optimization model, we choose a nonlinear dynamic inversion control approach. This approach uses the muscle models as nonlinear reference models and links them to the ski jumper movement by a control law. This strategy yields a linearized input-output behavior, which makes the optimal control problem easier to solve. The resulting model of the ski jumper can then be used for trajectory optimization whose results are compared to literature jumps. Ultimately, this enables the jumper to get a very detailed feedback of the flight. To achieve the maximal jump length, exact positioning of his body with respect to the air can be displayed.

Hierarchical Cluster-based Partial Least Squares Regression (HC-PLSR is an efficient tool for metamodelling of nonlinear dynamic models

Directory of Open Access Journals (Sweden)

Omholt Stig W

2011-06-01

Full Text Available Abstract Background Deterministic dynamic models of complex biological systems contain a large number of parameters and state variables, related through nonlinear differential equations with various types of feedback. A metamodel of such a dynamic model is a statistical approximation model that maps variation in parameters and initial conditions (inputs to variation in features of the trajectories of the state variables (outputs throughout the entire biologically relevant input space. A sufficiently accurate mapping can be exploited both instrumentally and epistemically. Multivariate regression methodology is a commonly used approach for emulating dynamic models. However, when the input-output relations are highly nonlinear or non-monotone, a standard linear regression approach is prone to give suboptimal results. We therefore hypothesised that a more accurate mapping can be obtained by locally linear or locally polynomial regression. We present here a new method for local regression modelling, Hierarchical Cluster-based PLS regression (HC-PLSR, where fuzzy C-means clustering is used to separate the data set into parts according to the structure of the response surface. We compare the metamodelling performance of HC-PLSR with polynomial partial least squares regression (PLSR and ordinary least squares (OLS regression on various systems: six different gene regulatory network models with various types of feedback, a deterministic mathematical model of the mammalian circadian clock and a model of the mouse ventricular myocyte function. Results Our results indicate that multivariate regression is well suited for emulating dynamic models in systems biology. The hierarchical approach turned out to be superior to both polynomial PLSR and OLS regression in all three test cases. The advantage, in terms of explained variance and prediction accuracy, was largest in systems with highly nonlinear functional relationships and in systems with positive feedback

Hierarchical cluster-based partial least squares regression (HC-PLSR) is an efficient tool for metamodelling of nonlinear dynamic models.

Science.gov (United States)

Tøndel, Kristin; Indahl, Ulf G; Gjuvsland, Arne B; Vik, Jon Olav; Hunter, Peter; Omholt, Stig W; Martens, Harald

2011-06-01

Deterministic dynamic models of complex biological systems contain a large number of parameters and state variables, related through nonlinear differential equations with various types of feedback. A metamodel of such a dynamic model is a statistical approximation model that maps variation in parameters and initial conditions (inputs) to variation in features of the trajectories of the state variables (outputs) throughout the entire biologically relevant input space. A sufficiently accurate mapping can be exploited both instrumentally and epistemically. Multivariate regression methodology is a commonly used approach for emulating dynamic models. However, when the input-output relations are highly nonlinear or non-monotone, a standard linear regression approach is prone to give suboptimal results. We therefore hypothesised that a more accurate mapping can be obtained by locally linear or locally polynomial regression. We present here a new method for local regression modelling, Hierarchical Cluster-based PLS regression (HC-PLSR), where fuzzy C-means clustering is used to separate the data set into parts according to the structure of the response surface. We compare the metamodelling performance of HC-PLSR with polynomial partial least squares regression (PLSR) and ordinary least squares (OLS) regression on various systems: six different gene regulatory network models with various types of feedback, a deterministic mathematical model of the mammalian circadian clock and a model of the mouse ventricular myocyte function. Our results indicate that multivariate regression is well suited for emulating dynamic models in systems biology. The hierarchical approach turned out to be superior to both polynomial PLSR and OLS regression in all three test cases. The advantage, in terms of explained variance and prediction accuracy, was largest in systems with highly nonlinear functional relationships and in systems with positive feedback loops. HC-PLSR is a promising approach for

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

International Nuclear Information System (INIS)

Faybishenko, Boris

2002-01-01

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 fractured 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

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

Energy Technology Data Exchange (ETDEWEB)

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 fractured 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.

Nonlinear Dynamics in Spear Wigglers

International Nuclear Information System (INIS)

2002-01-01

BL11, the most recently installed wiggler in the SPEAR storage ring at SSRL, produces a large nonlinear perturbation of the electron beam dynamics, which was not directly evident in the integrated magnetic field measurements. Measurements of tune shifts with betatron oscillation amplitude and with closed orbit shifts were used to characterize the nonlinear fields of the SPEAR insertion devices (IDs). Because of the narrow pole width in BL11, the nonlinear fields seen along the wiggling electron trajectory are dramatically different than the flip coil measurements made along a straight line. This difference explains the tune shift measurements and the observed degradation in dynamic aperture. Corrector magnets to cancel the BL11 nonlinear fields are presently under construction

Nonlinear dynamics analysis of a modified optically injected semiconductor lasers model

International Nuclear Information System (INIS)

Chu Yandong; Li Xianfeng; Zhang Jiangang; Chang Yingxiang

2009-01-01

In this paper, a new nonlinear autonomous system that was introduced by Chlouverakis and Sprott is studied further, to present very rich and complex nonlinear dynamical behaviors. Some basic dynamical properties are studied either analytically or numerically, such as Poincare mapping, Lyapunov exponents, fractal dimension, continuous power spectrum and so forth. Furthermore, the coexistence of different attractors is discovered on the Poincare maps. Meanwhile, chaotic oscillation of this system is converted into a stable periodic orbit with the method of time-delayed feedback, which demonstrated by numerical simulations and the robustness of this method is proved.

A Novel Numerical Approach for a Nonlinear Fractional Dynamical Model of Interpersonal and Romantic Relationships

Directory of Open Access Journals (Sweden)

Jagdev Singh

2017-07-01

Full Text Available In this paper, we propose a new numerical algorithm, namely q-homotopy analysis Sumudu transform method (q-HASTM, to obtain the approximate solution for the nonlinear fractional dynamical model of interpersonal and romantic relationships. The suggested algorithm examines the dynamics of love affairs between couples. The q-HASTM is a creative combination of Sumudu transform technique, q-homotopy analysis method and homotopy polynomials that makes the calculation very easy. To compare the results obtained by using q-HASTM, we solve the same nonlinear problem by Adomian’s decomposition method (ADM. The convergence of the q-HASTM series solution for the model is adapted and controlled by auxiliary parameter ℏ and asymptotic parameter n. The numerical results are demonstrated graphically and in tabular form. The result obtained by employing the proposed scheme reveals that the approach is very accurate, effective, flexible, simple to apply and computationally very nice.

A Two-Step Hybrid Approach for Modeling the Nonlinear Dynamic Response of Piezoelectric Energy Harvesters

Directory of Open Access Journals (Sweden)

Claudio Maruccio

2018-01-01

Full Text Available An effective hybrid computational framework is described here in order to assess the nonlinear dynamic response of piezoelectric energy harvesting devices. The proposed strategy basically consists of two steps. First, fully coupled multiphysics finite element (FE analyses are performed to evaluate the nonlinear static response of the device. An enhanced reduced-order model is then derived, where the global dynamic response is formulated in the state-space using lumped coefficients enriched with the information derived from the FE simulations. The electromechanical response of piezoelectric beams under forced vibrations is studied by means of the proposed approach, which is also validated by comparing numerical predictions with some experimental results. Such numerical and experimental investigations have been carried out with the main aim of studying the influence of material and geometrical parameters on the global nonlinear response. The advantage of the presented approach is that the overall computational and experimental efforts are significantly reduced while preserving a satisfactory accuracy in the assessment of the global behavior.

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

Science.gov (United States)

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.

Analytical and Computational Modeling of Mechanical Waves in Microscale Granular Crystals: Nonlinearity and Rotational Dynamics

Science.gov (United States)

Wallen, Samuel P.

Granular media are one of the most common, yet least understood forms of matter on earth. The difficulties in understanding the physics of granular media stem from the fact that they are typically heterogeneous and highly disordered, and the grains interact via nonlinear contact forces. Historically, one approach to reducing these complexities and gaining new insight has been the study of granular crystals, which are ordered arrays of similarly-shaped particles (typically spheres) in Hertzian contact. Using this setting, past works explored the rich nonlinear dynamics stemming from contact forces, and proposed avenues where such granular crystals could form designer, dynamically responsive materials, which yield beneficial functionality in dynamic regimes. In recent years, the combination of self-assembly fabrication methods and laser ultrasonic experimental characterization have enabled the study of granular crystals at microscale. While our intuition may suggest that these microscale granular crystals are simply scaled-down versions of their macroscale counterparts, in fact, the relevant physics change drastically; for example, short-range adhesive forces between particles, which are negligible at macroscale, are several orders of magnitude stronger than gravity at microscale. In this thesis, we present recent advances in analytical and computational modeling of microscale granular crystals, in particular concerning the interplay of nonlinearity, shear interactions, and particle rotations, which have previously been either absent, or included separately at macroscale. Drawing inspiration from past works on phononic crystals and nonlinear lattices, we explore problems involving locally-resonant metamaterials, nonlinear localized modes, amplitude-dependent energy partition, and other rich dynamical phenomena. This work enhances our understanding of microscale granular media, which may find applicability in fields such as ultrasonic wave tailoring, signal processing

Nonlinear dynamics aspects of modern storage rings

International Nuclear Information System (INIS)

Helleman, R.H.G.; Kheifets, S.A.

1986-01-01

It is argued that the nonlinearity of storage rings becomes an essential problem as the design parameters of each new machine are pushed further and further. Yet the familiar methods of classical mechanics do not allow determination of single particle orbits over reasonable lengths of time. It is also argued that the single particle dynamics of a storage ring is possibly one of the cleanest and simplest nonlinear dynamical systems available with very few degrees of freedom. Hence, reasons are found for accelerator physicists to be interested in nonlinear dynamics and for researchers in nonlinear dynamics to be interested in modern storage rings. The more familiar methods of treating nonlinear systems routinely used in acclerator theory are discussed, pointing out some of their limitations and pitfalls. 39 refs., 1 fig

Calibration of the nonlinear ring model at the Diamond Light Source

Directory of Open Access Journals (Sweden)

R. Bartolini

2011-05-01

Full Text Available Nonlinear beam dynamics plays a crucial role in defining the performance of a storage ring. The beam lifetime, the injection efficiency, and the dynamic and momentum apertures available to the beam are optimized during the design phase by a proper optimization of the linear lattice and of the distribution of sextupole families. The correct implementation of the design model, especially the nonlinear part, is a nontrivial accelerator physics task. Several parameters of the nonlinear dynamics can be used to compare the real machine with the model and eventually to correct the accelerator. Most of these parameters are extracted from the analysis of turn-by-turn data after the excitation of betatron oscillations of the particles in the ring. We present the experimental results of the campaign of measurements carried out at the Diamond storage ring to characterize the nonlinear beam dynamics. A combination of frequency map analysis with the detuning with momentum measurements has allowed for a precise calibration of the nonlinear model that can accurately reproduce the nonlinear beam dynamics in Diamond.

Threshold Dynamics in Stochastic SIRS Epidemic Models with Nonlinear Incidence and Vaccination

Directory of Open Access Journals (Sweden)

Lei Wang

2017-01-01

Full Text Available In this paper, the dynamical behaviors for a stochastic SIRS epidemic model with nonlinear incidence and vaccination are investigated. In the models, the disease transmission coefficient and the removal rates are all affected by noise. Some new basic properties of the models are found. Applying these properties, we establish a series of new threshold conditions on the stochastically exponential extinction, stochastic persistence, and permanence in the mean of the disease with probability one for the models. Furthermore, we obtain a sufficient condition on the existence of unique stationary distribution for the model. Finally, a series of numerical examples are introduced to illustrate our main theoretical results and some conjectures are further proposed.

Global investigation of the nonlinear dynamics of carbon nanotubes

KAUST Repository

Xu, Tiantian

2016-11-17

Understanding the complex nonlinear dynamics of carbon nanotubes (CNTs) is essential to enable utilization of these structures in devices and practical applications. We present in this work an investigation of the global nonlinear dynamics of a slacked CNT when actuated by large electrostatic and electrodynamic excitations. The coexistence of several attractors is observed. The CNT is modeled as an Euler–Bernoulli beam. A reduced-order model based on the Galerkin method is developed and utilized to simulate the static and dynamic responses. Critical computational challenges are posed due to the complicated form of the electrostatic force, which describes the interaction between the upper electrode, consisting of the cylindrically shaped CNT, and the lower electrode. Toward this, we approximate the electrostatic force using the Padé expansion. We explore the dynamics near the primary and superharmonic resonances. The nanostructure exhibits several attractors with different characteristics. To achieve deep insight and describe the complexity and richness of the behavior, we analyze the nonlinear response from an attractor-basins point of view. The competition of attractors is highlighted. Compactness and/or fractality of their basins are discussed. Both the effects of varying the excitation frequency and amplitude are examined up to the dynamic pull-in instability.

Device Applications of Nonlinear Dynamics

CERN Document Server

Baglio, Salvatore

2006-01-01

This edited book is devoted specifically to the applications of complex nonlinear dynamic phenomena to real systems and device applications. While in the past decades there has been significant progress in the theory of nonlinear phenomena under an assortment of system boundary conditions and preparations, there exist comparatively few devices that actually take this rich behavior into account. "Device Applications of Nonlinear Dynamics" applies and exploits this knowledge to make devices which operate more efficiently and cheaply, while affording the promise of much better performance. Given the current explosion of ideas in areas as diverse as molecular motors, nonlinear filtering theory, noise-enhanced propagation, stochastic resonance and networked systems, the time is right to integrate the progress of complex systems research into real devices.

Effect of initial strain and material nonlinearity on the nonlinear static and dynamic response of graphene sheets

Science.gov (United States)

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.

Parametric Identification of Nonlinear Dynamical Systems

Science.gov (United States)

Feeny, Brian

2002-01-01

In this project, we looked at the application of harmonic balancing as a tool for identifying parameters (HBID) in a nonlinear dynamical systems with chaotic responses. The main idea is to balance the harmonics of periodic orbits extracted from measurements of each coordinate during a chaotic response. The periodic orbits are taken to be approximate solutions to the differential equations that model the system, the form of the differential equations being known, but with unknown parameters to be identified. Below we summarize the main points addressed in this work. The details of the work are attached as drafts of papers, and a thesis, in the appendix. Our study involved the following three parts: (1) Application of the harmonic balance to a simulation case in which the differential equation model has known form for its nonlinear terms, in contrast to a differential equation model which has either power series or interpolating functions to represent the nonlinear terms. We chose a pendulum, which has sinusoidal nonlinearities; (2) Application of the harmonic balance to an experimental system with known nonlinear forms. We chose a double pendulum, for which chaotic response were easily generated. Thus we confronted a two-degree-of-freedom system, which brought forth challenging issues; (3) A study of alternative reconstruction methods. The reconstruction of the phase space is necessary for the extraction of periodic orbits from the chaotic responses, which is needed in this work. Also, characterization of a nonlinear system is done in the reconstructed phase space. Such characterizations are needed to compare models with experiments. Finally, some nonlinear prediction methods can be applied in the reconstructed phase space. We developed two reconstruction methods that may be considered if the common method (method of delays) is not applicable.

Estimation of dynamic reactivity using an H∞ optimal filter with a nonlinear term

International Nuclear Information System (INIS)

Suzuki, Katsuo; Watanabe, Koiti

1996-01-01

A method of nonlinear filtering is applied to the problem of estimating the dynamic reactivity of a nonlinear reactor system. The nonlinear filtering algorithm developed is a simple modification of a linear H ∞ optimal filter with a nonlinear feedback loop added. The linear filter is designed on the basis of a linearized dynamical system model that consists of linearized point reactor kinetic equations and a reactivity state equation driven by a fictitious signal. The latter is artificially introduced to deal with the reactivity as a state variable. The results of the computer simulation show that the nonlinear filtering algorithm can be applied to estimate the dynamic reactivity of the nonlinear reactor system, even under relatively large reactivity disturbances

Comparison of stochastic resonance in static and dynamical nonlinearities

International Nuclear Information System (INIS)

Ma, Yumei; Duan, Fabing

2014-01-01

We compare the stochastic resonance (SR) effects in parallel arrays of static and dynamical nonlinearities via the measure of output signal-to-noise ratio (SNR). For a received noisy periodic signal, parallel arrays of both static and dynamical nonlinearities can enhance the output SNR by optimizing the internal noise level. The static nonlinearity is easily implementable, while the dynamical nonlinearity has more parameters to be tuned, at the risk of not exploiting the beneficial role of internal noise components. It is of interest to note that, for an input signal buried in the external Laplacian noise, we show that the dynamical nonlinearity is superior to the static nonlinearity in obtaining a better output SNR. This characteristic is assumed to be closely associated with the kurtosis of noise distribution. - Highlights: • Comparison of SR effects in arrays of both static and dynamical nonlinearities. • Static nonlinearity is easily implementable for the SNR enhancement. • Dynamical nonlinearity yields a better output SNR for external Laplacian noise

Nonlinear dynamics and numerical uncertainties in CFD

Science.gov (United States)

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.

Nonlinear modelling of polymer electrolyte membrane fuel cell stack using nonlinear cancellation technique

Energy Technology Data Exchange (ETDEWEB)

Barus, R. P. P., E-mail: rismawan.ppb@gmail.com [Engineering Physics, Faculty of Industrial Technology, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung and Centre for Material and Technical Product, Jalan Sangkuriang No. 14 Bandung (Indonesia); Tjokronegoro, H. A.; Leksono, E. [Engineering Physics, Faculty of Industrial Technology, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung (Indonesia); Ismunandar [Chemistry Study, Faculty of Mathematics and Science, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung (Indonesia)

2014-09-25

Fuel cells are promising new energy conversion devices that are friendly to the environment. A set of control systems are required in order to operate a fuel cell based power plant system optimally. For the purpose of control system design, an accurate fuel cell stack model in describing the dynamics of the real system is needed. Currently, linear model are widely used for fuel cell stack control purposes, but it has limitations in narrow operation range. While nonlinear models lead to nonlinear control implemnetation whos more complex and hard computing. In this research, nonlinear cancellation technique will be used to transform a nonlinear model into a linear form while maintaining the nonlinear characteristics. The transformation is done by replacing the input of the original model by a certain virtual input that has nonlinear relationship with the original input. Then the equality of the two models is tested by running a series of simulation. Input variation of H2, O2 and H2O as well as disturbance input I (current load) are studied by simulation. The error of comparison between the proposed model and the original nonlinear model are less than 1 %. Thus we can conclude that nonlinear cancellation technique can be used to represent fuel cell nonlinear model in a simple linear form while maintaining the nonlinear characteristics and therefore retain the wide operation range.

Nonlinear modelling of polymer electrolyte membrane fuel cell stack using nonlinear cancellation technique

International Nuclear Information System (INIS)

Barus, R. P. P.; Tjokronegoro, H. A.; Leksono, E.; Ismunandar

2014-01-01

Fuel cells are promising new energy conversion devices that are friendly to the environment. A set of control systems are required in order to operate a fuel cell based power plant system optimally. For the purpose of control system design, an accurate fuel cell stack model in describing the dynamics of the real system is needed. Currently, linear model are widely used for fuel cell stack control purposes, but it has limitations in narrow operation range. While nonlinear models lead to nonlinear control implemnetation whos more complex and hard computing. In this research, nonlinear cancellation technique will be used to transform a nonlinear model into a linear form while maintaining the nonlinear characteristics. The transformation is done by replacing the input of the original model by a certain virtual input that has nonlinear relationship with the original input. Then the equality of the two models is tested by running a series of simulation. Input variation of H2, O2 and H2O as well as disturbance input I (current load) are studied by simulation. The error of comparison between the proposed model and the original nonlinear model are less than 1 %. Thus we can conclude that nonlinear cancellation technique can be used to represent fuel cell nonlinear model in a simple linear form while maintaining the nonlinear characteristics and therefore retain the wide operation range

Modeling, numerical simulation, and nonlinear dynamic behavior analysis of PV microgrid-connected inverter with capacitance catastrophe

Science.gov (United States)

Li, Sichen; Liao, Zhixian; Luo, Xiaoshu; Wei, Duqu; Jiang, Pinqun; Jiang, Qinghong

2018-02-01

The value of the output capacitance (C) should be carefully considered when designing a photovoltaic (PV) inverter since it can cause distortion in the working state of the circuit, and the circuit produces nonlinear dynamic behavior. According to Kirchhoff’s laws and the characteristics of an ideal operational amplifier for a strict piecewise linear state equation, a circuit simulation model is constructed to study the system parameters (time, C) for the current passing through an inductor with an inductance of L and the voltage across the capacitor with a capacitance of C. The developed simulation model uses Runge-Kutta methods to solve the state equations. This study focuses on predicting the fault of the circuit from the two aspects of the harmonic distortion and simulation results. Moreover, the presented model is also used to research the working state of the system in the case of a load capacitance catastrophe. The nonlinear dynamic behaviors in the inverter are simulated and verified.

Soliton dynamics in periodic system with different nonlinear media

International Nuclear Information System (INIS)

Zabolotskij, A.A.

2001-01-01

To analyze pulse dynamics in the optical system consisting of periodic sequence of nonlinear media one uses a composition model covering a model of resonance interaction of light ultrashort pulse with energy transition of medium with regard to pumping of the upper level and quasi-integrable model describing propagation of light field in another medium with cubic nonlinearity and dispersion. One additionally takes account of losses and other types of interaction in the from of perturbation members. On the basis of the method of scattering back problem and perturbation theory one developed a simple method to study peculiarities of soliton evolution in such periodic system. Due to its application one managed to describe different modes of soliton evolution in such a system including chaotic dynamics [ru

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

Science.gov (United States)

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.

Modeling and Analysis of Static and Dynamic Characteristics of Nonlinear Seat Suspension for Off-Road Vehicles

OpenAIRE

Yan, Zhenhua; Zhu, Bing; Li, Xuefei; Wang, Guoqiang

2015-01-01

Low-frequency vibrations (0.5–5 Hz) that harm drivers occur in off-road vehicles. Thus, researchers have focused on finding methods to effectively isolate or control low-frequency vibrations. A novel nonlinear seat suspension structure for off-road vehicles is designed, whose static characteristics and seat-human system dynamic response are modeled and analyzed, and experiments are conducted to verify the theoretical solutions. Results show that the stiffness of this nonlinear seat suspension...

Some Aspects of Nonlinear Dynamics and CFD

Science.gov (United States)

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.

Nonlinear evolution dynamics of holographic superconductor model with scalar self-interaction

Science.gov (United States)

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 process is then holographically dual to the dynamical superconducting phase transition process in the boundary theory. Furthermore, we also study the effect of the scalar self-interaction on time evolution of superconducting condensate operator, event and apparent horizon areas of the final hairy black hole.

Forecasting with nonlinear time series models

DEFF Research Database (Denmark)

Kock, Anders Bredahl; Teräsvirta, Timo

In this paper, nonlinear models are restricted to mean nonlinear parametric models. Several such models popular in time series econo- metrics are presented and some of their properties discussed. This in- cludes two models based on universal approximators: the Kolmogorov- Gabor polynomial model...... applied to economic fore- casting problems, is briefly highlighted. A number of large published studies comparing macroeconomic forecasts obtained using different time series models are discussed, and the paper also contains a small simulation study comparing recursive and direct forecasts in a partic...... and two versions of a simple artificial neural network model. Techniques for generating multi-period forecasts from nonlinear models recursively are considered, and the direct (non-recursive) method for this purpose is mentioned as well. Forecasting with com- plex dynamic systems, albeit less frequently...

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

Science.gov (United States)

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.

On the Theory of Nonlinear Dynamics and its Applications in Vehicle Systems Dynamics

DEFF Research Database (Denmark)

True, Hans

1999-01-01

We present a brief outline of nonlinear dynamics and its applications to vehicle systems dynamics problems. The concept of a phase space is introduced in order to illustrate the dynamics of nonlinear systems in a way that is easy to perceive. Various equilibrium states are defined...... of nonlinear dynamics in vehicle simulations is discussed, and it is argued that it is necessary to know the equilibrium states of the full nonlinear system before the simulation calculations are performed......., and the important case of multiple equilibrium states and their dependence on a parameter is discussed. It is argued that the analysis of nonlinear dynamic problems always should start with an analysis of the equilibrium states of the full nonlinear problem whereby great care must be taken in the choice...

Spin-current emission governed by nonlinear spin dynamics.

Science.gov (United States)

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.

Modeling and non-linear responses of MEMS capacitive accelerometer

Directory of Open Access Journals (Sweden)

Sri Harsha C.

2014-01-01

Full Text Available A theoretical investigation of an electrically actuated beam has been illustrated when the electrostatic-ally actuated micro-cantilever beam is separated from the electrode by a moderately large gap for two distinct types of geometric configurations of MEMS accelerometer. Higher order nonlinear terms have been taken into account for studying the pull in voltage analysis. A nonlinear model of gas film squeezing damping, another source of nonlinearity in MEMS devices is included in obtaining the dynamic responses. Moreover, in the present work, the possible source of nonlinearities while formulating the mathematical model of a MEMS accelerometer and their influences on the dynamic responses have been investigated. The theoretical results obtained by using MATLAB has been verified with the results obtained in FE software and has been found in good agreement. Criterion towards stable micro size accelerometer for each configuration has been investigated. This investigation clearly provides an understanding of nonlinear static and dynamics characteristics of electrostatically micro cantilever based device in MEMS.

Nonlinear Dynamics of Non-uniform Current-Vortex Sheets in Magnetohydrodynamic Flows

Science.gov (United States)

Matsuoka, C.; Nishihara, K.; Sano, T.

2017-04-01

A theoretical model is proposed to describe fully nonlinear dynamics of interfaces in two-dimensional MHD flows based on an idea of non-uniform current-vortex sheet. Application of vortex sheet model to MHD flows has a crucial difficulty because of non-conservative nature of magnetic tension. However, it is shown that when a magnetic field is initially parallel to an interface, the concept of vortex sheet can be extended to MHD flows (current-vortex sheet). Two-dimensional MHD flows are then described only by a one-dimensional Lagrange parameter on the sheet. It is also shown that bulk magnetic field and velocity can be calculated from their values on the sheet. The model is tested by MHD Richtmyer-Meshkov instability with sinusoidal vortex sheet strength. Two-dimensional ideal MHD simulations show that the nonlinear dynamics of a shocked interface with density stratification agrees fairly well with that for its corresponding potential flow. Numerical solutions of the model reproduce properly the results of the ideal MHD simulations, such as the roll-up of spike, exponential growth of magnetic field, and its saturation and oscillation. Nonlinear evolution of the interface is found to be determined by the Alfvén and Atwood numbers. Some of their dependence on the sheet dynamics and magnetic field amplification are discussed. It is shown by the model that the magnetic field amplification occurs locally associated with the nonlinear dynamics of the current-vortex sheet. We expect that our model can be applicable to a wide variety of MHD shear flows.

Describing pediatric dysphonia with nonlinear dynamic parameters

Science.gov (United States)

Meredith, Morgan L.; Theis, Shannon M.; McMurray, J. Scott; Zhang, Yu; Jiang, Jack J.

2008-01-01

Objective Nonlinear dynamic analysis has emerged as a reliable and objective tool for assessing voice disorders. However, it has only been tested on adult populations. In the present study, nonlinear dynamic analysis was applied to normal and dysphonic pediatric populations with the goal of collecting normative data. Jitter analysis was also applied in order to compare nonlinear dynamic and perturbation measures. This study’s findings will be useful in creating standards for the use of nonlinear dynamic analysis as a tool to describe dysphonia in the pediatric population. Methods The study included 38 pediatric subjects (23 children with dysphonia and 15 without). Recordings of sustained vowels were obtained from each subject and underwent nonlinear dynamic analysis and percent jitter analysis. The resulting correlation dimension (D2) and percent jitter values were compared across the two groups using t-tests set at a significance level of p = 0.05. Results It was shown that D2 values covary with the presence of pathology in children. D2 values were significantly higher in dysphonic children than in normal children (p = 0.002). Standard deviations indicated a higher level of variation in normal children’s D2 values than in dysphonic children’s D2 values. Jitter analysis showed markedly higher percent jitter in dysphonic children than in normal children (p = 0.025) and large standard deviations for both groups. Conclusion This study indicates that nonlinear dynamic analysis could be a viable tool for the detection and assessment of dysphonia in children. Further investigations and more normative data are needed to create standards for using nonlinear dynamic parameters for the clinical evaluation of pediatric dysphonia. PMID:18947887

Non-Linear Dynamics of Saturn's Rings

Science.gov (United States)

Esposito, L. W.

2016-12-01

Non-linear processes can explain why Saturn's rings are so active and dynamic. Ring systems differ from simple linear systems in two significant ways: 1. They are systems of granular material: where particle-to-particle collisions dominate; thus a kinetic, not a fluid description needed. Stresses are strikingly inhomogeneous and fluctuations are large compared to equilibrium. 2. They are strongly forced by resonances: which drive a non-linear response, that push the system across thresholds that lead to persistent states. Some of this non-linearity is captured in a simple Predator-Prey Model: Periodic forcing from the moon causes streamline crowding; This damps the relative velocity. About a quarter phase later, the aggregates stir the system to higher relative velocity and the limit cycle repeats each orbit, with relative velocity ranging from nearly zero to a multiple of the orbit average. Summary of Halo Results: A predator-prey model for ring dynamics produces transient structures like `straw' that can explain the halo morphology and spectroscopy: Cyclic velocity changes cause perturbed regions to reach higher collision speeds at some orbital phases, which preferentially removes small regolith particles; surrounding particles diffuse back too slowly to erase the effect: this gives the halo morphology; this requires energetic collisions (v ≈ 10m/sec, with throw distances about 200km, implying objects of scale R ≈ 20km).Transform to Duffing Eqn : With the coordinate transformation, z = M2/3, the Predator-Prey equations can be combined to form a single second-order differential equation with harmonic resonance forcing.Ring dynamics and history implications: Moon-triggered clumping explains both small and large particles at resonances. We calculate the stationary size distribution using a cell-to-cell mapping procedure that converts the phase-plane trajectories to a Markov chain. Approximating it as an asymmetric random walk with reflecting boundaries

Natural Poisson structures of nonlinear plasma dynamics

International Nuclear Information System (INIS)

Kaufman, A.N.

1982-01-01

Hamiltonian field theories, for models of nonlinear plasma dynamics, require a Poisson bracket structure for functionals of the field variables. These are presented, applied, and derived for several sets of field variables: coherent waves, incoherent waves, particle distributions, and multifluid electrodynamics. Parametric coupling of waves and plasma yields concise expressions for ponderomotive effects (in kinetic and fluid models) and for induced scattering. (Auth.)

Natural Poisson structures of nonlinear plasma dynamics

International Nuclear Information System (INIS)

Kaufman, A.N.

1982-06-01

Hamiltonian field theories, for models of nonlinear plasma dynamics, require a Poisson bracket structure for functionals of the field variables. These are presented, applied, and derived for several sets of field variables: coherent waves, incoherent waves, particle distributions, and multifluid electrodynamics. Parametric coupling of waves and plasma yields concise expressions for ponderomotive effects (in kinetic and fluid models) and for induced scattering

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

Science.gov (United States)

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.

Nonlinear dynamic modeling of a helicopter planetary gear train for carrier plate crack fault diagnosis

Directory of Open Access Journals (Sweden)

Fan Lei

2016-06-01

Full Text Available Planetary gear train plays a significant role in a helicopter operation and its health is of great importance for the flight safety of the helicopter. This paper investigates the effects of a planet carrier plate crack on the dynamic characteristics of a planetary gear train, and thus finds an effective method to diagnose crack fault. A dynamic model is developed to analyze the torsional vibration of a planetary gear train with a cracked planet carrier plate. The model takes into consideration nonlinear factors such as the time-varying meshing stiffness, gear backlash and viscous damping. Investigation of the deformation of the cracked carrier plate under static stress is performed in order to simulate the dynamic effects of the planet carrier crack on the angular displacement of carrier posts. Validation shows good accuracy of the developed dynamic model in predicting dynamic characteristics of a planetary gear train. Fault features extracted from predictions of the model reveal the correspondence between vibration characteristic and the conditions (length and position of a planet carrier crack clearly.

Intramolecular and nonlinear dynamics

Energy Technology Data Exchange (ETDEWEB)

Davis, M.J. [Argonne National Laboratory, IL (United States)

1993-12-01

Research in this program focuses on three interconnected areas. The first involves the study of intramolecular dynamics, particularly of highly excited systems. The second area involves the use of nonlinear dynamics as a tool for the study of molecular dynamics and complex kinetics. The third area is the study of the classical/quantum correspondence for highly excited systems, particularly systems exhibiting classical chaos.

Neural network based adaptive control for nonlinear dynamic regimes

Science.gov (United States)

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.

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

Science.gov (United States)

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.

Nonlinear dynamics of an electrically actuated imperfect microbeam resonator: Experimental investigation and reduced-order modeling

KAUST Repository

Ruzziconi, Laura

2013-06-10

We present a study of the dynamic behavior of a microelectromechanical systems (MEMS) device consisting of an imperfect clamped-clamped microbeam subjected to electrostatic and electrodynamic actuation. Our objective is to develop a theoretical analysis, which is able to describe and predict all the main relevant aspects of the experimental response. Extensive experimental investigation is conducted, where the main imperfections coming from microfabrication are detected, the first four experimental natural frequencies are identified and the nonlinear dynamics are explored at increasing values of electrodynamic excitation, in a neighborhood of the first symmetric resonance. Several backward and forward frequency sweeps are acquired. The nonlinear behavior is highlighted, which includes ranges of multistability, where the nonresonant and the resonant branch coexist, and intervals where superharmonic resonances are clearly visible. Numerical simulations are performed. Initially, two single mode reduced-order models are considered. One is generated via the Galerkin technique, and the other one via the combined use of the Ritz method and the Padé approximation. Both of them are able to provide a satisfactory agreement with the experimental data. This occurs not only at low values of electrodynamic excitation, but also at higher ones. Their computational efficiency is discussed in detail, since this is an essential aspect for systematic local and global simulations. Finally, the theoretical analysis is further improved and a two-degree-of-freedom reduced-order model is developed, which is also capable of capturing the measured second symmetric superharmonic resonance. Despite the apparent simplicity, it is shown that all the proposed reduced-order models are able to describe the experimental complex nonlinear dynamics of the device accurately and properly, which validates the proposed theoretical approach. © 2013 IOP Publishing Ltd.

Nonlinear dynamic model for skidding behavior of angular contact ball bearings

Science.gov (United States)

Han, Qinkai; Chu, Fulei

2015-10-01

A three-dimensional nonlinear dynamic model is proposed to predict the skidding behavior of angular contact ball bearings under combined load condition. The centrifugal and gyroscopic effects induced by ball rotation and revolution, Hertz contact between the ball and inner/outer races, discontinuous contact between the ball and cage and elastohydrodynamic lubrication are considered in the model. Through comparisons with the tested results of the reference, the dynamic model is verified. Based upon these, variations of ball slipping speed with time and space are discussed for the bearing under combined load condition. It is shown that radial load leads to the fluctuations in the slipping velocity of the ball contacting with inner/outer races, especially for the ball in load-decreasing regions. Adding the radial load would significantly increase the amplitude and range of slipping velocity, indicating that the skidding becomes more serious. As the ball still withstands contact load in the load-decreasing region, large slipping velocity would increase the temperature of both bearing and lubricant oil, intensify the wear and then might shorten the bearing service life. Therefore, the radial load should be considered carefully in the design and monitoring of rotating machinery.

Identifiability of large-scale non-linear dynamic network models applied to the ADM1-case study.

Science.gov (United States)

Nimmegeers, Philippe; Lauwers, Joost; Telen, Dries; Logist, Filip; Impe, Jan Van

2017-06-01

In this work, both the structural and practical identifiability of the Anaerobic Digestion Model no. 1 (ADM1) is investigated, which serves as a relevant case study of large non-linear dynamic network models. The structural identifiability is investigated using the probabilistic algorithm, adapted to deal with the specifics of the case study (i.e., a large-scale non-linear dynamic system of differential and algebraic equations). The practical identifiability is analyzed using a Monte Carlo parameter estimation procedure for a 'non-informative' and 'informative' experiment, which are heuristically designed. The model structure of ADM1 has been modified by replacing parameters by parameter combinations, to provide a generally locally structurally identifiable version of ADM1. This means that in an idealized theoretical situation, the parameters can be estimated accurately. Furthermore, the generally positive structural identifiability results can be explained from the large number of interconnections between the states in the network structure. This interconnectivity, however, is also observed in the parameter estimates, making uncorrelated parameter estimations in practice difficult. Copyright © 2017. Published by Elsevier Inc.

IUTAM Symposium on Nonlinear Dynamics for Advanced Technologies and Engineering Design

CERN Document Server

Rega, Giuseppe

2013-01-01

Nonlinear dynamics has been enjoying a vast development for nearly four decades resulting in a range of well established theory, with the potential to significantly enhance performance, effectiveness, reliability and safety of physical systems as well as offering novel technologies and designs. By critically appraising the state-of-the-art, it is now time to develop design criteria and technology for new generation products/processes operating on principles of nonlinear interaction and in the nonlinear regime, leading to more effective, sensitive, accurate, and durable methods than what is currently available. This new approach is expected to radically influence the design, control and exploitation paradigms, in a magnitude of contexts. With a strong emphasis on experimentally calibrated and validated models, contributions by top-level international experts will foster future directions for the development of engineering technologies and design using robust nonlinear dynamics modelling and analysis.  

Topological approximation of the nonlinear Anderson model

Science.gov (United States)

Milovanov, Alexander V.; Iomin, Alexander

2014-06-01

We study the phenomena of Anderson localization in the presence of nonlinear interaction on a lattice. A class of nonlinear Schrödinger models with arbitrary power nonlinearity is analyzed. We conceive the various regimes of behavior, depending on the topology of resonance overlap in phase space, ranging from a fully developed chaos involving Lévy flights to pseudochaotic dynamics at the onset of delocalization. It is demonstrated that the quadratic nonlinearity plays a dynamically very distinguished role in that it is the only type of power nonlinearity permitting an abrupt localization-delocalization transition with unlimited spreading already at the delocalization border. We describe this localization-delocalization transition as a percolation transition on the infinite Cayley tree (Bethe lattice). It is found in the vicinity of the criticality that the spreading of the wave field is subdiffusive in the limit t →+∞. The second moment of the associated probability distribution grows with time as a power law ∝ tα, with the exponent α =1/3 exactly. Also we find for superquadratic nonlinearity that the analog pseudochaotic regime at the edge of chaos is self-controlling in that it has feedback on the topology of the structure on which the transport processes concentrate. Then the system automatically (without tuning of parameters) develops its percolation point. We classify this type of behavior in terms of self-organized criticality dynamics in Hilbert space. For subquadratic nonlinearities, the behavior is shown to be sensitive to the details of definition of the nonlinear term. A transport model is proposed based on modified nonlinearity, using the idea of "stripes" propagating the wave process to large distances. Theoretical investigations, presented here, are the basis for consistency analysis of the different localization-delocalization patterns in systems with many coupled degrees of freedom in association with the asymptotic properties of the

Nonlinear Deformable-body Dynamics

CERN Document Server

Luo, Albert C J

2010-01-01

"Nonlinear Deformable-body Dynamics" mainly consists in a mathematical treatise of approximate theories for thin deformable bodies, including cables, beams, rods, webs, membranes, plates, and shells. The intent of the book is to stimulate more research in the area of nonlinear deformable-body dynamics not only because of the unsolved theoretical puzzles it presents but also because of its wide spectrum of applications. For instance, the theories for soft webs and rod-reinforced soft structures can be applied to biomechanics for DNA and living tissues, and the nonlinear theory of deformable bodies, based on the Kirchhoff assumptions, is a special case discussed. This book can serve as a reference work for researchers and a textbook for senior and postgraduate students in physics, mathematics, engineering and biophysics. Dr. Albert C.J. Luo is a Professor of Mechanical Engineering at Southern Illinois University, Edwardsville, IL, USA. Professor Luo is an internationally recognized scientist in the field of non...

Chaotic Dynamics and Application of LCR Oscillators Sharing Common Nonlinearity

Science.gov (United States)

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.

Nonlinear Model Predictive Control with Constraint Satisfactions for a Quadcopter

Science.gov (United States)

Wang, Ye; Ramirez-Jaime, Andres; Xu, Feng; Puig, Vicenç

2017-01-01

This paper presents a nonlinear model predictive control (NMPC) strategy combined with constraint satisfactions for a quadcopter. The full dynamics of the quadcopter describing the attitude and position are nonlinear, which are quite sensitive to changes of inputs and disturbances. By means of constraint satisfactions, partial nonlinearities and modeling errors of the control-oriented model of full dynamics can be transformed into the inequality constraints. Subsequently, the quadcopter can be controlled by an NMPC controller with the updated constraints generated by constraint satisfactions. Finally, the simulation results applied to a quadcopter simulator are provided to show the effectiveness of the proposed strategy.

Nonlinear dynamics in cardiac conduction

Science.gov (United States)

Kaplan, D. T.; Smith, J. M.; Saxberg, B. E.; Cohen, R. J.

1988-01-01

Electrical conduction in the heart shows many phenomena familiar from nonlinear dynamics. Among these phenomena are multiple basins of attraction, phase locking, and perhaps period-doubling bifurcations and chaos. We describe a simple cellular-automation model of electrical conduction which simulates normal conduction patterns in the heart as well as a wide range of disturbances of heart rhythm. In addition, we review the application of percolation theory to the analysis of the development of complex, self-sustaining conduction patterns.

Polynomic nonlinear dynamical systems - A residual sensitivity method for model reduction

Science.gov (United States)

Yurkovich, S.; Bugajski, D.; Sain, M.

1985-01-01

The motivation for using polynomic combinations of system states and inputs to model nonlinear dynamics systems is founded upon the classical theories of analysis and function representation. A feature of such representations is the need to make available all possible monomials in these variables, up to the degree specified, so as to provide for the description of widely varying functions within a broad class. For a particular application, however, certain monomials may be quite superfluous. This paper examines the possibility of removing monomials from the model in accordance with the level of sensitivity displayed by the residuals to their absence. Critical in these studies is the effect of system input excitation, and the effect of discarding monomial terms, upon the model parameter set. Therefore, model reduction is approached iteratively, with inputs redesigned at each iteration to ensure sufficient excitation of remaining monomials for parameter approximation. Examples are reported to illustrate the performance of such model reduction approaches.

Non-linear dynamics in Parkinsonism

Directory of Open Access Journals (Sweden)

Olivier eDarbin

2013-12-01

Full Text Available Over the last 30 years, the functions (and dysfunctions of the sensory-motor circuitry have been mostly conceptualized using linear modelizations which have resulted in two main models: the "rate hypothesis" and the "oscillatory hypothesis". In these two models, the basal ganglia data stream is envisaged as a random temporal combination of independent simple patterns issued from its probability distribution of interval interspikes or its spectrum of frequencies respectively.More recently, non-linear analyses have been introduced in the modelization of motor circuitry activities, and they have provided evidences that complex temporal organizations exist in basal ganglia neuronal activities. Regarding movement disorders, these complex temporal organizations in the basal ganglia data stream differ between conditions (i.e. parkinsonism, dyskinesia, healthy control and are responsive to treatments (i.e. L-DOPA,DBS. A body of evidence has reported that basal ganglia neuronal entropy (a marker for complexity/irregularity in time series is higher in hypokinetic state. In line with these findings, an entropy-based model has been recently formulated to introduce basal ganglia entropy as a marker for the alteration of motor processing and a factor of motor inhibition. Importantly, non-linear features have also been identified as a marker of condition and/or treatment effects in brain global signals (EEG, muscular activities (EMG or kinetic of motor symptoms (tremor, gait of patients with movement disorders. It is therefore warranted that the non-linear dynamics of motor circuitry will contribute to a better understanding of the neuronal dysfunctions underlying the spectrum of parkinsonian motor symptoms including tremor, rigidity and hypokinesia.

Model of anisotropic nonlinearity in self-defocusing photorefractive media.

Science.gov (United States)

Barsi, C; Fleischer, J W

2015-09-21

We develop a phenomenological model of anisotropy in self-defocusing photorefractive crystals. In addition to an independent term due to nonlinear susceptibility, we introduce a nonlinear, non-separable correction to the spectral diffraction operator. The model successfully describes the crossover between photovoltaic and photorefractive responses and the spatially dispersive shock wave behavior of a nonlinearly spreading Gaussian input beam. It should prove useful for characterizing internal charge dynamics in complex materials and for accurate image reconstruction through nonlinear media.

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

Science.gov (United States)

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.

Nonlinear laser dynamics from quantum dots to cryptography

CERN Document Server

Lüdge, Kathy

2012-01-01

A distinctive discussion of the nonlinear dynamical phenomena of semiconductor lasers. The book combines recent results of quantum dot laser modeling with mathematical details and an analytic understanding of nonlinear phenomena in semiconductor lasers and points out possible applications of lasers in cryptography and chaos control. This interdisciplinary approach makes it a unique and powerful source of knowledge for anyone intending to contribute to this field of research.By presenting both experimental and theoretical results, the distinguished authors consider solitary lase

Nonlinear behaviour of cantilevered carbon nanotube resonators based on a new nonlinear electrostatic load model

Science.gov (United States)

Farokhi, Hamed; Païdoussis, Michael P.; Misra, Arun K.

2018-04-01

The present study examines the nonlinear behaviour of a cantilevered carbon nanotube (CNT) resonator and its mass detection sensitivity, employing a new nonlinear electrostatic load model. More specifically, a 3D finite element model is developed in order to obtain the electrostatic load distribution on cantilevered CNT resonators. A new nonlinear electrostatic load model is then proposed accounting for the end effects due to finite length. Additionally, a new nonlinear size-dependent continuum model is developed for the cantilevered CNT resonator, employing the modified couple stress theory (to account for size-effects) together with the Kelvin-Voigt model (to account for nonlinear damping); the size-dependent model takes into account all sources of nonlinearity, i.e. geometrical and inertial nonlinearities as well as nonlinearities associated with damping, small-scale, and electrostatic load. The nonlinear equation of motion of the cantilevered CNT resonator is obtained based on the new models developed for the CNT resonator and the electrostatic load. The Galerkin method is then applied to the nonlinear equation of motion, resulting in a set of nonlinear ordinary differential equations, consisting of geometrical, inertial, electrical, damping, and size-dependent nonlinear terms. This high-dimensional nonlinear discretized model is solved numerically utilizing the pseudo-arclength continuation technique. The nonlinear static and dynamic responses of the system are examined for various cases, investigating the effect of DC and AC voltages, length-scale parameter, nonlinear damping, and electrostatic load. Moreover, the mass detection sensitivity of the system is examined for possible application of the CNT resonator as a nanosensor.

A Fully Nonlinear, Dynamically Consistent Numerical Model for Solid-Body Ship Motion. I. Ship Motion with Fixed Heading

Science.gov (United States)

Lin, Ray-Quing; Kuang, Weijia

2011-01-01

In this paper, we describe the details of our numerical model for simulating ship solidbody motion in a given environment. In this model, the fully nonlinear dynamical equations governing the time-varying solid-body ship motion under the forces arising from ship wave interactions are solved with given initial conditions. The net force and moment (torque) on the ship body are directly calculated via integration of the hydrodynamic pressure over the wetted surface and the buoyancy effect from the underwater volume of the actual ship hull with a hybrid finite-difference/finite-element method. Neither empirical nor free parametrization is introduced in this model, i.e. no a priori experimental data are needed for modelling. This model is benchmarked with many experiments of various ship hulls for heave, roll and pitch motion. In addition to the benchmark cases, numerical experiments are also carried out for strongly nonlinear ship motion with a fixed heading. These new cases demonstrate clearly the importance of nonlinearities in ship motion modelling.

A Compact Synchronous Cellular Model of Nonlinear Calcium Dynamics: Simulation and FPGA Synthesis Results.

Science.gov (United States)

Soleimani, Hamid; Drakakis, Emmanuel M

2017-06-01

Recent studies have demonstrated that calcium is a widespread intracellular ion that controls a wide range of temporal dynamics in the mammalian body. The simulation and validation of such studies using experimental data would benefit from a fast large scale simulation and modelling tool. This paper presents a compact and fully reconfigurable cellular calcium model capable of mimicking Hopf bifurcation phenomenon and various nonlinear responses of the biological calcium dynamics. The proposed cellular model is synthesized on a digital platform for a single unit and a network model. Hardware synthesis, physical implementation on FPGA, and theoretical analysis confirm that the proposed cellular model can mimic the biological calcium behaviors with considerably low hardware overhead. The approach has the potential to speed up large-scale simulations of slow intracellular dynamics by sharing more cellular units in real-time. To this end, various networks constructed by pipelining 10 k to 40 k cellular calcium units are compared with an equivalent simulation run on a standard PC workstation. Results show that the cellular hardware model is, on average, 83 times faster than the CPU version.

Overview of magnetic nonlinear beam dynamics in the RHIC

International Nuclear Information System (INIS)

Luo, Y.; Bai, M.; Beebe-Wang, J.; Bengtsson, J.; Calaga, R.; Fischer, W.; Jain, A.; Pilat, F.; Ptitsyn, V.; Malitsky, N.; Robert-Demolaize, G.; Satogata, T.; Tepikian, S.; Tomas, R.; Trbojevic, D.

2009-01-01

In this article we review our studies of nonlinear beam dynamics due to the nonlinear magnetic field errors in the Relativistic Heavy Ion Collider (RHIC). Nonlinear magnetic field errors, including magnetic field errors in interaction regions (IRs), chromatic sextupoles, and sextupole components from arc main dipoles are discussed. Their effects on beam dynamics and beam dynamic aperture are evaluated. The online methods to measure and correct the IR nonlinear field errors, second order chromaticities, and horizontal third order resonance are presented. The overall strategy for nonlinear corrections in RHIC is discussed

Stochastic Erosion of Fractal Structure in Nonlinear Dynamical Systems

Science.gov (United States)

Agarwal, S.; Wettlaufer, J. S.

2014-12-01

We analyze the effects of stochastic noise on the Lorenz-63 model in the chaotic regime to demonstrate a set of general issues arising in the interpretation of data from nonlinear dynamical systems typical in geophysics. The model is forced using both additive and multiplicative, white and colored noise and it is shown that, through a suitable choice of the noise intensity, both additive and multiplicative noise can produce similar dynamics. We use a recently developed measure, histogram distance, to show the similarity between the dynamics produced by additive and multiplicative forcing. This phenomenon, in a nonlinear fractal structure with chaotic dynamics can be explained by understanding how noise affects the Unstable Periodic Orbits (UPOs) of the system. For delta-correlated noise, the UPOs erode the fractal structure. In the presence of memory in the noise forcing, the time scale of the noise starts to interact with the period of some UPO and, depending on the noise intensity, stochastic resonance may be observed. This also explains the mixing in dissipative dynamical systems in presence of white noise; as the fractal structure is smoothed, the decay of correlations is enhanced, and hence the rate of mixing increases with noise intensity.

Electricity demand and spot price forecasting using evolutionary computation combined with chaotic nonlinear dynamic model

International Nuclear Information System (INIS)

Unsihuay-Vila, C.; Zambroni de Souza, A.C.; Marangon-Lima, J.W.; Balestrassi, P.P.

2010-01-01

This paper proposes a new hybrid approach based on nonlinear chaotic dynamics and evolutionary strategy to forecast electricity loads and prices. The main idea is to develop a new training or identification stage in a nonlinear chaotic dynamic based predictor. In the training stage five optimal parameters for a chaotic based predictor are searched through an optimization model based on evolutionary strategy. The objective function of the optimization model is the mismatch minimization between the multi-step-ahead forecasting of predictor and observed data such as it is done in identification problems. The first contribution of this paper is that the proposed approach is capable of capturing the complex dynamic of demand and price time series considered resulting in a more accuracy forecasting. The second contribution is that the proposed approach run on-line manner, i.e. the optimal set of parameters and prediction is executed automatically which can be used to prediction in real-time, it is an advantage in comparison with other models, where the choice of their input parameters are carried out off-line, following qualitative/experience-based recipes. A case study of load and price forecasting is presented using data from New England, Alberta, and Spain. A comparison with other methods such as autoregressive integrated moving average (ARIMA) and artificial neural network (ANN) is shown. The results show that the proposed approach provides a more accurate and effective forecasting than ARIMA and ANN methods. (author)

A comprehensive dynamic modeling approach for giant magnetostrictive material actuators

International Nuclear Information System (INIS)

Gu, Guo-Ying; Zhu, Li-Min; Li, Zhi; Su, Chun-Yi

2013-01-01

In this paper, a comprehensive modeling approach for a giant magnetostrictive material actuator (GMMA) is proposed based on the description of nonlinear electromagnetic behavior, the magnetostrictive effect and frequency response of the mechanical dynamics. It maps the relationships between current and magnetic flux at the electromagnetic part to force and displacement at the mechanical part in a lumped parameter form. Towards this modeling approach, the nonlinear hysteresis effect of the GMMA appearing only in the electrical part is separated from the linear dynamic plant in the mechanical part. Thus, a two-module dynamic model is developed to completely characterize the hysteresis nonlinearity and the dynamic behaviors of the GMMA. The first module is a static hysteresis model to describe the hysteresis nonlinearity, and the cascaded second module is a linear dynamic plant to represent the dynamic behavior. To validate the proposed dynamic model, an experimental platform is established. Then, the linear dynamic part and the nonlinear hysteresis part of the proposed model are identified in sequence. For the linear part, an approach based on axiomatic design theory is adopted. For the nonlinear part, a Prandtl–Ishlinskii model is introduced to describe the hysteresis nonlinearity and a constrained quadratic optimization method is utilized to identify its coefficients. Finally, experimental tests are conducted to demonstrate the effectiveness of the proposed dynamic model and the corresponding identification method. (paper)

From point process observations to collective neural dynamics: Nonlinear Hawkes process GLMs, low-dimensional dynamics and coarse graining.

Science.gov (United States)

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.

Nonlinear dynamics of rotating shallow water methods and advances

CERN Document Server

Zeitlin, Vladimir

2007-01-01

The rotating shallow water (RSW) model is of wide use as a conceptual tool in geophysical fluid dynamics (GFD), because, in spite of its simplicity, it contains all essential ingredients of atmosphere and ocean dynamics at the synoptic scale, especially in its two- (or multi-) layer version. The book describes recent advances in understanding (in the framework of RSW and related models) of some fundamental GFD problems, such as existence of the slow manifold, dynamical splitting of fast (inertia-gravity waves) and slow (vortices, Rossby waves) motions, nonlinear geostrophic adjustment and wa

Dynamical processes and epidemic threshold on nonlinear coupled multiplex networks

Science.gov (United States)

Gao, Chao; Tang, Shaoting; Li, Weihua; Yang, Yaqian; Zheng, Zhiming

2018-04-01

Recently, the interplay between epidemic spreading and awareness diffusion has aroused the interest of many researchers, who have studied models mainly based on linear coupling relations between information and epidemic layers. However, in real-world networks the relation between two layers may be closely correlated with the property of individual nodes and exhibits nonlinear dynamical features. Here we propose a nonlinear coupled information-epidemic model (I-E model) and present a comprehensive analysis in a more generalized scenario where the upload rate differs from node to node, deletion rate varies between susceptible and infected states, and infection rate changes between unaware and aware states. In particular, we develop a theoretical framework of the intra- and inter-layer dynamical processes with a microscopic Markov chain approach (MMCA), and derive an analytic epidemic threshold. Our results suggest that the change of upload and deletion rate has little effect on the diffusion dynamics in the epidemic layer.

Periodic precursors of nonlinear dynamical transitions

International Nuclear Information System (INIS)

Jiang Yu; Dong Shihai; Lozada-Cassou, M.

2004-01-01

We study the resonant response of a nonlinear system to external periodic perturbations. We show by numerical simulation that the periodic resonance curve may anticipate the dynamical instability of the unperturbed nonlinear periodic system, at parameter values far away from the bifurcation points. In the presence of noise, the buried intrinsic periodic dynamics can be picked out by analyzing the system's response to periodic modulation of appropriate intensity

Nonlinear and Stochastic Dynamics in the Heart

Science.gov (United States)

Qu, Zhilin; Hu, Gang; Garfinkel, Alan; Weiss, James N.

2014-01-01

In a normal human life span, the heart beats about 2 to 3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems. PMID:25267872

Nonlinear and stochastic dynamics in the heart

Energy Technology Data Exchange (ETDEWEB)

Qu, Zhilin, E-mail: zqu@mednet.ucla.edu [Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, CA 90095 (United States); Hu, Gang [Department of Physics, Beijing Normal University, Beijing 100875 (China); Garfinkel, Alan [Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, CA 90095 (United States); Department of Integrative Biology and Physiology, University of California, Los Angeles, CA 90095 (United States); Weiss, James N. [Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, CA 90095 (United States); Department of Physiology, David Geffen School of Medicine, University of California, Los Angeles, CA 90095 (United States)

2014-10-10

In a normal human life span, the heart beats about 2–3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems.

Nonlinear and stochastic dynamics in the heart

International Nuclear Information System (INIS)

Qu, Zhilin; Hu, Gang; Garfinkel, Alan; Weiss, James N.

2014-01-01

In a normal human life span, the heart beats about 2–3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems

Nonlinear analysis of renal autoregulation in rats using principal dynamic modes

DEFF Research Database (Denmark)

Marmarelis, V Z; Chon, K H; Holstein-Rathlou, N H

1999-01-01

This article presents results of the use of a novel methodology employing principal dynamic modes (PDM) for modeling the nonlinear dynamics of renal autoregulation in rats. The analyzed experimental data are broadband (0-0.5 Hz) blood pressure-flow data generated by pseudorandom forcing and colle......This article presents results of the use of a novel methodology employing principal dynamic modes (PDM) for modeling the nonlinear dynamics of renal autoregulation in rats. The analyzed experimental data are broadband (0-0.5 Hz) blood pressure-flow data generated by pseudorandom forcing...... and collected in normotensive and hypertensive rats for two levels of pressure forcing (as measured by the standard deviation of the pressure fluctuation). The PDMs are computed from first-order and second-order kernel estimates obtained from the data via the Laguerre expansion technique. The results...

Selected Problems in Nonlinear Dynamics and Sociophysics

Science.gov (United States)

Westley, Alexandra Renee

This Ph.D. dissertation focuses on a collection of problems on the dynamical behavior of nonlinear many-body systems, drawn from two substantially different areas. First, the dynamical behavior seen in strongly nonlinear lattices such as in the Fermi-Pasta-Ulam-Tsingou (FPUT) system (part I) and second, time evolution behavior of interacting living objects which can be broadly considered as sociophysics systems (part II). The studies on FPUT-like systems will comprise of five chapters, dedicated to the properties of solitary and anti-solitary waves in the system, how localized nonlinear excitations decay and spread throughout these lattices, how two colliding solitary waves can precipitate highly localized and stable excitations, a possible alternative way to view these localized excitations through Duffing oscillators, and finally an exploration of parametric resonance in an FPUT-like lattice. Part II consists of two problems in the context of sociophysics. I use molecular dynamics inspired simulations to study the size and the stability of social groups of chimpanzees (such as those seen in central Africa) and compare the results with existing observations on the stability of chimpanzee societies. Secondly, I use an agent-based model to simulate land battles between an intelligent army and an insurgency when both have access to equally powerful weaponry. The study considers genetic algorithm based adaptive strategies to infer the strategies needed for the intelligent army to win the battles.

Physics constrained nonlinear regression models for time series

International Nuclear Information System (INIS)

Majda, Andrew J; Harlim, John

2013-01-01

A central issue in contemporary science is the development of data driven statistical nonlinear dynamical models for time series of partial observations of nature or a complex physical model. It has been established recently that ad hoc quadratic multi-level regression (MLR) models can have finite-time blow up of statistical solutions and/or pathological behaviour of their invariant measure. Here a new class of physics constrained multi-level quadratic regression models are introduced, analysed and applied to build reduced stochastic models from data of nonlinear systems. These models have the advantages of incorporating memory effects in time as well as the nonlinear noise from energy conserving nonlinear interactions. The mathematical guidelines for the performance and behaviour of these physics constrained MLR models as well as filtering algorithms for their implementation are developed here. Data driven applications of these new multi-level nonlinear regression models are developed for test models involving a nonlinear oscillator with memory effects and the difficult test case of the truncated Burgers–Hopf model. These new physics constrained quadratic MLR models are proposed here as process models for Bayesian estimation through Markov chain Monte Carlo algorithms of low frequency behaviour in complex physical data. (paper)

Steady states and outbreaks of two-phase nonlinear age-structured model of population dynamics with discrete time delay.

Science.gov (United States)

Akimenko, Vitalii; Anguelov, Roumen

2017-12-01

In this paper we study the nonlinear age-structured model of a polycyclic two-phase population dynamics including delayed effect of population density growth on the mortality. Both phases are modelled as a system of initial boundary values problem for semi-linear transport equation with delay and initial problem for nonlinear delay ODE. The obtained system is studied both theoretically and numerically. Three different regimes of population dynamics for asymptotically stable states of autonomous systems are obtained in numerical experiments for the different initial values of population density. The quasi-periodical travelling wave solutions are studied numerically for the autonomous system with the different values of time delays and for the system with oscillating death rate and birth modulus. In both cases it is observed three types of travelling wave solutions: harmonic oscillations, pulse sequence and single pulse.

Nonlinear Dynamic Modeling and Controls Development for Supersonic Propulsion System Research

Science.gov (United States)

Connolly, Joseph W.; Kopasakis, George; Paxson, Daniel E.; Stuber, Eric; Woolwine, Kyle

2012-01-01

This paper covers the propulsion system component modeling and controls development of an integrated nonlinear dynamic simulation for an inlet and engine that can be used for an overall vehicle (APSE) model. The focus here is on developing a methodology for the propulsion model integration, which allows for controls design that prevents inlet instabilities and minimizes the thrust oscillation experienced by the vehicle. Limiting thrust oscillations will be critical to avoid exciting vehicle aeroelastic modes. Model development includes both inlet normal shock position control and engine rotor speed control for a potential supersonic commercial transport. A loop shaping control design process is used that has previously been developed for the engine and verified on linear models, while a simpler approach is used for the inlet control design. Verification of the modeling approach is conducted by simulating a two-dimensional bifurcated inlet and a representative J-85 jet engine previously used in a NASA supersonics project. Preliminary results are presented for the current supersonics project concept variable cycle turbofan engine design.

Self-Organized Biological Dynamics and Nonlinear Control

Science.gov (United States)

Walleczek, Jan

2006-04-01

The frontiers and challenges of biodynamics research Jan Walleczek; Part I. Nonlinear Dynamics in Biology and Response to Stimuli: 1. External signals and internal oscillation dynamics - principal aspects and response of stimulated rhythmic processes Friedemann Kaiser; 2. Nonlinear dynamics in biochemical and biophysical systems: from enzyme kinetics to epilepsy Raima Larter, Robert Worth and Brent Speelman; 3. Fractal mechanisms in neural control: human heartbeat and gait dynamics in health and disease Chung-Kang Peng, Jeffrey M. Hausdorff and Ary L. Goldberger; 4. Self-organising dynamics in human coordination and perception Mingzhou Ding, Yanqing Chen, J. A. Scott Kelso and Betty Tuller; 5. Signal processing in biochemical reaction networks Adam P. Arkin; Part II. Nonlinear Sensitivity of Biological Systems to Electromagnetic Stimuli: 6. Electrical signal detection and noise in systems with long-range coherence Paul C. Gailey; 7. Oscillatory signals in migrating neutrophils: effects of time-varying chemical and electrical fields Howard R. Petty; 8. Enzyme kinetics and nonlinear biochemical amplification in response to static and oscillating magnetic fields Jan Walleczek and Clemens F. Eichwald; 9. Magnetic field sensitivity in the hippocampus Stefan Engström, Suzanne Bawin and W. Ross Adey; Part III. Stochastic Noise-Induced Dynamics and Transport in Biological Systems: 10. Stochastic resonance: looking forward Frank Moss; 11. Stochastic resonance and small-amplitude signal transduction in voltage-gated ion channels Sergey M. Bezrukov and Igor Vodyanoy; 12. Ratchets, rectifiers and demons: the constructive role of noise in free energy and signal transduction R. Dean Astumian; 13. Cellular transduction of periodic and stochastic energy signals by electroconformational coupling Tian Y. Tsong; Part IV. Nonlinear Control of Biological and Other Excitable Systems: 14. Controlling chaos in dynamical systems Kenneth Showalter; 15. Electromagnetic fields and biological

Non-Linear Dynamics of Saturn’s Rings

Science.gov (United States)

Esposito, Larry W.

2015-11-01

Non-linear processes can explain why Saturn’s rings are so active and dynamic. Ring systems differ from simple linear systems in two significant ways: 1. They are systems of granular material: where particle-to-particle collisions dominate; thus a kinetic, not a fluid description needed. We find that stresses are strikingly inhomogeneous and fluctuations are large compared to equilibrium. 2. They are strongly forced by resonances: which drive a non-linear response, pushing the system across thresholds that lead to persistent states.Some of this non-linearity is captured in a simple Predator-Prey Model: Periodic forcing from the moon causes streamline crowding; This damps the relative velocity, and allows aggregates to grow. About a quarter phase later, the aggregates stir the system to higher relative velocity and the limit cycle repeats each orbit.Summary of Halo Results: A predator-prey model for ring dynamics produces transient structures like ‘straw’ that can explain the halo structure and spectroscopy: This requires energetic collisions (v ≈ 10m/sec, with throw distances about 200km, implying objects of scale R ≈ 20km).Transform to Duffing Eqn : With the coordinate transformation, z = M2/3, the Predator-Prey equations can be combined to form a single second-order differential equation with harmonic resonance forcing.Ring dynamics and history implications: Moon-triggered clumping at perturbed regions in Saturn’s rings creates both high velocity dispersion and large aggregates at these distances, explaining both small and large particles observed there. We calculate the stationary size distribution using a cell-to-cell mapping procedure that converts the phase-plane trajectories to a Markov chain. Approximating the Markov chain as an asymmetric random walk with reflecting boundaries allows us to determine the power law index from results of numerical simulations in the tidal environment surrounding Saturn. Aggregates can explain many dynamic aspects

Nonlinear switching dynamics in a photonic-crystal nanocavity

International Nuclear Information System (INIS)

Yu, Yi; Palushani, Evarist; Heuck, Mikkel; Vukovic, Dragana; Peucheret, Christophe; Yvind, Kresten; Mork, Jesper

2014-01-01

We report the experimental observation of nonlinear switching dynamics in an InP photonic crystal nanocavity. Usually, the regime of relatively small cavity perturbations is explored, where the signal transmitted through the cavity follows the temporal variation of the cavity resonance. When the cavity is perturbed by strong pulses, we observe several nonlinear effects, i.e., saturation of the switching contrast, broadening of the switching window, and even initial reduction of the transmission. The effects are analyzed by comparison with nonlinear coupled mode theory and explained in terms of large dynamical variations of the cavity resonance in combination with nonlinear losses. The results provide insight into the nonlinear optical processes that govern the dynamics of nanocavities and are important for applications in optical signal processing, where one wants to optimize the switching contrast.

Nonlinear switching dynamics in a photonic-crystal nanocavity

DEFF Research Database (Denmark)

Yu, Yi; Palushani, Evarist; Heuck, Mikkel

2014-01-01

We report the experimental observation of nonlinear switching dynamics in an InP photonic crystal nanocavity. Usually, the regime of relatively small cavity perturbations is explored, where the signal transmitted through the cavity follows the temporal variation of the cavity resonance. When...... of large dynamical variations of the cavity resonance in combination with nonlinear losses. The results provide insight into the nonlinear optical processes that govern the dynamics of nanocavities and are important for applications in optical signal processing, where one wants to optimize the switching...... the cavity is perturbed by strong pulses, we observe several nonlinear effects, i.e., saturation of the switching contrast, broadening of the switching window, and even initial reduction of the transmission. The effects are analyzed by comparison with nonlinear coupled mode theory and explained in terms...

Nonlinear and Nonequilibrium Dynamics in Geomaterials

OpenAIRE

TenCate, James A.; Pasqualini, Donatella; Habib, Salman; Heitmann, Katrin; Higdon, David; Johnson, Paul A.

2004-01-01

The transition from linear to nonlinear dynamical elasticity in rocks is of considerable interest in seismic wave propagation as well as in understanding the basic dynamical processes in consolidated granular materials. We have carried out a careful experimental investigation of this transition for Berea and Fontainebleau sandstones. Below a well-characterized strain, the materials behave linearly, transitioning beyond that point to a nonlinear behavior which can be accurately captured by a s...

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

Science.gov (United States)

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 response analysis of block foundations with nonlinear dry friction mounting system to impact loads

International Nuclear Information System (INIS)

Zheng, Enlai; Zhu, Sihong; Zhou, Xinlong

2014-01-01

It is essential to establish a dynamic model to predict and evaluate the dynamic performance of a nonlinear dry friction mounting system during design procedure, when it is impossible to carry out the test of prototype. Unlike the conventional ideal dry friction model where the direction of dry friction force is always considered to be opposite to that of relative velocity, a new equivalent resistance model of dry friction force is proposed based on the bilinear hysteretic model by introducing a parameter g in this work. The equivalent resistance contains spring force and damping force, whose direction is not opposite to that of relative velocity. Then, a dynamic model of the block foundation with nonlinear dry friction mounting system is established. When the equivalent resistance is applied to the dynamic model, its dynamic responses are obtained under common practical forms of press loads: rectangular pulse, half-sine pulse, and triangular pulse. Compared to experimental results, the dynamic responses based on the equivalent resistance model are more consistent with the simulation results based on the ideal dry friction model and the validity of the equivalent resistance model for the bilinear hysteretic model in this work is verified. Furthermore, the effect of the pulse shape and pulse duration on the dynamic responses of the block foundation with nonlinear dry friction mounting system is investigated.

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

Science.gov (United States)

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.

Nonlinear Modelling of Low Frequency Loudspeakers

DEFF Research Database (Denmark)

Olsen, Erling Sandermann

1997-01-01

In the Danish LoDist project on distortion from dynamic low frequency loudspeakers a detailed nonlinear model of loudspeakers has been developed. The model has been implemented in a PC program so that it can be used to create signals for listening tests and analysis. Also, different methods...

Nonlinear Modelling of Low Frequency Loudspeakers

DEFF Research Database (Denmark)

Olsen, Erling Sandermann

1997-01-01

In the Danish LoDist project on distortion from dynamic low-frequency loudspeakers, a detailed nonlinear model of loudspeakers has been developed. The model has been implemented in a PC program so that it can be used to create signals for listening tests and analysis. Also, different methods...

Nonlinear dynamics new directions theoretical aspects

CERN Document Server

Ugalde, Edgardo

2015-01-01

This book, along with its companion volume, Nonlinear Dynamics New Directions: Models and Applications, covers topics ranging from fractal analysis to very specific applications of the theory of dynamical systems to biology. This first volume is devoted to fundamental aspects and includes a number of important new contributions as well as some review articles that emphasize new development prospects. The second volume contains mostly new applications of the theory of dynamical systems to both engineering and biology. The topics addressed in the two volumes include a rigorous treatment of fluctuations in dynamical systems, topics in fractal analysis, studies of the transient dynamics in biological networks, synchronization in lasers, and control of chaotic systems, among others. This book also: ·         Presents a rigorous treatment of fluctuations in dynamical systems and explores a range of topics in fractal analysis, among other fundamental topics ·         Features recent developments on...

Nonlinear Kalman Filtering in Affine Term Structure Models

DEFF Research Database (Denmark)

Christoffersen, Peter; Dorion, Christian; Jacobs, Kris

When the relationship between security prices and state variables in dynamic term structure models is nonlinear, existing studies usually linearize this relationship because nonlinear fi…ltering is computationally demanding. We conduct an extensive investigation of this linearization and analyze...... the potential of the unscented Kalman …filter to properly capture nonlinearities. To illustrate the advantages of the unscented Kalman …filter, we analyze the cross section of swap rates, which are relatively simple non-linear instruments, and cap prices, which are highly nonlinear in the states. An extensive...

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

Science.gov (United States)

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.

Nonlinear dynamical triggering of slow slip

Energy Technology Data Exchange (ETDEWEB)

Johnson, Paul A [Los Alamos National Laboratory; Knuth, Matthew W [WISCONSIN; Kaproth, Bryan M [PENN STATE; Carpenter, Brett [PENN STATE; Guyer, Robert A [Los Alamos National Laboratory; Le Bas, Pierre - Yves [Los Alamos National Laboratory; Daub, Eric G [Los Alamos National Laboratory; Marone, Chris [PENN STATE

2010-12-10

Among the most fascinating, recent discoveries in seismology have been the phenomena of triggered slip, including triggered earthquakes and triggered-tremor, as well as triggered slow, silent-slip during which no seismic energy is radiated. Because fault nucleation depths cannot be probed directly, the physical regimes in which these phenomena occur are poorly understood. Thus determining physical properties that control diverse types of triggered fault sliding and what frictional constitutive laws govern triggered faulting variability is challenging. We are characterizing the physical controls of triggered faulting with the goal of developing constitutive relations by conducting laboratory and numerical modeling experiments in sheared granular media at varying load conditions. In order to simulate granular fault zone gouge in the laboratory, glass beads are sheared in a double-direct configuration under constant normal stress, while subject to transient perturbation by acoustic waves. We find that triggered, slow, silent-slip occurs at very small confining loads ({approx}1-3 MPa) that are smaller than those where dynamic earthquake triggering takes place (4-7 MPa), and that triggered slow-slip is associated with bursts of LFE-like acoustic emission. Experimental evidence suggests that the nonlinear dynamical response of the gouge material induced by dynamic waves may be responsible for the triggered slip behavior: the slip-duration, stress-drop and along-strike slip displacement are proportional to the triggering wave amplitude. Further, we observe a shear-modulus decrease corresponding to dynamic-wave triggering relative to the shear modulus of stick-slips. Modulus decrease in response to dynamical wave amplitudes of roughly a microstrain and above is a hallmark of elastic nonlinear behavior. We believe that the dynamical waves increase the material non-affine elastic deformation during shearing, simultaneously leading to instability and slow-slip. The inferred

Structure-preserving integrators in nonlinear structural dynamics and flexible multibody dynamics

CERN Document Server

2016-01-01

This book focuses on structure-preserving numerical methods for flexible multibody dynamics, including nonlinear elastodynamics and geometrically exact models for beams and shells. It also deals with the newly emerging class of variational integrators as well as Lie-group integrators. It discusses two alternative approaches to the discretization in space of nonlinear beams and shells. Firstly, geometrically exact formulations, which are typically used in the finite element community and, secondly, the absolute nodal coordinate formulation, which is popular in the multibody dynamics community. Concerning the discretization in time, the energy-momentum method and its energy-decaying variants are discussed. It also addresses a number of issues that have arisen in the wake of the structure-preserving discretization in space. Among them are the parameterization of finite rotations, the incorporation of algebraic constraints and the computer implementation of the various numerical methods. The practical application...

Supercritical nonlinear parametric dynamics of Timoshenko microbeams

Science.gov (United States)

Farokhi, Hamed; Ghayesh, Mergen H.

2018-06-01

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

Report of the working group on single-particle nonlinear dynamics

International Nuclear Information System (INIS)

Bazzani, A.; Bongini, L.; Corbett, J.; Dome, G.; Fedorova, A.; Freguglia, P.; Ng, K.; Ohmi, K.; Owen, H.; Papaphilippou, Y.; Robin, D.; Safranek, J.; Scandale, W.; Terebilo, A.; Turchetti, G.; Todesco, E.; Warnock, R.; Zeitlin, M.

1999-01-01

The Working Group on single-particle nonlinear dynamics has developed a set of tools to study nonlinear dynamics in a particle accelerator. The design of rings with large dynamic apertures is still far from automatic. The Working Group has concluded that nonlinear single-particle dynamics limits the performance of accelerators. (AIP) copyright 1999 American Institute of Physics

Nonlinear Dynamic Behavior of a Bi-Axial Torsional MEMS Mirror with Sidewall Electrodes

Directory of Open Access Journals (Sweden)

Mehmet Ozdogan

2016-03-01

Full Text Available Nonlinear dynamic responses of a Micro-Electro-Mechanical Systems (MEMS mirror with sidewall electrodes are presented that are in close agreement with previously-reported experimental data. An analysis of frequency responses reveals softening behavior, and secondary resonances originated from the dominant quadratic nonlinearity. The quadratic nonlinearity is an electromechanical coupling effect caused by the electrostatic force. This effect is reflected in our mathematical model used to simulate the dynamic response of the micro-mirror. The effects of increased forcing and decreased damping on the frequency response are investigated as the mirrors are mostly used in vacuum packages. The results can predict MEMS mirror behaviors in optical devices better than previously-reported models.

Effect of Friction-Induced Nonlinearity on OMA-Identified Dynamic Characteristics of Offshore Platform Models

DEFF Research Database (Denmark)

Friis, Tobias; Orfanos, Antonios; Katsanos, Evangelos

The identification of the modal characteristics of engineering systems under operational conditions is commonly conducted with the use of the Operational Modal Analysis (OMA), being a class of useful tools employed within various fields of structural, mechanical as well as marine and naval...... engineering. The current OMA methods have been advanced on the basis of two fundamental, though, restrictive assumptions: (i) linearity and (ii) stationarity. Nevertheless, there are several applications that are inherently related to various nonlinear mechanisms, which, in turn, violate the two cornerstones...... of OMA and hence, question its robustness and efficiency. Along these lines, the current study addresses the effect of friction-induced nonlinearity on OMA-identified dynamic characteristics of an experimental set up consisting of a pair of reduced scale offshore platform models that are connected...

Artificial Neural Networks for Nonlinear Dynamic Response Simulation in Mechanical Systems

DEFF Research Database (Denmark)

Christiansen, Niels Hørbye; Høgsberg, Jan Becker; Winther, Ole

2011-01-01

It is shown how artificial neural networks can be trained to predict dynamic response of a simple nonlinear structure. Data generated using a nonlinear finite element model of a simplified wind turbine is used to train a one layer artificial neural network. When trained properly the network is ab...... to perform accurate response prediction much faster than the corresponding finite element model. Initial result indicate a reduction in cpu time by two orders of magnitude....

Analysis of Nonlinear Dynamics by Square Matrix Method

Energy Technology Data Exchange (ETDEWEB)

Yu, Li Hua [Brookhaven National Lab. (BNL), Upton, NY (United States). Energy and Photon Sciences Directorate. National Synchrotron Light Source II

2016-07-25

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. And 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.

Calibration of the nonlinear ring model at the Diamond Light Source

CERN Document Server

Bartolini, R; Rehm, G; Martin, I P S

2011-01-01

Nonlinear beam dynamics plays a crucial role in defining the performance of a storage ring. The beam lifetime, the injection efficiency, and the dynamic and momentum apertures available to the beam are optimized during the design phase by a proper optimization of the linear lattice and of the distribution of sextupole families. The correct implementation of the design model, especially the nonlinear part, is a nontrivial accelerator physics task. Several parameters of the nonlinear dynamics can be used to compare the real machine with the model and eventually to correct the accelerator. Most of these parameters are extracted from the analysis of turn-by-turn data after the excitation of betatron oscillations of the particles in the ring. We present the experimental results of the campaign of measurements carried out at the Diamond storage ring to characterize the nonlinear beam dynamics. A combination of frequency map analysis with the detuning with momentum measurements has allowed for a precise calibration ...

Nonlinear dynamics of semiclassical coherent states in periodic potentials

International Nuclear Information System (INIS)

Carles, Rémi; Sparber, Christof

2012-01-01

We consider nonlinear Schrödinger equations with either local or nonlocal nonlinearities. In addition, we include periodic potentials as used, for example, in matter wave experiments in optical lattices. By considering the corresponding semiclassical scaling regime, we construct asymptotic solutions, which are concentrated both in space and in frequency around the effective semiclassical phase-space flow induced by Bloch’s spectral problem. The dynamics of these generalized coherent states is governed by a nonlinear Schrödinger model with effective mass. In the case of nonlocal nonlinearities, we establish a novel averaging-type result in the critical case. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’. (paper)

Non-Gaussian lineshapes and dynamics of time-resolved linear and nonlinear (correlation) spectra.

Science.gov (United States)

Dinpajooh, Mohammadhasan; Matyushov, Dmitry V

2014-07-17

Signatures of nonlinear and non-Gaussian dynamics in time-resolved linear and nonlinear (correlation) 2D spectra are analyzed in a model considering a linear plus quadratic dependence of the spectroscopic transition frequency on a Gaussian nuclear coordinate of the thermal bath (quadratic coupling). This new model is contrasted to the commonly assumed linear dependence of the transition frequency on the medium nuclear coordinates (linear coupling). The linear coupling model predicts equality between the Stokes shift and equilibrium correlation functions of the transition frequency and time-independent spectral width. Both predictions are often violated, and we are asking here the question of whether a nonlinear solvent response and/or non-Gaussian dynamics are required to explain these observations. We find that correlation functions of spectroscopic observables calculated in the quadratic coupling model depend on the chromophore's electronic state and the spectral width gains time dependence, all in violation of the predictions of the linear coupling models. Lineshape functions of 2D spectra are derived assuming Ornstein-Uhlenbeck dynamics of the bath nuclear modes. The model predicts asymmetry of 2D correlation plots and bending of the center line. The latter is often used to extract two-point correlation functions from 2D spectra. The dynamics of the transition frequency are non-Gaussian. However, the effect of non-Gaussian dynamics is limited to the third-order (skewness) time correlation function, without affecting the time correlation functions of higher order. The theory is tested against molecular dynamics simulations of a model polar-polarizable chromophore dissolved in a force field water.

Linear versus Nonlinear Filtering with Scale-Selective Corrections for Balanced Dynamics in a Simple Atmospheric Model

KAUST Repository

Subramanian, Aneesh C.

2012-11-01

This paper investigates the role of the linear analysis step of the ensemble Kalman filters (EnKF) in disrupting the balanced dynamics in a simple atmospheric model and compares it to a fully nonlinear particle-based filter (PF). The filters have a very similar forecast step but the analysis step of the PF solves the full Bayesian filtering problem while the EnKF analysis only applies to Gaussian distributions. The EnKF is compared to two flavors of the particle filter with different sampling strategies, the sequential importance resampling filter (SIRF) and the sequential kernel resampling filter (SKRF). The model admits a chaotic vortical mode coupled to a comparatively fast gravity wave mode. It can also be configured either to evolve on a so-called slow manifold, where the fast motion is suppressed, or such that the fast-varying variables are diagnosed from the slow-varying variables as slaved modes. Identical twin experiments show that EnKF and PF capture the variables on the slow manifold well as the dynamics is very stable. PFs, especially the SKRF, capture slaved modes better than the EnKF, implying that a full Bayesian analysis estimates the nonlinear model variables better. The PFs perform significantly better in the fully coupled nonlinear model where fast and slow variables modulate each other. This suggests that the analysis step in the PFs maintains the balance in both variables much better than the EnKF. It is also shown that increasing the ensemble size generally improves the performance of the PFs but has less impact on the EnKF after a sufficient number of members have been used.

Linear versus Nonlinear Filtering with Scale-Selective Corrections for Balanced Dynamics in a Simple Atmospheric Model

KAUST Repository

Subramanian, Aneesh C.; Hoteit, Ibrahim; Cornuelle, Bruce; Miller, Arthur J.; Song, Hajoon

2012-01-01

This paper investigates the role of the linear analysis step of the ensemble Kalman filters (EnKF) in disrupting the balanced dynamics in a simple atmospheric model and compares it to a fully nonlinear particle-based filter (PF). The filters have a very similar forecast step but the analysis step of the PF solves the full Bayesian filtering problem while the EnKF analysis only applies to Gaussian distributions. The EnKF is compared to two flavors of the particle filter with different sampling strategies, the sequential importance resampling filter (SIRF) and the sequential kernel resampling filter (SKRF). The model admits a chaotic vortical mode coupled to a comparatively fast gravity wave mode. It can also be configured either to evolve on a so-called slow manifold, where the fast motion is suppressed, or such that the fast-varying variables are diagnosed from the slow-varying variables as slaved modes. Identical twin experiments show that EnKF and PF capture the variables on the slow manifold well as the dynamics is very stable. PFs, especially the SKRF, capture slaved modes better than the EnKF, implying that a full Bayesian analysis estimates the nonlinear model variables better. The PFs perform significantly better in the fully coupled nonlinear model where fast and slow variables modulate each other. This suggests that the analysis step in the PFs maintains the balance in both variables much better than the EnKF. It is also shown that increasing the ensemble size generally improves the performance of the PFs but has less impact on the EnKF after a sufficient number of members have been used.

The SR Approach: a new Estimation Method for Non-Linear and Non-Gaussian Dynamic Term Structure Models

DEFF Research Database (Denmark)

Andreasen, Martin Møller; Christensen, Bent Jesper

This paper suggests a new and easy approach to estimate linear and non-linear dynamic term structure models with latent factors. We impose no distributional assumptions on the factors and they may therefore be non-Gaussian. The novelty of our approach is to use many observables (yields or bonds p...

Comparison of linear and nonlinear implementation of the compartmental tissue uptake model for dynamic contrast-enhanced MRI.

Science.gov (United States)

Kallehauge, Jesper F; Sourbron, Steven; Irving, Benjamin; Tanderup, Kari; Schnabel, Julia A; Chappell, Michael A

2017-06-01

Fitting tracer kinetic models using linear methods is much faster than using their nonlinear counterparts, although this comes often at the expense of reduced accuracy and precision. The aim of this study was to derive and compare the performance of the linear compartmental tissue uptake (CTU) model with its nonlinear version with respect to their percentage error and precision. The linear and nonlinear CTU models were initially compared using simulations with varying noise and temporal sampling. Subsequently, the clinical applicability of the linear model was demonstrated on 14 patients with locally advanced cervical cancer examined with dynamic contrast-enhanced magnetic resonance imaging. Simulations revealed equal percentage error and precision when noise was within clinical achievable ranges (contrast-to-noise ratio >10). The linear method was significantly faster than the nonlinear method, with a minimum speedup of around 230 across all tested sampling rates. Clinical analysis revealed that parameters estimated using the linear and nonlinear CTU model were highly correlated (ρ ≥ 0.95). The linear CTU model is computationally more efficient and more stable against temporal downsampling, whereas the nonlinear method is more robust to variations in noise. The two methods may be used interchangeably within clinical achievable ranges of temporal sampling and noise. Magn Reson Med 77:2414-2423, 2017. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine.

The topology of non-linear global carbon dynamics: from tipping points to planetary boundaries

International Nuclear Information System (INIS)

Anderies, J M; Carpenter, S R; Steffen, Will; Rockström, Johan

2013-01-01

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. (letter)

The topology of non-linear global carbon dynamics: from tipping points to planetary boundaries

Science.gov (United States)

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.

Model reduction of systems with localized nonlinearities.

Energy Technology Data Exchange (ETDEWEB)

Segalman, Daniel Joseph

2006-03-01

An LDRD funded approach to development of reduced order models for systems with local nonlinearities is presented. This method is particularly useful for problems of structural dynamics, but has potential application in other fields. The key elements of this approach are (1) employment of eigen modes of a reference linear system, (2) incorporation of basis functions with an appropriate discontinuity at the location of the nonlinearity. Galerkin solution using the above combination of basis functions appears to capture the dynamics of the system with a small basis set. For problems involving small amplitude dynamics, the addition of discontinuous (joint) modes appears to capture the nonlinear mechanics correctly while preserving the modal form of the predictions. For problems involving large amplitude dynamics of realistic joint models (macro-slip), the use of appropriate joint modes along with sufficient basis eigen modes to capture the frequencies of the system greatly enhances convergence, though the modal nature the result is lost. Also observed is that when joint modes are used in conjunction with a small number of elastic eigen modes in problems of macro-slip of realistic joint models, the resulting predictions are very similar to those of the full solution when seen through a low pass filter. This has significance both in terms of greatly reducing the number of degrees of freedom of the problem and in terms of facilitating the use of much larger time steps.

Nonlinear State Space Modeling and System Identification for Electrohydraulic Control

Directory of Open Access Journals (Sweden)

Jun Yan

2013-01-01

Full Text Available The paper deals with nonlinear modeling and identification of an electrohydraulic control system for improving its tracking performance. We build the nonlinear state space model for analyzing the highly nonlinear system and then develop a Hammerstein-Wiener (H-W model which consists of a static input nonlinear block with two-segment polynomial nonlinearities, a linear time-invariant dynamic block, and a static output nonlinear block with single polynomial nonlinearity to describe it. We simplify the H-W model into a linear-in-parameters structure by using the key term separation principle and then use a modified recursive least square method with iterative estimation of internal variables to identify all the unknown parameters simultaneously. It is found that the proposed H-W model approximates the actual system better than the independent Hammerstein, Wiener, and ARX models. The prediction error of the H-W model is about 13%, 54%, and 58% less than the Hammerstein, Wiener, and ARX models, respectively.

Nonlinear dynamics and chaotic phenomena an introduction

CERN Document Server

Shivamoggi, Bhimsen K

2014-01-01

This book starts with a discussion of nonlinear ordinary differential equations, bifurcation theory and Hamiltonian dynamics. It then embarks on a systematic discussion of the traditional topics of modern nonlinear dynamics  -- integrable systems, Poincaré maps, chaos, fractals and strange attractors. The Baker’s transformation, the logistic map and Lorenz system are discussed in detail in view of their central place in the subject. There is a detailed discussion of solitons centered around the Korteweg-deVries equation in view of its central place in integrable systems. Then, there is a discussion of the Painlevé property of nonlinear differential equations which seems to provide a test of integrability. Finally, there is a detailed discussion of the application of fractals and multi-fractals to fully-developed turbulence -- a problem whose understanding has been considerably enriched by the application of the concepts and methods of modern nonlinear dynamics. On the application side, there is a special...

Linear and nonlinear dynamic systems in financial time series prediction

Directory of Open Access Journals (Sweden)

Salim Lahmiri

2012-10-01

Full Text Available Autoregressive moving average (ARMA process and dynamic neural networks namely the nonlinear autoregressive moving average with exogenous inputs (NARX are compared by evaluating their ability to predict financial time series; for instance the S&P500 returns. Two classes of ARMA are considered. The first one is the standard ARMA model which is a linear static system. The second one uses Kalman filter (KF to estimate and predict ARMA coefficients. This model is a linear dynamic system. The forecasting ability of each system is evaluated by means of mean absolute error (MAE and mean absolute deviation (MAD statistics. Simulation results indicate that the ARMA-KF system performs better than the standard ARMA alone. Thus, introducing dynamics into the ARMA process improves the forecasting accuracy. In addition, the ARMA-KF outperformed the NARX. This result may suggest that the linear component found in the S&P500 return series is more dominant than the nonlinear part. In sum, we conclude that introducing dynamics into the ARMA process provides an effective system for S&P500 time series prediction.

Modelling of the nonlinear soliton dynamics in the ring fibre cavity

Science.gov (United States)

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.

Nonlinear dynamics of the m=1 kink-tearing instability in a modified magnetohydrodynamic model

International Nuclear Information System (INIS)

Wang, X.; Bhattacharjee, A.

1995-01-01

A theory is given for the nonlinear dynamical evolution of the collisionless m=1 kink-tearing instability, including the effects of electron inertia and electron pressure gradient in a generalized Ohm's law. It is demonstrated that electron pressure gradients can cause near-explosive growth in the nonlinear regime of a thin m=1 island. This near-explosive phase is followed by a rapid decay phase as the island width becomes comparable to the radius of the sawtooth region. An island equation is derived for the entire nonlinear evolution of the instability, extending recent work on the subject [X. Wang and A. Bhattacharjee, Phys. Rev. Lett. 70, 1627 (1993)] to include the effects of both electron inertia and electron pressure gradient. Comparisons are made with experimental data from present-day tokamaks. It is suggested that the present model not only accounts for fast sawtooth crashes, but also provides possible explanations for the problems of sudden onset and incomplete reconnection that have been, heretofore, unexplained features of observations. copyright 1995 American Institute of Physics

Calibration of the Nonlinear Accelerator Model at the Diamond Storage Ring

CERN Document Server

Bartolini, Riccardo; Rowland, James; Martin, Ian; Schmidt, Frank

2010-01-01

The correct implementation of the nonlinear ring model is crucial to achieve the top performance of a synchrotron light source. Several dynamics quantities can be used to compare the real machine with the model and eventually to correct the accelerator. Most of these methods are based on the analysis of turn-by-turn data of excited betatron oscillations. We present the experimental results of the campaign of measurements carried out at the Diamond. A combination of Frequency Map Analysis (FMA) and detuning with momentum measurements has allowed a precise calibration of the nonlinear model capable of reproducing the nonlinear beam dynamics in the storage ring

Experimental studies of nonlinear beam dynamics

International Nuclear Information System (INIS)

Caussyn, D.D.; Ball, M.; Brabson, B.; Collins, J.; Curtis, S.A.; Derenchuck, V.; DuPlantis, D.; East, G.; Ellison, M.; Ellison, T.; Friesel, D.; Hamilton, B.; Jones, W.P.; Lamble, W.; Lee, S.Y.; Li, D.; Minty, M.G.; Sloan, T.; Xu, G.; Chao, A.W.; Ng, K.Y.; Tepikian, S.

1992-01-01

The nonlinear beam dynamics of transverse betatron oscillations were studied experimentally at the Indiana University Cyclotron Facility cooler ring. Motion in one dimension was measured for betatron tunes near the third, fourth, fifth, and seventh integer resonances. This motion is described by coupling between the transverse modes of motion and nonlinear field errors. The Hamiltonian for nonlinear particle motion near the third- and fourth-integer-resonance conditions has been deduced

Success Stories in Control: Nonlinear Dynamic Inversion Control

Science.gov (United States)

Bosworth, John T.

2010-01-01

NASA plays an important role in advancing the state of the art in flight control systems. In the case of Nonlinear Dynamic Inversion (NDI) NASA supported initial implementation of the theory in an aircraft and demonstration in a space vehicle. Dr. Dale Enns of Honeywell Aerospace Advanced Technology performed this work in cooperation with NASA and under NASA contract. Honeywell and Lockheed Martin were subsequently contracted by AFRL to create "Design Guidelines for Multivariable Control Theory". This foundational work directly contributed to the advancement of the technology and the credibility of the control law as a design option. As a result Honeywell collaborated with Lockheed Martin to produce a Nonlinear Dynamic Inversion controller for the X-35 and subsequently Lockheed Martin did the same for the production Lockheed Martin F-35 vehicle. The theory behind NDI is to use a systematic generalized approach to controlling a vehicle. Using general aircraft nonlinear equations of motion and onboard aerodynamic, mass properties, and engine models specific to the vehicle, a relationship between control effectors and desired aircraft motion can be formulated. Using this formulation a control combination is used that provides a predictable response to commanded motion. Control loops around this formulation shape the response as desired and provide robustness to modeling errors. Once the control law is designed it can be used on a similar class of vehicle with only an update to the vehicle specific onboard models.

Nonlinearly coupled dynamics of irregularities in the equatorial electrojet

Energy Technology Data Exchange (ETDEWEB)

Atul, J.K., E-mail: jkatulphysics@gmail.com [Department of Physics, College of Commerce under Magadh University, Patna 800020 (India); Sarkar, S. [FCIPT, Institute for Plasma Research, Gandhinagar 382428 (India); Singh, S.K. [Department of Physics, College of Commerce under Magadh University, Patna 800020 (India)

2016-04-01

Kinetic wave description is used to study the nonlinear influence of background Farley Buneman (FB) modes on the Gradient Drift (GD) modes in the equatorial electrojet ionosphere. The dominant nonlinearity is mediated through the electron flux term in the governing fluid equation which further invokes a turbulent current into the system. Electron dynamics reveals the modification in electron collision frequency and inhomogeneity scale length. It is seen that the propagation and growth rate of GD modes get modified by the background FB modes. Also, a new quasimode gets excited through the quadratic dispersion relation. Physical significance of coupled dynamics between the participating modes is also discussed. - Highlights: • Nonlinear influence of Farley Buneman mode on the Gradient drift mode, is investigated. • Electron collision frequency and density gradient scale length get modified. • A new quasimode gets excited due to the competition between these modes. • It seems to be important for modelling of Equatorial Electrojet current system.

Nonlinearly coupled dynamics of irregularities in the equatorial electrojet

International Nuclear Information System (INIS)

Atul, J.K.; Sarkar, S.; Singh, S.K.

2016-01-01

Kinetic wave description is used to study the nonlinear influence of background Farley Buneman (FB) modes on the Gradient Drift (GD) modes in the equatorial electrojet ionosphere. The dominant nonlinearity is mediated through the electron flux term in the governing fluid equation which further invokes a turbulent current into the system. Electron dynamics reveals the modification in electron collision frequency and inhomogeneity scale length. It is seen that the propagation and growth rate of GD modes get modified by the background FB modes. Also, a new quasimode gets excited through the quadratic dispersion relation. Physical significance of coupled dynamics between the participating modes is also discussed. - Highlights: • Nonlinear influence of Farley Buneman mode on the Gradient drift mode, is investigated. • Electron collision frequency and density gradient scale length get modified. • A new quasimode gets excited due to the competition between these modes. • It seems to be important for modelling of Equatorial Electrojet current system.

Nonlinear price impact from linear models

Science.gov (United States)

Patzelt, Felix; Bouchaud, Jean-Philippe

2017-12-01

The impact of trades on asset prices is a crucial aspect of market dynamics for academics, regulators, and practitioners alike. Recently, universal and highly nonlinear master curves were observed for price impacts aggregated on all intra-day scales (Patzelt and Bouchaud 2017 arXiv:1706.04163). Here we investigate how well these curves, their scaling, and the underlying return dynamics are captured by linear ‘propagator’ models. We find that the classification of trades as price-changing versus non-price-changing can explain the price impact nonlinearities and short-term return dynamics to a very high degree. The explanatory power provided by the change indicator in addition to the order sign history increases with increasing tick size. To obtain these results, several long-standing technical issues for model calibration and testing are addressed. We present new spectral estimators for two- and three-point cross-correlations, removing the need for previously used approximations. We also show when calibration is unbiased and how to accurately reveal previously overlooked biases. Therefore, our results contribute significantly to understanding both recent empirical results and the properties of a popular class of impact models.

Nonlinear Dynamics Analysis of the Semiactive Suspension System with Magneto-Rheological Damper

Directory of Open Access Journals (Sweden)

Hailong Zhang

2015-01-01

Full Text Available This paper examines dynamical behavior of a nonlinear oscillator which models a quarter-car forced by the road profile. The magneto-rheological (MR suspension system has been established, by employing the modified Bouc-Wen force-velocity (F-v model of magneto-rheological damper (MRD. The possibility of chaotic motions in MR suspension is discovered by employing the method of nonlinear stability analysis. With the bifurcation diagrams and corresponding Lyapunov exponent (LE spectrum diagrams detected through numerical calculation, we can observe the complex dynamical behaviors and oscillating mechanism of alternating periodic oscillations, quasiperiodic oscillations, and chaotic oscillations with different profiles of road excitation, as well as the dynamical evolutions to chaos through period-doubling bifurcations, saddle-node bifurcations, and reverse period-doubling bifurcations.

An extended Kalman filtering approach to modeling nonlinear dynamic gene regulatory networks via short gene expression time series.

Science.gov (United States)

Wang, Zidong; Liu, Xiaohui; Liu, Yurong; Liang, Jinling; Vinciotti, Veronica

2009-01-01

In this paper, the extended Kalman filter (EKF) algorithm is applied to model the gene regulatory network from gene time series data. The gene regulatory network is considered as a nonlinear dynamic stochastic model that consists of the gene measurement equation and the gene regulation equation. After specifying the model structure, we apply the EKF algorithm for identifying both the model parameters and the actual value of gene expression levels. It is shown that the EKF algorithm is an online estimation algorithm that can identify a large number of parameters (including parameters of nonlinear functions) through iterative procedure by using a small number of observations. Four real-world gene expression data sets are employed to demonstrate the effectiveness of the EKF algorithm, and the obtained models are evaluated from the viewpoint of bioinformatics.

Dynamics of breathers in discrete nonlinear Schrodinger models

DEFF Research Database (Denmark)

Christiansen, Peter Leth; Johansson, Magnus; Aubry, Serge

1998-01-01

We review some recent results concerning the existence and stability of spatially localized and temporally quasiperiodic (non-stationary) excitations in discrete nonlinear Schrodinger (DNLS) models. In two dimensions, we show the existence of linearly stable, stationary and non-stationary localized...

Nonlinear dynamics and chaos in a pseudoelastic two-bar truss

International Nuclear Information System (INIS)

Savi, Marcelo A; Nogueira, Jefferson B

2010-01-01

Stability aspects of structures are usually treated by archetypal models that provide global comprehension of the system behavior. The two-bar truss is an example of this kind of model that presents snap-through behavior. This paper deals with the dynamical response of a pseudoelastic two-bar truss, representing an archetypal model of a structural system that exhibits both geometrical and constitutive nonlinearities. Adaptive trusses with shape memory alloy actuators are examples of dynamical systems that may behave like the structure considered in this paper. A constitutive model is employed in order to describe the SMA behavior, presenting close agreement with experimental data. An iterative numerical procedure based on the operator split technique, the orthogonal projection algorithm and the classical fourth order Runge–Kutta method is developed to deal with nonlinearities in the formulation. Numerical investigation is carried out considering free and forced responses of the pseudoelastic two-bar truss showing complex behaviors

Non-linear models for the detection of impaired cerebral blood flow autoregulation.

Science.gov (United States)

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.

Nonlinear chaotic model for predicting storm surges

Directory of Open Access Journals (Sweden)

M. Siek

2010-09-01

Full Text Available This paper addresses the use of the methods of nonlinear dynamics and chaos theory for building a predictive chaotic model from time series. The chaotic model predictions are made by the adaptive local models based on the dynamical neighbors found in the reconstructed phase space of the observables. We implemented the univariate and multivariate chaotic models with direct and multi-steps prediction techniques and optimized these models using an exhaustive search method. The built models were tested for predicting storm surge dynamics for different stormy conditions in the North Sea, and are compared to neural network models. The results show that the chaotic models can generally provide reliable and accurate short-term storm surge predictions.

Nonlinear dynamic range transformation in visual communication channels.

Science.gov (United States)

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.

Energy flow theory of nonlinear dynamical systems with applications

CERN Document Server

Xing, Jing Tang

2015-01-01

This monograph develops a generalised energy flow theory to investigate non-linear dynamical systems governed by ordinary differential equations in phase space and often met in various science and engineering fields. Important nonlinear phenomena such as, stabilities, periodical orbits, bifurcations and chaos are tack-led and the corresponding energy flow behaviors are revealed using the proposed energy flow approach. As examples, the common interested nonlinear dynamical systems, such as, Duffing’s oscillator, Van der Pol’s equation, Lorenz attractor, Rössler one and SD oscillator, etc, are discussed. This monograph lights a new energy flow research direction for nonlinear dynamics. A generalised Matlab code with User Manuel is provided for readers to conduct the energy flow analysis of their nonlinear dynamical systems. Throughout the monograph the author continuously returns to some examples in each chapter to illustrate the applications of the discussed theory and approaches. The book can be used as ...

Nonlinear modeling, strength-based design, and testing of flexible piezoelectric energy harvesters under large dynamic loads for rotorcraft applications

Science.gov (United States)

Leadenham, Stephen; Erturk, Alper

2014-04-01

There has been growing interest in enabling wireless health and usage monitoring for rotorcraft applications, such as helicopter rotor systems. Large dynamic loads and acceleration fluctuations available in these environments make the implementation of vibration-based piezoelectric energy harvesters a very promising choice. However, such extreme loads transmitted to the harvester can also be detrimental to piezoelectric laminates and overall system reliability. Particularly flexible resonant cantilever configurations tuned to match the dominant excitation frequency can be subject to very large deformations and failure of brittle piezoelectric laminates due to excessive bending stresses at the root of the harvester. Design of resonant piezoelectric energy harvesters for use in these environments require nonlinear electroelastic dynamic modeling and strength-based analysis to maximize the power output while ensuring that the harvester is still functional. This paper presents a mathematical framework to design and analyze the dynamics of nonlinear flexible piezoelectric energy harvesters under large base acceleration levels. A strength-based limit is imposed to design the piezoelectric energy harvester with a proof mass while accounting for material, geometric, and dissipative nonlinearities, with a focus on two demonstrative case studies having the same linear fundamental resonance frequency but different overhang length and proof mass values. Experiments are conducted at different excitation levels for validation of the nonlinear design approach proposed in this work. The case studies in this work reveal that harvesters exhibiting similar behavior and power generation performance at low excitation levels (e.g. less than 0.1g) can have totally different strength-imposed performance limitations under high excitations (e.g. above 1g). Nonlinear modeling and strength-based design is necessary for such excitation levels especially when using resonant cantilevers with no

On non-linear dynamics of a coupled electro-mechanical system

DEFF Research Database (Denmark)

Darula, Radoslav; Sorokin, Sergey

2012-01-01

Electro-mechanical devices are an example of coupled multi-disciplinary weakly non-linear systems. Dynamics of such systems is described in this paper by means of two mutually coupled differential equations. The first one, describing an electrical system, is of the first order and the second one...... excitation. The results are verified using a numerical model created in MATLAB Simulink environment. Effect of non-linear terms on dynamical response of the coupled system is investigated; the backbone and envelope curves are analyzed. The two phenomena, which exist in the electro-mechanical system: (a......, for mechanical system, is of the second order. The governing equations are coupled via linear and weakly non-linear terms. A classical perturbation method, a method of multiple scales, is used to find a steadystate response of the electro-mechanical system exposed to a harmonic close-resonance mechanical...

Nonlinear Modeling of the PEMFC Based On NNARX Approach

OpenAIRE

Shan-Jen Cheng; Te-Jen Chang; Kuang-Hsiung Tan; Shou-Ling Kuo

2015-01-01

Polymer Electrolyte Membrane Fuel Cell (PEMFC) is such a time-vary nonlinear dynamic system. The traditional linear modeling approach is hard to estimate structure correctly of PEMFC system. From this reason, this paper presents a nonlinear modeling of the PEMFC using Neural Network Auto-regressive model with eXogenous inputs (NNARX) approach. The multilayer perception (MLP) network is applied to evaluate the structure of the NNARX model of PEMFC. The validity and accurac...

Analysis of Nonlinear Dynamics in Linear Compressors Driven by Linear Motors

Science.gov (United States)

Chen, Liangyuan

2018-03-01

The analysis of dynamic characteristics of the mechatronics system is of great significance for the linear motor design and control. Steady-state nonlinear response characteristics of a linear compressor are investigated theoretically based on the linearized and nonlinear models. First, the influence factors considering the nonlinear gas force load were analyzed. Then, a simple linearized model was set up to analyze the influence on the stroke and resonance frequency. Finally, the nonlinear model was set up to analyze the effects of piston mass, spring stiffness, driving force as an example of design parameter variation. The simulating results show that the stroke can be obtained by adjusting the excitation amplitude, frequency and other adjustments, the equilibrium position can be adjusted by adjusting the DC input, and to make the more efficient operation, the operating frequency must always equal to the resonance frequency.

The numerical dynamic for highly nonlinear partial differential equations

Science.gov (United States)

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.

Quality of computerized blast load simulation for non-linear dynamic ...

African Journals Online (AJOL)

Quality of computerized blast load simulation for non-linear dynamic response ... commercial software system and a special-purpose, blast-specific software product to ... depend both on the analysis model of choice and the stand-off distances.

Nonlinear identification of process dynamics using neural networks

International Nuclear Information System (INIS)

Parlos, A.G.; Atiya, A.F.; Chong, K.T.

1992-01-01

In this paper the nonlinear identification of process dynamics encountered in nuclear power plant components is addressed, in an input-output sense, using artificial neural systems. A hybrid feedforward/feedback neural network, namely, a recurrent multilayer perceptron, is used as the model structure to be identified. The feedforward portion of the network architecture provides its well-known interpolation property, while through recurrency and cross-talk, the local information feedback enables representation of temporal variations in the system nonlinearities. The standard backpropagation learning algorithm is modified, and it is used for the supervised training of the proposed hybrid network. The performance of recurrent multilayer perceptron networks in identifying process dynamics is investigated via the case study of a U-tube steam generator. The response of representative steam generator is predicted using a neural network, and it is compared to the response obtained from a sophisticated computer model based on first principles. The transient responses compare well, although further research is warranted to determine the predictive capabilities of these networks during more severe operational transients and accident scenarios

Nonlinear stochastic dynamics of mesoscopic homogeneous biochemical reaction systems—an analytical theory

International Nuclear Information System (INIS)

Qian, Hong

2011-01-01

The nonlinear dynamics of biochemical reactions in a small-sized system on the order of a cell are stochastic. Assuming spatial homogeneity, the populations of n molecular species follow a multi-dimensional birth-and-death process on Z n . We introduce the Delbrück–Gillespie process, a continuous-time Markov jump process, whose Kolmogorov forward equation has been known as the chemical master equation, and whose stochastic trajectories can be computed via the Gillespie algorithm. Using simple models, we illustrate that a system of nonlinear ordinary differential equations on R n emerges in the infinite system size limit. For finite system size, transitions among multiple attractors of the nonlinear dynamical system are rare events with exponentially long transit times. There is a separation of time scales between the deterministic ODEs and the stochastic Markov jumps between attractors. No diffusion process can provide a global representation that is accurate on both short and long time scales for the nonlinear, stochastic population dynamics. On the short time scale and near deterministic stable fixed points, Ornstein–Uhlenbeck Gaussian processes give linear stochastic dynamics that exhibit time-irreversible circular motion for open, driven chemical systems. Extending this individual stochastic behaviour-based nonlinear population theory of molecular species to other biological systems is discussed. (invited article)

Digital Communication Devices Based on Nonlinear Dynamics and Chaos

National Research Council Canada - National Science Library

Larson, Lawrence

2003-01-01

The final report of the ARO MURI "Digital Communications Based on Chaos and Nonlinear Dynamics" contains research results in the areas of chaos and nonlinear dynamics applied to wireless and optical communications...

Design of advanced materials for linear and nonlinear dynamics

DEFF Research Database (Denmark)

Frandsen, Niels Morten Marslev

to reveal the fundamental dynamic characteristics and thus the relevant design parameters.The thesis is built around the characterization of two one-dimensional, periodic material systems. The first is a nonlinear mass-spring chain with periodically varying material properties, representing a simple......The primary catalyst of this PhD project has been an ambition to design advanced materials and structural systems including, and possibly even exploiting, nonlinear phenomena such as nonlinear modal interaction leading to energy conversion between modes. An important prerequisite for efficient...... but general model of inhomogeneous structural materials with nonlinear material characteristics. The second material system is an “engineered” material in the sense that a classical structural element, a linear elastic and homogeneous rod, is “enhanced” by applying a mechanism on its surface, amplifying...

Final report LDRD project 105816 : model reduction of large dynamic systems with localized nonlinearities.

Energy Technology Data Exchange (ETDEWEB)

Lehoucq, Richard B.; Segalman, Daniel Joseph; Hetmaniuk, Ulrich L. (University of Washington, Seattle, WA); Dohrmann, Clark R.

2009-10-01

Advanced computing hardware and software written to exploit massively parallel architectures greatly facilitate the computation of extremely large problems. On the other hand, these tools, though enabling higher fidelity models, have often resulted in much longer run-times and turn-around-times in providing answers to engineering problems. The impediments include smaller elements and consequently smaller time steps, much larger systems of equations to solve, and the inclusion of nonlinearities that had been ignored in days when lower fidelity models were the norm. The research effort reported focuses on the accelerating the analysis process for structural dynamics though combinations of model reduction and mitigation of some factors that lead to over-meshing.

Dynamical heterogeneities and mechanical non-linearities: Modeling the onset of plasticity in polymer in the glass transition.

Science.gov (United States)

Masurel, R J; Gelineau, P; Lequeux, F; Cantournet, S; Montes, H

2017-12-27

In this paper we focus on the role of dynamical heterogeneities on the non-linear response of polymers in the glass transition domain. We start from a simple coarse-grained model that assumes a random distribution of the initial local relaxation times and that quantitatively describes the linear viscoelasticity of a polymer in the glass transition regime. We extend this model to non-linear mechanics assuming a local Eyring stress dependence of the relaxation times. Implementing the model in a finite element mechanics code, we derive the mechanical properties and the local mechanical fields at the beginning of the non-linear regime. The model predicts a narrowing of distribution of relaxation times and the storage of a part of the mechanical energy --internal stress-- transferred to the material during stretching in this temperature range. We show that the stress field is not spatially correlated under and after loading and follows a Gaussian distribution. In addition the strain field exhibits shear bands, but the strain distribution is narrow. Hence, most of the mechanical quantities can be calculated analytically, in a very good approximation, with the simple assumption that the strain rate is constant.

Nonlinear Dynamical Analysis for a Plain Bearing

Directory of Open Access Journals (Sweden)

Ali Belhamra

2014-03-01

Full Text Available This paper investigates the nonlinear dynamic behavior for a plain classic bearing (fluid bearing lubricated by a non-Newtonian fluid of a turbo machine rotating with high speed; this type of fluid contains additives viscosity (couple-stress fluid film. The solution of the nonlinear dynamic problem of this type of bearing is determined with a spatial discretisation of the modified Reynolds' equation written in dynamic mode by using the optimized short bearing theory and a temporal discretisation for equations of rotor motion by the help of Euler's explicit diagram. This study analyzes the dynamic behavior of a rotor supported by two couple-stress fluid film journal lubricant enhances the dynamic stability of the rotor-bearing system considerably compared to that obtained when using a traditional Newtonian lubricant. The analysis shows that the dynamic behavior of a shaft which turns with high velocities is strongly nonlinear even for poor eccentricities of unbalance; the presence of parameters of couple stress allows strongly attenuating the will synchrony (unbalance and asynchrony (whipping amplitudes of vibrations of the shaft which supports more severe conditions (large unbalances.

Nonlinear dynamic simulation of optimal depletion of crude oil in the lower 48 United States

International Nuclear Information System (INIS)

Ruth, M.; Cleveland, C.J.

1993-01-01

This study combines the economic theory of optimal resource use with econometric estimates of demand and supply parameters to develop a nonlinear dynamic model of crude oil exploration, development, and production in the lower 48 United States. The model is simulated with the graphical programming language STELLA, for the years 1985 to 2020. The procedure encourages use of economic theory and econometrics in combination with nonlinear dynamic simulation to enhance our understanding of complex interactions present in models of optimal resource use. (author)

Hierarchical nonlinear dynamics of human attention.

Science.gov (United States)

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

2015-08-01

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

Nonlinear Dynamic Characteristics of the Railway Vehicle

Science.gov (United States)

Uyulan, Çağlar; Gokasan, Metin

2017-06-01

The nonlinear dynamic characteristics of a railway vehicle are checked into thoroughly by applying two different wheel-rail contact model: a heuristic nonlinear friction creepage model derived by using Kalker 's theory and Polach model including dead-zone clearance. This two models are matched with the quasi-static form of the LuGre model to obtain more realistic wheel-rail contact model. LuGre model parameters are determined using nonlinear optimization method, which it's objective is to minimize the error between the output of the Polach and Kalker model and quasi-static LuGre model for specific operating conditions. The symmetric/asymmetric bifurcation attitude and stable/unstable motion of the railway vehicle in the presence of nonlinearities which are yaw damping forces in the longitudinal suspension system are analyzed in great detail by changing the vehicle speed. Phase portraits of the lateral displacement of the leading wheelset of the railway vehicle are drawn below and on the critical speeds, where sub-critical Hopf bifurcation take place, for two wheel-rail contact model. Asymmetric periodic motions have been observed during the simulation in the lateral displacement of the wheelset under different vehicle speed range. The coexistence of multiple steady states cause bounces in the amplitude of vibrations, resulting instability problems of the railway vehicle. By using Lyapunov's indirect method, the critical hunting speeds are calculated with respect to the radius of the curved track parameter changes. Hunting, which is defined as the oscillation of the lateral displacement of wheelset with a large domain, is described by a limit cycle-type oscillation nature. The evaluated accuracy of the LuGre model adopted from Kalker's model results for prediction of critical speed is higher than the results of the LuGre model adopted from Polach's model. From the results of the analysis, the critical hunting speed must be resolved by investigating the track tests

COMPARISON OF NONLINEAR DYNAMICS OPTIMIZATION METHODS FOR APS-U

Energy Technology Data Exchange (ETDEWEB)

Sun, Y.; Borland, Michael

2017-06-25

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.

A Non-linear Stochastic Model for an Office Building with Air Infiltration

DEFF Research Database (Denmark)

Thavlov, Anders; Madsen, Henrik

2015-01-01

This paper presents a non-linear heat dynamic model for a multi-room office building with air infiltration. Several linear and non-linear models, with and without air infiltration, are investigated and compared. The models are formulated using stochastic differential equations and the model...

Nonlinear dynamics as an engine of computation.

Science.gov (United States)

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 Dynamic Modeling of a Supersonic Commercial Transport Turbo-Machinery Propulsion System for Aero-Propulso-Servo-Elasticity Research

Science.gov (United States)

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.

Is DNA a nonlinear dynamical system where solitary conformational ...

Indian Academy of Sciences (India)

Unknown

DNA is considered as a nonlinear dynamical system in which solitary conformational waves can be excited. The ... nonlinear differential equations and their soliton-like solu- .... structure and dynamics can be added till the most accurate.

Modeling of Nonlinear Dynamics and Synchronized Oscillations of Microbial Populations, Carbon and Oxygen Concentrations, Induced by Root Exudation in the Rhizosphere

Science.gov (United States)

Molz, F. J.; Faybishenko, B.; Jenkins, E. W.

2012-12-01

Mass and energy fluxes within the soil-plant-atmosphere continuum are highly coupled and inherently nonlinear. The main focus of this presentation is to demonstrate the results of numerical modeling of a system of 4 coupled, nonlinear ordinary differential equations (ODEs), which are used to describe the long-term, rhizosphere processes of soil microbial dynamics, including the competition between nitrogen-fixing bacteria and those unable to fix nitrogen, along with substrate concentration (nutrient supply) and oxygen concentration. Modeling results demonstrate the synchronized patterns of temporal oscillations of competing microbial populations, which are affected by carbon and oxygen concentrations. The temporal dynamics and amplitude of the root exudation process serve as a driving force for microbial and geochemical phenomena, and lead to the development of the Gompetzian dynamics, synchronized oscillations, and phase-space attractors of microbial populations and carbon and oxygen concentrations. The nonlinear dynamic analysis of time series concentrations from the solution of the ODEs was used to identify several types of phase-space attractors, which appear to be dependent on the parameters of the exudation function and Monod kinetic parameters. This phase space analysis was conducted by means of assessing the global and local embedding dimensions, correlation time, capacity and correlation dimensions, and Lyapunov exponents of the calculated model variables defining the phase space. Such results can be used for planning experimental and theoretical studies of biogeochemical processes in the fields of plant nutrition, phyto- and bio-remediation, and other ecological areas.

Nonlinear dynamics, chaos and complex cardiac arrhythmias

Science.gov (United States)

Glass, L.; Courtemanche, M.; Shrier, A.; Goldberger, A. L.

1987-01-01

Periodic stimulation of a nonlinear cardiac oscillator in vitro gives rise to complex dynamics that is well described by one-dimensional finite difference equations. As stimulation parameters are varied, a large number of different phase-locked and chaotic rhythms is observed. Similar rhythms can be observed in the intact human heart when there is interaction between two pacemaker sites. Simplified models are analyzed, which show some correspondence to clinical observations.

Photonic single nonlinear-delay dynamical node for information processing

Science.gov (United States)

Ortín, Silvia; San-Martín, Daniel; Pesquera, Luis; Gutiérrez, José Manuel

2012-06-01

An electro-optical system with a delay loop based on semiconductor lasers is investigated for information processing by performing numerical simulations. This system can replace a complex network of many nonlinear elements for the implementation of Reservoir Computing. We show that a single nonlinear-delay dynamical system has the basic properties to perform as reservoir: short-term memory and separation property. The computing performance of this system is evaluated for two prediction tasks: Lorenz chaotic time series and nonlinear auto-regressive moving average (NARMA) model. We sweep the parameters of the system to find the best performance. The results achieved for the Lorenz and the NARMA-10 tasks are comparable to those obtained by other machine learning methods.

A non-linear model of economic production processes

Science.gov (United States)

Ponzi, A.; Yasutomi, A.; Kaneko, K.

2003-06-01

We present a new two phase model of economic production processes which is a non-linear dynamical version of von Neumann's neoclassical model of production, including a market price-setting phase as well as a production phase. The rate of an economic production process is observed, for the first time, to depend on the minimum of its input supplies. This creates highly non-linear supply and demand dynamics. By numerical simulation, production networks are shown to become unstable when the ratio of different products to total processes increases. This provides some insight into observed stability of competitive capitalist economies in comparison to monopolistic economies. Capitalist economies are also shown to have low unemployment.

Nonlinear model of a rotating hub-beams structure: Equations of motion

Science.gov (United States)

Warminski, Jerzy

2018-01-01

Dynamics of a rotating structure composed of a rigid hub and flexible beams is presented in the paper. A nonlinear model of a beam takes into account bending, extension and nonlinear curvature. The influence of geometric nonlinearity and nonconstant angular velocity on dynamics of the rotating structure is presented. The exact equations of motion and associated boundary conditions are derived on the basis of the Hamilton's principle. The simplification of the exact nonlinear mathematical model is proposed taking into account the second order approximation. The reduced partial differential equations of motion together with associated boundary conditions can be used to study natural or forced vibrations of a rotating structure considering constant or nonconstant angular speed of a rigid hub and an arbitrary number of flexible blades.

Modeling and Analysis of Static and Dynamic Characteristics of Nonlinear Seat Suspension for Off-Road Vehicles

Directory of Open Access Journals (Sweden)

Zhenhua Yan

2015-01-01

Full Text Available Low-frequency vibrations (0.5–5 Hz that harm drivers occur in off-road vehicles. Thus, researchers have focused on finding methods to effectively isolate or control low-frequency vibrations. A novel nonlinear seat suspension structure for off-road vehicles is designed, whose static characteristics and seat-human system dynamic response are modeled and analyzed, and experiments are conducted to verify the theoretical solutions. Results show that the stiffness of this nonlinear seat suspension could achieve real zero stiffness through well-matched parameters, and precompression of the main spring could change the nonlinear seat suspension performance when a driver’s weight changes. The displacement transmissibility curve corresponds with the static characteristic curve of nonlinear suspension, where the middle part of the static characteristic curve is gentler and the resonance frequency of the displacement transmissibility curve and the isolation minimum frequency are lower. Damping should correspond with static characteristics, in which the corresponding suspension damping value should be smaller given a flatter static characteristic curve to prevent vibration isolation performance reduction.

Mean-field dynamics of a Bose-Einstein condensate in a time-dependent triple-well trap: Nonlinear eigenstates, Landau-Zener models, and stimulated Raman adiabatic passage

International Nuclear Information System (INIS)

Graefe, E. M.; Korsch, H. J.; Witthaut, D.

2006-01-01

We investigate the dynamics of a Bose-Einstein condensate in a triple-well trap in a three-level approximation. The interatomic interactions are taken into account in a mean-field approximation (Gross-Pitaevskii equation), leading to a nonlinear three-level model. Additional eigenstates emerge due to the nonlinearity, depending on the system parameters. Adiabaticity breaks down if such a nonlinear eigenstate disappears when the parameters are varied. The dynamical implications of this loss of adiabaticity are analyzed for two important special cases: A three-level Landau-Zener model and the stimulated Raman adiabatic passage (STIRAP) scheme. We discuss the emergence of looped levels for an equal-slope Landau-Zener model. The Zener tunneling probability does not tend to zero in the adiabatic limit and shows pronounced oscillations as a function of the velocity of the parameter variation. Furthermore we generalize the STIRAP scheme for adiabatic coherent population transfer between atomic states to the nonlinear case. It is shown that STIRAP breaks down if the nonlinearity exceeds the detuning

Nonlinear dynamic analysis of nuclear reactor primary coolant systems

International Nuclear Information System (INIS)

Saffell, B.F. Jr.; Macek, R.W.; Thompson, T.R.; Lippert, R.F.

1979-01-01

The ADINA computer code is utilized to perform mechanical response analysis of pressurized reactor primary coolant systems subjected to postulated loss-of-coolant accident (LOCA) loadings. Specifically, three plant analyses are performed utilizing the geometric and material nonlinear analysis capabilities of ADINA. Each reactor system finite element model represents the reactor vessel and internals, piping, major components, and component supports in a single coupled model. Material and geometric nonlinear capabilities of the beam and truss elements are employed in the formulation of each finite element model. Loadings applied to each plant for LOCA dynamic analysis include steady-state pressure, dead weight, strain energy release, transient piping hydraulic forces, and reactor vessel cavity pressurization. Representative results are presented with some suggestions for consideration in future ADINA code development

Nonlinear Coupled Dynamics of a Rod Fastening Rotor under Rub-Impact and Initial Permanent Deflection

Directory of Open Access Journals (Sweden)

Liang Hu

2016-10-01

Full Text Available A nonlinear coupled dynamic model of a rod fastening rotor under rub-impact and initial permanent deflection was developed in this paper. The governing motion equation was derived by the D’Alembert principle considering the contact characteristic between disks, nonlinear oil-film force, rub-impact force, unbalance mass, etc. The contact effects between disks was modeled as a flexural spring with cubical nonlinear stiffness. The coupled nonlinear dynamic phenomena of the rub-impact rod fastening rotor bearing system with initial permanent deflection were investigated by the fourth-order Runge-Kutta method. Bifurcation diagram, vibration waveform, frequency spectrum, shaft orbit and Poincaré map are used to illustrate the rich diversity of the system response with complicated dynamics. The studies indicate that the coupled dynamic responses of the rod fastening rotor bearing system under rub-impact and initial permanent deflection exhibit a rich nonlinear dynamic diversity, synchronous periodic-1 motion, multiple periodic motion, quasi-periodic motion and chaotic motion can be observed under certain conditions. Larger radial stiffness of the stator will simplify the system motion and make the oil whirl weaker or even disappear at a certain rotating speed. With the increase of initial permanent deflection length, the instability speed of the system gradually rises, and the chaotic motion region gets smaller and smaller. The corresponding results can provide guidance for the fault diagnosis of a rub-impact rod fastening rotor with initial permanent deflection and contribute to the further understanding of the nonlinear dynamic characteristics of the rod fastening rotor bearing system.

Nonlinear Model Predictive Control for Solid Oxide Fuel Cell System Based On Wiener Model

OpenAIRE

T. H. Lee; J. H. Park; S. M. Lee; S. C. Lee

2010-01-01

In this paper, we consider Wiener nonlinear model for solid oxide fuel cell (SOFC). The Wiener model of the SOFC consists of a linear dynamic block and a static output non-linearity followed by the block, in which linear part is approximated by state-space model and the nonlinear part is identified by a polynomial form. To control the SOFC system, we have to consider various view points such as operating conditions, another constraint conditions, change of load current and so on. A change of ...

Structure-based control of complex networks with nonlinear dynamics.

Science.gov (United States)

Zañudo, Jorge Gomez Tejeda; Yang, Gang; Albert, Réka

2017-07-11

What can we learn about controlling a system solely from its underlying network structure? Here we adapt a recently developed framework for control of networks governed by a broad class of nonlinear dynamics that includes the major dynamic models of biological, technological, and social processes. This feedback-based framework provides realizable node overrides that steer a system toward any of its natural long-term dynamic behaviors, regardless of the specific functional forms and system parameters. We use this framework on several real networks, identify the topological characteristics that underlie the predicted node overrides, and compare its predictions to those of structural controllability in control theory. Finally, we demonstrate this framework's applicability in dynamic models of gene regulatory networks and identify nodes whose override is necessary for control in the general case but not in specific model instances.

Nonlinear dynamical modes of climate variability: from curves to manifolds

Science.gov (United States)

Gavrilov, Andrey; Mukhin, Dmitry; Loskutov, Evgeny; Feigin, Alexander

2016-04-01

The necessity of efficient dimensionality reduction methods capturing dynamical properties of the system from observed data is evident. Recent study shows that nonlinear dynamical mode (NDM) expansion is able to solve this problem and provide adequate phase variables in climate data analysis [1]. A single NDM is logical extension of linear spatio-temporal structure (like empirical orthogonal function pattern): it is constructed as nonlinear transformation of hidden scalar time series to the space of observed variables, i. e. projection of observed dataset onto a nonlinear curve. Both the hidden time series and the parameters of the curve are learned simultaneously using Bayesian approach. The only prior information about the hidden signal is the assumption of its smoothness. The optimal nonlinearity degree and smoothness are found using Bayesian evidence technique. In this work we do further extension and look for vector hidden signals instead of scalar with the same smoothness restriction. As a result we resolve multidimensional manifolds instead of sum of curves. The dimension of the hidden manifold is optimized using also Bayesian evidence. The efficiency of the extension is demonstrated on model examples. Results of application to climate data are demonstrated and discussed. The study is supported by Government of Russian Federation (agreement #14.Z50.31.0033 with the Institute of Applied Physics of RAS). 1. Mukhin, D., Gavrilov, A., Feigin, A., Loskutov, E., & Kurths, J. (2015). Principal nonlinear dynamical modes of climate variability. Scientific Reports, 5, 15510. http://doi.org/10.1038/srep15510

Nonlinear beam mechanics

NARCIS (Netherlands)

Westra, H.J.R.

2012-01-01

In this Thesis, nonlinear dynamics and nonlinear interactions are studied from a micromechanical point of view. Single and doubly clamped beams are used as model systems where nonlinearity plays an important role. The nonlinearity also gives rise to rich dynamic behavior with phenomena like

Nonlinear modal analysis in NPP dynamics: a proposal

International Nuclear Information System (INIS)

Suarez Antola, R.

2005-07-01

We propose and briefly suggest how to apply the analytical tools of nonlinear modal analysis (NMA) to problems of nuclear reactor kinetics, NPP dynamics, and NPP instrumentation and control. The proposed method is closely related with recent approaches by modal analysis using the reactivity matrix with feedbacks to couple neutron kinetics with thermal hydraulics in the reactors core. A nonlinear system of ordinary differential equations for mode amplitudes is obtained, projecting the dynamic equations of a model of NPP onto the eigenfunctions of a suitable adjoint operator. A steady state solution of the equations is taken as a reference, and the behaviour of transient solutions in some neighbourhood of the steady state solution is studied by an extension of Liapunov's First Method that enables to cope directly with the non-linear terms in the dynamics. In NPP dynamics these differential equations for the mode amplitudes are of polynomial type of low degree A few dominant modes can usually be identified. These mode amplitudes evolve almost independently of the other modes, more slowly and tending to slave the other mode amplitudes. Using asymptotic methods, it is possible to calculate a closed form analytical approximation to the response to finite amplitude perturbations from the given steady spatial pattern (the origin of the space of mode amplitudes).When there is finite amplitude instability, the method allows us to calculate the threshold amplitude as a well defined function of system's parameters. This is a most significant accomplishment that the other methods cannot afford

Reduced-order computational model in nonlinear structural dynamics for structures having numerous local elastic modes in the low-frequency range. Application to fuel assemblies

International Nuclear Information System (INIS)

Batou, A.; Soize, C.; Brie, N.

2013-01-01

Highlights: • A ROM of a nonlinear dynamical structure is built with a global displacements basis. • The reduced order model of fuel assemblies is accurate and of very small size. • The shocks between grids of a row of seven fuel assemblies are computed. -- Abstract: We are interested in the construction of a reduced-order computational model for nonlinear complex dynamical structures which are characterized by the presence of numerous local elastic modes in the low-frequency band. This high modal density makes the use of the classical modal analysis method not suitable. Therefore the reduced-order computational model is constructed using a basis of a space of global displacements, which is constructed a priori and which allows the nonlinear dynamical response of the structure observed on the stiff part to be predicted with a good accuracy. The methodology is applied to a complex industrial structure which is made up of a row of seven fuel assemblies with possibility of collisions between grids and which is submitted to a seismic loading

Reduced-order computational model in nonlinear structural dynamics for structures having numerous local elastic modes in the low-frequency range. Application to fuel assemblies

Energy Technology Data Exchange (ETDEWEB)

Batou, A., E-mail: anas.batou@univ-paris-est.fr [Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-la-Vallee (France); Soize, C., E-mail: christian.soize@univ-paris-est.fr [Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-la-Vallee (France); Brie, N., E-mail: nicolas.brie@edf.fr [EDF R and D, Département AMA, 1 avenue du général De Gaulle, 92140 Clamart (France)

2013-09-15

Highlights: • A ROM of a nonlinear dynamical structure is built with a global displacements basis. • The reduced order model of fuel assemblies is accurate and of very small size. • The shocks between grids of a row of seven fuel assemblies are computed. -- Abstract: We are interested in the construction of a reduced-order computational model for nonlinear complex dynamical structures which are characterized by the presence of numerous local elastic modes in the low-frequency band. This high modal density makes the use of the classical modal analysis method not suitable. Therefore the reduced-order computational model is constructed using a basis of a space of global displacements, which is constructed a priori and which allows the nonlinear dynamical response of the structure observed on the stiff part to be predicted with a good accuracy. The methodology is applied to a complex industrial structure which is made up of a row of seven fuel assemblies with possibility of collisions between grids and which is submitted to a seismic loading.

Nonlinear joint models for individual dynamic prediction of risk of death using Hamiltonian Monte Carlo: application to metastatic prostate cancer

Directory of Open Access Journals (Sweden)

Solène Desmée

2017-07-01

Full Text Available Abstract Background Joint models of longitudinal and time-to-event data are increasingly used to perform individual dynamic prediction of a risk of event. However the difficulty to perform inference in nonlinear models and to calculate the distribution of individual parameters has long limited this approach to linear mixed-effect models for the longitudinal part. Here we use a Bayesian algorithm and a nonlinear joint model to calculate individual dynamic predictions. We apply this approach to predict the risk of death in metastatic castration-resistant prostate cancer (mCRPC patients with frequent Prostate-Specific Antigen (PSA measurements. Methods A joint model is built using a large population of 400 mCRPC patients where PSA kinetics is described by a biexponential function and the hazard function is a PSA-dependent function. Using Hamiltonian Monte Carlo algorithm implemented in Stan software and the estimated population parameters in this population as priors, the a posteriori distribution of the hazard function is computed for a new patient knowing his PSA measurements until a given landmark time. Time-dependent area under the ROC curve (AUC and Brier score are derived to assess discrimination and calibration of the model predictions, first on 200 simulated patients and then on 196 real patients that are not included to build the model. Results Satisfying coverage probabilities of Monte Carlo prediction intervals are obtained for longitudinal and hazard functions. Individual dynamic predictions provide good predictive performances for landmark times larger than 12 months and horizon time of up to 18 months for both simulated and real data. Conclusions As nonlinear joint models can characterize the kinetics of biomarkers and their link with a time-to-event, this approach could be useful to improve patient’s follow-up and the early detection of most at risk patients.

Dynamics of Nonlinear Time-Delay Systems

CERN Document Server

Lakshmanan, Muthusamy

2010-01-01

Synchronization of chaotic systems, a patently nonlinear phenomenon, has emerged as a highly active interdisciplinary research topic at the interface of physics, biology, applied mathematics and engineering sciences. In this connection, time-delay systems described by delay differential equations have developed as particularly suitable tools for modeling specific dynamical systems. Indeed, time-delay is ubiquitous in many physical systems, for example due to finite switching speeds of amplifiers in electronic circuits, finite lengths of vehicles in traffic flows, finite signal propagation times in biological networks and circuits, and quite generally whenever memory effects are relevant. This monograph presents the basics of chaotic time-delay systems and their synchronization with an emphasis on the effects of time-delay feedback which give rise to new collective dynamics. Special attention is devoted to scalar chaotic/hyperchaotic time-delay systems, and some higher order models, occurring in different bran...

Nonlinear dynamics of the human lumbar intervertebral disc.

Science.gov (United States)

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.

Nonlinear beam dynamics experimental program at SPEAR

International Nuclear Information System (INIS)

Tran, P.; Pellegrini, C.; Cornacchia, M.; Lee, M.; Corbett, W.

1995-01-01

Since nonlinear effects can impose strict performance limitations on modern colliders and storage rings, future performance improvements depend on further understanding of nonlinear beam dynamics. Experimental studies of nonlinear beam motion in three-dimensional space have begun in SPEAR using turn-by-turn transverse and longitudinal phase-space monitors. This paper presents preliminary results from an on-going experiment in SPEAR

Nonlinear Bubble Dynamics And The Effects On Propagation Through Near-Surface Bubble Layers

Science.gov (United States)

Leighton, Timothy G.

2004-11-01

Nonlinear bubble dynamics are often viewed as the unfortunate consequence of having to use high acoustic pressure amplitudes when the void fraction in the near-surface oceanic bubble layer is great enough to cause severe attenuation (e.g. >50 dB/m). This is seen as unfortunate since existing models for acoustic propagation in bubbly liquids are based on linear bubble dynamics. However, the development of nonlinear models does more than just allow quantification of the errors associated with the use of linear models. It also offers the possibility of propagation modeling and acoustic inversions which appropriately incorporate the bubble nonlinearity. Furthermore, it allows exploration and quantification of possible nonlinear effects which may be exploited. As a result, high acoustic pressure amplitudes may be desirable even in low void fractions, because they offer opportunities to gain information about the bubble cloud from the nonlinearities, and options to exploit the nonlinearities to enhance communication and sonar in bubbly waters. This paper presents a method for calculating the nonlinear acoustic cross-sections, scatter, attenuations and sound speeds from bubble clouds which may be inhomogeneous. The method allows prediction of the time dependency of these quantities, both because the cloud may vary and because the incident acoustic pulse may have finite and arbitrary time history. The method can be readily adapted for bubbles in other environments (e.g. clouds of interacting bubbles, sediments, structures, in vivo, reverberant conditions etc.). The possible exploitation of bubble acoustics by marine mammals, and for sonar enhancement, is explored.

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

Science.gov (United States)

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

2012-07-01

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

Nonlinear dynamics of the relativistic standard map

International Nuclear Information System (INIS)

Nomura, Y.; Ichikawa, Y.H.; Horton, W.

1991-01-01

Heating and acceleration of charged particles by RF fields have been extensively investigated by the standard map (ST). Thus, it is natural to pose the question asking how the relativistic effects change the nonlinear dynamical behavior described by the classical ST map. The authors show that the speed of light limits the rate of advance of the phase in the relativistic standard map (RST) and introduces KAM surfaces persisting in the high momentum region. The RST map is a two parameter (k, β = ω/kc) family of dynamics reducing to the ST map when β → 0. For β ≠ 0 the relativity suppresses the onset of stochasticity. Chernikov et al. has also reported this effect. They have carried out extensive studies of nonlinear dynamics of the RST map and found very intricate structure of mixing of the higher order periodic orbits and chaotic orbits. They have shown that no matter how its gets chaotic the symmetry properties of the RST map determines its nonlinear dynamical behavior. 1 ref

Analysis of the nonlinear dynamics of a 2-axle freight wagon in curves

DEFF Research Database (Denmark)

Di Gialleonardo, Egidio; Bruni, Stefano; True, Hans

2014-01-01

This paper deals with the study of the nonlinear dynamic behaviour of 2-axle freight wagons in curves, considering the case of one single wagon (neglecting inter-car coupling forces) and of multiple wagons interacting through the buffers and the couplers. A multi-body model of a single wagon...... and of a three-car assembly is introduced, paying particular attention to the nonlinear and nonsmooth modelling of the suspensions and of the inter-car coupling elements. Using this model, a numerical analysis of the steady-state solution reached after the negotiation of curve transition is presented......, it is shown that the coupling forces exchanged by the wagons significantly affect their dynamics in a curve, reducing the amplitude of vibration....

Predicting seizures in untreated temporal lobe epilepsy using point-process nonlinear models of heartbeat dynamics.

Science.gov (United States)

Valenza, G; Romigi, A; Citi, L; Placidi, F; Izzi, F; Albanese, M; Scilingo, E P; Marciani, M G; Duggento, A; Guerrisi, M; Toschi, N; Barbieri, R

2016-08-01

Symptoms of temporal lobe epilepsy (TLE) are frequently associated with autonomic dysregulation, whose underlying biological processes are thought to strongly contribute to sudden unexpected death in epilepsy (SUDEP). While abnormal cardiovascular patterns commonly occur during ictal events, putative patterns of autonomic cardiac effects during pre-ictal (PRE) periods (i.e. periods preceding seizures) are still unknown. In this study, we investigated TLE-related heart rate variability (HRV) through instantaneous, nonlinear estimates of cardiovascular oscillations during inter-ictal (INT) and PRE periods. ECG recordings from 12 patients with TLE were processed to extract standard HRV indices, as well as indices of instantaneous HRV complexity (dominant Lyapunov exponent and entropy) and higher-order statistics (bispectra) obtained through definition of inhomogeneous point-process nonlinear models, employing Volterra-Laguerre expansions of linear, quadratic, and cubic kernels. Experimental results demonstrate that the best INT vs. PRE classification performance (balanced accuracy: 73.91%) was achieved only when retaining the time-varying, nonlinear, and non-stationary structure of heartbeat dynamical features. The proposed approach opens novel important avenues in predicting ictal events using information gathered from cardiovascular signals exclusively.

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

Science.gov (United States)

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.

Parallel processors and nonlinear structural dynamics algorithms and software

Science.gov (United States)

Belytschko, Ted

1989-01-01

A nonlinear structural dynamics finite element program was developed to run on a shared memory multiprocessor with pipeline processors. The program, WHAMS, was used as a framework for this work. The program employs explicit time integration and has the capability to handle both the nonlinear material behavior and large displacement response of 3-D structures. The elasto-plastic material model uses an isotropic strain hardening law which is input as a piecewise linear function. Geometric nonlinearities are handled by a corotational formulation in which a coordinate system is embedded at the integration point of each element. Currently, the program has an element library consisting of a beam element based on Euler-Bernoulli theory and trianglar and quadrilateral plate element based on Mindlin theory.

Nonlinear analysis of dynamic signature

Science.gov (United States)

Rashidi, S.; Fallah, A.; Towhidkhah, F.

2013-12-01

Signature is a long trained motor skill resulting in well combination of segments like strokes and loops. It is a physical manifestation of complex motor processes. The problem, generally stated, is that how relative simplicity in behavior emerges from considerable complexity of perception-action system that produces behavior within an infinitely variable biomechanical and environmental context. To solve this problem, we present evidences which indicate that motor control dynamic in signing process is a chaotic process. This chaotic dynamic may explain a richer array of time series behavior in motor skill of signature. Nonlinear analysis is a powerful approach and suitable tool which seeks for characterizing dynamical systems through concepts such as fractal dimension and Lyapunov exponent. As a result, they can be analyzed in both horizontal and vertical for time series of position and velocity. We observed from the results that noninteger values for the correlation dimension indicates low dimensional deterministic dynamics. This result could be confirmed by using surrogate data tests. We have also used time series to calculate the largest Lyapunov exponent and obtain a positive value. These results constitute significant evidence that signature data are outcome of chaos in a nonlinear dynamical system of motor control.

Non-linear hybrid control oriented modelling of a digital displacement machine

DEFF Research Database (Denmark)

Pedersen, Niels Henrik; Johansen, Per; Andersen, Torben O.

2017-01-01

Proper feedback control of digital fluid power machines (Pressure, flow, torque or speed control) requires a control oriented model, from where the system dynamics can be analyzed, stability can be proven and design criteria can be specified. The development of control oriented models for hydraulic...... Digital Displacement Machines (DDM) is complicated due to non-smooth machine behavior, where the dynamics comprises both analog, digital and non-linear elements. For a full stroke operated DDM the power throughput is altered in discrete levels based on the ratio of activated pressure chambers....... In this paper, a control oriented hybrid model is established, which combines the continuous non-linear pressure chamber dynamics and the discrete shaft position dependent activation of the pressure chambers. The hybrid machine model is further extended to describe the dynamics of a Digital Fluid Power...

Modeling and nonlinear heading control for sailing yachts

DEFF Research Database (Denmark)

Xiao, Lin; Jouffroy, Jerome

2014-01-01

This paper presents a study on the development and testing of a model-based heading controller for a sailing yacht. Using Fossen’s compact notation for marine vehicles, we first describe a nonlinear four-degree-of-freedom (DOF) dynamic model for a sailing yacht, including roll. Our model also...

Modeling and nonlinear heading control for sailing yachts

DEFF Research Database (Denmark)

Xiao, Lin; Jouffroy, Jerome

2011-01-01

This paper presents a study on the development and testing of a model-based heading controller for a sailing yacht. Using Fossen's compact notation for marine vehicles, we first describe a nonlinear 4-DOF dynamic model for a sailing yacht, including roll. Starting from this model, we then design...

Neural-Based Compensation of Nonlinearities in an Airplane Longitudinal Model with Dynamic-Inversion Control

Directory of Open Access Journals (Sweden)

YanBin Liu

2017-01-01

Full Text Available The inversion design approach is a very useful tool for the complex multiple-input-multiple-output nonlinear systems to implement the decoupling control goal, such as the airplane model and spacecraft model. In this work, the flight control law is proposed using the neural-based inversion design method associated with the nonlinear compensation for a general longitudinal model of the airplane. First, the nonlinear mathematic model is converted to the equivalent linear model based on the feedback linearization theory. Then, the flight control law integrated with this inversion model is developed to stabilize the nonlinear system and relieve the coupling effect. Afterwards, the inversion control combined with the neural network and nonlinear portion is presented to improve the transient performance and attenuate the uncertain effects on both external disturbances and model errors. Finally, the simulation results demonstrate the effectiveness of this controller.

A Nonlinear Dynamic Subscale Model for Partially Resolved Numerical Simulation (PRNS)/Very Large Eddy Simulation (VLES) of Internal Non-Reacting Flows

Science.gov (United States)

Shih, Tsan-Hsing; Liu, nan-Suey

2010-01-01

A brief introduction of the temporal filter based partially resolved numerical simulation/very large eddy simulation approach (PRNS/VLES) and its distinct features are presented. A nonlinear dynamic subscale model and its advantages over the linear subscale eddy viscosity model are described. In addition, a guideline for conducting a PRNS/VLES simulation is provided. Results are presented for three turbulent internal flows. The first one is the turbulent pipe flow at low and high Reynolds numbers to illustrate the basic features of PRNS/VLES; the second one is the swirling turbulent flow in a LM6000 single injector to further demonstrate the differences in the calculated flow fields resulting from the nonlinear model versus the pure eddy viscosity model; the third one is a more complex turbulent flow generated in a single-element lean direct injection (LDI) combustor, the calculated result has demonstrated that the current PRNS/VLES approach is capable of capturing the dynamically important, unsteady turbulent structures while using a relatively coarse grid.

Nonlinear dynamics non-integrable systems and chaotic dynamics

CERN Document Server

Borisov, Alexander

2017-01-01

This monograph reviews advanced topics in the area of nonlinear dynamics. Starting with theory of integrable systems – including methods to find and verify integrability – the remainder of the book is devoted to non-integrable systems with an emphasis on dynamical chaos. Topics include structural stability, mechanisms of emergence of irreversible behaviour in deterministic systems as well as chaotisation occurring in dissipative systems.

Nonlinear and Complex Dynamics in Real Systems

OpenAIRE

William Barnett; Apostolos Serletis; Demitre Serletis

2005-01-01

This paper was produced for the El-Naschie Symposium on Nonlinear Dynamics in Shanghai in December 2005. In this paper we provide a review of the literature with respect to fluctuations in real systems and chaos. In doing so, we contrast the order and organization hypothesis of real systems with nonlinear chaotic dynamics and discuss some techniques used in distinguishing between stochastic and deterministic behavior. Moreover, we look at the issue of where and when the ideas of chaos could p...

Reproducing the nonlinear dynamic behavior of a structured beam with a generalized continuum model

Science.gov (United States)

Vila, J.; Fernández-Sáez, J.; Zaera, R.

2018-04-01

In this paper we study the coupled axial-transverse nonlinear vibrations of a kind of one dimensional structured solids by application of the so called Inertia Gradient Nonlinear continuum model. To show the accuracy of this axiomatic model, previously proposed by the authors, its predictions are compared with numeric results from a previously defined finite discrete chain of lumped masses and springs, for several number of particles. A continualization of the discrete model equations based on Taylor series allowed us to set equivalent values of the mechanical properties in both discrete and axiomatic continuum models. Contrary to the classical continuum model, the inertia gradient nonlinear continuum model used herein is able to capture scale effects, which arise for modes in which the wavelength is comparable to the characteristic distance of the structured solid. The main conclusion of the work is that the proposed generalized continuum model captures the scale effects in both linear and nonlinear regimes, reproducing the behavior of the 1D nonlinear discrete model adequately.

Robust flight control using incremental nonlinear dynamic inversion and angular acceleration prediction

NARCIS (Netherlands)

Sieberling, S.; Chu, Q.P.; Mulder, J.A.

2010-01-01

This paper presents a flight control strategy based on nonlinear dynamic inversion. The approach presented, called incremental nonlinear dynamic inversion, uses properties of general mechanical systems and nonlinear dynamic inversion by feeding back angular accelerations. Theoretically, feedback of

On the Boundary between Nonlinear Jump Phenomenon and Linear Response of Hypoid Gear Dynamics

Directory of Open Access Journals (Sweden)

Jun Wang

2011-01-01

Full Text Available A nonlinear time-varying (NLTV dynamic model of a hypoid gear pair system with time-dependent mesh point, line-of-action vector, mesh stiffness, mesh damping, and backlash nonlinearity is formulated to analyze the transitional phase between nonlinear jump phenomenon and linear response. It is found that the classical jump discontinuity will occur if the dynamic mesh force exceeds the mean value of tooth mesh force. On the other hand, the propensity for the gear response to jump disappears when the dynamic mesh force is lower than the mean mesh force. Furthermore, the dynamic analysis is able to distinguish the specific tooth impact types from analyzing the behaviors of the dynamic mesh force. The proposed theory is general and also applicable to high-speed spur, helical and spiral bevel gears even though those types of gears are not the primary focus of this paper.

Nonlinear dynamics: Challenges and perspectives

Indian Academy of Sciences (India)

fields such as economics, social dynamics and so on [6–10]. These nonlinear ..... developing all-optical computers in homogeneous bulk media such as pho- ... suggestions have been given to develop effective chaos-based cryptographic.

Bubble nonlinear dynamics and stimulated scattering process

Science.gov (United States)

Jie, Shi; De-Sen, Yang; Sheng-Guo, Shi; Bo, Hu; Hao-Yang, Zhang; Shi-Yong, Hu

2016-02-01

A complete understanding of the bubble dynamics is deemed necessary in order to achieve their full potential applications in industry and medicine. For this purpose it is first needed to expand our knowledge of a single bubble behavior under different possible conditions including the frequency and pressure variations of the sound field. In addition, stimulated scattering of sound on a bubble is a special effect in sound field, and its characteristics are associated with bubble oscillation mode. A bubble in liquid can be considered as a representative example of nonlinear dynamical system theory with its resonance, and its dynamics characteristics can be described by the Keller-Miksis equation. The nonlinear dynamics of an acoustically excited gas bubble in water is investigated by using theoretical and numerical analysis methods. Our results show its strongly nonlinear behavior with respect to the pressure amplitude and excitation frequency as the control parameters, and give an intuitive insight into stimulated sound scattering on a bubble. It is seen that the stimulated sound scattering is different from common dynamical behaviors, such as bifurcation and chaos, which is the result of the nonlinear resonance of a bubble under the excitation of a high amplitude acoustic sound wave essentially. The numerical analysis results show that the threshold of stimulated sound scattering is smaller than those of bifurcation and chaos in the common condition. Project supported by the Program for Changjiang Scholars and Innovative Research Team in University, China (Grant No. IRT1228) and the Young Scientists Fund of the National Natural Science Foundation of China (Grant Nos. 11204050 and 11204049).

Complex motion in nonlinear-map model of elevators in energy-saving traffic

International Nuclear Information System (INIS)

Nagatani, Takashi

2011-01-01

We have studied the dynamic behavior and dynamic transitions of elevators in a system for reducing energy consumption. We present a nonlinear-map model for the dynamics of M elevators. The motion of elevators depends on the loading parameter and their number M. The dependence of the fixed points on the loading parameter is derived. The dynamic transitions occur at 2(M-1) stages with increasing the value of loading parameter. At the dynamic transition point, the motion of elevators changes from a stable state to an unstable state and vice versa. The elevators display periodic motions with various periods in the unstable state. In the unstable state, the number of riding passengers fluctuates in a complex manner over various trips. - Highlights: → We propose the nonlinear-map model in energy-saving traffic of elevators. → We study the dynamical behavior and dynamical transitions in the system of elevators. → We derive the fixed point of the nonlinear map analytically. → We clarify the dependence of the motion on the loading parameter and the number.

Complex motion in nonlinear-map model of elevators in energy-saving traffic

Energy Technology Data Exchange (ETDEWEB)

Nagatani, Takashi, E-mail: tmtnaga@ipc.shizuoka.ac.j [Department of Mechanical Engineering, Division of Thermal Science, Shizuoka University, Hamamatsu 432-8561 (Japan)

2011-05-16

We have studied the dynamic behavior and dynamic transitions of elevators in a system for reducing energy consumption. We present a nonlinear-map model for the dynamics of M elevators. The motion of elevators depends on the loading parameter and their number M. The dependence of the fixed points on the loading parameter is derived. The dynamic transitions occur at 2(M-1) stages with increasing the value of loading parameter. At the dynamic transition point, the motion of elevators changes from a stable state to an unstable state and vice versa. The elevators display periodic motions with various periods in the unstable state. In the unstable state, the number of riding passengers fluctuates in a complex manner over various trips. - Highlights: We propose the nonlinear-map model in energy-saving traffic of elevators. We study the dynamical behavior and dynamical transitions in the system of elevators. We derive the fixed point of the nonlinear map analytically. We clarify the dependence of the motion on the loading parameter and the number.

Nonlinear absorption dynamics using field-induced surface hopping: zinc porphyrin in water.

Science.gov (United States)

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.

The application of nonlinear dynamics in the study of ferroelectric materials

International Nuclear Information System (INIS)

Blochwitz, S.; Habel, R.; Diestelhorst, M.; Beige, H.

1996-01-01

It is well known that the structural phase transitions in ferroelectric materials are connected with strong nonlinear properties. So we can expect all features of nonlinear dynamical systems such as period-doubling cascades and chaos in a dynamical system that contains ferroelectric materials. Therefore we can apply nonlinear dynamics to these ferroelectric materials and we are doing it in two directions: (i) We study the structural phase transitions by analyzing the large signal behaviour with means of nonlinear dynamics. (ii) We control the chaotic behaviour of the system with the method proposed by Ott, Grebogi and Yorke. (authors)

On-line supercapacitor dynamic models for energy conversion and management

International Nuclear Information System (INIS)

Wu, C.H.; Hung, Y.H.; Hong, C.W.

2012-01-01

Highlights: ► On-line supercapacitor dynamic models are derived from time and frequency domains. ► Equivalent circuits with an ANN identifier are derived for nonlinear effects. ► Nonlinear effects include environmental temperature and operating voltage. ► Supercapacitor models can achieve both system fidelity and computation efficiency. - Abstract: This paper develops on-line nonlinear dynamic models of electrochemical supercapacitors which are for energy conversion and management. Based on the theory of electrochemical impedance spectroscopy, extensive alternative current impedance tests have been conducted to investigate the frequency-domain dynamics of these supercapacitors. A Nyquist diagram is plotted to help establish an equivalent electric circuit, which is regarded as the first-phase linear model. Two performance-influencing factors, environmental temperature and operating voltage, are considered as nonlinear effects. The nonlinear relationships among parameters of the capacitances and resistances in the first-phase model are established by a multi-layer artificial neural network. The neural parameters are trained using a back-propagation algorithm by feeding the experimental data bank. Combining the first-phase model and the on-line neural “parameter identifier”, the algorithm produces an on-line nonlinear dynamic model. Simulation results have proved that this proposed model is able to achieve both system fidelity and computational efficiency.

Time Domain Modeling and Simulation of Nonlinear Slender Viscoelastic Beams Associating Cosserat Theory and a Fractional Derivative Model

Directory of Open Access Journals (Sweden)

Adailton S. Borges

Full Text Available Abstract A broad class of engineering systems can be satisfactory modeled under the assumptions of small deformations and linear material properties. However, many mechanical systems used in modern applications, like structural elements typical of aerospace and petroleum industries, have been characterized by increased slenderness and high static and dynamic loads. In such situations, it becomes indispensable to consider the nonlinear geometric effects and/or material nonlinear behavior. At the same time, in many cases involving dynamic loads, there comes the need for attenuation of vibration levels. In this context, this paper describes the development and validation of numerical models of viscoelastic slender beam-like structures undergoing large displacements. The numerical approach is based on the combination of the nonlinear Cosserat beam theory and a viscoelastic model based on Fractional Derivatives. Such combination enables to derive nonlinear equations of motion that, upon finite element discretization, can be used for predicting the dynamic behavior of the structure in the time domain, accounting for geometric nonlinearity and viscoelastic damping. The modeling methodology is illustrated and validated by numerical simulations, the results of which are compared to others available in the literature.

Ultrahigh energy neutrinos and nonlinear QCD dynamics

International Nuclear Information System (INIS)

Machado, Magno V.T.

2004-01-01

The ultrahigh energy neutrino-nucleon cross sections are computed taking into account different phenomenological implementations of the nonlinear QCD dynamics. Based on the color dipole framework, the results for the saturation model supplemented by the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution as well as for the Balitskii-Fadin-Kuraev-Lipatov (BFKL) formalism in the geometric scaling regime are presented. They are contrasted with recent calculations using next-to-leading order DGLAP and unified BFKL-DGLAP formalisms

Nonlinear Dynamics of Silicon Nanowire Resonator Considering Nonlocal Effect.

Science.gov (United States)

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.

Bifurcation methods of dynamical systems for handling nonlinear ...

Indian Academy of Sciences (India)

physics pp. 863–868. Bifurcation methods of dynamical systems for handling nonlinear wave equations. DAHE FENG and JIBIN LI. Center for Nonlinear Science Studies, School of Science, Kunming University of Science and Technology .... (b) It can be shown from (15) and (18) that the balance between the weak nonlinear.

Nonlinear dynamic macromodeling techniques for audio systems

Science.gov (United States)

Ogrodzki, Jan; Bieńkowski, Piotr

2015-09-01

This paper develops a modelling method and a models identification technique for the nonlinear dynamic audio systems. Identification is performed by means of a behavioral approach based on a polynomial approximation. This approach makes use of Discrete Fourier Transform and Harmonic Balance Method. A model of an audio system is first created and identified and then it is simulated in real time using an algorithm of low computational complexity. The algorithm consists in real time emulation of the system response rather than in simulation of the system itself. The proposed software is written in Python language using object oriented programming techniques. The code is optimized for a multithreads environment.

Three-dimensional finite element nonlinear dynamic analysis of pile groups for lateral transient and seismic excitations

International Nuclear Information System (INIS)

Maheshwari, B.K.; Truman, K.Z.; El Naggar, M.H.; Gould, P.L.

2004-01-01

The effects of material nonlinearity of soil and separation at the soil-pile interface on the dynamic behaviour of a single pile and pile groups are investigated. An advanced plasticity-based soil model, hierarchical single surface (HiSS), is incorporated in the finite element formulation. To simulate radiation effects, proper boundary conditions are used. The model and algorithm are verified with analytical results that are available for elastic and elastoplastic soil models. Analyses are performed for seismic excitation and for the load applied on the pile cap. For seismic analysis, both harmonic and transient excitations are considered. For loading on the pile cap, dynamic stiffness of the soil-pile system is derived and the effect of nonlinearity is investigated. The effects of spacing between piles are investigated, and it was found that the effect of soil nonlinearity on the seismic response is very much dependent on the frequency of excitation. For the loading on a pile cap, the nonlinearity increases the response for most of the frequencies of excitation while decreasing the dynamic stiffness of the soil-pile system. (author)

Nonlinear dynamics aspects of modern storage rings

International Nuclear Information System (INIS)

Helleman, R.H.G.; Kheifets, S.A.

1986-01-01

The authors try to address the following two questions: a. Why should accelerator physicists to be interested in the recent, sometimes abstract, developments in Nonlinear Dynamics, a field which will recently was mainly studied by mathematicians, theoretical physicists and astronomers? That such an interest to some extent already exists is apparent from the fact that many accelerator physicists attended this School and several analogous meetings in the past. b. Why should researchers from nonlinear dynamics be interested in modern Storage Rings which are largely designed and built by experimental physicists and engineers? At the moment few 'nonlinear scientists' work on storage rings (or in the field of accelerator physics). It is a hopeful sign that many (more) attended this School

A quasi-sequential parameter estimation for nonlinear dynamic systems based on multiple data profiles

Energy Technology Data Exchange (ETDEWEB)

Zhao, Chao [FuZhou University, FuZhou (China); Vu, Quoc Dong; Li, Pu [Ilmenau University of Technology, Ilmenau (Germany)

2013-02-15

A three-stage computation framework for solving parameter estimation problems for dynamic systems with multiple data profiles is developed. The dynamic parameter estimation problem is transformed into a nonlinear programming (NLP) problem by using collocation on finite elements. The model parameters to be estimated are treated in the upper stage by solving an NLP problem. The middle stage consists of multiple NLP problems nested in the upper stage, representing the data reconciliation step for each data profile. We use the quasi-sequential dynamic optimization approach to solve these problems. In the lower stage, the state variables and their gradients are evaluated through ntegrating the model equations. Since the second-order derivatives are not required in the computation framework this proposed method will be efficient for solving nonlinear dynamic parameter estimation problems. The computational results obtained on a parameter estimation problem for two CSTR models demonstrate the effectiveness of the proposed approach.

A quasi-sequential parameter estimation for nonlinear dynamic systems based on multiple data profiles

International Nuclear Information System (INIS)

Zhao, Chao; Vu, Quoc Dong; Li, Pu

2013-01-01

A three-stage computation framework for solving parameter estimation problems for dynamic systems with multiple data profiles is developed. The dynamic parameter estimation problem is transformed into a nonlinear programming (NLP) problem by using collocation on finite elements. The model parameters to be estimated are treated in the upper stage by solving an NLP problem. The middle stage consists of multiple NLP problems nested in the upper stage, representing the data reconciliation step for each data profile. We use the quasi-sequential dynamic optimization approach to solve these problems. In the lower stage, the state variables and their gradients are evaluated through ntegrating the model equations. Since the second-order derivatives are not required in the computation framework this proposed method will be efficient for solving nonlinear dynamic parameter estimation problems. The computational results obtained on a parameter estimation problem for two CSTR models demonstrate the effectiveness of the proposed approach

Influence of forced respiration on nonlinear dynamics in heart rate variability

DEFF Research Database (Denmark)

Kanters, J K; Højgaard, M V; Agner, E

1997-01-01

Although it is doubtful whether the normal sinus rhythm can be described as low-dimensional chaos, there is evidence for inherent nonlinear dynamics and determinism in time series of consecutive R-R intervals. However, the physiological origin for these nonlinearities is unknown. The aim...... with a metronome set to 12 min(-1). Nonlinear dynamics were measured as the correlation dimension and the nonlinear prediction error. Complexity expressed as correlation dimension was unchanged from normal respiration, 9.1 +/- 0.5, compared with forced respiration, 9.3 +/- 0.6. Also, nonlinear determinism...... expressed as the nonlinear prediction error did not differ between spontaneous respiration, 32.3 +/- 3.4 ms, and forced respiration, 31.9 +/- 5.7. It is concluded that the origin of the nonlinear dynamics in heart rate variability is not a nonlinear input from the respiration into the cardiovascular...

Nonlinear dynamic characterization of two-dimensional materials

NARCIS (Netherlands)

Davidovikj, D.; Alijani, F.; Cartamil Bueno, S.J.; van der Zant, H.S.J.; Amabili, M.; Steeneken, P.G.

2017-01-01

Owing to their atomic-scale thickness, the resonances of two-dimensional (2D) material membranes show signatures of nonlinearities at forces of only a few picoNewtons. Although the linear dynamics of membranes is well understood, the exact relation between the nonlinear response and the resonator's

Nonlinear dynamic behaviors of an optically injected vertical-cavity surface-emitting laser

International Nuclear Information System (INIS)