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

Nonlinear chaos-dynamical approach to analysis of atmospheric ...

Indian Academy of Sciences (India)

false nearest neighbors, Lyapunov's exponents, surrogate data, nonlinear prediction ... Chaotic dynamics; time series of the 222Rn concentration; universal complex ... tems is due to a number of applications, including the ..... Computer Engineering. ... Ternovsky,Quantum Systems in Physics, Chemistry, and. Biology, pp.

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

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

Science.gov (United States)

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

2017-12-19

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

Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear partial differential evolution equations of dynamical systems

Institute of Scientific and Technical Information of China (English)

2008-01-01

Using functional derivative technique in quantum field theory, the algebraic dy-namics approach for solution of ordinary differential evolution equations was gen-eralized to treat partial differential evolution equations. The partial differential evo-lution equations were lifted to the corresponding functional partial differential equations in functional space by introducing the time translation operator. The functional partial differential evolution equations were solved by algebraic dynam-ics. The algebraic dynamics solutions are analytical in Taylor series in terms of both initial functions and time. Based on the exact analytical solutions, a new nu-merical algorithm—algebraic dynamics algorithm was proposed for partial differ-ential evolution equations. The difficulty of and the way out for the algorithm were discussed. The application of the approach to and computer numerical experi-ments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution equations both analytically and numerically.

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)

On the Complete Integrability of Nonlinear Dynamical Systems on Discrete Manifolds within the Gradient-Holonomic Approach

International Nuclear Information System (INIS)

Prykarpatsky, Yarema A.; Bogolubov, Nikolai N. Jr.; Prykarpatsky, Anatoliy K.; Samoylenko, Valeriy H.

2010-12-01

A gradient-holonomic approach for the Lax type integrability analysis of differential-discrete dynamical systems is devised. The asymptotical solutions to the related Lax equation are studied and the related gradient identity is stated. The integrability of a discrete nonlinear Schroedinger type dynamical system is treated in detail. The integrability of a generalized Riemann type discrete hydrodynamical system is discussed. (author)

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.

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...

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.  

Flow Equation Approach to the Statistics of Nonlinear Dynamical Systems

Science.gov (United States)

Marston, J. B.; Hastings, M. B.

2005-03-01

The probability distribution function of non-linear dynamical systems is governed by a linear framework that resembles quantum many-body theory, in which stochastic forcing and/or averaging over initial conditions play the role of non-zero . Besides the well-known Fokker-Planck approach, there is a related Hopf functional methodootnotetextUriel Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press, 1995) chapter 9.5.; in both formalisms, zero modes of linear operators describe the stationary non-equilibrium statistics. To access the statistics, we investigate the method of continuous unitary transformationsootnotetextS. D. Glazek and K. G. Wilson, Phys. Rev. D 48, 5863 (1993); Phys. Rev. D 49, 4214 (1994). (also known as the flow equation approachootnotetextF. Wegner, Ann. Phys. 3, 77 (1994).), suitably generalized to the diagonalization of non-Hermitian matrices. Comparison to the more traditional cumulant expansion method is illustrated with low-dimensional attractors. The treatment of high-dimensional dynamical systems is also discussed.

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)

Quantifying non-linear dynamics of mass-springs in series oscillators via asymptotic approach

Science.gov (United States)

Starosta, Roman; Sypniewska-Kamińska, Grażyna; Awrejcewicz, Jan

2017-05-01

Dynamical regular response of an oscillator with two serially connected springs with nonlinear characteristics of cubic type and governed by a set of differential-algebraic equations (DAEs) is studied. The classical approach of the multiple scales method (MSM) in time domain has been employed and appropriately modified to solve the governing DAEs of two systems, i.e. with one- and two degrees-of-freedom. The approximate analytical solutions have been verified by numerical simulations.

Nonlinear approaches in engineering applications applied mechanics, vibration control, and numerical analysis

CERN Document Server

Jazar, Reza

2015-01-01

This book focuses on the latest applications of nonlinear approaches in different disciplines of engineering. For each selected topic, detailed concept development, derivations, and relevant knowledge are provided for the convenience of the readers. The topics range from dynamic systems and control to optimal approaches in nonlinear dynamics. The volume includes invited chapters from world class experts in the field. The selected topics are of great interest in the fields of engineering and physics and this book is ideal for engineers and researchers working in a broad range of practical topics and approaches. This book also: ·         Explores the most up-to-date applications and underlying principles of nonlinear approaches to problems in engineering and physics, including sections on analytic nonlinearity and practical nonlinearity ·         Enlightens readers to the conceptual significance of nonlinear approaches with examples of applications in scientific and engineering problems from v...

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

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)

Minimax terminal approach problem in two-level hierarchical nonlinear discrete-time dynamical system

Energy Technology Data Exchange (ETDEWEB)

Shorikov, A. F., E-mail: afshorikov@mail.ru [Ural Federal University, 19 S. Mira, Ekaterinburg, 620002, Russia Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences, 16 S. Kovalevskaya, Ekaterinburg, 620990 (Russian Federation)

2015-11-30

We consider a discrete–time dynamical system consisting of three controllable objects. The motions of all objects are given by the corresponding vector nonlinear or linear discrete–time recurrent vector relations, and control system for its has two levels: basic (first or I level) that is dominating and subordinate level (second or II level) and both have different criterions of functioning and united a priori by determined informational and control connections defined in advance. For the dynamical system in question, we propose a mathematical formalization in the form of solving a multistep problem of two-level hierarchical minimax program control over the terminal approach process with incomplete information and give a general scheme for its solving.

Dynamics of elliptic breathers in saturable nonlinear media with linear anisotropy

International Nuclear Information System (INIS)

Liang, Guo; Guo, Qi; Shou, Qian; Ren, Zhanmei

2014-01-01

We have introduced a class of dynamic elliptic breathers in saturable nonlinear media with linear anisotropy. Two kinds of evolution behavior for the dynamic breathers, rotations and molecule-like librations, are both predicted by the variational approach, and confirmed in numerical simulations. The dynamic elliptic breathers can rotate even though they have no initial orbital angular momentum (OAM). As the media are linear anisotropic, OAM is no longer conserved, and hence the angular velocity is not constant but a periodic function of the propagation distance. When the linear anisotropy is large enough, the dynamic elliptic breathers librate like molecules. The dynamic elliptic breathers are present in media with not only saturable nonlinearity but also nonlocal nonlinearity; indeed, they are universal in nonlinear media with linear anisotropy. (paper)

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.

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.

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.

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 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 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.

A nonlinear dynamical system approach for the yielding behaviour of a viscoplastic material.

Science.gov (United States)

Burghelea, Teodor; Moyers-Gonzalez, Miguel; Sainudiin, Raazesh

2017-03-08

A nonlinear dynamical system model that approximates a microscopic Gibbs field model for the yielding of a viscoplastic material subjected to varying external stresses recently reported in R. Sainudiin, M. Moyers-Gonzalez and T. Burghelea, Soft Matter, 2015, 11(27), 5531-5545 is presented. The predictions of the model are in fair agreement with microscopic simulations and are in very good agreement with the micro-structural semi-empirical model reported in A. M. V. Putz and T. I. Burghelea, Rheol. Acta, 2009, 48, 673-689. With only two internal parameters, the nonlinear dynamical system model captures several key features of the solid-fluid transition observed in experiments: the effect of the interactions between microscopic constituents on the yield point, the abruptness of solid-fluid transition and the emergence of a hysteresis of the micro-structural states upon increasing/decreasing external forces. The scaling behaviour of the magnitude of the hysteresis with the degree of the steadiness of the flow is consistent with previous experimental observations. Finally, the practical usefulness of the approach is demonstrated by fitting a rheological data set measured with an elasto-viscoplastic material.

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.

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 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.

Gradient-based optimization in nonlinear structural dynamics

DEFF Research Database (Denmark)

Dou, Suguang

The intrinsic nonlinearity of mechanical structures can give rise to rich nonlinear dynamics. Recently, nonlinear dynamics of micro-mechanical structures have contributed to developing new Micro-Electro-Mechanical Systems (MEMS), for example, atomic force microscope, passive frequency divider......, frequency stabilization, and disk resonator gyroscope. For advanced design of these structures, it is of considerable value to extend current optimization in linear structural dynamics into nonlinear structural dynamics. In this thesis, we present a framework for modelling, analysis, characterization......, and optimization of nonlinear structural dynamics. In the modelling, nonlinear finite elements are used. In the analysis, nonlinear frequency response and nonlinear normal modes are calculated based on a harmonic balance method with higher-order harmonics. In the characterization, nonlinear modal coupling...

Structural optimization for nonlinear dynamic response

DEFF Research Database (Denmark)

Dou, Suguang; Strachan, B. Scott; Shaw, Steven W.

2015-01-01

by a single vibrating mode, or by a pair of internally resonant modes. The approach combines techniques from nonlinear dynamics, computational mechanics and optimization, and it allows one to relate the geometric and material properties of structural elements to terms in the normal form for a given resonance......Much is known about the nonlinear resonant response of mechanical systems, but methods for the systematic design of structures that optimize aspects of these responses have received little attention. Progress in this area is particularly important in the area of micro-systems, where nonlinear...... resonant behaviour is being used for a variety of applications in sensing and signal conditioning. In this work, we describe a computational method that provides a systematic means for manipulating and optimizing features of nonlinear resonant responses of mechanical structures that are described...

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.

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 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)

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 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).

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

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...

A nonlinear optimal control approach for chaotic finance dynamics

Science.gov (United States)

Rigatos, G.; Siano, P.; Loia, V.; Tommasetti, A.; Troisi, O.

2017-11-01

A new nonlinear optimal control approach is proposed for stabilization of the dynamics of a chaotic finance model. The dynamic model of the financial system, which expresses interaction between the interest rate, the investment demand, the price exponent and the profit margin, undergoes approximate linearization round local operating points. These local equilibria are defined at each iteration of the control algorithm and consist of the present value of the systems state vector and the last value of the control inputs vector that was exerted on it. The approximate linearization makes use of Taylor series expansion and of the computation of the associated Jacobian matrices. The truncation of higher order terms in the Taylor series expansion is considered to be a modelling error that is compensated by the robustness of the control loop. As the control algorithm runs, the temporary equilibrium is shifted towards the reference trajectory and finally converges to it. The control method needs to compute an H-infinity feedback control law at each iteration, and requires the repetitive solution of an algebraic Riccati equation. Through Lyapunov stability analysis it is shown that an H-infinity tracking performance criterion holds for the control loop. This implies elevated robustness against model approximations and external perturbations. Moreover, under moderate conditions the global asymptotic stability of the control loop is proven.

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 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 dynamics and predictability in the atmospheric sciences

Science.gov (United States)

Ghil, M.; Kimoto, M.; Neelin, J. D.

1991-01-01

Systematic applications of nonlinear dynamics to studies of the atmosphere and climate are reviewed for the period 1987-1990. Problems discussed include paleoclimatic applications, low-frequency atmospheric variability, and interannual variability of the ocean-atmosphere system. Emphasis is placed on applications of the successive bifurcation approach and the ergodic theory of dynamical systems to understanding and prediction of intraseasonal, interannual, and Quaternary climate changes.

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.

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

Science.gov (United States)

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

2018-05-01

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

Nonlinear 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

An Improved Dynamic Programming Decomposition Approach for Network Revenue Management

OpenAIRE

Dan Zhang

2011-01-01

We consider a nonlinear nonseparable functional approximation to the value function of a dynamic programming formulation for the network revenue management (RM) problem with customer choice. We propose a simultaneous dynamic programming approach to solve the resulting problem, which is a nonlinear optimization problem with nonlinear constraints. We show that our approximation leads to a tighter upper bound on optimal expected revenue than some known bounds in the literature. Our approach can ...

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

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 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

Machine learning control taming nonlinear dynamics and turbulence

CERN Document Server

Duriez, Thomas; Noack, Bernd R

2017-01-01

This is the first book on a generally applicable control strategy for turbulence and other complex nonlinear systems. The approach of the book employs powerful methods of machine learning for optimal nonlinear control laws. This machine learning control (MLC) is motivated and detailed in Chapters 1 and 2. In Chapter 3, methods of linear control theory are reviewed. In Chapter 4, MLC is shown to reproduce known optimal control laws for linear dynamics (LQR, LQG). In Chapter 5, MLC detects and exploits a strongly nonlinear actuation mechanism of a low-dimensional dynamical system when linear control methods are shown to fail. Experimental control demonstrations from a laminar shear-layer to turbulent boundary-layers are reviewed in Chapter 6, followed by general good practices for experiments in Chapter 7. The book concludes with an outlook on the vast future applications of MLC in Chapter 8. Matlab codes are provided for easy reproducibility of the presented results. The book includes interviews with leading r...

Streamflow disaggregation: a nonlinear deterministic approach

Directory of Open Access Journals (Sweden)

B. Sivakumar

2004-01-01

Full Text Available This study introduces a nonlinear deterministic approach for streamflow disaggregation. According to this approach, the streamflow transformation process from one scale to another is treated as a nonlinear deterministic process, rather than a stochastic process as generally assumed. The approach follows two important steps: (1 reconstruction of the scalar (streamflow series in a multi-dimensional phase-space for representing the transformation dynamics; and (2 use of a local approximation (nearest neighbor method for disaggregation. The approach is employed for streamflow disaggregation in the Mississippi River basin, USA. Data of successively doubled resolutions between daily and 16 days (i.e. daily, 2-day, 4-day, 8-day, and 16-day are studied, and disaggregations are attempted only between successive resolutions (i.e. 2-day to daily, 4-day to 2-day, 8-day to 4-day, and 16-day to 8-day. Comparisons between the disaggregated values and the actual values reveal excellent agreements for all the cases studied, indicating the suitability of the approach for streamflow disaggregation. A further insight into the results reveals that the best results are, in general, achieved for low embedding dimensions (2 or 3 and small number of neighbors (less than 50, suggesting possible presence of nonlinear determinism in the underlying transformation process. A decrease in accuracy with increasing disaggregation scale is also observed, a possible implication of the existence of a scaling regime in streamflow.

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 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

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.

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.

Visual Analysis of Nonlinear Dynamical Systems: Chaos, Fractals, Self-Similarity and the Limits of Prediction

Directory of Open Access Journals (Sweden)

Geoff Boeing

2016-11-01

Full Text Available Nearly all nontrivial real-world systems are nonlinear dynamical systems. Chaos describes certain nonlinear dynamical systems that have a very sensitive dependence on initial conditions. Chaotic systems are always deterministic and may be very simple, yet they produce completely unpredictable and divergent behavior. Systems of nonlinear equations are difficult to solve analytically, and scientists have relied heavily on visual and qualitative approaches to discover and analyze the dynamics of nonlinearity. Indeed, few fields have drawn as heavily from visualization methods for their seminal innovations: from strange attractors, to bifurcation diagrams, to cobweb plots, to phase diagrams and embedding. Although the social sciences are increasingly studying these types of systems, seminal concepts remain murky or loosely adopted. This article has three aims. First, it argues for several visualization methods to critically analyze and understand the behavior of nonlinear dynamical systems. Second, it uses these visualizations to introduce the foundations of nonlinear dynamics, chaos, fractals, self-similarity and the limits of prediction. Finally, it presents Pynamical, an open-source Python package to easily visualize and explore nonlinear dynamical systems’ behavior.

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

A New Approach for Studying Nonlinear Dynamic Response of a Thin Plate with Internal Resonance in a Fractional Viscoelastic Medium

Directory of Open Access Journals (Sweden)

Yury A. Rossikhin

2015-01-01

Full Text Available In the previous analysis, the dynamic behaviour of a nonlinear plate embedded into a fractional derivative viscoelastic medium has been studied by the method of multiple time scales under the conditions of the internal resonances two-to-one and one-to-one, as well as the internal combinational resonances for the case when the linear parts of nonlinear equations of motion occur to be coupled. A new approach proposed in this paper allows one to uncouple the linear parts of equations of motion of the plate, while the same method, the method of multiple time scales, has been utilized for solving nonlinear equations. The influence of viscosity on the energy exchange mechanism between interacting nonlinear modes has been analyzed. It has been shown that for some internal resonances there exist such particular cases when it is possible to obtain two first integrals, namely, the energy integral and the stream function, which allows one to reduce the problem to the calculation of elliptic integrals. The new approach enables one to solve the problems of vibrations of thin bodies more efficiently.

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.)

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...

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.

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.

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

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...

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.

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...

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...

Nonlinear structural mechanics theory, dynamical phenomena and modeling

CERN Document Server

Lacarbonara, Walter

2013-01-01

Nonlinear Structural Mechanics: Theory, Dynamical Phenomena and Modeling offers a concise, coherent presentation of the theoretical framework of nonlinear structural mechanics, computational methods, applications, parametric investigations of nonlinear phenomena and their mechanical interpretation towards design. The theoretical and computational tools that enable the formulation, solution, and interpretation of nonlinear structures are presented in a systematic fashion so as to gradually attain an increasing level of complexity of structural behaviors, under the prevailing assumptions on the geometry of deformation, the constitutive aspects and the loading scenarios. Readers will find a treatment of the foundations of nonlinear structural mechanics towards advanced reduced models, unified with modern computational tools in the framework of the prominent nonlinear structural dynamic phenomena while tackling both the mathematical and applied sciences. Nonlinear Structural Mechanics: Theory, Dynamical Phenomena...

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.

Nonlinear dynamic soil-structure interaction in earthquake engineering

International Nuclear Information System (INIS)

Nieto-Ferro, Alex

2013-01-01

The present work addresses a computational methodology to solve dynamic problems coupling time and Laplace domain discretizations within a domain decomposition approach. In particular, the proposed methodology aims at meeting the industrial need of performing more accurate seismic risk assessments by accounting for three-dimensional dynamic soil-structure interaction (DSSI) in nonlinear analysis. Two subdomains are considered in this problem. On the one hand, the linear and unbounded domain of soil which is modelled by an impedance operator computed in the Laplace domain using a Boundary Element (BE) method; and, on the other hand, the superstructure which refers not only to the structure and its foundations but also to a region of soil that possibly exhibits nonlinear behaviour. The latter sub-domain is formulated in the time domain and discretized using a Finite Element (FE) method. In this framework, the DSSI forces are expressed as a time convolution integral whose kernel is the inverse Laplace transform of the soil impedance matrix. In order to evaluate this convolution in the time domain by means of the soil impedance matrix (available in the Laplace domain), a Convolution Quadrature-based approach called the Hybrid Laplace-Time domain Approach (HLTA), is thus introduced. Its numerical stability when coupled to Newmark time integration schemes is subsequently investigated through several numerical examples of DSSI applications in linear and nonlinear analyses. The HLTA is finally tested on a more complex numerical model, closer to that of an industrial seismic application, and good results are obtained when compared to the reference solutions. (author)

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.

Reconfigurable Flight Control Using Nonlinear Dynamic Inversion with a Special Accelerometer Implementation

Science.gov (United States)

Bacon, Barton J.; Ostroff, Aaron J.

2000-01-01

This paper presents an approach to on-line control design for aircraft that have suffered either actuator failure, missing effector surfaces, surface damage, or any combination. The approach is based on a modified version of nonlinear dynamic inversion. The approach does not require a model of the baseline vehicle (effectors at zero deflection), but does require feedback of accelerations and effector positions. Implementation issues are addressed and the method is demonstrated on an advanced tailless aircraft. An experimental simulation analysis tool is used to directly evaluate the nonlinear system's stability robustness.

Asymptotic approach for the nonlinear equatorial long wave interactions

International Nuclear Information System (INIS)

Ramirez Gutierrez, Enver; Silva Dias, Pedro L; Raupp, Carlos

2011-01-01

In the present work we use an asymptotic approach to obtain the long wave equations. The shallow water equation is put as a function of an external parameter that is a measure of both the spatial scales anisotropy and the fast to slow time ratio. The values given to the external parameters are consistent with those computed using typical values of the perturbations in tropical dynamics. Asymptotically, the model converge toward the long wave model. Thus, it is possible to go toward the long wave approximation through intermediate realizable states. With this approach, the resonant nonlinear wave interactions are studied. To simplify, the reduced dynamics of a single resonant triad is used for some selected equatorial trios. It was verified by both theoretical and numerical results that the nonlinear energy exchange period increases smoothly as we move toward the long wave approach. The magnitude of the energy exchanges is also modified, but in this case depends on the particular triad used and also on the initial energy partition among the triad components. Some implications of the results for the tropical dynamics are discussed. In particular, we discuss the implications of the results for El Nino and the Madden-Julian in connection with other scales of time and spatial variability.

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.

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.  

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...

Complexity analyses show two distinct types of nonlinear dynamics in short heart period variability recordings

Science.gov (United States)

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

2015-01-01

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

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 approaches in engineering applications 2

CERN Document Server

Jazar, Reza N

2013-01-01

Provides updated principles and applications of the nonlinear approaches in solving engineering and physics problems Demonstrates how nonlinear approaches may open avenues to better, safer, cheaper systems with less energy consumption Has a strong emphasis on the application, physical meaning, and methodologies of nonlinear approaches in different engineering and science problems

Static and Dynamic Nonlinearity of A/D Converters

Directory of Open Access Journals (Sweden)

M. Villa

2005-04-01

Full Text Available The dynamic range of broadband digital system is mostly limited byharmonics and spurious arising from ADC nonlinearity. The nonlinearitymay be described in several ways. The distinction between static anddynamic contributions has strong theoretical motivations but it isdifficult to independently measure these contributions. A morepractical approach is based upon analysis of the complex spectrum,which is well defined, easily measured, and may be used to optimize theADC working point and to somehow characterize both static and dynamicnonlinearity. To minimize harmonics and spurious components we need asufficient level of input noise (dither, which destroys theperiodicity at multistage pipelined ADC, combined with a carefulanalysis of the different sources of nonlinearity.

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

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.

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

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

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

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.

Analytical description of critical dynamics for two-dimensional dissipative nonlinear maps

International Nuclear Information System (INIS)

Méndez-Bermúdez, J.A.; Oliveira, Juliano A. de; Leonel, Edson D.

2016-01-01

The critical dynamics near the transition from unlimited to limited action diffusion for two families of well known dissipative nonlinear maps, namely the dissipative standard and dissipative discontinuous maps, is characterized by the use of an analytical approach. The approach is applied to explicitly obtain the average squared action as a function of the (discrete) time and the parameters controlling nonlinearity and dissipation. This allows to obtain a set of critical exponents so far obtained numerically in the literature. The theoretical predictions are verified by extensive numerical simulations. We conclude that all possible dynamical cases, independently on the map parameter values and initial conditions, collapse into the universal exponential decay of the properly normalized average squared action as a function of a normalized time. The formalism developed here can be extended to many other different types of mappings therefore making the methodology generic and robust. - Highlights: • We analytically approach scaling properties of a family of two-dimensional dissipative nonlinear maps. • We derive universal scaling functions that were obtained before only approximately. • We predict the unexpected condition where diffusion and dissipation compensate each other exactly. • We find a new universal scaling function that embraces all possible dissipative behaviors.

Functional integral approach to classical statistical dynamics

International Nuclear Information System (INIS)

Jensen, R.V.

1980-04-01

A functional integral method is developed for the statistical solution of nonlinear stochastic differential equations which arise in classical dynamics. The functional integral approach provides a very natural and elegant derivation of the statistical dynamical equations that have been derived using the operator formalism of Martin, Siggia, and Rose

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

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

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...

Advances in dynamic relaxation techniques for nonlinear finite element analysis

International Nuclear Information System (INIS)

Sauve, R.G.; Metzger, D.R.

1995-01-01

Traditionally, the finite element technique has been applied to static and steady-state problems using implicit methods. When nonlinearities exist, equilibrium iterations must be performed using Newton-Raphson or quasi-Newton techniques at each load level. In the presence of complex geometry, nonlinear material behavior, and large relative sliding of material interfaces, solutions using implicit methods often become intractable. A dynamic relaxation algorithm is developed for inclusion in finite element codes. The explicit nature of the method avoids large computer memory requirements and makes possible the solution of large-scale problems. The method described approaches the steady-state solution with no overshoot, a problem which has plagued researchers in the past. The method is included in a general nonlinear finite element code. A description of the method along with a number of new applications involving geometric and material nonlinearities are presented. They include: (1) nonlinear geometric cantilever plate; (2) moment-loaded nonlinear beam; and (3) creep of nuclear fuel channel assemblies

Nonlinear dynamic analysis of flexible multibody systems

Science.gov (United States)

Bauchau, Olivier A.; Kang, Nam Kook

1991-01-01

Two approaches are developed to analyze the dynamic behavior of flexible multibody systems. In the first approach each body is modeled with a modal methodology in a local non-inertial frame of reference, whereas in the second approach, each body is modeled with a finite element methodology in the inertial frame. In both cases, the interaction among the various elastic bodies is represented by constraint equations. The two approaches were compared for accuracy and efficiency: the first approach is preferable when the nonlinearities are not too strong but it becomes cumbersome and expensive to use when many modes must be used. The second approach is more general and easier to implement but could result in high computation costs for a large system. The constraints should be enforced in a time derivative fashion for better accuracy and stability.

Nonlinear normal vibration modes in the dynamics of nonlinear elastic systems

International Nuclear Information System (INIS)

Mikhlin, Yu V; Perepelkin, N V; Klimenko, A A; Harutyunyan, E

2012-01-01

Nonlinear normal modes (NNMs) are a generalization of the linear normal vibrations. By the Kauderer-Rosenberg concept in the regime of the NNM all position coordinates are single-values functions of some selected position coordinate. By the Shaw-Pierre concept, the NNM is such a regime when all generalized coordinates and velocities are univalent functions of a couple of dominant (active) phase variables. The NNMs approach is used in some applied problems. In particular, the Kauderer-Rosenberg NNMs are analyzed in the dynamics of some pendulum systems. The NNMs of forced vibrations are investigated in a rotor system with an isotropic-elastic shaft. A combination of the Shaw-Pierre NNMs and the Rauscher method is used to construct the forced NNMs and the frequency responses in the rotor dynamics.

Nonlinear Dynamic Models in Advanced Life Support

Science.gov (United States)

Jones, Harry

2002-01-01

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

Nonlinear Bayesian filtering and learning: a neuronal dynamics for perception.

Science.gov (United States)

Kutschireiter, Anna; Surace, Simone Carlo; Sprekeler, Henning; Pfister, Jean-Pascal

2017-08-18

The robust estimation of dynamical hidden features, such as the position of prey, based on sensory inputs is one of the hallmarks of perception. This dynamical estimation can be rigorously formulated by nonlinear Bayesian filtering theory. Recent experimental and behavioral studies have shown that animals' performance in many tasks is consistent with such a Bayesian statistical interpretation. However, it is presently unclear how a nonlinear Bayesian filter can be efficiently implemented in a network of neurons that satisfies some minimum constraints of biological plausibility. Here, we propose the Neural Particle Filter (NPF), a sampling-based nonlinear Bayesian filter, which does not rely on importance weights. We show that this filter can be interpreted as the neuronal dynamics of a recurrently connected rate-based neural network receiving feed-forward input from sensory neurons. Further, it captures properties of temporal and multi-sensory integration that are crucial for perception, and it allows for online parameter learning with a maximum likelihood approach. The NPF holds the promise to avoid the 'curse of dimensionality', and we demonstrate numerically its capability to outperform weighted particle filters in higher dimensions and when the number of particles is limited.

Dimensionality of heavy metal distribution in waste disposal sites using nonlinear dynamics

International Nuclear Information System (INIS)

Modis, Kostas; Komnitsas, Kostas

2008-01-01

Mapping of heavy metal contamination in mining and waste disposal sites usually relies on geostatistical approaches and linear stochastic dynamics. The present paper aims to identify, using the Grassberger-Procaccia correlation dimension (CD) algorithm, the existence of a nonlinear deterministic and chaotic dynamic behaviour in the spatial pattern of arsenic, manganese and zinc concentration in a Russian coal waste disposal site. The analysis carried out yielded embedding dimension values ranging between 7 and 8 suggesting thus from a chaotic dynamic perspective that arsenic, manganese and zinc concentration in space is a medium dimensional problem for the regionalized scale considered in this study. This alternative nonlinear dynamics approach may complement conventional geostatistical studies and may be also used for the estimation of risk and the subsequent screening and selection of a feasible remediation scheme in wider mining and waste disposal sites. Finally, the synergistic effect of this study may be further elaborated if additional factors including among others presence of hot spots, density and depth of sampling, mineralogy of wastes and sensitivity of analytical techniques are taken into account

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 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.

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...

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.

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

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

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...

Nonlinear dynamics in human behavior

Energy Technology Data Exchange (ETDEWEB)

Huys, Raoul [Centre National de la Recherche Scientifique (CNRS), 13 - Marseille (France); Marseille Univ. (France). Movement Science Inst.; Jirsa, Viktor K. (eds.) [Centre National de la Recherche Scientifique (CNRS), 13 - Marseille (France); Marseille Univ. (France). Movement Science Inst.; Florida Atlantic Univ., Boca Raton, FL (United States). Center for Complex Systems and Brain Sciences

2010-07-01

Humans engage in a seemingly endless variety of different behaviors, of which some are found across species, while others are conceived of as typically human. Most generally, behavior comes about through the interplay of various constraints - informational, mechanical, neural, metabolic, and so on - operating at multiple scales in space and time. Over the years, consensus has grown in the research community that, rather than investigating behavior only from bottom up, it may be also well understood in terms of concepts and laws on the phenomenological level. Such top down approach is rooted in theories of synergetics and self-organization using tools from nonlinear dynamics. The present compendium brings together scientists from all over the world that have contributed to the development of their respective fields departing from this background. It provides an introduction to deterministic as well as stochastic dynamical systems and contains applications to motor control and coordination, visual perception and illusion, as well as auditory perception in the context of speech and music. (orig.)

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).

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

Application of a nonlinear spring element to analysis of circumferentially cracked pipe under dynamic loading

International Nuclear Information System (INIS)

Olson, R.; Scott, P.; Wilkowski, G.M.

1992-01-01

As part of the US NRC's Degraded Piping Program, the concept of using a nonlinear spring element to simulate the response of cracked pipe in dynamic finite element pipe evaluations was initially proposed. The nonlinear spring element is used to represent the moment versus rotation response of the cracked pipe section. The moment-rotation relationship for the crack size and material of interest is determined from either J-estimation scheme analyses or experimental data. In this paper, a number of possible approaches for modeling the nonlinear stiffness of the cracked pipe section are introduced. One approach, modeling the cracked section moment rotation response with a series of spring-slider elements, is discussed in detail. As part of this discussion, results from a series of finite element predictions using the spring-slider nonlinear spring element are compared with the results from a series of dynamic cracked pipe system experiments from the International Piping Integrity Research Group (IPIRG) program

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

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.

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.

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.

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...

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.

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.

Nonlinear Dynamics of Controlled Synchronizations of Manipulator System

Directory of Open Access Journals (Sweden)

Qingkai Han

2014-01-01

Full Text Available The nonlinear dynamics of the manipulator system which is controlled to achieve the synchronization motions is investigated in the paper. Firstly, the control strategies and modeling approaches of the manipulator system are given, in which the synchronization goal is defined by both synchronization errors and its derivatives. The synchronization controllers applied on the manipulator system include neuron synchronization controller, improved OPCL synchronization controller, and MRAC-PD synchronization controller. Then, an improved adaptive synchronized control strategy is proposed in order to estimate online the unknown structure parameters and state variables of the manipulator system and to realize the needed synchronous compensation. Furthermore, a robust adaptive synchronization controller is also researched to guarantee the dynamic stability of the system. Finally, the stability of motion synchronizations of the manipulator system possessing nonlinear component is discussed, together with the effect of control parameters and joint friction and others. Some typical motions such as motion bifurcations and the loss of synchronization of it are obtained and illustrated as periodic, multiperiodic, and/or chaotic motion patterns.

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 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.

Neurobiologically Inspired Approaches to Nonlinear Process Control and Modeling

Science.gov (United States)

1999-12-31

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

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.

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 approaches in engineering applications advanced analysis of vehicle related technologies

CERN Document Server

Dai, Liming

2016-01-01

This book looks at the broad field of engineering science through the lens of nonlinear approaches. Examples focus on issues in vehicle technology, including vehicle dynamics, vehicle-road interaction, steering, and control for electric and hybrid vehicles. Also included are discussions on train and tram systems, aerial vehicles, robot-human interaction, and contact and scratch analysis at the micro/nanoscale. Chapters are based on invited contributions from world-class experts in the field who advance the future of engineering by discussing the development of more optimal, accurate, efficient, and cost and energy effective systems. This book is appropriate for researchers, students, and practicing engineers who are interested in the applications of nonlinear approaches to solving engineering and science problems.

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.

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

Bending localization of nitrous oxide under anharmonicity and Fermi coupling: the dynamical potential approach

International Nuclear Information System (INIS)

Zhang Chi; Wu Guo-Zhen; Fang Chao

2010-01-01

This paper studies the vibrational nonlinear dynamics of nitrous oxide with Fermi coupling between the symmetric stretching and bending coordinates by classical dynamical potential approach. This is a global approach in the sense that the overall dynamics is evidenced by the classical nonlinear variables such as the fixed points and the focus are on a set of levels instead of individual ones. The dynamics of nitrous oxide is demonstrated to be not so much dependent on the excitation energy. Moreover, the localized bending mode is shown to be ubiquitous in all the energy range studied

Nonlinear Damping Identification in Nonlinear Dynamic System Based on Stochastic Inverse Approach

Directory of Open Access Journals (Sweden)

S. L. Han

2012-01-01

Full Text Available The nonlinear model is crucial to prepare, supervise, and analyze mechanical system. In this paper, a new nonparametric and output-only identification procedure for nonlinear damping is studied. By introducing the concept of the stochastic state space, we formulate a stochastic inverse problem for a nonlinear damping. The solution of the stochastic inverse problem is designed as probabilistic expression via the hierarchical Bayesian formulation by considering various uncertainties such as the information insufficiency in parameter of interests or errors in measurement. The probability space is estimated using Markov chain Monte Carlo (MCMC. The applicability of the proposed method is demonstrated through numerical experiment and particular application to a realistic problem related to ship roll motion.

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

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.

Application of Dynamic Systems Family for Synthesis of Fuzzy Control with Account of Non-linearities

Directory of Open Access Journals (Sweden)

Andriy Lozynskyy

2016-01-01

Full Text Available Dynamic system with nonlinearities has been considered. This system has been divided into a set of linear subsystems. A fuzzy controller of the considered system has been synthesized. It takes into account nonlinearities of the system and provides smooth switching between controllers of the linear subsystems. An unstable subsystem has been utilized, which provides better dynamic characteristics of the considered system. Comparison with traditional controller has been conducted. Corresponding qualitative and quantitative estimates have been provided. They testify the expediency of the proposed approach.

Nonlinear dynamics and anisotropic structure of rotating sheared turbulence.

Science.gov (United States)

Salhi, A; Jacobitz, F G; Schneider, K; Cambon, C

2014-01-01

Homogeneous turbulence in rotating shear flows is studied by means of pseudospectral direct numerical simulation and analytical spectral linear theory (SLT). The ratio of the Coriolis parameter to shear rate is varied over a wide range by changing the rotation strength, while a constant moderate shear rate is used to enable significant contributions to the nonlinear interscale energy transfer and to the nonlinear intercomponental redistribution terms. In the destabilized and neutral cases, in the sense of kinetic energy evolution, nonlinearity cannot saturate the growth of the largest scales. It permits the smallest scale to stabilize by a scale-by-scale quasibalance between the nonlinear energy transfer and the dissipation spectrum. In the stabilized cases, the role of rotation is mainly nonlinear, and interacting inertial waves can affect almost all scales as in purely rotating flows. In order to isolate the nonlinear effect of rotation, the two-dimensional manifold with vanishing spanwise wave number is revisited and both two-component spectra and single-point two-dimensional energy components exhibit an important effect of rotation, whereas the SLT as well as the purely two-dimensional nonlinear analysis are unaffected by rotation as stated by the Proudman theorem. The other two-dimensional manifold with vanishing streamwise wave number is analyzed with similar tools because it is essential for any shear flow. Finally, the spectral approach is used to disentangle, in an analytical way, the linear and nonlinear terms in the dynamical equations.

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 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...

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 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.

A statistical state dynamics approach to wall turbulence.

Science.gov (United States)

Farrell, B F; Gayme, D F; Ioannou, P J

2017-03-13

This paper reviews results obtained using statistical state dynamics (SSD) that demonstrate the benefits of adopting this perspective for understanding turbulence in wall-bounded shear flows. The SSD approach used in this work employs a second-order closure that retains only the interaction between the streamwise mean flow and the streamwise mean perturbation covariance. This closure restricts nonlinearity in the SSD to that explicitly retained in the streamwise constant mean flow together with nonlinear interactions between the mean flow and the perturbation covariance. This dynamical restriction, in which explicit perturbation-perturbation nonlinearity is removed from the perturbation equation, results in a simplified dynamics referred to as the restricted nonlinear (RNL) dynamics. RNL systems, in which a finite ensemble of realizations of the perturbation equation share the same mean flow, provide tractable approximations to the SSD, which is equivalent to an infinite ensemble RNL system. This infinite ensemble system, referred to as the stochastic structural stability theory system, introduces new analysis tools for studying turbulence. RNL systems provide computationally efficient means to approximate the SSD and produce self-sustaining turbulence exhibiting qualitative features similar to those observed in direct numerical simulations despite greatly simplified dynamics. The results presented show that RNL turbulence can be supported by as few as a single streamwise varying component interacting with the streamwise constant mean flow and that judicious selection of this truncated support or 'band-limiting' can be used to improve quantitative accuracy of RNL turbulence. These results suggest that the SSD approach provides new analytical and computational tools that allow new insights into wall turbulence.This article is part of the themed issue 'Toward the development of high-fidelity models of wall turbulence at large Reynolds number'. © 2017 The Author(s).

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).

On-line control of the nonlinear dynamics for synchrotrons

Science.gov (United States)

Bengtsson, J.; Martin, I. P. S.; Rowland, J. H.; Bartolini, R.

2015-07-01

We propose a simple approach to the on-line control of the nonlinear dynamics in storage rings, based on compensation of the nonlinear resonance driving terms using beam losses as the main indicator of the strength of a resonance. The correction scheme is built on the analysis of the resonance driving terms in first perturbative order and on the possibility of using independent power supplies in the sextupole magnets, which is nowadays present in many synchrotron light sources. Such freedom allows the definition of "smart sextupole knobs" attacking each resonance separately. The compensation scheme has been tested at the Diamond light source and proved to be effective in opening up the betatron tune space, resonance free, available to the electron beam and to improve the beam lifetime.

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)

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

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 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

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...

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.

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

Electric generating capacity planning: A nonlinear programming approach

Energy Technology Data Exchange (ETDEWEB)

Yakin, M.Z.; McFarland, J.W.

1987-02-01

This paper presents a nonlinear programming approach for long-range generating capacity expansion planning in electrical power systems. The objective in the model is the minimization of total cost consisting of investment cost plus generation cost for a multi-year planning horizon. Reliability constraints are imposed by using standard and practical reserve margin requirements. State equations representing the dynamic aspect of the problem are included. The electricity demand (load) and plant availabilities are treated as random variables, and the method of cumulants is used to calculate the expected energy generated by each plant in each year of the planning horizon. The resulting model has a (highly) nonlinear objective function and linear constraints. The planning model is solved over the multiyear planning horizon instead of decomposing it into one-year period problems. This approach helps the utility decision maker to carry out extensive sensitivity analysis easily. A case study example is provided using EPRI test data. Relationships among the reserve margin, total cost and surplus energy generating capacity over the planning horizon are explored by analyzing the model.

Weighted fractional permutation entropy and fractional sample entropy for nonlinear Potts financial dynamics

Energy Technology Data Exchange (ETDEWEB)

Xu, Kaixuan, E-mail: kaixuanxubjtu@yeah.net; Wang, Jun

2017-02-26

In this paper, recently introduced permutation entropy and sample entropy are further developed to the fractional cases, weighted fractional permutation entropy (WFPE) and fractional sample entropy (FSE). The fractional order generalization of information entropy is utilized in the above two complexity approaches, to detect the statistical characteristics of fractional order information in complex systems. The effectiveness analysis of proposed methods on the synthetic data and the real-world data reveals that tuning the fractional order allows a high sensitivity and more accurate characterization to the signal evolution, which is useful in describing the dynamics of complex systems. Moreover, the numerical research on nonlinear complexity behaviors is compared between the returns series of Potts financial model and the actual stock markets. And the empirical results confirm the feasibility of the proposed model. - Highlights: • Two new entropy approaches for estimation of nonlinear complexity are proposed for the financial market. • Effectiveness analysis of proposed methods is presented and their respective features are studied. • Empirical research of proposed analysis on seven world financial market indices. • Numerical simulation of Potts financial dynamics is preformed for nonlinear complexity behaviors.

Weighted fractional permutation entropy and fractional sample entropy for nonlinear Potts financial dynamics

International Nuclear Information System (INIS)

Xu, Kaixuan; Wang, Jun

2017-01-01

In this paper, recently introduced permutation entropy and sample entropy are further developed to the fractional cases, weighted fractional permutation entropy (WFPE) and fractional sample entropy (FSE). The fractional order generalization of information entropy is utilized in the above two complexity approaches, to detect the statistical characteristics of fractional order information in complex systems. The effectiveness analysis of proposed methods on the synthetic data and the real-world data reveals that tuning the fractional order allows a high sensitivity and more accurate characterization to the signal evolution, which is useful in describing the dynamics of complex systems. Moreover, the numerical research on nonlinear complexity behaviors is compared between the returns series of Potts financial model and the actual stock markets. And the empirical results confirm the feasibility of the proposed model. - Highlights: • Two new entropy approaches for estimation of nonlinear complexity are proposed for the financial market. • Effectiveness analysis of proposed methods is presented and their respective features are studied. • Empirical research of proposed analysis on seven world financial market indices. • Numerical simulation of Potts financial dynamics is preformed for nonlinear complexity behaviors.

Nonlinear Dynamic Response of Compliant Journal Bearings

Directory of Open Access Journals (Sweden)

Glavatskih S.

2012-07-01

Full Text Available This paper investigates the dynamic response of the compliant tilting pad journal bearings subjected to synchronous excitation. Bearing compliance is affected by the properties of pad liner and pad support geometry. Different unbalance eccentricities are considered. It is shown that bearing dynamic response is non-linear. Journal orbit complexity increases with pad compliance though the orbit amplitudes are marginally affected at low loads. At high loads, the journal is forced to operate outside the bearing clearance. The polymer liner reduces the maximum oil film pressure by a factor of 2 when compared to the white metal liner. The nonlinear dynamic response of compliant tilting pad journal bearings is thoroughly discussed.

Nonlinear dynamics of a coherent polariton-biexciton system

International Nuclear Information System (INIS)

Nguyen Trung Dan; Vo Tinh

1994-08-01

The nonlinear dynamics of a coherent interacting polariton-biexciton system in optically excited semiconductors is investigated. We consider the case when two macroscopically coherent modes - a lower branch polariton and a biexciton existing simultaneously in a direct-gap semiconductor. The conditions for exhibiting optical bistability in stationary regime are obtained. Numerical simulation for the nonlinear dynamics equations of the system is also carried out. (author). 16 refs, 4 figs

Nonlinear relativistic plasma resonance: Renormalization group approach

Energy Technology Data Exchange (ETDEWEB)

Metelskii, I. I., E-mail: metelski@lebedev.ru [Russian Academy of Sciences, Lebedev Physical Institute (Russian Federation); Kovalev, V. F., E-mail: vfkvvfkv@gmail.com [Dukhov All-Russian Research Institute of Automatics (Russian Federation); Bychenkov, V. Yu., E-mail: bychenk@lebedev.ru [Russian Academy of Sciences, Lebedev Physical Institute (Russian Federation)

2017-02-15

An analytical solution to the nonlinear set of equations describing the electron dynamics and electric field structure in the vicinity of the critical density in a nonuniform plasma is constructed using the renormalization group approach with allowance for relativistic effects of electron motion. It is demonstrated that the obtained solution describes two regimes of plasma oscillations in the vicinity of the plasma resonance— stationary and nonstationary. For the stationary regime, the spatiotemporal and spectral characteristics of the resonantly enhanced electric field are investigated in detail and the effect of the relativistic nonlinearity on the spatial localization of the energy of the plasma relativistic field is considered. The applicability limits of the obtained solution, which are determined by the conditions of plasma wave breaking in the vicinity of the resonance, are established and analyzed in detail for typical laser and plasma parameters. The applicability limits of the earlier developed nonrelativistic theories are refined.

Nonlinear Dynamics and Strong Cavity Cooling of Levitated Nanoparticles.

Science.gov (United States)

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

2016-10-21

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

Nonlinear Dynamics and Strong Cavity Cooling of Levitated Nanoparticles

Science.gov (United States)

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

2016-10-01

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

Motion Cueing Algorithm Development: Human-Centered Linear and Nonlinear Approaches

Science.gov (United States)

Houck, Jacob A. (Technical Monitor); Telban, Robert J.; Cardullo, Frank M.

2005-01-01

While the performance of flight simulator motion system hardware has advanced substantially, the development of the motion cueing algorithm, the software that transforms simulated aircraft dynamics into realizable motion commands, has not kept pace. Prior research identified viable features from two algorithms: the nonlinear "adaptive algorithm", and the "optimal algorithm" that incorporates human vestibular models. A novel approach to motion cueing, the "nonlinear algorithm" is introduced that combines features from both approaches. This algorithm is formulated by optimal control, and incorporates a new integrated perception model that includes both visual and vestibular sensation and the interaction between the stimuli. Using a time-varying control law, the matrix Riccati equation is updated in real time by a neurocomputing approach. Preliminary pilot testing resulted in the optimal algorithm incorporating a new otolith model, producing improved motion cues. The nonlinear algorithm vertical mode produced a motion cue with a time-varying washout, sustaining small cues for longer durations and washing out large cues more quickly compared to the optimal algorithm. The inclusion of the integrated perception model improved the responses to longitudinal and lateral cues. False cues observed with the NASA adaptive algorithm were absent. The neurocomputing approach was crucial in that the number of presentations of an input vector could be reduced to meet the real time requirement without degrading the quality of the motion cues.

A sampling approach to constructing Lyapunov functions for nonlinear continuous–time systems

NARCIS (Netherlands)

Bobiti, R.V.; Lazar, M.

2016-01-01

The problem of constructing a Lyapunov function for continuous-time nonlinear dynamical systems is tackled in this paper via a sampling-based approach. The main idea of the sampling-based method is to verify a Lyapunov-type inequality for a finite number of points (known state vectors) in the

Multiscale Support Vector Learning With Projection Operator Wavelet Kernel for Nonlinear Dynamical System Identification.

Science.gov (United States)

Lu, Zhao; Sun, Jing; Butts, Kenneth

2016-02-03

A giant leap has been made in the past couple of decades with the introduction of kernel-based learning as a mainstay for designing effective nonlinear computational learning algorithms. In view of the geometric interpretation of conditional expectation and the ubiquity of multiscale characteristics in highly complex nonlinear dynamic systems [1]-[3], this paper presents a new orthogonal projection operator wavelet kernel, aiming at developing an efficient computational learning approach for nonlinear dynamical system identification. In the framework of multiresolution analysis, the proposed projection operator wavelet kernel can fulfill the multiscale, multidimensional learning to estimate complex dependencies. The special advantage of the projection operator wavelet kernel developed in this paper lies in the fact that it has a closed-form expression, which greatly facilitates its application in kernel learning. To the best of our knowledge, it is the first closed-form orthogonal projection wavelet kernel reported in the literature. It provides a link between grid-based wavelets and mesh-free kernel-based methods. Simulation studies for identifying the parallel models of two benchmark nonlinear dynamical systems confirm its superiority in model accuracy and sparsity.

Analysis of Nonlinear Dynamic Structures

African Journals Online (AJOL)

Bheema

work a two degrees of freedom nonlinear system with zero memory was ... FRF is the most widely used method in structural dynamics which gives information about the ..... 3.6, which is the waterfall diagram of the same response, as well.

A nonlinear dynamics of trunk kinematics during manual lifting tasks.

Science.gov (United States)

Khalaf, Tamer; Karwowski, Waldemar; Sapkota, Nabin

2015-01-01

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

Semiconductor Nonlinear Dynamics Study by Broadband Terahertz Spectroscopy

Science.gov (United States)

Ho, I.-Chen

Semiconductor nonlinearity in the terahertz (THz) frequency range has been attracting considerable attention due to the recent development of high-power semiconductor-based nanodevices. However, the underlying physics concerning carrier dynamics in the presence of high-field THz transients is still obscure. This thesis introduces an ultrafast, time-resolved THz pump/THz probe approach to the study of semiconductor properties in the nonlinear regime. The carrier dynamics regarding two mechanisms, intervalley scattering and impact ionization, is observed for doped InAs on a sub-picosecond time scale. In addition, polaron modulation driven by intense THz pulses is experimentally and theoretically investigated. The observed polaron dynamics verifies the interaction between energetic electrons and a phonon field. In contrast to previous work which reports optical phonon responses, acoustic phonon modulations are addressed in this study. A further understanding of the intense field interacting with solid materials will accelerate the development of semiconductor devices. This thesis starts with the design and performance of a table-top THz spectrometer which has the advantages of ultra-broad bandwidth (one order higher bandwidth compared to a conventional ZnTe sensor) and high electric field strength (>100 kV/cm). Unlike the conventional THz time-domain spectroscopy, the spectrometer integrates a novel THz air-biased-coherent-detection (THz-ABCD) technique and utilizes selected gases as THz emitters and sensors. In comparison with commonly used electro-optic (EO) crystals or photoconductive (PC) dipole antennas, the gases have the benefits of no phonon absorption as existing in EO crystals and no carrier life time limitation as observed in PC dipole antennas. The newly development THz-ABCD spectrometer with a strong THz field strength capability provides a platform for various research topics especially on the nonlinear carrier dynamics of semiconductors. Two mechanisms

Poromechanical approach describing the moisture influence on the non-linear quasi-static and dynamic behaviour of porous building materials

NARCIS (Netherlands)

Carmeliet, J.; Abeele, van den K.E.A.

2004-01-01

The non-linear quasi-static and dynamic elastic behaviour of Berea sandstone has been experimentally analysed showing hysteresis and a strong influence of moisture especially in the lower saturation range. It is shown that non-linear hysteretic response originates within the "bond system" of the

Passivation and control of partially known SISO nonlinear systems via dynamic neural networks

Directory of Open Access Journals (Sweden)

Reyes-Reyes J.

2000-01-01

Full Text Available In this paper, an adaptive technique is suggested to provide the passivity property for a class of partially known SISO nonlinear systems. A simple Dynamic Neural Network (DNN, containing only two neurons and without any hidden-layers, is used to identify the unknown nonlinear system. By means of a Lyapunov-like analysis the new learning law for this DNN, guarantying both successful identification and passivation effects, is derived. Based on this adaptive DNN model, an adaptive feedback controller, serving for wide class of nonlinear systems with an a priori incomplete model description, is designed. Two typical examples illustrate the effectiveness of the suggested approach.

On-line control of the nonlinear dynamics for synchrotrons

Directory of Open Access Journals (Sweden)

J. Bengtsson

2015-07-01

Full Text Available We propose a simple approach to the on-line control of the nonlinear dynamics in storage rings, based on compensation of the nonlinear resonance driving terms using beam losses as the main indicator of the strength of a resonance. The correction scheme is built on the analysis of the resonance driving terms in first perturbative order and on the possibility of using independent power supplies in the sextupole magnets, which is nowadays present in many synchrotron light sources. Such freedom allows the definition of “smart sextupole knobs” attacking each resonance separately. The compensation scheme has been tested at the Diamond light source and proved to be effective in opening up the betatron tune space, resonance free, available to the electron beam and to improve the beam lifetime.

Detecting dynamic causal inference in nonlinear two-phase fracture flow

Science.gov (United States)

Faybishenko, Boris

2017-08-01

Identifying dynamic causal inference involved in flow and transport processes in complex fractured-porous media is generally a challenging task, because nonlinear and chaotic variables may be positively coupled or correlated for some periods of time, but can then become spontaneously decoupled or non-correlated. In his 2002 paper (Faybishenko, 2002), the author performed a nonlinear dynamical and chaotic analysis of time-series data obtained from the fracture flow experiment conducted by Persoff and Pruess (1995), and, based on the visual examination of time series data, hypothesized that the observed pressure oscillations at both inlet and outlet edges of the fracture result from a superposition of both forward and return waves of pressure propagation through the fracture. In the current paper, the author explores an application of a combination of methods for detecting nonlinear chaotic dynamics behavior along with the multivariate Granger Causality (G-causality) time series test. Based on the G-causality test, the author infers that his hypothesis is correct, and presents a causation loop diagram of the spatial-temporal distribution of gas, liquid, and capillary pressures measured at the inlet and outlet of the fracture. The causal modeling approach can be used for the analysis of other hydrological processes, for example, infiltration and pumping tests in heterogeneous subsurface media, and climatic processes, for example, to find correlations between various meteorological parameters, such as temperature, solar radiation, barometric pressure, etc.

Mathematical modeling and applications in nonlinear dynamics

CERN Document Server

Merdan, Hüseyin

2016-01-01

The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems. Provides methods for mathematical models with switching, thresholds, and impulses, each of particular importance for discontinuous processes Includes qualitative analysis of behaviors on Tumor-Immune Systems and methods of analysis for DNA, neural networks and epidemiology Introduces...

XXIII International Conference on Nonlinear Dynamics of Electronic Systems

CERN Document Server

Stoop, Ruedi; Stramaglia, Sebastiano

2017-01-01

This book collects contributions to the XXIII international conference “Nonlinear dynamics of electronic systems”. Topics range from non-linearity in electronic circuits to synchronisation effects in complex networks to biological systems, neural dynamics and the complex organisation of the brain. Resting on a solid mathematical basis, these investigations address highly interdisciplinary problems in physics, engineering, biology and biochemistry.

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.

Applications of Nonlinear Dynamics Model and Design of Complex Systems

CERN Document Server

In, Visarath; Palacios, Antonio

2009-01-01

This edited book is aimed at interdisciplinary, device-oriented, applications of nonlinear science theory and methods in complex systems. In particular, applications directed to nonlinear phenomena with space and time characteristics. Examples include: complex networks of magnetic sensor systems, coupled nano-mechanical oscillators, nano-detectors, microscale devices, stochastic resonance in multi-dimensional chaotic systems, biosensors, and stochastic signal quantization. "applications of nonlinear dynamics: model and design of complex systems" brings together the work of scientists and engineers that are applying ideas and methods from nonlinear dynamics to design and fabricate complex systems.

Physical dynamics of quasi-particles in nonlinear wave equations

International Nuclear Information System (INIS)

Christov, Ivan; Christov, C.I.

2008-01-01

By treating the centers of solitons as point particles and studying their discrete dynamics, we demonstrate a new approach to the quantization of the soliton solutions of the sine-Gordon equation, one of the first model nonlinear field equations. In particular, we show that a linear superposition of the non-interacting shapes of two solitons offers a qualitative (and to a good approximation quantitative) description of the true two-soliton solution, provided that the trajectories of the centers of the superimposed solitons are considered unknown. Via variational calculus, we establish that the dynamics of the quasi-particles obey a pseudo-Newtonian law, which includes cross-mass terms. The successful identification of the governing equations of the (discrete) quasi-particles from the (continuous) field equation shows that the proposed approach provides a basis for the passage from the continuous to a discrete description of the field

Physical dynamics of quasi-particles in nonlinear wave equations

Energy Technology Data Exchange (ETDEWEB)

Christov, Ivan [Department of Mathematics, Texas A and M University, College Station, TX 77843-3368 (United States)], E-mail: christov@alum.mit.edu; Christov, C.I. [Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504-1010 (United States)], E-mail: christov@louisiana.edu

2008-02-04

By treating the centers of solitons as point particles and studying their discrete dynamics, we demonstrate a new approach to the quantization of the soliton solutions of the sine-Gordon equation, one of the first model nonlinear field equations. In particular, we show that a linear superposition of the non-interacting shapes of two solitons offers a qualitative (and to a good approximation quantitative) description of the true two-soliton solution, provided that the trajectories of the centers of the superimposed solitons are considered unknown. Via variational calculus, we establish that the dynamics of the quasi-particles obey a pseudo-Newtonian law, which includes cross-mass terms. The successful identification of the governing equations of the (discrete) quasi-particles from the (continuous) field equation shows that the proposed approach provides a basis for the passage from the continuous to a discrete description of the field.

Optimal control of dissipative nonlinear dynamical systems with triggers of coupled singularities

International Nuclear Information System (INIS)

Hedrih, K

2008-01-01

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

Optimal control of dissipative nonlinear dynamical systems with triggers of coupled singularities

Science.gov (United States)

Stevanović Hedrih, K.

2008-02-01

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

Nonlinear dynamics research in the former Soviet Union

International Nuclear Information System (INIS)

McKenney, B.L.; Krafsig, J.; Moon, F.C.; Shlesinger, M.F.

1992-08-01

This assessment of nonlinear dynamics research in the former Soviet Union was performed by seven US scientists and engineers active in the fields examined. The topics covered include: solid-state systems and circuits, information theory and signal analysis, chaos in mechanical systems, turbulence and vortex dynamics, ocean processes, image processing, and lasers and nonlinear optics. The field of nonlinear dynamics and chaos blossomed in academic settings in both the West and the former Soviet Union during the 1980s. The field went from mathematical abstraction to interesting engineering application areas. Several generalizations can be drawn from the review of Soviet work: Soviet work generally began earlier than Western work, and, in areas that do not require extensive computational resources, that work has kept up with, and often leads, the West. This is especially true in the mathematical analysis of nonlinear phenomena. Soviet researchers have shown an ability to combine numerical or analytic ideas with laboratory experimentation in a smoother, less erratic fashion than Western researchers. Furthermore, contrary to Western practice, the same researchers often do both theoretical and experimental work. In areas that require numerical verification of ideas in the field, the Western work is leading that of the former Soviet Union. This is especially true in the areas of signal processing, simulations of turbulence, and communications. No evidence was found of any significant penetration of ideas of nonlinear dynamics into technological applications of a military or commercial area in the former Soviet Union. Opportunities abound, but specific applications are not apparent

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

Nonlinear dynamics of laser systems with elements of a chaos: Advanced computational code

Science.gov (United States)

Buyadzhi, V. V.; Glushkov, A. V.; Khetselius, O. Yu; Kuznetsova, A. A.; Buyadzhi, A. A.; Prepelitsa, G. P.; Ternovsky, V. B.

2017-10-01

A general, uniform chaos-geometric computational approach to analysis, modelling and prediction of the non-linear dynamics of quantum and laser systems (laser and quantum generators system etc) with elements of the deterministic chaos is briefly presented. The approach is based on using the advanced generalized techniques such as the wavelet analysis, multi-fractal formalism, mutual information approach, correlation integral analysis, false nearest neighbour algorithm, the Lyapunov’s exponents analysis, and surrogate data method, prediction models etc There are firstly presented the numerical data on the topological and dynamical invariants (in particular, the correlation, embedding, Kaplan-York dimensions, the Lyapunov’s exponents, Kolmogorov’s entropy and other parameters) for laser system (the semiconductor GaAs/GaAlAs laser with a retarded feedback) dynamics in a chaotic and hyperchaotic regimes.

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.

Modeling of Macroeconomics by a Novel Discrete Nonlinear Fractional Dynamical System

Directory of Open Access Journals (Sweden)

Zhenhua Hu

2013-01-01

Full Text Available We propose a new nonlinear economic system with fractional derivative. According to the Jumarie’s definition of fractional derivative, we obtain a discrete fractional nonlinear economic system. Three variables, the gross domestic production, inflation, and unemployment rate, are considered by this nonlinear system. Based on the concrete macroeconomic data of USA, the coefficients of this nonlinear system are estimated by the method of least squares. The application of discrete fractional economic model with linear and nonlinear structure is shown to illustrate the efficiency of modeling the macroeconomic data with discrete fractional dynamical system. The empirical study suggests that the nonlinear discrete fractional dynamical system can describe the actual economic data accurately and predict the future behavior more reasonably than the linear dynamic system. The method proposed in this paper can be applied to investigate other macroeconomic variables of more states.

Nonlinear dynamics analysis of a low-temperature-differential kinematic Stirling heat engine

Science.gov (United States)

Izumida, Yuki

2018-03-01

The low-temperature-differential (LTD) Stirling heat engine technology constitutes one of the important sustainable energy technologies. The basic question of how the rotational motion of the LTD Stirling heat engine is maintained or lost based on the temperature difference is thus a practically and physically important problem that needs to be clearly understood. Here, we approach this problem by proposing and investigating a minimal nonlinear dynamic model of an LTD kinematic Stirling heat engine. Our model is described as a driven nonlinear pendulum where the motive force is the temperature difference. The rotational state and the stationary state of the engine are described as a stable limit cycle and a stable fixed point of the dynamical equations, respectively. These two states coexist under a sufficient temperature difference, whereas the stable limit cycle does not exist under a temperature difference that is too small. Using a nonlinear bifurcation analysis, we show that the disappearance of the stable limit cycle occurs via a homoclinic bifurcation, with the temperature difference being the bifurcation parameter.

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).

EVA – a non-linear Eulerian approach for assessment of health-cost externalities of air pollution

DEFF Research Database (Denmark)

Andersen, Mikael Skou; Frohn, Lise Marie; Nielsen, Jytte Seested

2006-01-01

of the emissions. External cost estimates based on the Eulerian approach, on the other hand, are in mutual conformity. The existence of non-linear dynamics and possible thresholds, both in the atmospheric modelling and in the dose-response functions for health effects, need further attention and should......Integrated models which are used to account for the external costs of air pollution have to a considerable extent ignored the non-linear dynamics of atmospheric science. In order to bridge the gap between economic analysis and environmental modelling an integrated model EVA, based on a Eulerian...... for the final external cost estimates of the Eulerian approach is explored. Uncertainties in the health costs estimates are endemic in particular for mortality, but in order to achieve a common baseline the approach recommended by the OECD has been employed for the valuation part. This approach implies the use...

Nonlinear dynamics of fractional order Duffing system

International Nuclear Information System (INIS)

Li, Zengshan; Chen, Diyi; Zhu, Jianwei; Liu, Yongjian

2015-01-01

In this paper, we analyze the nonlinear dynamics of fractional order Duffing system. First, we present the fractional order Duffing system and the numerical algorithm. Second, nonlinear dynamic behaviors of Duffing system with a fixed fractional order is studied by using bifurcation diagrams, phase portraits, Poincare maps and time domain waveforms. The fractional order Duffing system shows some interesting dynamical behaviors. Third, a series of Duffing systems with different fractional orders are analyzed by using bifurcation diagrams. The impacts of fractional orders on the tendency of dynamical motion, the periodic windows in chaos, the bifurcation points and the distance between the first and the last bifurcation points are respectively studied, in which some basic laws are discovered and summarized. This paper reflects that the integer order system and the fractional order one have close relationship and an integer order system is a special case of fractional order ones.

Bayesian inversion analysis of nonlinear dynamics in surface heterogeneous reactions.

Science.gov (United States)

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

2016-09-01

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

Role of nonlinear dynamics and chaos in applied sciences

International Nuclear Information System (INIS)

Lawande, Quissan V.; Maiti, Nirupam

2000-02-01

Nonlinear dynamics manifests itself in a number of phenomena in both laboratory and day to day dealings. However, little attention was being paid to this dynamically rich field. With the advent of high speed computers with visual graphics, the field has proliferated over past few years. One of the most rewarding realization from nonlinear dynamics is the universally acclaimed field of chaos. Chaos has brought in order and has broken the disciplinary boundaries that existed until recently. With its universal phenomena, almost all disciplines following an evolutionary character can be treated on same footing. Chaotic dynamics has its grounding in the multidisciplinary field of synergetics founded by Professor Hermann Haken. In this report, we address some of the basics related to the field of chaos. We have discussed simple mechanisms for generating chaotic trajectories, ways and means of characterizing such systems and the manifestation of their signatures in the evolutions. We have mentioned the links of this field with other existing theories. We have outlined the topics on bifurcation and stability of dynamical systems. Information theoretic aspects and notions on fractal geometry are reviewed in the light of dynamical characterization of chaotic systems. Application oriented views of this novel dynamical phenomena are discussed through examples on simple nonlinear electronic circuits and a BWR reactor. Some ideas relating to control and synchronization in chaotic systems also addressed. In conclusion, we have explored the possibilities of exploiting nonlinear dynamics and chaos in the context of multidisciplinary character of BARC. (author)

Statistical methods in nonlinear dynamics

Indian Academy of Sciences (India)

Sensitivity to initial conditions in nonlinear dynamical systems leads to exponential divergence of trajectories that are initially arbitrarily close, and hence to unpredictability. Statistical methods have been found to be helpful in extracting useful information about such systems. In this paper, we review briefly some statistical ...

Molecular nonlinear dynamics and protein thermal uncertainty quantification

Science.gov (United States)

Xia, Kelin; Wei, Guo-Wei

2014-01-01

This work introduces molecular nonlinear dynamics (MND) as a new approach for describing protein folding and aggregation. By using a mode system, we show that the MND of disordered proteins is chaotic while that of folded proteins exhibits intrinsically low dimensional manifolds (ILDMs). The stability of ILDMs is found to strongly correlate with protein energies. We propose a novel method for protein thermal uncertainty quantification based on persistently invariant ILDMs. Extensive comparison with experimental data and the state-of-the-art methods in the field validate the proposed new method for protein B-factor prediction. PMID:24697365

Cumulative effect of structural nonlinearities: chaotic dynamics of cantilever beam system with impacts

International Nuclear Information System (INIS)

Emans, Joseph; Wiercigroch, Marian; Krivtsov, Anton M.

2005-01-01

The nonlinear analysis of a common beam system was performed, and the method for such, outlined and presented. Nonlinear terms for the governing dynamic equations were extracted and the behaviour of the system was investigated. The analysis was carried out with and without physically realistic parameters, to show the characteristics of the system, and the physically realistic responses. Also, the response as part of a more complex system was considered, in order to investigate the cumulative effects of nonlinearities. Chaos, as well as periodic motion was found readily for the physically unrealistic parameters. In addition, nonlinear behaviour such as co-existence of attractors was found even at modest oscillation levels during investigations with realistic parameters. When considered as part of a more complex system with further nonlinearities, comparisons with linear beam theory show the classical approach to be lacking in accuracy of qualitative predictions, even at weak oscillations

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.

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.

Nonlinear dynamics and cavity cooling of levitated nanoparticles

Science.gov (United States)

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

2016-09-01

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

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...

Recurrence phase shift in Fermi-Pasta-Ulam nonlinear dynamics

Energy Technology Data Exchange (ETDEWEB)

Devine, N., E-mail: nnd124@rsphysse.anu.edu.au [Optical Sciences Group, Research School of Physics and Engineering, The Australian National University, Canberra ACT 0200 (Australia); Ankiewicz, A. [Optical Sciences Group, Research School of Physics and Engineering, The Australian National University, Canberra ACT 0200 (Australia); Genty, G. [Tampere University of Technology, Optics Laboratory, FI-33101 Tampere (Finland); Dudley, J.M. [Institut FEMTO-ST UMR 6174 CNRS/Universite de Franche-Comte, Besancon (France); Akhmediev, N. [Optical Sciences Group, Research School of Physics and Engineering, The Australian National University, Canberra ACT 0200 (Australia)

2011-11-07

We show that the dynamics of Fermi-Pasta-Ulam recurrence is associated with a nonlinear phase shift between initial and final states that are otherwise identical, after a full growth-return cycle. The properties of this phase shift are studied for the particular case of the self-focussing nonlinear Schroedinger equation, and we describe the magnitude of the phase shift in terms of the system parameters. This phase shift, accumulated during the nonlinear recurrence cycle, is a previously-unremarked feature of the Fermi-Pasta-Ulam problem, and we anticipate its wide significance as an essential feature of related dynamics in other systems. -- Highlights: → The dynamics of FPU recurrence is associated with a phase shift between initial and final states. → The properties of this phase shift are studied for the self-focussing NLS equation. → This phase shift is a previously-unremarked feature of the FPU growth-return cycle. → We anticipate its wide significance as an essential feature of related dynamics in other systems.

Recurrence phase shift in Fermi-Pasta-Ulam nonlinear dynamics

International Nuclear Information System (INIS)

Devine, N.; Ankiewicz, A.; Genty, G.; Dudley, J.M.; Akhmediev, N.

2011-01-01

We show that the dynamics of Fermi-Pasta-Ulam recurrence is associated with a nonlinear phase shift between initial and final states that are otherwise identical, after a full growth-return cycle. The properties of this phase shift are studied for the particular case of the self-focussing nonlinear Schroedinger equation, and we describe the magnitude of the phase shift in terms of the system parameters. This phase shift, accumulated during the nonlinear recurrence cycle, is a previously-unremarked feature of the Fermi-Pasta-Ulam problem, and we anticipate its wide significance as an essential feature of related dynamics in other systems. -- Highlights: → The dynamics of FPU recurrence is associated with a phase shift between initial and final states. → The properties of this phase shift are studied for the self-focussing NLS equation. → This phase shift is a previously-unremarked feature of the FPU growth-return cycle. → We anticipate its wide significance as an essential feature of related dynamics in other systems.

Nonlinear effects in dynamic analysis and design of nuclear power plant components: research status and needs

Energy Technology Data Exchange (ETDEWEB)

Stoykovich, M [Burns and Roe, Inc., New York (USA)

1978-10-01

This paper encompasses nonlinear effects in dynamic analysis and design of nuclear power plant facilities. The history of plasticity as a science is briefly discussed, and nonlinear cases of special interest are described. Approaches to some of the nonlinear problems are presented. These include the nonlinearity due to foundation-structure interaction associated with the base slab uplift during seismic disturbances, the nonlinear base-isolation system for the reduction of earthquake-generated forces and deformations of superstructures, nonlinear systems having restoring-force functions in case of gaps and liift-off conditions, and nonlinearity of viscoelastic systems due to inelastic deformations. Available computer programs information for the solution of various types of nonlinear problems are provided. Advantages and disadvantages of some of the nonlinear and linear analyses are discussed. Comparison of some nonlinear and linear results of analyses are presented. Conclusions are reached with regard to research status and recommendations for further studies and for performing non-linear analyses associated with the problems of nonlinearity are presented.

Nonlinear effects in dynamic analysis and design of nuclear power plant components: research status and needs

International Nuclear Information System (INIS)

Stoykovich, M.

1978-01-01

This paper encompasses nonlinear effects in dynamic analysis and design of nuclear power plant facilities. The history of plasticity as a science is briefly discussed, and nonlinear cases of special interest are described. Approaches to some of the nonlinear problems are presented. These include the nonlinearity due to foundation-structure interaction associated with the base slab uplift during seismic disturbances, the nonlinear base-isolation system for the reduction of earthquake-generated forces and deformations of superstructures, nonlinear systems having restoring-force functions in case of gaps and liift-off conditions, and nonlinearity of viscoelastic systems due to inelastic deformations. Available computer programs information for the solution of various types of nonlinear problems are provided. Advantages and disadvantages of some of the nonlinear and linear analyses are discussed. Comparison of some nonlinear and linear results of analyses are presented. Conclusions are reached with regard to research status and recommendations for further studies and for performing non-linear analyses associated with the problems of nonlinearity are presented. (Auth.)

Dynamics and control of quadcopter using linear model predictive control approach

Science.gov (United States)

Islam, M.; Okasha, M.; Idres, M. M.

2017-12-01

This paper investigates the dynamics and control of a quadcopter using the Model Predictive Control (MPC) approach. The dynamic model is of high fidelity and nonlinear, with six degrees of freedom that include disturbances and model uncertainties. The control approach is developed based on MPC to track different reference trajectories ranging from simple ones such as circular to complex helical trajectories. In this control technique, a linearized model is derived and the receding horizon method is applied to generate the optimal control sequence. Although MPC is computer expensive, it is highly effective to deal with the different types of nonlinearities and constraints such as actuators’ saturation and model uncertainties. The MPC parameters (control and prediction horizons) are selected by trial-and-error approach. Several simulation scenarios are performed to examine and evaluate the performance of the proposed control approach using MATLAB and Simulink environment. Simulation results show that this control approach is highly effective to track a given reference trajectory.

Predicting Mood Changes in Bipolar Disorder through Heartbeat Nonlinear Dynamics.

Science.gov (United States)

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

2016-04-20

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

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

Science.gov (United States)

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

2016-07-01

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

Nonlinear dynamical system identification using unscented Kalman filter

Science.gov (United States)

Rehman, M. Javvad ur; Dass, Sarat Chandra; Asirvadam, Vijanth Sagayan

2016-11-01

Kalman Filter is the most suitable choice for linear state space and Gaussian error distribution from decades. In general practical systems are not linear and Gaussian so these assumptions give inconsistent results. System Identification for nonlinear dynamical systems is a difficult task to perform. Usually, Extended Kalman Filter (EKF) is used to deal with non-linearity in which Jacobian method is used for linearizing the system dynamics, But it has been observed that in highly non-linear environment performance of EKF is poor. Unscented Kalman Filter (UKF) is proposed here as a better option because instead of analytical linearization of state space, UKF performs statistical linearization by using sigma point calculated from deterministic samples. Formation of the posterior distribution is based on the propagation of mean and covariance through sigma points.

The lie-algebraic structures and integrability of differential and differential-difference nonlinear dynamical systems

International Nuclear Information System (INIS)

Prykarpatsky, A.K.; Blackmore, D.L.; Bogolubov, N.N. Jr.

2007-05-01

The infinite-dimensional operator Lie algebras of the related integrable nonlocal differential-difference dynamical systems are treated as their hidden symmetries. As a result of their dimerization the Lax type representations for both local differential-difference equations and nonlocal ones are obtained. An alternative approach to the Lie-algebraic interpretation of the integrable local differential-difference systems is also proposed. The Hamiltonian representation for a hierarchy of Lax type equations on a dual space to the centrally extended Lie algebra of integro-differential operators with matrix-valued coefficients coupled with suitable eigenfunctions and adjoint eigenfunctions evolutions of associated spectral problems is obtained by means of a specially constructed Baecklund transformation. The Hamiltonian description for the corresponding set of additional symmetry hierarchies is represented. The relation of these hierarchies with Lax type integrable (3+1)-dimensional nonlinear dynamical systems and their triple Lax type linearizations is analyzed. The Lie-algebraic structures, related with centrally extended current operator Lie algebras are discussed with respect to constructing new nonlinear integrable dynamical systems on functional manifolds and super-manifolds. Special Poisson structures and related with them factorized integrable operator dynamical systems having interesting applications in modern mathematical physics, quantum computing mathematics and other fields are constructed. The previous purely computational results are explained within the approach developed. (author)

Non-Linear Dynamics and Fundamental Interactions

CERN Document Server

Khanna, Faqir

2006-01-01

The book is directed to researchers and graduate students pursuing an advanced degree. It provides details of techniques directed towards solving problems in non-linear dynamics and chos that are, in general, not amenable to a perturbative treatment. The consideration of fundamental interactions is a prime example where non-perturbative techniques are needed. Extension of these techniques to finite temperature problems is considered. At present these ideas are primarily used in a perturbative context. However, non-perturbative techniques have been considered in some specific cases. Experts in the field on non-linear dynamics and chaos and fundamental interactions elaborate the techniques and provide a critical look at the present status and explore future directions that may be fruitful. The text of the main talks will be very useful to young graduate students who are starting their studies in these areas.

Thermospheric dynamics - A system theory approach

Science.gov (United States)

Codrescu, M.; Forbes, J. M.; Roble, R. G.

1990-01-01

A system theory approach to thermospheric modeling is developed, based upon a linearization method which is capable of preserving nonlinear features of a dynamical system. The method is tested using a large, nonlinear, time-varying system, namely the thermospheric general circulation model (TGCM) of the National Center for Atmospheric Research. In the linearized version an equivalent system, defined for one of the desired TGCM output variables, is characterized by a set of response functions that is constructed from corresponding quasi-steady state and unit sample response functions. The linearized version of the system runs on a personal computer and produces an approximation of the desired TGCM output field height profile at a given geographic location.

Homotopy Analysis Method for Nonlinear Dynamical System of an Electrostatically Actuated Microcantilever

Directory of Open Access Journals (Sweden)

Y. M. Chen

2011-01-01

Full Text Available The homotopy analysis method (HAM is employed to propose an approach for solving the nonlinear dynamical system of an electrostatically actuated micro-cantilever in MEMS. There are two relative merits of the presented HAM compared with some usual procedures of the HAM. First, a new auxiliary linear operator is constructed. This operator makes it unnecessary to eliminate any secular terms. Furthermore, all the deformation equations are purely linear. Numerical examples show the excellent agreement of the attained solutions with numerical ones. The respective effects of applied voltage, cubic nonlinear stiffness, gap distance, and squeeze film damping on vibration responses are analyzed detailedly.

Data based identification and prediction of nonlinear and complex dynamical systems

Science.gov (United States)

Wang, Wen-Xu; Lai, Ying-Cheng; Grebogi, Celso

2016-07-01

The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and economics. The classic approach to phase-space reconstruction through the methodology of delay-coordinate embedding has been practiced for more than three decades, but the paradigm is effective mostly for low-dimensional dynamical systems. Often, the methodology yields only a topological correspondence of the original system. There are situations in various fields of science and engineering where the systems of interest are complex and high dimensional with many interacting components. A complex system typically exhibits a rich variety of collective dynamics, and it is of great interest to be able to detect, classify, understand, predict, and control the dynamics using data that are becoming increasingly accessible due to the advances of modern information technology. To accomplish these goals, especially prediction and control, an accurate reconstruction of the original system is required. Nonlinear and complex systems identification aims at inferring, from data, the mathematical equations that govern the dynamical evolution and the complex interaction patterns, or topology, among the various components of the system. With successful reconstruction of the system equations and the connecting topology, it may be possible to address challenging and significant problems such as identification of causal relations among the interacting components and detection of hidden nodes. The "inverse" problem thus presents a grand challenge, requiring new paradigms beyond the traditional delay-coordinate embedding methodology. The past fifteen years have witnessed rapid development of contemporary complex graph theory with broad applications in interdisciplinary science and engineering. The combination of graph, information, and nonlinear dynamical

Data based identification and prediction of nonlinear and complex dynamical systems

Energy Technology Data Exchange (ETDEWEB)

Wang, Wen-Xu [School of Systems Science, Beijing Normal University, Beijing, 100875 (China); Business School, University of Shanghai for Science and Technology, Shanghai 200093 (China); Lai, Ying-Cheng, E-mail: Ying-Cheng.Lai@asu.edu [School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287 (United States); Department of Physics, Arizona State University, Tempe, AZ 85287 (United States); Institute for Complex Systems and Mathematical Biology, King’s College, University of Aberdeen, Aberdeen AB24 3UE (United Kingdom); Grebogi, Celso [Institute for Complex Systems and Mathematical Biology, King’s College, University of Aberdeen, Aberdeen AB24 3UE (United Kingdom)

2016-07-12

The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and economics. The classic approach to phase-space reconstruction through the methodology of delay-coordinate embedding has been practiced for more than three decades, but the paradigm is effective mostly for low-dimensional dynamical systems. Often, the methodology yields only a topological correspondence of the original system. There are situations in various fields of science and engineering where the systems of interest are complex and high dimensional with many interacting components. A complex system typically exhibits a rich variety of collective dynamics, and it is of great interest to be able to detect, classify, understand, predict, and control the dynamics using data that are becoming increasingly accessible due to the advances of modern information technology. To accomplish these goals, especially prediction and control, an accurate reconstruction of the original system is required. Nonlinear and complex systems identification aims at inferring, from data, the mathematical equations that govern the dynamical evolution and the complex interaction patterns, or topology, among the various components of the system. With successful reconstruction of the system equations and the connecting topology, it may be possible to address challenging and significant problems such as identification of causal relations among the interacting components and detection of hidden nodes. The “inverse” problem thus presents a grand challenge, requiring new paradigms beyond the traditional delay-coordinate embedding methodology. The past fifteen years have witnessed rapid development of contemporary complex graph theory with broad applications in interdisciplinary science and engineering. The combination of graph, information, and nonlinear

Data based identification and prediction of nonlinear and complex dynamical systems

International Nuclear Information System (INIS)

Wang, Wen-Xu; Lai, Ying-Cheng; Grebogi, Celso

2016-01-01

The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and economics. The classic approach to phase-space reconstruction through the methodology of delay-coordinate embedding has been practiced for more than three decades, but the paradigm is effective mostly for low-dimensional dynamical systems. Often, the methodology yields only a topological correspondence of the original system. There are situations in various fields of science and engineering where the systems of interest are complex and high dimensional with many interacting components. A complex system typically exhibits a rich variety of collective dynamics, and it is of great interest to be able to detect, classify, understand, predict, and control the dynamics using data that are becoming increasingly accessible due to the advances of modern information technology. To accomplish these goals, especially prediction and control, an accurate reconstruction of the original system is required. Nonlinear and complex systems identification aims at inferring, from data, the mathematical equations that govern the dynamical evolution and the complex interaction patterns, or topology, among the various components of the system. With successful reconstruction of the system equations and the connecting topology, it may be possible to address challenging and significant problems such as identification of causal relations among the interacting components and detection of hidden nodes. The “inverse” problem thus presents a grand challenge, requiring new paradigms beyond the traditional delay-coordinate embedding methodology. The past fifteen years have witnessed rapid development of contemporary complex graph theory with broad applications in interdisciplinary science and engineering. The combination of graph, information, and nonlinear

Asymptotic investigation of the nonlinear boundary value dynamic problem for the systems with finite sizes

International Nuclear Information System (INIS)

Andrianov, I.V.; Danishevsky, V.V.

1994-01-01

Asymptotic approaches for nonlinear dynamics of continual system are developed well for the infinite in spatial variables. For the systems with finite sizes we have an infinite number of resonance, and Poincare-Lighthill-Go method does riot work. Using of averaging procedure or method of multiple scales leads to the infinite systems of nonlinear algebraic or ordinary differential equations systems and then using truncation method. which does not gives possibility to obtain all important properties of the solutions

Study nonlinear dynamics of stratospheric ozone concentration at Pakistan Terrestrial region

Science.gov (United States)

Jan, Bulbul; Zai, Muhammad Ayub Khan Yousuf; Afradi, Faisal Khan; Aziz, Zohaib

2018-03-01

This study investigates the nonlinear dynamics of the stratospheric ozone layer at Pakistan atmospheric region. Ozone considered now the most important issue in the world because of its diverse effects on earth biosphere, including human health, ecosystem, marine life, agriculture yield and climate change. Therefore, this paper deals with total monthly time series data of stratospheric ozone over the Pakistan atmospheric region from 1970 to 2013. Two approaches, basic statistical analysis and Fractal dimension (D) have adapted to study the nature of nonlinear dynamics of stratospheric ozone level. Results obtained from this research have shown that the Hurst exponent values of both methods of fractal dimension revealed an anti-persistent behavior (negatively correlated), i.e. decreasing trend for all lags and Rescaled range analysis is more appropriate as compared to Detrended fluctuation analysis. For seasonal time series all month follows an anti-persistent behavior except in the month of November which shown persistence behavior i.e. time series is an independent and increasing trend. The normality test statistics also confirmed the nonlinear behavior of ozone and the rejection of hypothesis indicates the strong evidence of the complexity of data. This study will be useful to the researchers working in the same field in the future to verify the complex nature of stratospheric ozone.

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 robust control of hypersonic aircrafts with interactions between flight dynamics and propulsion systems.

Science.gov (United States)

Li, Zhaoying; Zhou, Wenjie; Liu, Hao

2016-09-01

This paper addresses the nonlinear robust tracking controller design problem for hypersonic vehicles. This problem is challenging due to strong coupling between the aerodynamics and the propulsion system, and the uncertainties involved in the vehicle dynamics including parametric uncertainties, unmodeled model uncertainties, and external disturbances. By utilizing the feedback linearization technique, a linear tracking error system is established with prescribed references. For the linear model, a robust controller is proposed based on the signal compensation theory to guarantee that the tracking error dynamics is robustly stable. Numerical simulation results are given to show the advantages of the proposed nonlinear robust control method, compared to the robust loop-shaping control approach. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

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

Nonlinear dynamics and plasma transport

International Nuclear Information System (INIS)

Antonsen, T.M. Jr.; Drake, J.F.; Finn, J.M.; Guzdar, P.N.; Hassam, A.B.; Sagdeev, R.Z.

1992-01-01

In this paper we summarize the progress made over the last year in three different areas of research: (a) shear flow generation and reduced transport in fluids and plasma, (b) nonlinear dynamics and visualization of 3D flows, and (c) application of wavelet analysis to the study of fractal dimensions in experimental and numerical data

The nonlinear dynamics of a coupled fission system

International Nuclear Information System (INIS)

Bilanovic, Z.; Harms, A.A.

1993-01-01

The dynamic properties of a nonlinear and in situ vibrationally perturbed nuclear-to-thermal coupled neutron multiplying medium are examined. Some unique self-organizational temporal patterns appear in such fission systems and suggest a complex underlying dynamic. (Author)

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 dynamic mechanism of vocal tremor from voice analysis and model simulations

Science.gov (United States)

Zhang, Yu; Jiang, Jack J.

2008-09-01

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

A new approach to nonlinear constrained Tikhonov regularization

KAUST Repository

Ito, Kazufumi

2011-09-16

We present a novel approach to nonlinear constrained Tikhonov regularization from the viewpoint of optimization theory. A second-order sufficient optimality condition is suggested as a nonlinearity condition to handle the nonlinearity of the forward operator. The approach is exploited to derive convergence rate results for a priori as well as a posteriori choice rules, e.g., discrepancy principle and balancing principle, for selecting the regularization parameter. The idea is further illustrated on a general class of parameter identification problems, for which (new) source and nonlinearity conditions are derived and the structural property of the nonlinearity term is revealed. A number of examples including identifying distributed parameters in elliptic differential equations are presented. © 2011 IOP Publishing Ltd.

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

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 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

On modulated complex non-linear dynamical systems

International Nuclear Information System (INIS)

Mahmoud, G.M.; Mohamed, A.A.; Rauh, A.

1999-01-01

This paper is concerned with the development of an approximate analytical method to investigate periodic solutions and their stability in the case of modulated non-linear dynamical systems whose equation of motion is describe. Such differential equations appear, for example, in problems of colliding particle beams in high-energy accelerators or one-mass systems with two or more degrees of freedom, e.g. rotors. The significance of periodic solutions lies on the fact that all non-periodic responses, if convergent, would approach to periodic solutions at the steady-state conditions. The example shows a good agreement between numerical and analytical results for small values of ε. The effect of the periodic modulation on the stability of the 2π-periodic solutions is discussed

Dynamic bounds for power and efficiency of non-ideal energy converters under nonlinear transfer laws

International Nuclear Information System (INIS)

Sieniutycz, Stanislaw

2009-01-01

We present a thermodynamic approach to simulation and modeling of nonlinear energy converters, in particular radiation engines. Novel results are obtained especially for dynamical engines when the temperature of the propelling medium decreases in time due to a continual decrease of the medium's internal energy caused by the power production. Basic thermodynamic principles determine the converter's efficiency and work limits in terms of the entropy production. The real work is a cumulative effect obtained in a system of a resource fluid, a sequence of engines, and an infinite bath. Nonlinear modeling involves dynamic optimization in which the classical expression for efficiency at maximum power is generalized to endoirreversible machines and nonlinear transfer laws. The primary result is a finite-rate generalization of the classical, reversible work potential (exergy). The generalized work function depends on thermal coordinates and a dissipation index, h, i.e. a Hamiltonian of the minimum entropy production problem. This generalized work function implies stronger bounds on work delivered or supplied than the reversible work potential. The role of the nonlinear analyses and dynamic optimization is shown especially for radiation engines. As an example of the kinetic work limit, generalized exergy of radiation fluid is estimated in terms of finite rates, quantified by the Hamiltonian h

Nonlinear dynamics of semiconductors in strong THz electric fields

DEFF Research Database (Denmark)

Tarekegne, Abebe Tilahun

In this thesis, we investigate nonlinear interactions of an intense terahertz (THz) field with semiconductors, in particular the technologically relevant materials silicon and silicon carbide. We reveal the time-resolved dynamics of the nonlinear processes by pump-probe experiments that involve...

Nonlinear dynamic response of an electrically actuated imperfect microbeam resonator

KAUST Repository

Ruzziconi, Laura

2013-08-04

We present a study of the dynamic behavior of a MEMS device constituted 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 and the nonlinear dynamics are explored at increasing values of electrodynamic excitation, in a neighborhood of the first symmetric resonance. The nonlinear behavior is highlighted, which includes ranges of multistability, where the non-resonant 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 capable also to capture 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. Copyright © 2013 by ASME.

Third Conference on nonlinear science and complexity (NSC)

CERN Document Server

Machado, José; Baleanu, Dumitru; Dynamical Systems and Methods

2012-01-01

Nonlinear Systems and Methods For Mechanical, Electrical and Biosystems presents topics observed at the 3rd Conference on Nonlinear Science and Complexity(NSC), focusing on energy transfer and synchronization in hybrid nonlinear systems. The studies focus on fundamental theories and principles,analytical and symbolic approaches, computational techniques in nonlinear physical science and mathematics. Broken into three parts, the text covers:\\ Parametrical excited pendulum, nonlinear dynamics in hybrid systems, dynamical system synchronization and (N+1) body dynamics as well as new views different from the existing results in nonlinear dynamics. Mathematical methods for dynamical systems including conservation laws, dynamical symmetry in nonlinear differential equations and invex energies. Nonlinear phenomena in physical problems such as solutions, complex flows, chemical kinetics, Toda lattices and parallel manipulator. This book is useful to scholars, researchers and advanced technical members of industrial l...

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

Dynamics of electron wave packet in a disordered chain with delayed nonlinear response

International Nuclear Information System (INIS)

Zhu Hongjun; Xiong Shijie

2010-01-01

We investigate the dynamics of one electron wave packet in a linear chain with random on-site energies and a nonadiabatic electron-phonon interaction which is described by a delayed cubic nonlinear term in the time-dependent Schroedinger equation. We show that in the regime where the wave packet is delocalized in the case with only the delayed nonlinearity, the wave packet becomes localized when the disorder is added and the localization is enhanced by increasing the disorder. In the regime where the self-trapping phenomenon occurs in the case with only the delayed nonlinearity, by adding the disorder the general dynamical features of the wave packet do not change if the nonlinearity parameter is small, but the dynamics shows the subdiffusive behavior if the nonlinearity parameter is large. The numerical results demonstrate complicated wave packet dynamics of systems with both the disorder and nonlinearity.

Dynamic nonlinear analysis of shells of revolution

International Nuclear Information System (INIS)

Riesemann, W.A. von; Stricklin, J.A.; Haisler, W.E.

1975-01-01

Over the past few years a series of finite element computer programs have been developed at Texas A and M University for the static and dynamic nonlinear analysis of shells of revolution. This paper discusses one of these, DYNAPLAS, which is a program for the transient response of ring stiffened shells of revolution subjected to either asymmetric initial velocities or to asymmetric pressure loadings. Both material and geometric nonlinearities may be considered. (Auth.)

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.

A simple approach to nonlinear oscillators

International Nuclear Information System (INIS)

Ren Zhongfu; He Jihuan

2009-01-01

A very simple and effective approach to nonlinear oscillators is suggested. Anyone with basic knowledge of advanced calculus can apply the method to finding approximately the amplitude-frequency relationship of a nonlinear oscillator. Some examples are given to illustrate its extremely simple solution procedure and an acceptable accuracy of the obtained solutions.

Non-linear wave packet dynamics of coherent states

Indian Academy of Sciences (India)

In recent years, the non-linear quantum dynamics of these states have revealed some striking features. It was found that under the action of a Hamil- tonian which is a non-linear function of the photon operator(s) only, an initial coherent state loses its coherent structure quickly due to quantum dephasing induced by the non-.

Nonlinear Dynamics: Integrability, Chaos and Patterns

International Nuclear Information System (INIS)

Grammaticos, B

2004-01-01

's staircase'. I do not quite grasp the usefulness of such project-like exercises. Projects must be assigned by the person who indeed teaches the course. There are things that I really like a lot in this book. For instance, the section on 'chaos in nonlinear electronic circuits' is particularly interesting. It offers a simple and rather inexpensive way to visualize chaos in the laboratory. The closing section of the book devoted to technological applications of nonlinear dynamics is also quite useful. The fact that the treatment remains rather elementary, based on review articles and monographs rather than research articles, adds to the intelligibility of the chapter, which will certainly prove stimulating to many a student. Of course, not everything can be perfect, and a 600-page book is bound to have some weak points. I find the treatment of quantum chaos rather sketchy and that of chaotic scattering even more so. Also, while the authors are aware of the importance of complex time in integrability, they do not attempt an explanation of the fundamental puzzle: 'why, while the physical time is par excellence real, do we need a complex time in order to study the long-time behaviour of dynamical systems?'. Also the book devotes just four pages to integrable discrete systems. Given the tremendous development of this domain over the past decade, this short presentation is not doing justice to the subject. (However as the present reviewer is editing Springer Lecture Notes in Physics on precisely 'Integrable Discrete Systems', to appear in early 2004, he would be the last one to complain about the absence of more details on the matter in the present book.) To sum it up, the monograph of Lakshmanan and Rajasekar is a book written by physicists and for physicists. It will be of interest to both the experienced practitioner and to the uninitiated. Its main quality resides in its thorough, pedagogical approach to the matter. Moreover the relaxed, not too formal, style makes for easy

Nonlinear Dynamics: Integrability, Chaos and Patterns

Energy Technology Data Exchange (ETDEWEB)

Grammaticos, B [GMPIB, Universite Paris VII, Tour 24--14, 5e etage, Case 7021, 75251 Paris (France)

2004-02-06

-locking and b) devil's staircase'. I do not quite grasp the usefulness of such project-like exercises. Projects must be assigned by the person who indeed teaches the course. There are things that I really like a lot in this book. For instance, the section on 'chaos in nonlinear electronic circuits' is particularly interesting. It offers a simple and rather inexpensive way to visualize chaos in the laboratory. The closing section of the book devoted to technological applications of nonlinear dynamics is also quite useful. The fact that the treatment remains rather elementary, based on review articles and monographs rather than research articles, adds to the intelligibility of the chapter, which will certainly prove stimulating to many a student. Of course, not everything can be perfect, and a 600-page book is bound to have some weak points. I find the treatment of quantum chaos rather sketchy and that of chaotic scattering even more so. Also, while the authors are aware of the importance of complex time in integrability, they do not attempt an explanation of the fundamental puzzle: 'why, while the physical time is par excellence real, do we need a complex time in order to study the long-time behaviour of dynamical systems?'. Also the book devotes just four pages to integrable discrete systems. Given the tremendous development of this domain over the past decade, this short presentation is not doing justice to the subject. (However as the present reviewer is editing Springer Lecture Notes in Physics on precisely 'Integrable Discrete Systems', to appear in early 2004, he would be the last one to complain about the absence of more details on the matter in the present book.) To sum it up, the monograph of Lakshmanan and Rajasekar is a book written by physicists and for physicists. It will be of interest to both the experienced practitioner and to the uninitiated. Its main quality resides in its thorough, pedagogical approach to the matter

Nonlinear Dynamic Modeling of Langevin-Type Piezoelectric Transducers

Directory of Open Access Journals (Sweden)

Nicolás Peréz Alvarez

2015-11-01

Full Text Available Langevin transducers are employed in several applications, such as power ultrasound systems, naval hydrophones, and high-displacement actuators. Nonlinear effects can influence their performance, especially at high vibration amplitude levels. These nonlinear effects produce variations in the resonant frequency, harmonics of the excitation frequency, in addition to loss of symmetry in the frequency response and “frequency domain hysteresis”. In this context, this paper presents a simplified nonlinear dynamic model of power ultrasound transducers requiring only two parameters for simulating the most relevant nonlinear effects. One parameter reproduces the changes in the resonance frequency and the other introduces the dependence of the frequency response on the history of the system. The piezoelectric constitutive equations are extended by a linear dependence of the elastic constant on the mechanical displacement amplitude. For introducing the frequency hysteresis, the elastic constant is computed by combining the current value of the mechanical amplitude with the previous state amplitude. The model developed in this work is applied for predicting the dynamic responses of a 26 kHz ultrasonic transducer. The comparison of theoretical and experimental responses, obtained at several input voltages around the tuned frequency, shows a good agreement, indicating that the model can accurately describe the transducer nonlinear behavior.

Neuromechanical tuning of nonlinear postural control dynamics

Science.gov (United States)

Ting, Lena H.; van Antwerp, Keith W.; Scrivens, Jevin E.; McKay, J. Lucas; Welch, Torrence D. J.; Bingham, Jeffrey T.; DeWeerth, Stephen P.

2009-06-01

Postural control may be an ideal physiological motor task for elucidating general questions about the organization, diversity, flexibility, and variability of biological motor behaviors using nonlinear dynamical analysis techniques. Rather than presenting "problems" to the nervous system, the redundancy of biological systems and variability in their behaviors may actually be exploited to allow for the flexible achievement of multiple and concurrent task-level goals associated with movement. Such variability may reflect the constant "tuning" of neuromechanical elements and their interactions for movement control. The problem faced by researchers is that there is no one-to-one mapping between the task goal and the coordination of the underlying elements. We review recent and ongoing research in postural control with the goal of identifying common mechanisms underlying variability in postural control, coordination of multiple postural strategies, and transitions between them. We present a delayed-feedback model used to characterize the variability observed in muscle coordination patterns during postural responses to perturbation. We emphasize the significance of delays in physiological postural systems, requiring the modulation and coordination of both the instantaneous, "passive" response to perturbations as well as the delayed, "active" responses to perturbations. The challenge for future research lies in understanding the mechanisms and principles underlying neuromechanical tuning of and transitions between the diversity of postural behaviors. Here we describe some of our recent and ongoing studies aimed at understanding variability in postural control using physical robotic systems, human experiments, dimensional analysis, and computational models that could be enhanced from a nonlinear dynamics approach.

Nonlinear dynamics and quantum chaos an introduction

CERN Document Server

Wimberger, Sandro

2014-01-01

The field of nonlinear dynamics and chaos has grown very much over the last few decades and is becoming more and more relevant in different disciplines. This book presents a clear and concise introduction to the field of nonlinear dynamics and chaos, suitable for graduate students in mathematics, physics, chemistry, engineering, and in natural sciences in general. It provides a thorough and modern introduction to the concepts of Hamiltonian dynamical systems' theory combining in a comprehensive way classical and quantum mechanical description. It covers a wide range of topics usually not found in similar books. Motivations of the respective subjects and a clear presentation eases the understanding. The book is based on lectures on classical and quantum chaos held by the author at Heidelberg University. It contains exercises and worked examples, which makes it ideal for an introductory course for students as well as for researchers starting to work in the field.

Accurate detection of hierarchical communities in complex networks based on nonlinear dynamical evolution

Science.gov (United States)

Zhuo, Zhao; Cai, Shi-Min; Tang, Ming; Lai, Ying-Cheng

2018-04-01

One of the most challenging problems in network science is to accurately detect communities at distinct hierarchical scales. Most existing methods are based on structural analysis and manipulation, which are NP-hard. We articulate an alternative, dynamical evolution-based approach to the problem. The basic principle is to computationally implement a nonlinear dynamical process on all nodes in the network with a general coupling scheme, creating a networked dynamical system. Under a proper system setting and with an adjustable control parameter, the community structure of the network would "come out" or emerge naturally from the dynamical evolution of the system. As the control parameter is systematically varied, the community hierarchies at different scales can be revealed. As a concrete example of this general principle, we exploit clustered synchronization as a dynamical mechanism through which the hierarchical community structure can be uncovered. In particular, for quite arbitrary choices of the nonlinear nodal dynamics and coupling scheme, decreasing the coupling parameter from the global synchronization regime, in which the dynamical states of all nodes are perfectly synchronized, can lead to a weaker type of synchronization organized as clusters. We demonstrate the existence of optimal choices of the coupling parameter for which the synchronization clusters encode accurate information about the hierarchical community structure of the network. We test and validate our method using a standard class of benchmark modular networks with two distinct hierarchies of communities and a number of empirical networks arising from the real world. Our method is computationally extremely efficient, eliminating completely the NP-hard difficulty associated with previous methods. The basic principle of exploiting dynamical evolution to uncover hidden community organizations at different scales represents a "game-change" type of approach to addressing the problem of community

Structural predictor for nonlinear sheared dynamics in simple glass-forming liquids.

Science.gov (United States)

Ingebrigtsen, Trond S; Tanaka, Hajime

2018-01-02

Glass-forming liquids subjected to sufficiently strong shear universally exhibit striking nonlinear behavior; for example, a power-law decrease of the viscosity with increasing shear rate. This phenomenon has attracted considerable attention over the years from both fundamental and applicational viewpoints. However, the out-of-equilibrium and nonlinear nature of sheared fluids have made theoretical understanding of this phenomenon very challenging and thus slower to progress. We find here that the structural relaxation time as a function of the two-body excess entropy, calculated for the extensional axis of the shear flow, collapses onto the corresponding equilibrium curve for a wide range of pair potentials ranging from harsh repulsive to soft and finite. This two-body excess entropy collapse provides a powerful approach to predicting the dynamics of nonequilibrium liquids from their equilibrium counterparts. Furthermore, the two-body excess entropy scaling suggests that sheared dynamics is controlled purely by the liquid structure captured in the form of the two-body excess entropy along the extensional direction, shedding light on the perplexing mechanism behind shear thinning.

Structural predictor for nonlinear sheared dynamics in simple glass-forming liquids

Science.gov (United States)

Ingebrigtsen, Trond S.; Tanaka, Hajime

2018-01-01

Glass-forming liquids subjected to sufficiently strong shear universally exhibit striking nonlinear behavior; for example, a power-law decrease of the viscosity with increasing shear rate. This phenomenon has attracted considerable attention over the years from both fundamental and applicational viewpoints. However, the out-of-equilibrium and nonlinear nature of sheared fluids have made theoretical understanding of this phenomenon very challenging and thus slower to progress. We find here that the structural relaxation time as a function of the two-body excess entropy, calculated for the extensional axis of the shear flow, collapses onto the corresponding equilibrium curve for a wide range of pair potentials ranging from harsh repulsive to soft and finite. This two-body excess entropy collapse provides a powerful approach to predicting the dynamics of nonequilibrium liquids from their equilibrium counterparts. Furthermore, the two-body excess entropy scaling suggests that sheared dynamics is controlled purely by the liquid structure captured in the form of the two-body excess entropy along the extensional direction, shedding light on the perplexing mechanism behind shear thinning.

Nonlinear Dynamic Theory of Acute Cell Injuries and Brain Ischemia

Science.gov (United States)

Taha, Doaa; Anggraini, Fika; Degracia, Donald; Huang, Zhi-Feng

2015-03-01

Cerebral ischemia in the form of stroke and cardiac arrest brain damage affect over 1 million people per year in the USA alone. In spite of close to 200 clinical trials and decades of research, there are no treatments to stop post-ischemic neuron death. We have argued that a major weakness of current brain ischemia research is lack of a deductive theoretical framework of acute cell injury to guide empirical studies. A previously published autonomous model based on the concept of nonlinear dynamic network was shown to capture important facets of cell injury, linking the concept of therapeutic to bistable dynamics. Here we present an improved, non-autonomous formulation of the nonlinear dynamic model of cell injury that allows multiple acute injuries over time, thereby allowing simulations of both therapeutic treatment and preconditioning. Our results are connected to the experimental data of gene expression and proteomics of neuron cells. Importantly, this new model may be construed as a novel approach to pharmacodynamics of acute cell injury. The model makes explicit that any pro-survival therapy is always a form of sub-lethal injury. This insight is expected to widely influence treatment of acute injury conditions that have defied successful treatment to date. This work is supported by NIH NINDS (NS081347) and Wayne State University President's Research Enhancement Award.

Lifespan Differences in Nonlinear Dynamics during Rest and Auditory Oddball Performance

Science.gov (United States)

Muller, Viktor; Lindenberger, Ulman

2012-01-01

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

DYNAMICS OF FINANCIAL SYSTEM: A SYSTEM DYNAMICS APPROACH

Directory of Open Access Journals (Sweden)

Girish K Nair

2013-01-01

Full Text Available There are several ratios which define the financial health of an organization but the importance of Net cash flow, Gross income, Net income, Pending bills, Receivable bills, Debt, and Book value can never be undermined as they give the exact picture of the financial condition. While there are several approaches to study the dynamics of these variables, system dynamics based modelling and simulation is one of the modern techniques. The paper explores this method to simulate the before mentioned parameters during production capacity expansion in an electronic industry. Debt and Book value have shown a non-linear pattern of variation which is discussed. The model can be used by the financial experts as a decision support tool in arriving at conclusions in connection to the expansion plans of the organization.

Nonlinear quantum dynamics in diatomic molecules: Vibration, rotation and spin

International Nuclear Information System (INIS)

Yang, Ciann-Dong; Weng, Hung-Jen

2012-01-01

Highlights: ► This paper reveals the internal nonlinear dynamics embedded in a molecular quantum state. ► Analyze quantum molecular dynamics in a deterministic way, while preserving the consistency with probability interpretation. ► Molecular vibration–rotation interaction and spin–orbital coupling are considered simultaneously. ► Spin is just the remnant angular motion when orbital angular momentum is zero. ► Spin is the “zero dynamics” of nonlinear quantum dynamics. - Abstract: For a given molecular wavefunction Ψ, the probability density function Ψ ∗ Ψ is not the only information that can be extracted from Ψ. We point out in this paper that nonlinear quantum dynamics of a diatomic molecule, completely consistent with the probability prediction of quantum mechanics, does exist and can be derived from the quantum Hamilton equations of motion determined by Ψ. It can be said that the probability density function Ψ ∗ Ψ is an external representation of the quantum state Ψ, while the related Hamilton dynamics is an internal representation of Ψ, which reveals the internal mechanism underlying the externally observed random events. The proposed internal representation of Ψ establishes a bridge between nonlinear dynamics and quantum mechanics, which allows the methods and tools already developed by the former to be applied to the latter. Based on the quantum Hamilton equations of motion derived from Ψ, vibration, rotation and spin motions of a diatomic molecule and the interactions between them can be analyzed simultaneously. The resulting dynamic analysis of molecular motion is compared with the conventional probability analysis and the consistency between them is demonstrated.

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.

Laser acceleration and nonlinear beam dynamics

International Nuclear Information System (INIS)

Pellegrini, C.

1991-01-01

This research contract covers the period April 1990, September 1991. The work to be done under the contract was theoretical research in the areas of nonlinear beam dynamics and laser acceleration. In this final report we will discuss the motivation for this work and the results obtained

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.

Dynamic modeling of moment wheel assemblies with nonlinear rolling bearing supports

Science.gov (United States)

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

2017-10-01

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

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

Stability and nonlinear dynamics of gyrotrons at cyclotron harmonics

International Nuclear Information System (INIS)

Saraph, G.P.; Nusinovich, G.S.; Antonsen, T.M. Jr.; Levush, B.

1992-01-01

Gyrotrons operating at higher harmonics of the cyclotron frequency can overcome the frequency limitations caused by achievable strength of the magnetic field. However, the excitation of modes at the fundamental frequency exhibit a major problem for stable operation of harmonic gyrotron at high power with high efficiency. Therefore the issues of stability of gyrotron operation at the cyclotron harmonics and nonlinear dynamics of mode interaction are of great importance. The results of the authors stability analysis and multimode simulation are presented here. A detailed nonlinear theory of steady state single mode operation at cyclotron harmonics has been presented previously, taking into account beam-wave coupling and nonlinear gain function at cyclotron harmonics. A set of equations describing low gain regime interaction of modes resonant at different cyclotron harmonics was studied before. The multifrequency time-dependent nonlinear analysis presented here is based on previous gyrotron studies and beam-wave interaction at cyclotron harmonics. The authors have determined the parameter space for stable single mode operation at the second harmonic. The nonlinear dynamics of mode evolution and mode interaction for a harmonic gyrotron is presented. A new nonlinear effect in which the parasite at the fundamental harmonic helps excite the operating mode at the second harmonic has been demonstrated

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

Science.gov (United States)

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

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 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 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.

Topics in Nonlinear Dynamics

DEFF Research Database (Denmark)

Mosekilde, Erik

Through a significant number of detailed and realistic examples this book illustrates how the insights gained over the past couple of decades in the fields of nonlinear dynamics and chaos theory can be applied in practice. Aomng the topics considered are microbiological reaction systems, ecological...... food-web systems, nephron pressure and flow regulation, pulsatile secretion of hormones, thermostatically controlled radiator systems, post-stall maneuvering of aircrafts, transfer electron devices for microwave generation, economic long waves, human decision making behavior, and pattern formation...... in chemical reaction-diffusion systems....

Nonlinear dynamic effects in a two-wave CO2 laser

International Nuclear Information System (INIS)

Gorobets, V A; Kozlov, K V; Kuntsevich, B F; Petukhov, V O

1999-01-01

Theoretical and experimental investigations were made of nonlinear dynamic regimes of the operation of a two-wave CO 2 laser with cw excitation in an electric discharge and loss modulation in one of the channels. Nonlinear amplitude - frequency characteristics of each of the laser channels have two low-frequency resonance spikes, associated with forced linear oscillations of two coupled oscillators, and high-frequency spikes, corresponding to doubling of the period of the output radiation oscillations. At low loss-modulation frequencies the intensity oscillations of the output radiation in the coupled channels are in antiphase, whereas at high modulation frequencies the dynamics is cophasal. Nonlinear dynamic effects, such as doubling of the period and of the repetition frequency of the pulses and chaotic oscillations of the output radiation intensity, are observed for certain system parameters. (control of laser radiation parameters)

Local interaction simulation approach to modelling nonclassical, nonlinear elastic behavior in solids.

Science.gov (United States)

Scalerandi, Marco; Agostini, Valentina; Delsanto, Pier Paolo; Van Den Abeele, Koen; Johnson, Paul A

2003-06-01

Recent studies show that a broad category of materials share "nonclassical" nonlinear elastic behavior much different from "classical" (Landau-type) nonlinearity. Manifestations of "nonclassical" nonlinearity include stress-strain hysteresis and discrete memory in quasistatic experiments, and specific dependencies of the harmonic amplitudes with respect to the drive amplitude in dynamic wave experiments, which are remarkably different from those predicted by the classical theory. These materials have in common soft "bond" elements, where the elastic nonlinearity originates, contained in hard matter (e.g., a rock sample). The bond system normally comprises a small fraction of the total material volume, and can be localized (e.g., a crack in a solid) or distributed, as in a rock. In this paper a model is presented in which the soft elements are treated as hysteretic or reversible elastic units connected in a one-dimensional lattice to elastic elements (grains), which make up the hard matrix. Calculations are performed in the framework of the local interaction simulation approach (LISA). Experimental observations are well predicted by the model, which is now ready both for basic investigations about the physical origins of nonlinear elasticity and for applications to material damage diagnostics.

Mental-disorder detection using chaos and nonlinear dynamical analysis of photoplethysmographic signals

International Nuclear Information System (INIS)

Pham, Tuan D.; Thang, Truong Cong; Oyama-Higa, Mayumi; Sugiyama, Masahide

2013-01-01

Highlights: • Chaos and nonlinear dynamical analysis are applied for mental-disorder detection. • Experimental results show significant detection improvement with feature synergy. • Proposed approach is effective for analysis of photoplethysmographic signals. • Proposed approach is promising for developing automated mental-health systems. -- Abstract: Mental disorder can be defined as a psychological disturbance of thought or emotion. In particular, depression is a mental disease which can ultimately lead to death from suicide. If depression is identified, it can be treated with medication and psychotherapy. However, the diagnosis of depression is difficult and there are currently no any quick and reliable medical tests to detect if someone is depressed. This is because the exact cause of depression is still unknown given the belief that depression results in chemical brain changes, genetic disorder, stress, or the combination of these problems. Photoplethysmography has recently been realized as a non-invasive optical technique that can give new insights into the physiology and pathophysiology of the central and peripheral nervous systems. We present in this paper an automated mental-disorder detection approach in a general sense based on a novel synergy of chaos and nonlinear dynamical methods for the analysis of photoplethysmographic finger pulse waves of mental and control subjects. Such an approach can be applied for automated detection of depression as a special case. Because of the computational effectiveness of the studied methods and low cost of generation of the physiological signals, the proposed automated detection of mental illness is feasible for real-life applications including self-assessment, self-monitoring, and computerized health care

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

Science.gov (United States)

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

2017-06-12

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

Dynamics of nonlinear dielectric susceptibility of ferroelectrics near the morphotropic phase boundary

International Nuclear Information System (INIS)

Ibrahim, Abdel-Baset M A; Osman, Junaidah

2013-01-01

The dynamics of the nonlinear (NL) dielectric susceptibility of ferroelectrics (FE) near the morphotropic phase boundary (MPB) is theoretically investigated based on the Landau–Devonshire free energy approach and the concept of FE soft modes. To do so, the NL dielectric susceptibility elements of FE material in the tetragonal phase are expressed as functions of optical phonon modes. These are the E modes with normal characteristic frequency ω E 2 and the A modes with ω A 2 . On the one hand, the tetragonal E modes appear to exhibit a double soft-mode character, i.e. the mode softens either when the thermodynamic temperature T approaches the transition temperature T c or when the free energy parameter β 1 approaches β 2 . On the other hand, the A modes exhibit single soft-mode character when T approaches T c . Within this formulation, the dynamics of first-, second- and third-order NL susceptibility elements are investigated. The origin of the anomalous behavior of certain NL elements at the MPB appears to be a manifestation of FE mode-softening. This approach provides a simple yet powerful technique to understand the dynamics of the NL dielectric susceptibility elements of FE material near the MPB. (paper)

NONLINEAR FILTER METHOD OF GPS DYNAMIC POSITIONING BASED ON BANCROFT ALGORITHM

Institute of Scientific and Technical Information of China (English)

ZHANGQin; TAOBen-zao; ZHAOChao-ying; WANGLi

2005-01-01

Because of the ignored items after linearization, the extended Kalman filter (EKF) becomes a form of suboptimal gradient descent algorithm. The emanative tendency exists in GPS solution when the filter equations are ill-posed. The deviation in the estimation cannot be avoided. Furthermore, the true solution may be lost in pseudorange positioning because the linearized pseudorange equations are partial solutions. To solve the above problems in GPS dynamic positioning by using EKF, a closed-form Kalman filter method called the two-stage algorithm is presented for the nonlinear algebraic solution of GPS dynamic positioning based on the global nonlinear least squares closed algorithm--Bancroft numerical algorithm of American. The method separates the spatial parts from temporal parts during processing the GPS filter problems, and solves the nonlinear GPS dynamic positioning, thus getting stable and reliable dynamic positioning solutions.

Nonlinear Dynamics of Electrostatically Actuated MEMS Arches

KAUST Repository

Al Hennawi, Qais M.

2015-01-01

In this thesis, we present theoretical and experimental investigation into the nonlinear statics and dynamics of clamped-clamped in-plane MEMS arches when excited by an electrostatic force. Theoretically, we first solve the equation of motion using

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)

Nonlinear Dynamics of a Diffusing Interface

Science.gov (United States)

Duval, Walter M. B.

2001-01-01

Excitation of two miscible-viscous liquids inside a bounded enclosure in a microgravity environment has shown the evolution of quasi-stationary waves of various modes for a range of parameters. We examine computationally the nonlinear dynamics of the system as the interface breakup and bifurcates to resonance structures typified by the Rayleigh-Taylor instability mechanism. Results show that when the mean steady field is much smaller than the amplitude of the sinusoidal excitation, the system behaves linearly, and growth of quasi-stationary waves occurs through the Kelvin-Helmholtz instability mechanism. However, as the amplitude of excitation increases, nonlinearity occurs through subharmonic bifurcation prior to broadband chaos.

Nonlinear analysis and dynamic structure in the energy market

Science.gov (United States)

Aghababa, Hajar

This research assesses the dynamic structure of the energy sector of the aggregate economy in the context of nonlinear mechanisms. Earlier studies have focused mainly on the price of the energy products when detecting nonlinearities in time series data of the energy market, and there is little mention of the production side of the market. Moreover, there is a lack of exploration about the implication of high dimensionality and time aggregation when analyzing the market's fundamentals. This research will address these gaps by including the quantity side of the market in addition to the price and by systematically incorporating various frequencies for sample sizes in three essays. The goal of this research is to provide an inclusive and exhaustive examination of the dynamics in the energy markets. The first essay begins with the application of statistical techniques, and it incorporates the most well-known univariate tests for nonlinearity with distinct power functions over alternatives and tests different null hypotheses. It utilizes the daily spot price observations on five major products in the energy market. The results suggest that the time series daily spot prices of the energy products are highly nonlinear in their nature. They demonstrate apparent evidence of general nonlinear serial dependence in each individual series, as well as nonlinearity in the first, second, and third moments of the series. The second essay examines the underlying mechanism of crude oil production and identifies the nonlinear structure of the production market by utilizing various monthly time series observations of crude oil production: the U.S. field, Organization of the Petroleum Exporting Countries (OPEC), non-OPEC, and the world production of crude oil. The finding implies that the time series data of the U.S. field, OPEC, and the world production of crude oil exhibit deep nonlinearity in their structure and are generated by nonlinear mechanisms. However, the dynamics of the non

Dynamics of metastable breathers in nonlinear chains in acoustic vacuum

Science.gov (United States)

Sen, Surajit; Mohan, T. R. Krishna

2009-03-01

The study of the dynamics of one-dimensional chains with both harmonic and nonlinear interactions, as in the Fermi-Pasta-Ulam and related problems, has played a central role in efforts to identify the broad consequences of nonlinearity in these systems. Nevertheless, little is known about the dynamical behavior of purely nonlinear chains where there is a complete absence of the harmonic term, and hence sound propagation is not admissible, i.e., under conditions of “acoustic vacuum.” Here we study the dynamics of highly localized excitations, or breathers, which are known to be initiated by the quasistatic stretching of the bonds between adjacent particles. We show via detailed particle-dynamics-based studies that many low-energy pulses also form in the vicinity of the perturbation, and the breathers that form are “fragile” in the sense that they can be easily delocalized by scattering events in the system. We show that the localized excitations eventually disperse, allowing the system to attain an equilibrium-like state that is realizable in acoustic vacuum. We conclude with a discussion of how the dynamics is affected by the presence of acoustic oscillations.

An equivalent frequency approach for determining non-linear effects on pre-tensioned-cable cross-braced structures

Science.gov (United States)

Giaccu, Gian Felice

2018-05-01

Pre-tensioned cable braces are widely used as bracing systems in various structural typologies. This technology is fundamentally utilized for stiffening purposes in the case of steel and timber structures. The pre-stressing force imparted to the braces provides to the system a remarkable increment of stiffness. On the other hand, the pre-tensioning force in the braces must be properly calibrated in order to satisfactorily meet both serviceability and ultimate limit states. Dynamic properties of these systems are however affected by non-linear behavior due to potential slackening of the pre-tensioned brace. In the recent years the author has been working on a similar problem regarding the non-linear response of cables in cable-stayed bridges and braced structures. In the present paper a displacement-based approach is used to examine the non-linear behavior of a building system. The methodology operates through linearization and allows obtaining an equivalent linearized frequency to approximately characterize, mode by mode, the dynamic behavior of the system. The equivalent frequency depends on both the mechanical characteristics of the system, the pre-tensioning level assigned to the braces and a characteristic vibration amplitude. The proposed approach can be used as a simplified technique, capable of linearizing the response of structural systems, characterized by non-linearity induced by the slackening of pre-tensioned braces.

Nonlinear dynamics in psychology

Directory of Open Access Journals (Sweden)

Stephen J. Guastello

2001-01-01

Full Text Available This article provides a survey of the applications of nonlinear dynamical systems theory to substantive problems encountered in the full scope of psychological science. Applications are organized into three topical areas – cognitive science, social and organizational psychology, and personality and clinical psychology. Both theoretical and empirical studies are considered with an emphasis on works that capture the broadest scope of issues that are of substantive interest to psychological theory. A budding literature on the implications of NDS principles in professional practice is reported also.

Dynamic nonlinear elasticity in geo materials

International Nuclear Information System (INIS)

Ostrovsky, L.A.; Johnson, P.A.

2001-01-01

The nonlinear elastic behaviour of earth materials is an extremely rich topic, one that has broad implications to earth and materials sciences, including strong ground motion, rock physics, nondestructive evaluation and materials science. The mechanical properties of rock appear to place it in a broader class of materials, it can be named the Structural nonlinear elasticity class (also Mesoscopic/nano scale elasticity, or MS/NSE class). These terms are in contrast to materials that display classical, Atomic Elasticity, such as most fluids and monocrystalline solids. The difference between these two categories of materials is both in intensity and origin of their nonlinear response. The nonlinearity of atomic elastic materials is due to the atomic/molecular lattice anharmonicity. The latter is relatively small because the intermolecular forces are extremely strong. In contrast, the materials considered below contain small soft features that it is called the bond system (cracks, grain contacts, dislocations, etc.) within a hard matrix and relaxation (slow dynamical effects) are characteristic, non of which appear in atomic elastic materials. The research begins with a brief historical background from nonlinear acoustics to the recent developments in rock nonlinearity. This is followed by an overview of some representative laboratory measurements which serve as primary indicators of nonlinear behaviour, followed by theoretical development, and finally, mention a variety of observations of nonlinearity under field conditions and applications to nondestructive testing of materials. The goal is not to survey all papers published in the are but to demonstrate some experimental and theoretical results and ideas that will the reader to become oriented in this broad and rapidly growing area bridging macro-, meso- and microscale (nano scale) phenomena in physics, materials science, and geophysics

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 of cortical responses to color in the human cVEP.

Science.gov (United States)

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

2017-09-01

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

Nonlinear dynamics and control of a vibrating rectangular plate

Science.gov (United States)

Shebalin, J. V.

1983-01-01

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

Noise Response Data Reveal Novel Controllability Gramian for Nonlinear Network Dynamics

Science.gov (United States)

Kashima, Kenji

2016-01-01

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

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

Temporal nonlinear beam dynamics in infiltrated photonic crystal fibers

DEFF Research Database (Denmark)

Bennet, Francis; Rosberg, Christian Romer; Neshev, Dragomir N.

Liquid-infiltrated photonic crystal fibers (PCFs) offer a new way of studying light propagation in periodic and discrete systems. A wide range of available fiber structures combined with the ease of infiltration opens up a range of novel experimental opportunities for optical detection and bio...... the evolution of the fiber output beam in the few micro or milliseconds after the beam is turned on. The characterization of the temporal behavior of the thermal nonlinear response provides important information about the nonlocality associated with heat diffusion inside the fiber, thus enabling studies of long...... and technological potential of liquid-infiltrated PCFs it is important to understand the temporal dynamics of nonlinear beam propagation in such structures. In this work we consider thermally induced spatial nonlinear effects in infiltrated photonic crystal fibers. We experimentally study the temporal dynamics...

Possibilities of fractal analysis of the competitive dynamics: Approaches and procedures

Science.gov (United States)

Zagornaya, T. O.; Medvedeva, M. A.; Panova, V. L.; Isaichik, K. F.; Medvedev, A. N.

2017-11-01

The possibilities of the fractal approach are used for the study of non-linear nature of the competitive dynamics of the market of trading intermediaries. Based on a statistical study of the functioning of retail indicators in the region, the approach to the analysis of the characteristics of the competitive behavior of market participants is developed. The authors postulate the principles of studying the dynamics of competition as a result of changes in the characteristics of the vector and the competitive behavior of market agents.

Spurious Solutions Of Nonlinear Differential Equations

Science.gov (United States)

Yee, H. C.; Sweby, P. K.; Griffiths, D. F.

1992-01-01

Report utilizes nonlinear-dynamics approach to investigate possible sources of errors and slow convergence and non-convergence of steady-state numerical solutions when using time-dependent approach for problems containing nonlinear source terms. Emphasizes implications for development of algorithms in CFD and computational sciences in general. Main fundamental conclusion of study is that qualitative features of nonlinear differential equations cannot be adequately represented by finite-difference method and vice versa.

Nonlinear dynamics of charged particles in the magnetotail

Science.gov (United States)

Chen, James

1992-01-01

An important region of the earth's magnetosphere is the nightside magnetotail, which is believed to play a significant role in energy storage and release associated with substorms. The magnetotail contains a current sheet which separates regions of oppositely directed magnetic field. Particle motion in the collisionless magnetotail has been a long-standing problem. Recent research from the dynamical point of view has yielded considerable new insights into the fundamental properties of orbits and of particle distribution functions. A new framework of understanding magnetospheric plasma properties is emerging. Some novel predictions based directly on nonlinear dynamics have proved to be robust and in apparent good agreement with observation. The earth's magnetotail may serve as a paradigm, one accessible by in situ observation, of a broad class of boundary regions with embedded current sheets. This article reviews the nonlinear dynamics of charged particles in the magnetotail configuration. The emphasis is on the relationships between the dynamics and physical observables. At the end of the introduction, sections containing basic material are indicated.

Nonlinear optical systems

CERN Document Server

Lugiato, Luigi; Brambilla, Massimo

2015-01-01

Guiding graduate students and researchers through the complex world of laser physics and nonlinear optics, this book provides an in-depth exploration of the dynamics of lasers and other relevant optical systems, under the umbrella of a unitary spatio-temporal vision. Adopting a balanced approach, the book covers traditional as well as special topics in laser physics, quantum electronics and nonlinear optics, treating them from the viewpoint of nonlinear dynamical systems. These include laser emission, frequency generation, solitons, optically bistable systems, pulsations and chaos and optical pattern formation. It also provides a coherent and up-to-date treatment of the hierarchy of nonlinear optical models and of the rich variety of phenomena they describe, helping readers to understand the limits of validity of each model and the connections among the phenomena. It is ideal for graduate students and researchers in nonlinear optics, quantum electronics, laser physics and photonics.

Differential Neural Networks for Identification and Filtering in Nonlinear Dynamic Games

Directory of Open Access Journals (Sweden)

Emmanuel García

2014-01-01

Full Text Available This paper deals with the problem of identifying and filtering a class of continuous-time nonlinear dynamic games (nonlinear differential games subject to additive and undesired deterministic perturbations. Moreover, the mathematical model of this class is completely unknown with the exception of the control actions of each player, and even though the deterministic noises are known, their power (or their effect is not. Therefore, two differential neural networks are designed in order to obtain a feedback (perfect state information pattern for the mentioned class of games. In this way, the stability conditions for two state identification errors and for a filtering error are established, the upper bounds of these errors are obtained, and two new learning laws for each neural network are suggested. Finally, an illustrating example shows the applicability of this approach.

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 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.

Discretization model for nonlinear dynamic analysis of three dimensional structures

International Nuclear Information System (INIS)

Hayashi, Y.

1982-12-01

A discretization model for nonlinear dynamic analysis of three dimensional structures is presented. The discretization is achieved through a three dimensional spring-mass system and the dynamic response obtained by direct integration of the equations of motion using central diferences. First the viability of the model is verified through the analysis of homogeneous linear structures and then its performance in the analysis of structures subjected to impulsive or impact loads, taking into account both geometrical and physical nonlinearities is evaluated. (Author) [pt

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

An introduction to complex systems society, ecology, and nonlinear dynamics

CERN Document Server

Fieguth, Paul

2017-01-01

This undergraduate text explores a variety of large-scale phenomena - global warming, ice ages, water, poverty - and uses these case studies as a motivation to explore nonlinear dynamics, power-law statistics, and complex systems. Although the detailed mathematical descriptions of these topics can be challenging, the consequences of a system being nonlinear, power-law, or complex are in fact quite accessible. This book blends a tutorial approach to the mathematical aspects of complex systems together with a complementary narrative on the global/ecological/societal implications of such systems. Nearly all engineering undergraduate courses focus on mathematics and systems which are small scale, linear, and Gaussian. Unfortunately there is not a single large-scale ecological or social phenomenon that is scalar, linear, and Gaussian. This book offers students insights to better understand the large-scale problems facing the world and to realize that these cannot be solved by a single, narrow academic field or per...

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.

Any order approximate analytical solution of the nonlinear Volterra's integral equation for accelerator dynamic systems

International Nuclear Information System (INIS)

Liu Chunliang; Xie Xi; Chen Yinbao

1991-01-01

The universal nonlinear dynamic system equation is equivalent to its nonlinear Volterra's integral equation, and any order approximate analytical solution of the nonlinear Volterra's integral equation is obtained by exact analytical method, thus giving another derivation procedure as well as another computation algorithm for the solution of the universal nonlinear dynamic system equation

Effect of sample shape on nonlinear magnetization dynamics under an external magnetic field

International Nuclear Information System (INIS)

Vagin, Dmitry V.; Polyakov, Oleg P.

2008-01-01

Effect of sample shape on the nonlinear collective dynamics of magnetic moments in the presence of oscillating and constant external magnetic fields is studied using the Landau-Lifshitz-Gilbert (LLG) approach. The uniformly magnetized sample is considered to be an ellipsoidal axially symmetric particle described by demagnetization factors and uniaxial crystallographic anisotropy formed some angle with an applied field direction. It is investigated as to how the change in particle shape affects its nonlinear magnetization dynamics. To produce a regular study, all results are presented in the form of bifurcation diagrams for all sufficient dynamics regimes of the considered system. In this paper, we show that the sample's (particle's) shape and its orientation with respect to the external field (system configuration) determine the character of magnetization dynamics: deterministic behavior and appearance of chaotic states. A simple change in the system's configuration or in the shapes of its parts can transfer it from chaotic to periodic or even static regime and back. Moreover, the effect of magnetization precession stall and magnetic moments alignment parallel or antiparallel to the external oscillating field is revealed and the way of control of such 'polarized' states is found. Our results suggest that varying the particle's shape and fields' geometry may provide a useful way of magnetization dynamics control in complex magnetic systems

Numerical simulation of nonlinear dynamical systems driven by commutative noise

International Nuclear Information System (INIS)

Carbonell, F.; Biscay, R.J.; Jimenez, J.C.; Cruz, H. de la

2007-01-01

The local linearization (LL) approach has become an effective technique for the numerical integration of ordinary, random and stochastic differential equations. One of the reasons for this success is that the LL method achieves a convenient trade-off between numerical stability and computational cost. Besides, the LL method reproduces well the dynamics of nonlinear equations for which other classical methods fail. However, in the stochastic case, most of the reported works has been focused in Stochastic Differential Equations (SDE) driven by additive noise. This limits the applicability of the LL method since there is a number of interesting dynamics observed in equations with multiplicative noise. On the other hand, recent results show that commutative noise SDEs can be transformed into a random differential equation (RDE) by means of a random diffeomorfism (conjugacy). This paper takes advantages of such conjugacy property and the LL approach for defining a LL scheme for SDEs driven by commutative noise. The performance of the proposed method is illustrated by means of numerical simulations

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...

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.

Nonlinear Dynamic Buckling of Damaged Composite Cylindrical Shells

Institute of Scientific and Technical Information of China (English)

WANG Tian-lin; TANG Wen-yong; ZHANG Sheng-kun

2007-01-01

Based on the first order shear deformation theory(FSDT), the nonlinear dynamic equations involving transverse shear deformation and initial geometric imperfections were obtained by Hamilton's philosophy. Geometric deformation of the composite cylindrical shell was treated as the initial geometric imperfection in the dynamic equations, which were solved by the semi-analytical method in this paper. Stiffness reduction was employed for the damaged sub-layer, and the equivalent stiffness matrix was obtained for the delaminated area. By circumferential Fourier series expansions for shell displacements and loads and by using Galerkin technique, the nonlinear partial differential equations were transformed to ordinary differential equations which were finally solved by the finite difference method. The buckling was judged from shell responses by B-R criteria, and critical loads were then determined. The effect of the initial geometric deformation on the dynamic response and buckling of composite cylindrical shell was also discussed, as well as the effects of concomitant delamination and sub-layer matrix damages.

Nonlinear control and filtering using differential flatness approaches applications to electromechanical systems

CERN Document Server

Rigatos, Gerasimos G

2015-01-01

This monograph presents recent advances in differential flatness theory and analyzes its use for nonlinear control and estimation. It shows how differential flatness theory can provide solutions to complicated control problems, such as those appearing in highly nonlinear multivariable systems and distributed-parameter systems. Furthermore, it shows that differential flatness theory makes it possible to perform filtering and state estimation for a wide class of nonlinear dynamical systems and provides several descriptive test cases. The book focuses on the design of nonlinear adaptive controllers and nonlinear filters, using exact linearization based on differential flatness theory. The adaptive controllers obtained can be applied to a wide class of nonlinear systems with unknown dynamics, and assure reliable functioning of the control loop under uncertainty and varying operating conditions. The filters obtained outperform other nonlinear filters in terms of accuracy of estimation and computation speed. The bo...

Nonlinear dynamics in integrated coupled DFB lasers with ultra-short delay.

Science.gov (United States)

Liu, Dong; Sun, Changzheng; Xiong, Bing; Luo, Yi

2014-03-10

We report rich nonlinear dynamics in integrated coupled lasers with ultra-short coupling delay. Mutually stable locking, period-1 oscillation, frequency locking, quasi-periodicity and chaos are observed experimentally. The dynamic behaviors are reproduced numerically by solving coupled delay differential equations that take the variation of both frequency detuning and coupling phase into account. Moreover, it is pointed out that the round-trip frequency is not involved in the above nonlinear dynamical behaviors. Instead, the relationship between the frequency detuning Δν and the relaxation oscillation frequency νr under mutual injection are found to be critical for the various observed dynamics in mutually coupled lasers with very short delay.

Microtubules Nonlinear Models Dynamics Investigations through the exp(−Φ(ξ-Expansion Method Implementation

Directory of Open Access Journals (Sweden)

Nur Alam

2016-02-01

Full Text Available In this research article, we present exact solutions with parameters for two nonlinear model partial differential equations(PDEs describing microtubules, by implementing the exp(−Φ(ξ-Expansion Method. The considered models, describing highly nonlinear dynamics of microtubules, can be reduced to nonlinear ordinary differential equations. While the first PDE describes the longitudinal model of nonlinear dynamics of microtubules, the second one describes the nonlinear model of dynamics of radial dislocations in microtubules. The acquired solutions are then graphically presented, and their distinct properties are enumerated in respect to the corresponding dynamic behavior of the microtubules they model. Various patterns, including but not limited to regular, singular kink-like, as well as periodicity exhibiting ones, are detected. Being the method of choice herein, the exp(−Φ(ξ-Expansion Method not disappointing in the least, is found and declared highly efficient.

Introduction to nonlinear science

CERN Document Server

Nicolis, G

1995-01-01

One of the most unexpected results in science in recent years is that quite ordinary systems obeying simple laws can give rise to complex, nonlinear or chaotic, behavior. In this book, the author presents a unified treatment of the concepts and tools needed to analyze nonlinear phenomena and to outline some representative applications drawn from the physical, engineering, and biological sciences. Some of the interesting topics covered include: dynamical systems with a finite number of degrees of freedom, linear stability analysis of fixed points, nonlinear behavior of fixed points, bifurcation analysis, spatially distributed systems, broken symmetries, pattern formation, and chaotic dynamics. The author makes a special effort to provide a logical connection between ordinary dynamical systems and spatially extended systems, and to balance the emphasis on chaotic behavior and more classical nonlinear behavior. He also develops a statistical approach to complex systems and compares it to traditional deterministi...

The nonlinear response of the complex structural system in nuclear reactors using dynamic substructure method

International Nuclear Information System (INIS)

Zheng, Z.C.; Xie, G.; Du, Q.H.

1987-01-01

Because of the existence of nonlinear characteristics in practical engineering structures, such as large steam turbine-foundation system and offshore platform, it is necessary to predict nonlinear dynamic responses for these very large and complex structural systems subjected extreme load. Due to the limited storage and high executing cost of computers, there are still some difficulties in the analysis for such systems although the traditional finite element methods provide basic available methods to the problems. The dynamic substructure methods, which were developed as a branch of general structural dynamics in the past more than 20 years and have been widely used from aircraft, space vehicles to other mechanical and civil engineering structures, present a powerful method to the analysis of very large structural systems. The key to success is due to the considerable reduction in the number of degrees of freedom while not changing the physical essence of the problems investigated. The dynamic substructure method has been extended to nonlinear system and applicated to the analysis of nonlinear dynamic response of an offshore platform by Z.C. Zheng, et al. (1983, 1985a, b, c). In this paper, the method is presented to analyze dynamic responses of the systems contained intrinsic nonlinearities and with nonlinear attachments and nonlinear supports of nuclear structural systems. The efficiency of the method becomes more clear for nonlinear dynamic problems due to the adoption of iterating processes. For simplicity, the analysis procedure is demonstrated briefly. The generalized substructure method of nonlinear systems is similar to linear systems, only the nonlinear terms are treated as pseudo-forces. Interface coordinates are classified into two categories, the connecting interface coordinates which connect with each other directly in the global system and the linking interface coordinates which link to each other through attachments. (orig./GL)

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.

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)

Nonlinear dynamic response of electro-thermo-mechanically loaded piezoelectric cylindrical shell reinforced with BNNTs

International Nuclear Information System (INIS)

Yang, J H; Yang, J; Kitipornchai, S

2012-01-01

This paper presents an investigation on the nonlinear dynamic response of piezoelectric cylindrical shells reinforced with boron nitride nanotubes (BNNTs) under a combined axisymmetric electro-thermo-mechanical loading. By employing the classical Donnell shell theory, the von Kármán–Donnell kinematic relationship, and a piezo-elastic constitutive law including thermal effects, the nonlinear governing equations of motion of the shell are derived through the Reissner variational principle. The finite difference method and a time-integration scheme are used to obtain the nonlinear dynamic response of the BNNT-reinforced piezoelectric shell. A parametric study is conducted, showing the effects of geometrically nonlinear deformation, applied voltage, temperature change, mechanical load, BNNT volume fraction and boundary conditions on the nonlinear dynamic response. (paper)

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...

Analysis of the Nonlinear Static and Dynamic Behavior of Offshore Structures

KAUST Repository

Alfosail, Feras

2015-01-01

Understanding static and dynamic nonlinear behavior of pipes and risers is crucial for the design aspects in offshore engineering fields. In this work, we examine two nonlinear problems in offshore engineering field: vortex Induced vibration

Summary report of the group on single-particle nonlinear dynamics

International Nuclear Information System (INIS)

Axinescu, S.; Bartolini, R.; Bazzani, A.

1996-10-01

This report summarizes the research on single-particle nonlinear beam dynamics. It discusses the following topics: analytical and semi-analytical tools; early prediction of the dynamic aperture; how the results are commonly presented; Is the mechanism of the dynamic aperture understand; ripple effects; and beam-beam effects

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.

Nonlinear Relaxation in Population Dynamics

Science.gov (United States)

Cirone, Markus A.; de Pasquale, Ferdinando; Spagnolo, Bernardo

We analyze the nonlinear relaxation of a complex ecosystem composed of many interacting species. The ecological system is described by generalized Lotka-Volterra equations with a multiplicative noise. The transient dynamics is studied in the framework of the mean field theory and with random interaction between the species. We focus on the statistical properties of the asymptotic behaviour of the time integral of the ith population and on the distribution of the population and of the local field.

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.

Nonlinear robust hierarchical control for nonlinear uncertain systems

Directory of Open Access Journals (Sweden)

Leonessa Alexander

1999-01-01

Full Text Available A nonlinear robust control-system design framework predicated on a hierarchical switching controller architecture parameterized over a set of moving nominal system equilibria is developed. Specifically, using equilibria-dependent Lyapunov functions, a hierarchical nonlinear robust control strategy is developed that robustly stabilizes a given nonlinear system over a prescribed range of system uncertainty by robustly stabilizing a collection of nonlinear controlled uncertain subsystems. The robust switching nonlinear controller architecture is designed based on a generalized (lower semicontinuous Lyapunov function obtained by minimizing a potential function over a given switching set induced by the parameterized nominal system equilibria. The proposed framework robustly stabilizes a compact positively invariant set of a given nonlinear uncertain dynamical system with structured parametric uncertainty. Finally, the efficacy of the proposed approach is demonstrated on a jet engine propulsion control problem with uncertain pressure-flow map data.

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.

A nonlinear optimal control approach to stabilization of a macroeconomic development model

Science.gov (United States)

Rigatos, G.; Siano, P.; Ghosh, T.; Sarno, D.

2017-11-01

A nonlinear optimal (H-infinity) control approach is proposed for the problem of stabilization of the dynamics of a macroeconomic development model that is known as the Grossman-Helpman model of endogenous product cycles. The dynamics of the macroeconomic development model is divided in two parts. The first one describes economic activities in a developed country and the second part describes variation of economic activities in a country under development which tries to modify its production so as to serve the needs of the developed country. The article shows that through control of the macroeconomic model of the developed country, one can finally control the dynamics of the economy in the country under development. The control method through which this is achieved is the nonlinear H-infinity control. The macroeconomic model for the country under development undergoes approximate linearization round a temporary operating point. This is defined at each time instant by the present value of the system's state vector and the last value of the control input vector that was exerted on it. The linearization is based on Taylor series expansion and the computation of the associated Jacobian matrices. For the linearized model an H-infinity feedback controller is computed. The controller's gain is calculated by solving an algebraic Riccati equation at each iteration of the control method. The asymptotic stability of the control approach is proven through Lyapunov analysis. This assures that the state variables of the macroeconomic model of the country under development will finally converge to the designated reference values.

Polarization dynamics in nonlinear anisotropic fibers

International Nuclear Information System (INIS)

Komarov, Andrey; Komarov, Konstantin; Meshcheriakov, Dmitry; Amrani, Foued; Sanchez, Francois

2010-01-01

We give an extensive study of polarization dynamics in anisotropic fibers exhibiting a third-order index nonlinearity. The study is performed in the framework of the Stokes parameters with the help of the Poincare sphere. Stationary states are determined, and their stability is investigated. The number of fixed points and their stability depend on the respective magnitude of the linear and nonlinear birefringence. A conservation relation analogous to the energy conservation in mechanics allows evidencing a close analogy between the movement of the polarization in the Poincare sphere and the motion of a particle in a potential well. Two distinct potentials are found, leading to the existence of two families of solutions, according to the sign of the total energy of the equivalent mechanical system. The mechanical analogy allows us to fully characterize the solutions and also to determine analytically the associated beat lengths. General analytical solutions are given for the two families in terms of Jacobi's functions. The intensity-dependent transmission of a fiber placed between two crossed polarizers is calculated. Optimal conditions for efficient nonlinear switching compatible with mode-locking applications are determined. The general case of a nonlinear fiber ring with an intracavity polarizer placed between two polarization controllers is also considered.

Nonlinear Dynamics and the Growth of Literature.

Science.gov (United States)

Tabah, Albert N.

1992-01-01

Discussion of nonlinear dynamic mechanisms focuses on whether information production and dissemination can be described by similar mechanisms. The exponential versus linear growth of literature is discussed, the time factor is considered, an example using literature from the field of superconductivity is given, and implications for information…

Wave transmission in nonlinear lattices

International Nuclear Information System (INIS)

Hennig, D.; Tsironis, G.P.

1999-01-01

The interplay of nonlinearity with lattice discreteness leads to phenomena and propagation properties quite distinct from those appearing in continuous nonlinear systems. For a large variety of condensed matter and optics applications the continuous wave approximation is not appropriate. In the present review we discuss wave transmission properties in one dimensional nonlinear lattices. Our paradigmatic equations are discrete nonlinear Schroedinger equations and their study is done through a dynamical systems approach. We focus on stationary wave properties and utilize well known results from the theory of dynamical systems to investigate various aspects of wave transmission and wave localization. We analyze in detail the more general dynamical system corresponding to the equation that interpolates between the non-integrable discrete nonlinear Schroedinger equation and the integrable Albowitz-Ladik equation. We utilize this analysis in a nonlinear Kronig-Penney model and investigate transmission and band modification properties. We discuss the modifications that are effected through an electric field and the nonlinear Wannier-Stark localization effects that are induced. Several applications are described, such as polarons in one dimensional lattices, semiconductor superlattices and one dimensional nonlinear photonic band gap systems. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)

Nonlinear Cointegration Approach for Condition Monitoring of Wind Turbines

Directory of Open Access Journals (Sweden)

Konrad Zolna

2015-01-01

Full Text Available Monitoring of trends and removal of undesired trends from operational/process parameters in wind turbines is important for their condition monitoring. This paper presents the homoscedastic nonlinear cointegration for the solution to this problem. The cointegration approach used leads to stable variances in cointegration residuals. The adapted Breusch-Pagan test procedure is developed to test for the presence of heteroscedasticity in cointegration residuals obtained from the nonlinear cointegration analysis. Examples using three different time series data sets—that is, one with a nonlinear quadratic deterministic trend, another with a nonlinear exponential deterministic trend, and experimental data from a wind turbine drivetrain—are used to illustrate the method and demonstrate possible practical applications. The results show that the proposed approach can be used for effective removal of nonlinear trends form various types of data, allowing for possible condition monitoring applications.

Dynamic nonlinear thermal optical effects in coupled ring resonators

Directory of Open Access Journals (Sweden)

Chenguang Huang

2012-09-01

Full Text Available We investigate the dynamic nonlinear thermal optical effects in a photonic system of two coupled ring resonators. A bus waveguide is used to couple light in and out of one of the coupled resonators. Based on the coupling from the bus to the resonator, the coupling between the resonators and the intrinsic loss of each individual resonator, the system transmission spectrum can be classified by three different categories: coupled-resonator-induced absorption, coupled-resonator-induced transparency and over coupled resonance splitting. Dynamic thermal optical effects due to linear absorption have been analyzed for each category as a function of the input power. The heat power in each resonator determines the thermal dynamics in this coupled resonator system. Multiple “shark fins” and power competition between resonators can be foreseen. Also, the nonlinear absorption induced thermal effects have been discussed.

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.

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.

Nonlinear dynamics of thin current sheets

International Nuclear Information System (INIS)

Daughton, William

2002-01-01

Observations indicate that the current sheet in the Earth's geomagnetic tail may compress to a thickness comparable to an ion gyro-radius prior to substorm onset. In recent years, there has been considerable controversy regarding the kinetic stability of these thin structures. In particular, the growth rate of the kink instability and its relevance to magnetotail dynamics is still being debated. In this work, a series of fully kinetic particle-in-cell simulations are performed for a thin Harris sheet. The ion to electron mass ratio is varied between m i /m e =4→400 and careful comparisons are made with a formally exact approach to the linear Vlasov theory. At low mass ratio m i /m e <64, the simulations are in excellent agreement with the linear theory, but at high mass ratio the kink instability is observed to grow more rapidly in the kinetic simulations than predicted by theory. The resolution to this apparent discrepancy involves the lower hybrid instability which is active on the edge of the sheet and rapidly produces nonlinear modifications to the initial equilibrium. The nature of this nonlinear deformation is characterized and a simple model is proposed to explain the physics. After the growth and saturation of the lower hybrid fluctuations, the deformed current sheet is similar in structure to a Harris equilibrium with an additional background population. This may explain the large growth rate of the kink instability at later times, since this type of modification to the Harris sheet has been shown to greatly enhance the growth rate of the kink mode

Dynamic beam cleaning by a nonlinear resonance

Energy Technology Data Exchange (ETDEWEB)

Chao, A W; Month, M [Brookhaven National Lab., Upton, N.Y. (USA)

1976-03-15

The general framework for the dynamic cleaning of a stored proton beam by passing the beam through a nonlinear resonance is developed. The limitations and advantages of this technique are discussed. The method is contrasted with physical beam scraping, which is currently in use at the CERN ISR.

Reconstructing a nonlinear dynamical framework for testing quantum mechanics

International Nuclear Information System (INIS)

Jordan, T.F.

1993-01-01

The nonlinear generalization of quantum dynamics constructed by Weinberg as a basis for experimental tests is reconstructed in terms of density-matrix elements to allow independent dynamics for subsystems. Dynamics is generated with a Lie bracket and a nonlinear Hamiltonian function. It takes density matrices to density matrices and pure states to pure states. Each density matrix has a Hamiltonian operator that makes its evolution for an infinitesimal time, but the Hamiltonian operator may be different for different density matrices and may change in time as the density matrix changes. A Hamiltonian function for a subsystem serves also for the entire system. Independence of separate subsystems is confirmed by seeing that brackets are zero for functions from different subsystems and by looking at the Hamiltonian operator for each density matrix. Scaling properties of Hamiltonian functions are found to be important in connection with locality. An example of all this is obtained from every one of the local nonlinear Schroedinger equations described by Bialynicki-Birula and Mycielski. Examples are worked out for spins coupled together or to fields, demonstrating Hamiltonian functions and equations of motion written directly in terms of physical mean values. Observables and states are taken to be the same as in ordinary quantum mechanics. An attempt to find nonlinear representations of observables by characterizing propositions as functions equal to their squares yields a negative result. Sharper interpretation of mixed states is proposed. In a mixture of parts that are prepared separately, time dependence must be calculated separately for each part so different mixtures that yield the same density matrix can be distinguished. No criticism has shown that a consistent interpretation cannot be made this way. Thus, nonlinearity remains a viable hypothesis for experimental tests. 16 refs

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.

Application of homotopy-perturbation method to nonlinear population dynamics models

International Nuclear Information System (INIS)

Chowdhury, M.S.H.; Hashim, I.; Abdulaziz, O.

2007-01-01

In this Letter, the homotopy-perturbation method (HPM) is employed to derive approximate series solutions of nonlinear population dynamics models. The nonlinear models considered are the multispecies Lotka-Volterra equations. The accuracy of this method is examined by comparison with the available exact and the fourth-order Runge-Kutta method (RK4)

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.

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.

Energy harvester for rotating environments using offset pendulum and nonlinear dynamics

International Nuclear Information System (INIS)

Roundy, Shad; Tola, Jeffry

2014-01-01

We present an energy harvester for environments that rotate through the Earth’s gravitational field. Example applications include shafts connected to motors, axles, propellers, fans, and wheels or tires. Our approach uses the unique dynamics of an offset pendulum along with a nonlinear bistable restoring spring to improve the operational bandwidth of the system. Depending on the speed of the rotating environment, the system can act as a bistable oscillator, monostable stiffening oscillator, or linear oscillator. We apply our approach to a tire pressure monitoring system mounted on a car rim. Simulation and experimental test results show that the prototype generator is capable of directly powering an RF transmission every 60 s or less over a speed range of 10 to 155 kph. (paper)

Energy harvester for rotating environments using offset pendulum and nonlinear dynamics

Science.gov (United States)

Roundy, Shad; Tola, Jeffry

2014-10-01

We present an energy harvester for environments that rotate through the Earth’s gravitational field. Example applications include shafts connected to motors, axles, propellers, fans, and wheels or tires. Our approach uses the unique dynamics of an offset pendulum along with a nonlinear bistable restoring spring to improve the operational bandwidth of the system. Depending on the speed of the rotating environment, the system can act as a bistable oscillator, monostable stiffening oscillator, or linear oscillator. We apply our approach to a tire pressure monitoring system mounted on a car rim. Simulation and experimental test results show that the prototype generator is capable of directly powering an RF transmission every 60 s or less over a speed range of 10 to 155 kph.

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 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)

Some Nonlinear Dynamic Inequalities on Time Scales

Indian Academy of Sciences (India)

The aim of this paper is to investigate some nonlinear dynamic inequalities on time scales, which provide explicit bounds on unknown functions. The inequalities given here unify and extend some inequalities in (B G Pachpatte, On some new inequalities related to a certain inequality arising in the theory of differential ...

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.

Collective Dynamics of Nonlinear and Disordered Systems

CERN Document Server

Radons, G; Just, W

2005-01-01

Phase transitions in disordered systems and related dynamical phenomena are a topic of intrinsically high interest in theoretical and experimental physics. This book presents a unified view, adopting concepts from each of the disjoint fields of disordered systems and nonlinear dynamics. Special attention is paid to the glass transition, from both experimental and theoretical viewpoints, to modern concepts of pattern formation, and to the application of the concepts of dynamical systems for understanding equilibrium and nonequilibrium properties of fluids and solids. The content is accessible to graduate students, but will also be of benefit to specialists, since the presentation extends as far as the topics of ongoing research work.

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.

Dissipative quantum dynamics and nonlinear sigma-model

International Nuclear Information System (INIS)

Tarasov, V.E.

1992-01-01

Sedov variational principle which is the generalization of the least action principle for the dissipative and irreversible processes and the classical dissipative mechanics in the phase space is considered. Quantum dynamics for the dissipative and irreversible processes is constructed. As an example of the dissipative quantum theory the nonlinear two-dimensional sigma-model is considered. The conformal anomaly of the energy momentum tensor trace for closed bosonic string on the affine-metric manifold is investigated. The two-loop metric beta-function for nonlinear dissipative sigma-model was calculated. The results are compared with the ultraviolet two-loop conterterms for affine-metric sigma model. 71 refs

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.

Chaotic dynamics with high complexity in a simplified new nonautonomous nonlinear electronic circuit

International Nuclear Information System (INIS)

Arulgnanam, A.; Thamilmaran, K.; Daniel, M.

2009-01-01

A two dimensional nonautonomous dissipative forced series LCR circuit with a simple nonlinear element exhibiting an immense variety of dynamical features is proposed for the first time. Unlike the usual cases of nonlinear element, the nonlinear element used here possesses three segment piecewise linear character with one positive and one negative slope. This nonlinearity is verified to be sufficient to produce chaos with high complexity in many established nonautonomous nonlinear circuits, such as MLC, MLCV, driven Chua, etc., thus indicating an universal behavior similar to the familiar Chua's diode. The dynamics of the proposed circuit is studied experimentally, confirmed numerically, simulated through PSPICE and proved mathematically. An important feature of the circuit is its ability to show dual chaotic behavior.

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

Science.gov (United States)

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

2011-01-01

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

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...

Optimum Control for Nonlinear Dynamic Radial Deformation of Turbine Casing with Time-Varying LSSVM

Directory of Open Access Journals (Sweden)

Cheng-Wei Fei

2015-01-01

Full Text Available With the development of the high performance and high reliability of aeroengine, the blade-tip radial running clearance (BTRRC of high pressure turbine seriously influences the reliability and performance of aeroengine, wherein the radial deformation control of turbine casing has to be concerned in BTRRC design. To improve BTRRC design, the optimum control-based probabilistic optimization of turbine casing radial deformation was implemented using time-varying least square support vector machine (T-LSSVM by considering nonlinear material properties and dynamic thermal load. First the T-LSSVM method was proposed and its mathematical model was established. And then the nonlinear dynamic optimal control model of casing radial deformation was constructed with T-LSSVM. Thirdly, through the numerical experiments, the T-LSSVM method is demonstrated to be a promising approach in reducing additional design samples and improving computational efficiency with acceptable computational precision. Through the optimum control-based probabilistic optimization for nonlinear dynamic radial turbine casing deformation, the optimum radial deformation is 7.865 × 10−4 m with acceptable reliability degree 0.995 6, which is reduced by 7.86 × 10−5 m relative to that before optimization. These results validate the effectiveness and feasibility of the proposed T-LSSVM method, which provides a useful insight into casing radial deformation, BTRRC control, and the development of gas turbine with high performance and high reliability.

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.

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

Science.gov (United States)

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

2015-01-01

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

Discrete Localized States and Localization Dynamics in Discrete Nonlinear Schrödinger Equations

DEFF Research Database (Denmark)

Christiansen, Peter Leth; Gaididei, Yu.B.; Mezentsev, V.K.

1996-01-01

Dynamics of two-dimensional discrete structures is studied in the framework of the generalized two-dimensional discrete nonlinear Schrodinger equation. The nonlinear coupling in the form of the Ablowitz-Ladik nonlinearity is taken into account. Stability properties of the stationary solutions...

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

Science.gov (United States)

Wang, Hong; Han, Qinkai; Zhou, Daning

2017-02-01

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

Nonparametric identification of nonlinear dynamic systems using a synchronisation-based method

Science.gov (United States)

Kenderi, Gábor; Fidlin, Alexander

2014-12-01

The present study proposes an identification method for highly nonlinear mechanical systems that does not require a priori knowledge of the underlying nonlinearities to reconstruct arbitrary restoring force surfaces between degrees of freedom. This approach is based on the master-slave synchronisation between a dynamic model of the system as the slave and the real system as the master using measurements of the latter. As the model synchronises to the measurements, it becomes an observer of the real system. The optimal observer algorithm in a least-squares sense is given by the Kalman filter. Using the well-known state augmentation technique, the Kalman filter can be turned into a dual state and parameter estimator to identify parameters of a priori characterised nonlinearities. The paper proposes an extension of this technique towards nonparametric identification. A general system model is introduced by describing the restoring forces as bilateral spring-dampers with time-variant coefficients, which are estimated as augmented states. The estimation procedure is followed by an a posteriori statistical analysis to reconstruct noise-free restoring force characteristics using the estimated states and their estimated variances. Observability is provided using only one measured mechanical quantity per degree of freedom, which makes this approach less demanding in the number of necessary measurement signals compared with truly nonparametric solutions, which typically require displacement, velocity and acceleration signals. Additionally, due to the statistical rigour of the procedure, it successfully addresses signals corrupted by significant measurement noise. In the present paper, the method is described in detail, which is followed by numerical examples of one degree of freedom (1DoF) and 2DoF mechanical systems with strong nonlinearities of vibro-impact type to demonstrate the effectiveness of the proposed technique.

Molecular dynamics simulation of nonlinear spectroscopies of intermolecular motions in liquid water.

Science.gov (United States)

Yagasaki, Takuma; Saito, Shinji

2009-09-15

Water is the most extensively studied of liquids because of both its ubiquity and its anomalous thermodynamic and dynamic properties. The properties of water are dominated by hydrogen bonds and hydrogen bond network rearrangements. Fundamental information on the dynamics of liquid water has been provided by linear infrared (IR), Raman, and neutron-scattering experiments; molecular dynamics simulations have also provided insights. Recently developed higher-order nonlinear spectroscopies open new windows into the study of the hydrogen bond dynamics of liquid water. For example, the vibrational lifetimes of stretches and a bend, intramolecular features of water dynamics, can be accurately measured and are found to be on the femtosecond time scale at room temperature. Higher-order nonlinear spectroscopy is expressed by a multitime correlation function, whereas traditional linear spectroscopy is given by a one-time correlation function. Thus, nonlinear spectroscopy yields more detailed information on the dynamics of condensed media than linear spectroscopy. In this Account, we describe the theoretical background and methods for calculating higher order nonlinear spectroscopy; equilibrium and nonequilibrium molecular dynamics simulations, and a combination of both, are used. We also present the intermolecular dynamics of liquid water revealed by fifth-order two-dimensional (2D) Raman spectroscopy and third-order IR spectroscopy. 2D Raman spectroscopy is sensitive to couplings between modes; the calculated 2D Raman signal of liquid water shows large anharmonicity in the translational motion and strong coupling between the translational and librational motions. Third-order IR spectroscopy makes it possible to examine the time-dependent couplings. The 2D IR spectra and three-pulse photon echo peak shift show the fast frequency modulation of the librational motion. A significant effect of the translational motion on the fast frequency modulation of the librational motion is

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

Science.gov (United States)

Shaw, H.R.

1987-01-01

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

A non-linear dynamical approach to belief revision in cognitive behavioral therapy

Science.gov (United States)

Kronemyer, David; Bystritsky, Alexander

2014-01-01

Belief revision is the key change mechanism underlying the psychological intervention known as cognitive behavioral therapy (CBT). It both motivates and reinforces new behavior. In this review we analyze and apply a novel approach to this process based on AGM theory of belief revision, named after its proponents, Carlos Alchourrón, Peter Gärdenfors and David Makinson. AGM is a set-theoretical model. We reconceptualize it as describing a non-linear, dynamical system that occurs within a semantic space, which can be represented as a phase plane comprising all of the brain's attentional, cognitive, affective and physiological resources. Triggering events, such as anxiety-producing or depressing situations in the real world, or their imaginal equivalents, mobilize these assets so they converge on an equilibrium point. A preference function then evaluates and integrates evidentiary data associated with individual beliefs, selecting some of them and comprising them into a belief set, which is a metastable state. Belief sets evolve in time from one metastable state to another. In the phase space, this evolution creates a heteroclinic channel. AGM regulates this process and characterizes the outcome at each equilibrium point. Its objective is to define the necessary and sufficient conditions for belief revision by simultaneously minimizing the set of new beliefs that have to be adopted, and the set of old beliefs that have to be discarded or reformulated. Using AGM, belief revision can be modeled using three (and only three) fundamental syntactical operations performed on belief sets, which are expansion; revision; and contraction. Expansion is like adding a new belief without changing any old ones. Revision is like adding a new belief and changing old, inconsistent ones. Contraction is like changing an old belief without adding any new ones. We provide operationalized examples of this process in action. PMID:24860491

Quasi-ideal dynamics of vortex solitons embedded in flattop nonlinear Bessel beams.

Science.gov (United States)

Porras, Miguel A; Ramos, Francisco

2017-09-01

The applications of vortex solitons are severely limited by the diffraction and self-defocusing spreading of the background beam where they are nested. Nonlinear Bessel beams in self-defocusing media are nondiffracting, flattop beams where the nested vortex solitons can survive for propagation distances that are one order of magnitude larger than in the Gaussian or super-Gaussian beams. The dynamics of the vortex solitons is studied numerically and found to approach that in the ideal, uniform background, preventing vortex spiraling and decay, which eases vortex steering for applications.

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...

Nonlinear dynamic processes in modified ionospheric plasma

Science.gov (United States)

Kochetov, A.; Terina, G.

Presented work is a contribution to the experimental and theoretical study of nonlinear effects arising on ionospheric plasma under the action of powerful radio emission (G.I. Terina, J. Atm. Terr. Phys., 1995, v.57, p.273; A.V. Kochetov et. al., Advances in Space Research, 2002, in press). The experimental results were obtained by the method of sounding of artificially disturbed ionosphere by short radio pulses. The amplitude and phase characteristics of scattered signal as of "caviton" type (CS) (analogy of narrow-band component of stimulation electromagnetic emission (SEE)) as the main signal (MS) of probing transmitter are considered. The theoretical model is based on numerical solution of driven nonlinear Shrödinger equation (NSE) in inhomogeneous plasma. The simulation allows us to study a self-consistent spatial-temporal dynamics of field and plasma. The observed evolution of phase characteristics of MS and CS qualitatively correspond to the results of numerical simulation and demonstrate the penetration processes of powerful electromagnetic wave in supercritical (in linear approach) plasma regions. The modeling results explain also the periodic generation of CS, the travel CS maximum down to density gradient, the aftereffect of CS. The obtained results show the excitation of strong turbulence and allow us to interpret CS, NC and so far inexplicable phenomena as "spikes" too. The work was supported in part by Russian Foundation for Basic Research (grants Nos. 99-02-16642, 99-02- 16399).

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.

Dynamic behaviors for a perturbed nonlinear Schrödinger equation with the power-law nonlinearity in a non-Kerr medium

Science.gov (United States)

Chai, Jun; Tian, Bo; Zhen, Hui-Ling; Sun, Wen-Rong; Liu, De-Yin

2017-04-01

Effects of quantic nonlinearity on the propagation of the ultrashort optical pulses in a non-Kerr medium, like an optical fiber, can be described by a perturbed nonlinear Schrödinger equation with the power law nonlinearity, which is studied in this paper from a planar-dynamic-system view point. We obtain the equivalent two-dimensional planar dynamic system of such an equation, for which, according to the bifurcation theory and qualitative theory, phase portraits are given. Through the analysis of those phase portraits, we present the relations among the Hamiltonian, orbits of the dynamic system and types of the analytic solutions. Analytic expressions of the periodic-wave solutions, kink- and bell-shaped solitary-wave solutions are derived, and we find that the periodic-wave solutions can be reduced to the kink- and bell-shaped solitary-wave solutions.

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 dynamic analysis using Petrov-Galerkin natural element method

International Nuclear Information System (INIS)

Lee, Hong Woo; Cho, Jin Rae

2004-01-01

According to our previous study, it is confirmed that the Petrov-Galerkin Natural Element Method (PG-NEM) completely resolves the numerical integration inaccuracy in the conventional Bubnov-Galerkin Natural Element Method (BG-NEM). This paper is an extension of PG-NEM to two-dimensional nonlinear dynamic problem. For the analysis, a constant average acceleration method and a linearized total Lagrangian formulation is introduced with the PG-NEM. At every time step, the grid points are updated and the shape functions are reproduced from the relocated nodal distribution. This process enables the PG-NEM to provide more accurate and robust approximations. The representative numerical experiments performed by the test Fortran program, and the numerical results confirmed that the PG-NEM effectively and accurately approximates the nonlinear dynamic problem

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

Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics

CERN Document Server

Wu, Shen R

2012-01-01

A systematic introduction to the theories and formulations of the explicit finite element method As numerical technology continues to grow and evolve with industrial applications, understanding the explicit finite element method has become increasingly important, particularly in the areas of crashworthiness, metal forming, and impact engineering. Introduction to the Explicit FiniteElement Method for Nonlinear Transient Dynamics is the first book to address specifically what is now accepted as the most successful numerical tool for nonlinear transient dynamics. The book aids readers in master

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).

A Semi-Analytical Approach for the Response of Nonlinear Conservative Systems

DEFF Research Database (Denmark)

Kimiaeifar, Amin; Barari, Amin; Fooladi, M

2011-01-01

This work applies Parameter expanding method (PEM) as a powerful analytical technique in order to obtain the exact solution of nonlinear problems in the classical dynamics. Lagrange method is employed to derive the governing equations. The nonlinear governing equations are solved analytically by ...

Bubble and Drop Nonlinear Dynamics (BDND)

Science.gov (United States)

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

1998-01-01

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

Nonlinear dynamical systems for theory and research in ergonomics.

Science.gov (United States)

Guastello, Stephen J

2017-02-01

Nonlinear dynamical systems (NDS) theory offers new constructs, methods and explanations for phenomena that have in turn produced new paradigms of thinking within several disciplines of the behavioural sciences. This article explores the recent developments of NDS as a paradigm in ergonomics. The exposition includes its basic axioms, the primary constructs from elementary dynamics and so-called complexity theory, an overview of its methods, and growing areas of application within ergonomics. The applications considered here include: psychophysics, iconic displays, control theory, cognitive workload and fatigue, occupational accidents, resilience of systems, team coordination and synchronisation in systems. Although these applications make use of different subsets of NDS constructs, several of them share the general principles of the complex adaptive system. Practitioner Summary: Nonlinear dynamical systems theory reframes problems in ergonomics that involve complex systems as they change over time. The leading applications to date include psychophysics, control theory, cognitive workload and fatigue, biomechanics, occupational accidents, resilience of systems, team coordination and synchronisation of system components.

Bifurcation and Nonlinear Dynamic Analysis of Externally Pressurized Double Air Films Bearing System

Directory of Open Access Journals (Sweden)

Cheng-Chi Wang

2014-01-01

Full Text Available This paper studies the chaotic and nonlinear dynamic behaviors of a rigid rotor supported by externally pressurized double air films (EPDAF bearing system. A hybrid numerical method combining the differential transformation method and the finite difference method is used to calculate pressure distribution of EPDAF bearing system and bifurcation phenomenon of rotor center orbits. The results obtained for the orbits of the rotor center are in good agreement with those obtained using the traditional finite difference approach. The results presented summarize the changes which take place in the dynamic behavior of the EPDAF bearing system as the rotor mass and bearing number are increased and therefore provide a useful guideline for the bearing system.

The landscape of nonlinear structural dynamics: an introduction.

Science.gov (United States)

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

2015-09-28

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

Modified dynamic Stark shift and depopulation rate of an atom inside a Kerr nonlinear blackbody

International Nuclear Information System (INIS)

Yin Miao; Cheng Ze

2009-01-01

We investigate the dynamic Stark shift and atomic depopulation rate induced by real photons in a Kerr nonlinear blackbody. We found that the dynamic Stark shift and atomic depopulation rate are equally modified by a nonlinear contribution factor and a linear contribution factor under a transition temperature T c . The nonlinear contribution factor depends on the Kerr nonlinear coefficient as well as the absolute temperature. Below T c , the absolute values of the dynamic Stark shift and depopulation rate of a single atomic state (not the ground state) are correspondingly larger than those in a normal blackbody whose interior is filled with a nonabsorbing linear medium. Above T c , the dynamic Stark shift and atomic depopulation rate are correspondingly equal to those in a normal blackbody with a nonabsorbing linear medium in its interior.

BOOK REVIEW: Nonlinear Dynamics: Integrability, Chaos and Patterns

Science.gov (United States)

Grammaticos, B.

2004-02-01

's staircase'. I do not quite grasp the usefulness of such project-like exercises. Projects must be assigned by the person who indeed teaches the course. There are things that I really like a lot in this book. For instance, the section on `chaos in nonlinear electronic circuits' is particularly interesting. It offers a simple and rather inexpensive way to visualize chaos in the laboratory. The closing section of the book devoted to technological applications of nonlinear dynamics is also quite useful. The fact that the treatment remains rather elementary, based on review articles and monographs rather than research articles, adds to the intelligibility of the chapter, which will certainly prove stimulating to many a student. Of course, not everything can be perfect, and a 600-page book is bound to have some weak points. I find the treatment of quantum chaos rather sketchy and that of chaotic scattering even more so. Also, while the authors are aware of the importance of complex time in integrability, they do not attempt an explanation of the fundamental puzzle: `why, while the physical time is par excellence real, do we need a complex time in order to study the long-time behaviour of dynamical systems?'. Also the book devotes just four pages to integrable discrete systems. Given the tremendous development of this domain over the past decade, this short presentation is not doing justice to the subject. (However as the present reviewer is editing Springer Lecture Notes in Physics on precisely `Integrable Discrete Systems', to appear in early 2004, he would be the last one to complain about the absence of more details on the matter in the present book.) To sum it up, the monograph of Lakshmanan and Rajasekar is a book written by physicists and for physicists. It will be of interest to both the experienced practitioner and to the uninitiated. Its main quality resides in its thorough, pedagogical approach to the matter. Moreover the relaxed, not too formal, style makes for easy

Short- and long-term variations in non-linear dynamics of heart rate variability

DEFF Research Database (Denmark)

Kanters, J K; Højgaard, M V; Agner, E

1996-01-01

OBJECTIVES: The purpose of the study was to investigate the short- and long-term variations in the non-linear dynamics of heart rate variability, and to determine the relationships between conventional time and frequency domain methods and the newer non-linear methods of characterizing heart rate...... rate and describes mainly linear correlations. Non-linear predictability is correlated with heart rate variability measured as the standard deviation of the R-R intervals and the respiratory activity expressed as power of the high-frequency band. The dynamics of heart rate variability changes suddenly...

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

Science.gov (United States)

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

2018-01-01

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

Unraveling complex nonlinear elastic behaviors in rocks using dynamic acousto-elasticity

Science.gov (United States)

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

2012-12-01

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

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.

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.

Adaptive neural network output feedback control for stochastic nonlinear systems with unknown dead-zone and unmodeled dynamics.

Science.gov (United States)

Tong, Shaocheng; Wang, Tong; Li, Yongming; Zhang, Huaguang

2014-06-01

This paper discusses the problem of adaptive neural network output feedback control for a class of stochastic nonlinear strict-feedback systems. The concerned systems have certain characteristics, such as unknown nonlinear uncertainties, unknown dead-zones, unmodeled dynamics and without the direct measurements of state variables. In this paper, the neural networks (NNs) are employed to approximate the unknown nonlinear uncertainties, and then by representing the dead-zone as a time-varying system with a bounded disturbance. An NN state observer is designed to estimate the unmeasured states. Based on both backstepping design technique and a stochastic small-gain theorem, a robust adaptive NN output feedback control scheme is developed. It is proved that all the variables involved in the closed-loop system are input-state-practically stable in probability, and also have robustness to the unmodeled dynamics. Meanwhile, the observer errors and the output of the system can be regulated to a small neighborhood of the origin by selecting appropriate design parameters. Simulation examples are also provided to illustrate the effectiveness of the proposed approach.