WorldWideScience

Sample records for nonlinear systems theory

  1. Nonlinear system theory: another look at dependence.

    Science.gov (United States)

    Wu, Wei Biao

    2005-10-04

    Based on the nonlinear system theory, we introduce previously undescribed dependence measures for stationary causal processes. Our physical and predictive dependence measures quantify the degree of dependence of outputs on inputs in physical systems. The proposed dependence measures provide a natural framework for a limit theory for stationary processes. In particular, under conditions with quite simple forms, we present limit theorems for partial sums, empirical processes, and kernel density estimates. The conditions are mild and easily verifiable because they are directly related to the data-generating mechanisms.

  2. Geometric Theory of Reduction of Nonlinear Control Systems

    Science.gov (United States)

    Elkin, V. I.

    2018-02-01

    The foundations of a differential geometric theory of nonlinear control systems are described on the basis of categorical concepts (isomorphism, factorization, restrictions) by analogy with classical mathematical theories (of linear spaces, groups, etc.).

  3. Perturbation Theory for Open Two-Level Nonlinear Quantum Systems

    International Nuclear Information System (INIS)

    Zhang Zhijie; Jiang Dongguang; Wang Wei

    2011-01-01

    Perturbation theory is an important tool in quantum mechanics. In this paper, we extend the traditional perturbation theory to open nonlinear two-level systems, treating decoherence parameter γ as a perturbation. By this virtue, we give a perturbative solution to the master equation, which describes a nonlinear open quantum system. The results show that for small decoherence rate γ, the ratio of the nonlinear rate C to the tunneling coefficient V (i.e., r = C/V) determines the validity of the perturbation theory. For small ratio r, the perturbation theory is valid, otherwise it yields wrong results. (general)

  4. Nonlinear PI control of chaotic systems using singular perturbation theory

    International Nuclear Information System (INIS)

    Wang Jiang; Wang Jing; Li Huiyan

    2005-01-01

    In this paper, we develop the nonlinear PI controllers for a class of chaotic systems based on singular perturbation theory. The original system is decomposed into two reduced order systems, to which the nonlinear uncertain terms belongs. In order to alleviate the deterioration of these nonlinear uncertainties, the nonlinear PI controllers are applied to each subsystem and combined to construct the composite controller for the full order system. The effectiveness and feasibility of the proposed control scheme is demonstrated through numerical simulations on the chaotic Chua's circuit

  5. Mathematical Systems Theory : from Behaviors to Nonlinear Control

    CERN Document Server

    Julius, A; Pasumarthy, Ramkrishna; Rapisarda, Paolo; Scherpen, Jacquelien

    2015-01-01

    This treatment of modern topics related to mathematical systems theory forms the proceedings of a workshop, Mathematical Systems Theory: From Behaviors to Nonlinear Control, held at the University of Groningen in July 2015. The workshop celebrated the work of Professors Arjan van der Schaft and Harry Trentelman, honouring their 60th Birthdays. The first volume of this two-volume work covers a variety of topics related to nonlinear and hybrid control systems. After giving a detailed account of the state of the art in the related topic, each chapter presents new results and discusses new directions. As such, this volume provides a broad picture of the theory of nonlinear and hybrid control systems for scientists and engineers with an interest in the interdisciplinary field of systems and control theory. The reader will benefit from the expert participants’ ideas on exciting new approaches to control and system theory and their predictions of future directions for the subject that were discussed at the worksho...

  6. On nonequilibrium many-body systems III: nonlinear transport theory

    International Nuclear Information System (INIS)

    Luzzi, R.; Vasconcellos, A.R.; Algarte, A.C.S.

    1986-01-01

    A nonlinear transport theory for many-body systems arbitrarily away from equilibrium, based on the nonequilibrium statistical operator (NSO) method, is presented. Nonlinear transport equations for a basis set of dynamical quantities are derived using two equivalent treatments that may be considered far reaching generalizations of the Hilbert-Chapman-Enskog method and Mori's generalized Langevin equations method. The first case is considered in some detail and the general characteristics of the theory are discussed. (Author) [pt

  7. Energy flow theory of nonlinear dynamical systems with applications

    CERN Document Server

    Xing, Jing Tang

    2015-01-01

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

  8. 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.

  9. A general sensitivity theory for simulations of nonlinear systems

    International Nuclear Information System (INIS)

    Kenton, M.A.

    1981-01-01

    A general sensitivity theory is developed for nonlinear lumped-parameter system simulations. The point-of-departure is general perturbation theory, which has long been used for linear systems in nuclear engineering and reactor physics. The theory allows the sensitivity of particular figures-of-merit of the system behavior to be calculated with respect to any parameter.An explicit procedure is derived for applying the theory to physical systems undergoing sudden events (e.g., reactor scrams, tank ruptures). A related problem, treating figures-of-merit defined as functions of extremal values of system variables occurring at sudden events, is handled by the same procedure. The general calculational scheme for applying the theory to numerical codes is discussed. It is shown that codes which use pre-packaged implicit integration subroutines can be augmented to include sensitivity theory: a companion set of subroutines to solve the sensitivity problem is listed. This combined system analysis code is applied to a simple model for loss of post-accident heat removal in a liquid metal-cooled fast breeder reactor. The uses of the theory for answering more general sensitivity questions are discussed. One application of the theory is to systematically determine whether specific physical processes in a model contribute significantly to the figures-of-merit. Another application of the theory is for selecting parameter values which enable a model to match experimentally observed behavior

  10. Information theory and stochastics for multiscale nonlinear systems

    CERN Document Server

    Majda, Andrew J; Grote, Marcus J

    2005-01-01

    This book introduces mathematicians to the fascinating emerging mathematical interplay between ideas from stochastics and information theory and important practical issues in studying complex multiscale nonlinear systems. It emphasizes the serendipity between modern applied mathematics and applications where rigorous analysis, the development of qualitative and/or asymptotic models, and numerical modeling all interact to explain complex phenomena. After a brief introduction to the emerging issues in multiscale modeling, the book has three main chapters. The first chapter is an introduction to information theory with novel applications to statistical mechanics, predictability, and Jupiter's Red Spot for geophysical flows. The second chapter discusses new mathematical issues regarding fluctuation-dissipation theorems for complex nonlinear systems including information flow, various approximations, and illustrates applications to various mathematical models. The third chapter discusses stochastic modeling of com...

  11. Nonlinear closure relations theory for transport processes in nonequilibrium systems

    International Nuclear Information System (INIS)

    Sonnino, Giorgio

    2009-01-01

    A decade ago, a macroscopic theory for closure relations has been proposed for systems out of Onsager's region. This theory is referred to as the thermodynamic field theory (TFT). The aim of this work was to determine the nonlinear flux-force relations that respect the thermodynamic theorems for systems far from equilibrium. We propose a formulation of the TFT where one of the basic restrictions, namely, the closed-form solution for the skew-symmetric piece of the transport coefficients, has been removed. In addition, the general covariance principle is replaced by the De Donder-Prigogine thermodynamic covariance principle (TCP). The introduction of TCP requires the application of an appropriate mathematical formalism, which is referred to as the entropy-covariant formalism. By geometrical arguments, we prove the validity of the Glansdorff-Prigogine universal criterion of evolution. A new set of closure equations determining the nonlinear corrections to the linear ('Onsager') transport coefficients is also derived. The geometry of the thermodynamic space is non-Riemannian. However, it tends to be Riemannian for high values of the entropy production. In this limit, we recover the transport equations found by the old theory. Applications of our approach to transport in magnetically confined plasmas, materials submitted to temperature, and electric potential gradients or to unimolecular triangular chemical reactions can be found at references cited herein. Transport processes in tokamak plasmas are of particular interest. In this case, even in the absence of turbulence, the state of the plasma remains close to (but, it is not in) a state of local equilibrium. This prevents the transport relations from being linear.

  12. Linear theory for filtering nonlinear multiscale systems with model error.

    Science.gov (United States)

    Berry, Tyrus; Harlim, John

    2014-07-08

    In this paper, we study filtering of multiscale dynamical systems with model error arising from limitations in resolving the smaller scale processes. In particular, the analysis assumes the availability of continuous-time noisy observations of all components of the slow variables. Mathematically, this paper presents new results on higher order asymptotic expansion of the first two moments of a conditional measure. In particular, we are interested in the application of filtering multiscale problems in which the conditional distribution is defined over the slow variables, given noisy observation of the slow variables alone. From the mathematical analysis, we learn that for a continuous time linear model with Gaussian noise, there exists a unique choice of parameters in a linear reduced model for the slow variables which gives the optimal filtering when only the slow variables are observed. Moreover, these parameters simultaneously give the optimal equilibrium statistical estimates of the underlying system, and as a consequence they can be estimated offline from the equilibrium statistics of the true signal. By examining a nonlinear test model, we show that the linear theory extends in this non-Gaussian, nonlinear configuration as long as we know the optimal stochastic parametrization and the correct observation model. However, when the stochastic parametrization model is inappropriate, parameters chosen for good filter performance may give poor equilibrium statistical estimates and vice versa; this finding is based on analytical and numerical results on our nonlinear test model and the two-layer Lorenz-96 model. Finally, even when the correct stochastic ansatz is given, it is imperative to estimate the parameters simultaneously and to account for the nonlinear feedback of the stochastic parameters into the reduced filter estimates. In numerical experiments on the two-layer Lorenz-96 model, we find that the parameters estimated online , as part of a filtering

  13. Untangling the drivers of nonlinear systems with information theory

    Science.gov (United States)

    Wing, S.; Johnson, J.

    2017-12-01

    Many systems found in nature are nonlinear. The drivers of the system are often nonlinearly correlated with one another, which makes it a challenge to understand the effects of an individual driver. For example, solar wind velocity (Vsw) and density (nsw) are both found to correlate well with radiation belt fluxes and are thought to be drivers of the magnetospheric dynamics; however, the Vsw is anti-correlated with nsw, which can potentially confuse interpretation of these relationships as causal or coincidental. Information theory can untangle the drivers of these systems, describe the underlying dynamics, and offer constraints to modelers and theorists, leading to better understanding of the systems. Two examples are presented. In the first example, the solar wind drivers of geosynchronous electrons with energy range of 1.8-3.5 MeV are investigated using mutual information (MI), conditional mutual information (CMI), and transfer entropy (TE). The information transfer from Vsw to geosynchronous MeV electron flux (Je) peaks with a lag time (t) of 2 days. As previously reported, Je is anticorrelated with nsw with a lag of 1 day. However, this lag time and anticorrelation can be attributed mainly to the Je(t + 2 days) correlation with Vsw(t) and nsw(t + 1 day) anticorrelation with Vsw(t). Analyses of solar wind driving of the magnetosphere need to consider the large lag times, up to 3 days, in the (Vsw, nsw) anticorrelation. Using CMI to remove the effects of Vsw, the response of Je to nsw is 30% smaller and has a lag time < 24 hr, suggesting that the loss mechanism due to nsw or solar wind dynamic pressure has to start operating in < 24 hr. nsw transfers about 36% as much information as Vsw (the primary driver) to Je. Nonstationarity in the system dynamics are investigated using windowed TE. When the data is ordered according to high or low transfer entropy it is possible to understand details of the triangle distribution that has been identified between Je(t + 2

  14. Nonlinear systems

    CERN Document Server

    Palmero, Faustino; Lemos, M; Sánchez-Rey, Bernardo; Casado-Pascual, Jesús

    2018-01-01

    This book presents an overview of the most recent advances in nonlinear science. It provides a unified view of nonlinear properties in many different systems and highlights many  new developments. While volume 1 concentrates on mathematical theory and computational techniques and challenges, which are essential for the study of nonlinear science, this second volume deals with nonlinear excitations in several fields. These excitations can be localized and transport energy and matter in the form of breathers, solitons, kinks or quodons with very different characteristics, which are discussed in the book. They can also transport electric charge, in which case they are known as polarobreathers or solectrons. Nonlinear excitations can influence function and structure in biology, as for example, protein folding. In crystals and other condensed matter, they can modify transport properties, reaction kinetics and interact with defects. There are also engineering applications in electric lattices, Josephson junction a...

  15. Nonlinear optimal control theory

    CERN Document Server

    Berkovitz, Leonard David

    2012-01-01

    Nonlinear Optimal Control Theory presents a deep, wide-ranging introduction to the mathematical theory of the optimal control of processes governed by ordinary differential equations and certain types of differential equations with memory. Many examples illustrate the mathematical issues that need to be addressed when using optimal control techniques in diverse areas. Drawing on classroom-tested material from Purdue University and North Carolina State University, the book gives a unified account of bounded state problems governed by ordinary, integrodifferential, and delay systems. It also dis

  16. Classical and Quantum Nonlinear Integrable Systems: Theory and Application

    International Nuclear Information System (INIS)

    Brzezinski, Tomasz

    2003-01-01

    This is a very interesting collection of introductory and review articles on the theory and applications of classical and quantum integrable systems. The book reviews several integrable systems such as the KdV equation, vertex models, RSOS and IRF models, spin chains, integrable differential equations, discrete systems, Ising, Potts and other lattice models and reaction--diffusion processes, as well as outlining major methods of solving integrable systems. These include Lax pairs, Baecklund and Miura transformations, the inverse scattering method, various types of the Bethe Ansatz, Painleve methods, the dbar method and fusion methods to mention just a few. The book is divided into two parts, each containing five chapters. The first part is devoted to classical integrable systems and introduces the subject through the KdV equation, and then proceeds through Painleve analysis, discrete systems and two-dimensional integrable partial differential equations, to culminate in the review of solvable lattice models in statistical physics, solved through the coordinate and algebraic Bethe Ansatz methods. The second part deals with quantum integrable systems, and begins with an outline of unifying approaches to quantum, statistical, ultralocal and non-ultralocal systems. The theory and methods of solving quantum integrable spin chains are then described. Recent developments in applying Bethe Ansatz methods in condensed matter physics, including superconductivity and nanoscale physics, are reviewed. The book concludes with an introduction to diffusion-reaction processes. Every chapter is devoted to a different subject and is self-contained, and thus can be read separately. A reader interesting in classical methods of solitons, such as the methods of solving the KdV equation, can start from Chapter 1, while a reader interested in the Bethe Ansatz method can immediately proceed to Chapter 5, and so on. Thus the book should appeal and be useful to a wide range of theoretical

  17. Extension of a nonlinear systems theory to general-frequency unsteady transonic aerodynamic responses

    Science.gov (United States)

    Silva, Walter A.

    1993-01-01

    A methodology for modeling nonlinear unsteady aerodynamic responses, for subsequent use in aeroservoelastic analysis and design, using the Volterra-Wiener theory of nonlinear systems is presented. The methodology is extended to predict nonlinear unsteady aerodynamic responses of arbitrary frequency. The Volterra-Wiener theory uses multidimensional convolution integrals to predict the response of nonlinear systems to arbitrary inputs. The CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code is used to generate linear and nonlinear unit impulse responses that correspond to each of the integrals for a rectangular wing with a NACA 0012 section with pitch and plunge degrees of freedom. The computed kernels then are used to predict linear and nonlinear unsteady aerodynamic responses via convolution and compared to responses obtained using the CAP-TSD code directly. The results indicate that the approach can be used to predict linear unsteady aerodynamic responses exactly for any input amplitude or frequency at a significant cost savings. Convolution of the nonlinear terms results in nonlinear unsteady aerodynamic responses that compare reasonably well with those computed using the CAP-TSD code directly but at significant computational cost savings.

  18. Nonlinear systems

    National Research Council Canada - National Science Library

    Drazin, P. G

    1992-01-01

    This book is an introduction to the theories of bifurcation and chaos. It treats the solution of nonlinear equations, especially difference and ordinary differential equations, as a parameter varies...

  19. Using system theory and energy methods to prove existence of non-linear PDE's

    NARCIS (Netherlands)

    Zwart, H.J.

    2015-01-01

    In this discussion paper we present an idea of combining techniques known from systems theory with energy estimates to show existence for a class of non-linear partial differential equations (PDE's). At the end of the paper a list of research questions with possible approaches is given.

  20. The iteration formula of the Maslov-type index theory with applications to nonlinear Hamiltonian systems

    International Nuclear Information System (INIS)

    Di Dong; Yiming Long.

    1994-10-01

    In this paper, the iteration formula of the Maslov-type index theory for linear Hamiltonian systems with continuous periodic and symmetric coefficients is established. This formula yields a new method to determine the minimality of the period for solutions of nonlinear autonomous Hamiltonian systems via their Maslov-type indices. Applications of this formula give new results on the existence of periodic solutions with prescribed minimal period for such systems. (author). 40 refs

  1. Nonlinear field theories and non-Gaussian fluctuations for near-critical many-body systems

    International Nuclear Information System (INIS)

    Tuszynski, J.A.; Dixon, J.M.; Grundland, A.M.

    1994-01-01

    This review article outlines a number of efforts made over the past several decades to understand the physics of near critical many-body systems. Beginning with the phenomenological theories of Landau and Ginzburg the paper discusses the two main routes adopted in the past. The first approach is based on statistical calculations while the second investigates the underlying nonlinear field equations. In the last part of the paper we outline a generalisation of these methods which combines classical and quantum properties of the many-body systems studied. (orig.)

  2. Time series analyses of breathing patterns of lung cancer patients using nonlinear dynamical system theory.

    Science.gov (United States)

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

    2011-04-07

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

  3. Time series analyses of breathing patterns of lung cancer patients using nonlinear dynamical system theory

    Energy Technology Data Exchange (ETDEWEB)

    Tewatia, D K; Tolakanahalli, R P; Paliwal, B R; Tome, W A, E-mail: tewatia@wisc.edu [Department of Human Oncology, University of Wisconsin, Madison, WI (United States)

    2011-04-07

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

  4. Time series analyses of breathing patterns of lung cancer patients using nonlinear dynamical system theory

    International Nuclear Information System (INIS)

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

    2011-01-01

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

  5. Non-linear quenching of current fluctuations in a self-exciting homopolar dynamo, proved by feedback system theory

    Science.gov (United States)

    de Paor, A. M.

    Hide (Nonlinear Processes in Geophysics, 1998) has produced a new mathematical model of a self-exciting homopolar dynamo driving a series- wound motor, as a continuing contribution to the theory of the geomagnetic field. By a process of exact perturbation analysis, followed by combination and partial solution of differential equations, the complete nonlinear quenching of current fluctuations reported by Hide in the case that a parameter ɛ has the value 1 is proved via the Popov theorem from feedback system stability theory.

  6. H∞ Excitation Control Design for Stochastic Power Systems with Input Delay Based on Nonlinear Hamiltonian System Theory

    Directory of Open Access Journals (Sweden)

    Weiwei Sun

    2015-01-01

    Full Text Available This paper presents H∞ excitation control design problem for power systems with input time delay and disturbances by using nonlinear Hamiltonian system theory. The impact of time delays introduced by remote signal transmission and processing in wide-area measurement system (WAMS is well considered. Meanwhile, the systems under investigation are disturbed by random fluctuation. First, under prefeedback technique, the power systems are described as a nonlinear Hamiltonian system. Then the H∞ excitation controller of generators connected to distant power systems with time delay and stochasticity is designed. Based on Lyapunov functional method, some sufficient conditions are proposed to guarantee the rationality and validity of the proposed control law. The closed-loop systems under the control law are asymptotically stable in mean square independent of the time delay. And we through a simulation of a two-machine power system prove the effectiveness of the results proposed in this paper.

  7. 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...

  8. On projective synchronization of hyperchaotic complex nonlinear systems based on passive theory for secure communications

    International Nuclear Information System (INIS)

    Mahmoud, Gamal M; Mahmoud, Emad E; Arafa, Ayman A

    2013-01-01

    In this paper we deal with the projective synchronization (PS) of hyperchaotic complex nonlinear systems and its application in secure communications based on passive theory. The unpredictability of the scaling factor in PS can additionally enhance the security of communications. In this paper, a scheme for secure message transmission is proposed, and we try to transmit more than one large or bounded message from the transmitter to the receiver. The new hyperchaotic complex Lorenz system is employed to encrypt these messages. In the transmitter, the original messages are modulated into its parameter. In the receiver, we assume that the parameter of the receiver system is uncertain. The controllers and corresponding parameter update law are constructed to achieve PS between the transmitter and receiver system with an uncertain parameter, and identify the unknown parameter via passive theory. The original messages can be recovered successfully through some simple operations by the estimated parameter. Numerical results have verified the effectiveness and feasibility of the presented method. (paper)

  9. Theory of coherent Stark nonlinear spectroscopy in a three-level system

    International Nuclear Information System (INIS)

    Loiko, Yurii; Serrat, Carles

    2007-01-01

    Coherent Stark nonlinear spectroscopy (CSNS) is a spectroscopic tool based on the cancellation of the phase sensitivity at frequency 5ω in the ultrafast four-wave mixing (FWM) of two-color pulses with frequencies ω and 3ω. We develop a theory for CSNS in three-level V-type systems, and reveal that the mechanism for the phase sensitivity at 5ω is the quantum interference between the two primary paths in the FWM of the ω and 3ω fields. We find that the cancellation phenomenon occurs when the probability amplitude of one of these two primary pathways becomes equal to zero due to the competition effect between the two allowed transitions in the V-type system. The analytical expressions that describe the phase-sensitivity phenomenon and the conditions for its cancellation have been derived on the basis of perturbation theory, and are confirmed by numerical integration of the density matrix and Maxwell equations. We argue that CSNS can be utilized, in particular, for the investigation of optically dense media

  10. Nonlinear theory of elastic shells

    International Nuclear Information System (INIS)

    Costa Junior, J.A.

    1979-08-01

    Nonlinear theory of elastic shells is developed which incorporates both geometric and physical nonlinearities and which does not make use of the well known Love-Kirchhoff hypothesis. The resulting equations are formulated in tensorial notation and are reduced to the ones of common use when simplifying assumptions encountered in the especific litterature are taken. (Author) [pt

  11. Functional stochastic differential equations: mathematical theory of nonlinear parabolic systems with applications in field theory and statistical mechanics

    International Nuclear Information System (INIS)

    Doering, C.R.

    1985-01-01

    Applications of nonlinear parabolic stochastic differential equations with additive colored noise in equilibrium and nonequilibrium statistical mechanics and quantum field theory are developed in detail, providing a new unified mathematical approach to many problems. The existence and uniqueness of solutions to these equations is established, and some of the properties of the solutions are investigated. In particular, asymptotic expansions for the correlation functions of the solutions are introduced and compared to rigorous nonperturbative bounds on the moments. It is found that the perturbative analysis is in qualitative disagreement with the exact result in models corresponding to cut-off self-interacting nonperturbatively renormalizable scalar quantum field theories. For these theories the nonlinearities cannot be considered as perturbations of the linearized theory

  12. Non-linear quenching of current fluctuations in a self-exciting homopolar dynamo, proved by feedback system theory

    Directory of Open Access Journals (Sweden)

    A. M. de Paor

    1998-01-01

    Full Text Available Hide (Nonlinear Processes in Geophysics, 1998 has produced a new mathematical model of a self-exciting homopolar dynamo driving a series- wound motor, as a continuing contribution to the theory of the geomagnetic field. By a process of exact perturbation analysis, followed by combination and partial solution of differential equations, the complete nonlinear quenching of current fluctuations reported by Hide in the case that a parameter ε has the value 1 is proved via the Popov theorem from feedback system stability theory.

  13. Spectral theory and nonlinear functional analysis

    CERN Document Server

    Lopez-Gomez, Julian

    2001-01-01

    This Research Note addresses several pivotal problems in spectral theory and nonlinear functional analysis in connection with the analysis of the structure of the set of zeroes of a general class of nonlinear operators. It features the construction of an optimal algebraic/analytic invariant for calculating the Leray-Schauder degree, new methods for solving nonlinear equations in Banach spaces, and general properties of components of solutions sets presented with minimal use of topological tools. The author also gives several applications of the abstract theory to reaction diffusion equations and systems.The results presented cover a thirty-year period and include recent, unpublished findings of the author and his coworkers. Appealing to a broad audience, Spectral Theory and Nonlinear Functional Analysis contains many important contributions to linear algebra, linear and nonlinear functional analysis, and topology and opens the door for further advances.

  14. Thresholds, switches and hysteresis in hydrology from the pedon to the catchment scale: a non-linear systems theory

    Directory of Open Access Journals (Sweden)

    2007-01-01

    Full Text Available Hysteresis is a rate-independent non-linearity that is expressed through thresholds, switches, and branches. Exceedance of a threshold, or the occurrence of a turning point in the input, switches the output onto a particular output branch. Rate-independent branching on a very large set of switches with non-local memory is the central concept in the new definition of hysteresis. Hysteretic loops are a special case. A self-consistent mathematical description of hydrological systems with hysteresis demands a new non-linear systems theory of adequate generality. The goal of this paper is to establish this and to show how this may be done. Two results are presented: a conceptual model for the hysteretic soil-moisture characteristic at the pedon scale and a hysteretic linear reservoir at the catchment scale. Both are based on the Preisach model. A result of particular significance is the demonstration that the independent domain model of the soil moisture characteristic due to Childs, Poulavassilis, Mualem and others, is equivalent to the Preisach hysteresis model of non-linear systems theory, a result reminiscent of the reduction of the theory of the unit hydrograph to linear systems theory in the 1950s. A significant reduction in the number of model parameters is also achieved. The new theory implies a change in modelling paradigm.

  15. Oscillations in nonlinear systems

    CERN Document Server

    Hale, Jack K

    2015-01-01

    By focusing on ordinary differential equations that contain a small parameter, this concise graduate-level introduction to the theory of nonlinear oscillations provides a unified approach to obtaining periodic solutions to nonautonomous and autonomous differential equations. It also indicates key relationships with other related procedures and probes the consequences of the methods of averaging and integral manifolds.Part I of the text features introductory material, including discussions of matrices, linear systems of differential equations, and stability of solutions of nonlinear systems. Pa

  16. Connection between perturbation theory, projection-operator techniques, and statistical linearization for nonlinear systems

    International Nuclear Information System (INIS)

    Budgor, A.B.; West, B.J.

    1978-01-01

    We employ the equivalence between Zwanzig's projection-operator formalism and perturbation theory to demonstrate that the approximate-solution technique of statistical linearization for nonlinear stochastic differential equations corresponds to the lowest-order β truncation in both the consolidated perturbation expansions and in the ''mass operator'' of a renormalized Green's function equation. Other consolidated equations can be obtained by selectively modifying this mass operator. We particularize the results of this paper to the Duffing anharmonic oscillator equation

  17. Nonlinear classical theory of electromagnetism

    International Nuclear Information System (INIS)

    Pisello, D.

    1977-01-01

    A topological theory of electric charge is given. Einstein's criteria for the completion of classical electromagnetic theory are summarized and their relation to quantum theory and the principle of complementarity is indicated. The inhibiting effect that this principle has had on the development of physical thought is discussed. Developments in the theory of functions on nonlinear spaces provide the conceptual framework required for the completion of electromagnetism. The theory is based on an underlying field which is a continuous mapping of space-time into points on the two-sphere. (author)

  18. Nonlinearity and disorder: Theory and applications

    DEFF Research Database (Denmark)

    Bang, Ole; Sørensen, Mads Peter

    Proceedings of the NATO Advanced Research Workshop (ARW) entitled Nonlinearity and Disorder: Theory and Applications, held in Tashkent, Uzbekistan, October 2-6, 2001. Phenomena of coherent structures in nonlinear systems and disorder are considered opposite in nature. For example one of the most...... of the photorefractive solitons. Another very fast growing area induced by the technological development is statistical phenomena in nonlinear pulse propagation in optical fibers. Intrinsic randomness of existing optical communication systems has an important impact on the performance of planned soliton communication...

  19. Nonlinear Dynamics in Complex Systems Theory and Applications for the Life-, Neuro- and Natural Sciences

    CERN Document Server

    Fuchs, Armin

    2013-01-01

    With many areas of science reaching across their boundaries and becoming more and more interdisciplinary, students and researchers in these fields are confronted with techniques and tools not covered by their particular education. Especially in the life- and neurosciences quantitative models based on nonlinear dynamics and complex systems are becoming as frequently implemented as traditional statistical analysis. Unfamiliarity with the terminology and rigorous mathematics may discourage many scientists to adopt these methods for their own work, even though such reluctance in most cases is not justified.This book bridges this gap by introducing the procedures and methods used for analyzing nonlinear dynamical systems. In Part I, the concepts of fixed points, phase space, stability and transitions, among others, are discussed in great detail and implemented on the basis of example elementary systems. Part II is devoted to specific, non-trivial applications: coordination of human limb movement (Haken-Kelso-Bunz ...

  20. The Nonlinear Field Space Theory

    Energy Technology Data Exchange (ETDEWEB)

    Mielczarek, Jakub, E-mail: jakub.mielczarek@uj.edu.pl [Institute of Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków (Poland); Trześniewski, Tomasz, E-mail: tbwbt@ift.uni.wroc.pl [Institute of Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków (Poland); Institute for Theoretical Physics, University of Wrocław, pl. Borna 9, 50-204 Wrocław (Poland)

    2016-08-10

    In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values) that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum) Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the “Principle of finiteness” of physical theories, which once motivated the Born–Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity), as well as in condensed matter physics (e.g. continuous spin chains), and can shed new light on the issue of divergences in quantum field theories.

  1. The Nonlinear Field Space Theory

    International Nuclear Information System (INIS)

    Mielczarek, Jakub; Trześniewski, Tomasz

    2016-01-01

    In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values) that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum) Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the “Principle of finiteness” of physical theories, which once motivated the Born–Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity), as well as in condensed matter physics (e.g. continuous spin chains), and can shed new light on the issue of divergences in quantum field theories.

  2. Uncertainty analysis of time-dependent nonlinear systems: theory and application to transient thermal hydraulics

    International Nuclear Information System (INIS)

    Barhen, J.; Bjerke, M.A.; Cacuci, D.G.; Mullins, C.B.; Wagschal, G.G.

    1982-01-01

    An advanced methodology for performing systematic uncertainty analysis of time-dependent nonlinear systems is presented. This methodology includes a capability for reducing uncertainties in system parameters and responses by using Bayesian inference techniques to consistently combine prior knowledge with additional experimental information. The determination of best estimates for the system parameters, for the responses, and for their respective covariances is treated as a time-dependent constrained minimization problem. Three alternative formalisms for solving this problem are developed. The two ''off-line'' formalisms, with and without ''foresight'' characteristics, require the generation of a complete sensitivity data base prior to performing the uncertainty analysis. The ''online'' formalism, in which uncertainty analysis is performed interactively with the system analysis code, is best suited for treatment of large-scale highly nonlinear time-dependent problems. This methodology is applied to the uncertainty analysis of a transient upflow of a high pressure water heat transfer experiment. For comparison, an uncertainty analysis using sensitivities computed by standard response surface techniques is also performed. The results of the analysis indicate the following. Major reduction of the discrepancies in the calculation/experiment ratios is achieved by using the new methodology. Incorporation of in-bundle measurements in the uncertainty analysis significantly reduces system uncertainties. Accuracy of sensitivities generated by response-surface techniques should be carefully assessed prior to using them as a basis for uncertainty analyses of transient reactor safety problems

  3. Global Stability and Dynamics of Strongly Nonlinear Systems Using Koopman Operator Theory

    Science.gov (United States)

    2017-03-01

    Koopman operator theory to systems with memory in time made during Year 1, during Year 2 we worked toward developing a test capable of determining...using this term. Approved for public release; distribution is unlimited. 6 Furthermore, a key element of an approach that is fully capable of dealing...Operator Theory by Bryan Glaz and Adam Svenkeson Approved for public release; distribution is unlimited. NOTICES

  4. Theory and design of nonlinear metamaterials

    Science.gov (United States)

    Rose, Alec Daniel

    If electronics are ever to be completely replaced by optics, a significant possibility in the wake of the fiber revolution, it is likely that nonlinear materials will play a central and enabling role. Indeed, nonlinear optics is the study of the mechanisms through which light can change the nature and properties of matter and, as a corollary, how one beam or color of light can manipulate another or even itself within such a material. However, of the many barriers preventing such a lofty goal, the narrow and limited range of properties supported by nonlinear materials, and natural materials in general, stands at the forefront. Many industries have turned instead to artificial and composite materials, with homogenizable metamaterials representing a recent extension of such composites into the electromagnetic domain. In particular, the inclusion of nonlinear elements has caused metamaterials research to spill over into the field of nonlinear optics. Through careful design of their constituent elements, nonlinear metamaterials are capable of supporting an unprecedented range of interactions, promising nonlinear devices of novel design and scale. In this context, I cast the basic properties of nonlinear metamaterials in the conventional formalism of nonlinear optics. Using alternately transfer matrices and coupled mode theory, I develop two complementary methods for characterizing and designing metamaterials with arbitrary nonlinear properties. Subsequently, I apply these methods in numerical studies of several canonical metamaterials, demonstrating enhanced electric and magnetic nonlinearities, as well as predicting the existence of nonlinear magnetoelectric and off-diagonal nonlinear tensors. I then introduce simultaneous design of the linear and nonlinear properties in the context of phase matching, outlining five different metamaterial phase matching methods, with special emphasis on the phase matching of counter propagating waves in mirrorless parametric amplifiers

  5. Time-dependent density functional theory for nonlinear properties of open-shell systems.

    Science.gov (United States)

    Rinkevicius, Zilvinas; Jha, Prakash Chandra; Oprea, Corneliu I; Vahtras, Olav; Agren, Hans

    2007-09-21

    This paper presents response theory based on a spin-restricted Kohn-Sham formalism for computation of time-dependent and time-independent nonlinear properties of molecules with a high spin ground state. The developed approach is capable to handle arbitrary perturbations and constitutes an efficient procedure for evaluation of electric, magnetic, and mixed properties. Apart from presenting the derivation of the proposed approach, we show results from illustrating calculations of static and dynamic hyperpolarizabilities of small Si(3n+1)H(6n+3) (n=0,1,2) clusters which mimic Si(111) surfaces with dangling bond defects. The results indicate that the first hyperpolarizability tensor components of Si(3n+1)H(6n+3) have an ordering compatible with the measurements of second harmonic generation in SiO2/Si(111) interfaces and, therefore, support the hypothesis that silicon surface defects with dangling bonds are responsible for this phenomenon. The results exhibit a strong dependence on the quality of basis set and exchange-correlation functional, showing that an appropriate set of diffuse functions is required for reliable predictions of the first hyperpolarizability of open-shell compounds.

  6. Spectral theory and nonlinear analysis with applications to spatial ecology

    CERN Document Server

    Cano-Casanova, S; Mora-Corral , C

    2005-01-01

    This volume details some of the latest advances in spectral theory and nonlinear analysis through various cutting-edge theories on algebraic multiplicities, global bifurcation theory, non-linear Schrödinger equations, non-linear boundary value problems, large solutions, metasolutions, dynamical systems, and applications to spatial ecology. The main scope of the book is bringing together a series of topics that have evolved separately during the last decades around the common denominator of spectral theory and nonlinear analysis - from the most abstract developments up to the most concrete applications to population dynamics and socio-biology - in an effort to fill the existing gaps between these fields.

  7. Exact solutions to nonlinear symmetron theory: One- and two-mirror systems

    Science.gov (United States)

    Brax, Philippe; Pitschmann, Mario

    2018-03-01

    We derive the exact analytical solutions to the symmetron field theory equations in the presence of a one- or two-mirror system. The one-dimensional equations of motion are integrated exactly for both systems and their solutions can be expressed in terms of Jacobi elliptic functions. Surprisingly, in the case of two parallel mirrors, the equations of motion generically provide not a unique solution but a discrete set of solutions with increasing number of nodes and energies. The solutions obtained herein can be applied to q BOUNCE experiments, neutron interferometry and for the calculation of the symmetron-field-induced "Casimir force" in the CANNEX experiment.

  8. Complex motions and chaos in nonlinear systems

    CERN Document Server

    Machado, José; Zhang, Jiazhong

    2016-01-01

    This book brings together 10 chapters on a new stream of research examining complex phenomena in nonlinear systems—including engineering, physics, and social science. Complex Motions and Chaos in Nonlinear Systems provides readers a particular vantage of the nature and nonlinear phenomena in nonlinear dynamics that can develop the corresponding mathematical theory and apply nonlinear design to practical engineering as well as the study of other complex phenomena including those investigated within social science.

  9. Detection of seizures from small samples using nonlinear dynamic system theory.

    Science.gov (United States)

    Yaylali, I; Koçak, H; Jayakar, P

    1996-07-01

    The electroencephalogram (EEG), like many other biological phenomena, is quite likely governed by nonlinear dynamics. Certain characteristics of the underlying dynamics have recently been quantified by computing the correlation dimensions (D2) of EEG time series data. In this paper, D2 of the unbiased autocovariance function of the scalp EEG data was used to detect electrographic seizure activity. Digital EEG data were acquired at a sampling rate of 200 Hz per channel and organized in continuous frames (duration 2.56 s, 512 data points). To increase the reliability of D2 computations with short duration data, raw EEG data were initially simplified using unbiased autocovariance analysis to highlight the periodic activity that is present during seizures. The D2 computation was then performed from the unbiased autocovariance function of each channel using the Grassberger-Procaccia method with Theiler's box-assisted correlation algorithm. Even with short duration data, this preprocessing proved to be computationally robust and displayed no significant sensitivity to implementation details such as the choices of embedding dimension and box size. The system successfully identified various types of seizures in clinical studies.

  10. Stability analysis of nonlinear autonomous systems - General theory and application to flutter

    Science.gov (United States)

    Smith, L. L.; Morino, L.

    1975-01-01

    The analysis makes use of a singular perturbation method, the multiple time scaling. Concepts of stable and unstable limit cycles are introduced. The solution is obtained in the form of an asymptotic expansion. Numerical results are presented for the nonlinear flutter of panels and airfoils in supersonic flow. The approach used is an extension of a method for analyzing nonlinear panel flutter reported by Morino (1969).

  11. Non-linear quenching of current fluctuations in a self-exciting homopolar dynamo, proved by feedback system theory

    OpenAIRE

    A. M. de Paor

    1998-01-01

    International audience; Hide (Nonlinear Processes in Geophysics, 1998) has produced a new mathematical model of a self-exciting homopolar dynamo driving a series- wound motor, as a continuing contribution to the theory of the geomagnetic field. By a process of exact perturbation analysis, followed by combination and partial solution of differential equations, the complete nonlinear quenching of current fluctuations reported by Hide in the case that a parameter ? has the value 1 is proved via ...

  12. 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.

  13. Balancing for nonlinear systems

    NARCIS (Netherlands)

    Scherpen, J.M.A.

    1993-01-01

    We present a method of balancing for nonlinear systems which is an extension of balancing for linear systems in the sense that it is based on the input and output energy of a system. It is a local result, but gives 'broader' results than we obtain by just linearizing the system. Furthermore, the

  14. Nonlinear closed-loop control theory

    International Nuclear Information System (INIS)

    Perez, R.B.; Otaduy, P.J.; Abdalla, M.

    1992-01-01

    Traditionally, the control of nuclear power plants has been implemented by the use of proportional-integral (PI) control systems. PI controllers are both simple and, within their calibration range, highly reliable. However, PIs provide little performance information that could be used to diagnose out-of-range events or the nature of unanticipated transients that may occur in the plant. To go beyond the PI controller, the new control algorithms must deal with the physical system nonlinearities and with the reality of uncertain dynamics terms in its mathematical model. The tool to develop a new kind of control algorithm is provided by Optimal Control Theory. In this theory, a norm is minimized which incorporates the constraint that the model equations should be satisfied at all times by means of the Lagrange multipliers. Optimal control algorithms consist of two sets of coupled equations: (1) the model equations, integrated forward in time; and (2) the equations for the Lagrange multipliers (adjoints), integrated backwards in time. There are two challenges: dealing with large sets of coupled nonlinear equations and with a two-point boundary value problem that must be solved iteratively. In this paper, the rigorous conversion of the two-point boundary value problem into an initial value problem is presented. In addition, the incorporation into the control algorithm of ''real world'' constraints such as sensors and actuators, dynamic response functions and time lags introduced by the digitalization of analog signals is presented. (Author)

  15. Nonlinear dynamics of a pseudoelastic shape memory alloy system - theory and experiment

    DEFF Research Database (Denmark)

    Enemark, Søren; A Savi, M.; Santos, Ilmar

    2014-01-01

    In this work, a helical spring made from a pseudoelastic shape memory alloy was embedded in a dynamic system also composed of a mass, a linear spring and an excitation system. The mechanical behaviour of shape memory alloys is highly complex, involving hysteresis, which leads to damping capabilit...

  16. Gradient $L^q$ theory for a class of non-diagonal nonlinear elliptic systems

    Czech Academy of Sciences Publication Activity Database

    Bulíček, M.; Kalousek, M.; Kaplický, P.; Mácha, Václav

    2018-01-01

    Roč. 171, June (2018), s. 156-169 ISSN 0362-546X R&D Projects: GA ČR GA16-03230S Institutional support: RVO:67985840 Keywords : regularity * gradient estimates * non-diagonal elliptic systems Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.192, year: 2016 https://www.sciencedirect.com/science/ article /pii/S0362546X18300385

  17. Gradient $L^q$ theory for a class of non-diagonal nonlinear elliptic systems

    Czech Academy of Sciences Publication Activity Database

    Bulíček, M.; Kalousek, M.; Kaplický, P.; Mácha, Václav

    2018-01-01

    Roč. 171, June (2018), s. 156-169 ISSN 0362-546X R&D Projects: GA ČR GA16-03230S Institutional support: RVO:67985840 Keywords : regularity * gradient estimates * non-diagonal elliptic systems Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.192, year: 2016 https://www.sciencedirect.com/science/article/pii/S0362546X18300385

  18. Overview of nonlinear theory of kinetically driven instabilities

    International Nuclear Information System (INIS)

    Berk, H.L.; Breizman, B.N.

    1998-09-01

    An overview is presented of the theory for the nonlinear behavior of instabilities driven by the resonant wave particle interaction. The approach should be applicable to a wide variety of kinetic systems in magnetic fusion devices and accelerators. Here the authors emphasize application to Alfven were driven instability, and the principles of the theory are used to interpret experimental data

  19. A Geometrically—Nonlinear Plate Theory 12

    Institute of Scientific and Technical Information of China (English)

    AlbertC.J.LUO

    1999-01-01

    An approximate plate theory developed in this paper is based on an assumed displacement field,the strains described by a Taylor series in the normal distance from the middle surface,the exact strains of the middle surface and the equations of equilibrium governing the exact configuration of the deformed middle surface,In this theory the exact geometry of the deformed middle surface is used to derive the strains and equilibrium of the plate.Application of this theory does not depend on the constitutive law.THis theory can reduce to some existing nonlinear theories through imposition of constraints.

  20. Nonlinear Lorentz-invariant theory of gravitation

    International Nuclear Information System (INIS)

    Petry, W.

    1976-01-01

    A nonlinear Lorentz-invariant theory of gravitation and a Lorentz-invariant Hamiltonian for a particle with spin in the gravitational field are developed. The equations of motions are studied. The theory is applied to the three well known tests of General Relativity. In the special case of the red shift of spectral lines and of the deflection of light, the theory gives the same results as the General Theory of Relativity, whereas in the case of the perihelion of the Mercury, the theory gives 40,3'', in good agreement with experimental results of Dicke. (author)

  1. Nonlinear Hamiltonian systems

    DEFF Research Database (Denmark)

    Jørgensen, Michael Finn

    1995-01-01

    It is generally very difficult to solve nonlinear systems, and such systems often possess chaotic solutions. In the rare event that a system is completely solvable, it is said to integrable. Such systems never have chaotic solutions. Using the Inverse Scattering Transform Method (ISTM) two...... particular configurations of the Discrete Self-Trapping (DST) system are shown to be completely solvable. One of these systems includes the Toda lattice in a certain limit. An explicit integration is carried through for this Near-Toda lattice. The Near-Toda lattice is then generalized to include singular...

  2. Rigorous theory of molecular orientational nonlinear optics

    International Nuclear Information System (INIS)

    Kwak, Chong Hoon; Kim, Gun Yeup

    2015-01-01

    Classical statistical mechanics of the molecular optics theory proposed by Buckingham [A. D. Buckingham and J. A. Pople, Proc. Phys. Soc. A 68, 905 (1955)] has been extended to describe the field induced molecular orientational polarization effects on nonlinear optics. In this paper, we present the generalized molecular orientational nonlinear optical processes (MONLO) through the calculation of the classical orientational averaging using the Boltzmann type time-averaged orientational interaction energy in the randomly oriented molecular system under the influence of applied electric fields. The focal points of the calculation are (1) the derivation of rigorous tensorial components of the effective molecular hyperpolarizabilities, (2) the molecular orientational polarizations and the electronic polarizations including the well-known third-order dc polarization, dc electric field induced Kerr effect (dc Kerr effect), optical Kerr effect (OKE), dc electric field induced second harmonic generation (EFISH), degenerate four wave mixing (DFWM) and third harmonic generation (THG). We also present some of the new predictive MONLO processes. For second-order MONLO, second-order optical rectification (SOR), Pockels effect and difference frequency generation (DFG) are described in terms of the anisotropic coefficients of first hyperpolarizability. And, for third-order MONLO, third-order optical rectification (TOR), dc electric field induced difference frequency generation (EFIDFG) and pump-probe transmission are presented

  3. Lectures in nonlinear mechanics and chaos theory

    CERN Document Server

    Stetz, Albert W

    2016-01-01

    This elegant book presents a rigorous introduction to the theory of nonlinear mechanics and chaos. It turns out that many simple mechanical systems suffer from a peculiar malady. They are deterministic in the sense that their motion can be described with partial differential equations, but these equations have no proper solutions and the behavior they describe can be wildly unpredictable. This is implicit in Newtonian physics, and although it was analyzed in the pioneering work of Poincaré in the 19th century, its full significance has only been realized since the advent of modern computing. This book follows this development in the context of classical mechanics as it is usually taught in most graduate programs in physics. It starts with the seminal work of Laplace, Hamilton, and Liouville in the early 19th century and shows how their formulation of mechanics inevitably leads to systems that cannot be 'solved' in the usual sense of the word. It then discusses perturbation theory which, rather than providing...

  4. Nonlinear theory of electroelastic and magnetoelastic interactions

    CERN Document Server

    Dorfmann, Luis

    2014-01-01

    This book provides a unified theory of nonlinear electro-magnetomechanical interactions of soft materials capable of large elastic deformations. The authors include an overview of the basic principles of the classical theory of electromagnetism from the fundamental notions of point charges and magnetic dipoles through to distributions of charge and current in a non-deformable continuum, time-dependent electromagnetic fields and Maxwell’s equations. They summarize the basic ingredients of continuum mechanics that are required to account for the deformability of material and present nonlinear constitutive frameworks for electroelastic and magnetoelastic interactions in a highly deformable material. The equations contained in the book are used to formulate and solve a variety of representative boundary-value problems for both nonlinear electroelasticity and magnetoelasticity.

  5. Inverse operator theory method and its applications in nonlinear physics

    International Nuclear Information System (INIS)

    Fang Jinqing

    1993-01-01

    Inverse operator theory method, which has been developed by G. Adomian in recent years, and its applications in nonlinear physics are described systematically. The method can be an unified effective procedure for solution of nonlinear and/or stochastic continuous dynamical systems without usual restrictive assumption. It is realized by Mathematical Mechanization by us. It will have a profound on the modelling of problems of physics, mathematics, engineering, economics, biology, and so on. Some typical examples of the application are given and reviewed

  6. H∞ Balancing for Nonlinear Systems

    NARCIS (Netherlands)

    Scherpen, Jacquelien M.A.

    1996-01-01

    In previously obtained balancing methods for nonlinear systems a past and a future energy function are used to bring the nonlinear system in balanced form. By considering a different pair of past and future energy functions that are related to the H∞ control problem for nonlinear systems we define

  7. A nonlinear theory of generalized functions

    CERN Document Server

    1990-01-01

    This book provides a simple introduction to a nonlinear theory of generalized functions introduced by J.F. Colombeau, which gives a meaning to any multiplication of distributions. This theory extends from pure mathematics (it presents a faithful generalization of the classical theory of C? functions and provides a synthesis of most existing multiplications of distributions) to physics (it permits the resolution of ambiguities that appear in products of distributions), passing through the theory of partial differential equations both from the theoretical viewpoint (it furnishes a concept of weak solution of pde's leading to existence-uniqueness results in many cases where no distributional solution exists) and the numerical viewpoint (it introduces new and efficient methods developed recently in elastoplasticity, hydrodynamics and acoustics). This text presents basic concepts and results which until now were only published in article form. It is in- tended for mathematicians but, since the theory and applicati...

  8. FRF decoupling of nonlinear systems

    Science.gov (United States)

    Kalaycıoğlu, Taner; Özgüven, H. Nevzat

    2018-03-01

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

  9. 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.

  10. Nonlinear model predictive control theory and algorithms

    CERN Document Server

    Grüne, Lars

    2017-01-01

    This book offers readers a thorough and rigorous introduction to nonlinear model predictive control (NMPC) for discrete-time and sampled-data systems. NMPC schemes with and without stabilizing terminal constraints are detailed, and intuitive examples illustrate the performance of different NMPC variants. NMPC is interpreted as an approximation of infinite-horizon optimal control so that important properties like closed-loop stability, inverse optimality and suboptimality can be derived in a uniform manner. These results are complemented by discussions of feasibility and robustness. An introduction to nonlinear optimal control algorithms yields essential insights into how the nonlinear optimization routine—the core of any nonlinear model predictive controller—works. Accompanying software in MATLAB® and C++ (downloadable from extras.springer.com/), together with an explanatory appendix in the book itself, enables readers to perform computer experiments exploring the possibilities and limitations of NMPC. T...

  11. Balancing for Unstable Nonlinear Systems

    NARCIS (Netherlands)

    Scherpen, J.M.A.

    1993-01-01

    A previously obtained method of balancing for stable nonlinear systems is extended to unstable nonlinear systems. The similarity invariants obtained by the concept of LQG balancing for an unstable linear system can also be obtained by considering a past and future energy function of the system. By

  12. Topics in nonlinear wave theory with applications

    International Nuclear Information System (INIS)

    Tracy, E.R.

    1984-01-01

    Selected topics in nonlinear wave theory are discussed, and applications to the study of modulational instabilities are presented. A historical survey is given of topics relating to solitons and modulational problems. A method is then presented for generating exact periodic and quasi-periodic solutions to several nonlinear wave equations, which have important physical applications. The method is then specialized for the purposes of studying the modulational instability of a plane wave solution of the nonlinear Schroedinger equation, an equation with general applicability in one-dimensional modulational problems. Some numerical results obtained in conjunction with the analytic study are presented. The analytic approach explains the recurrence phenomena seen in the numerical studies, and the numerical work of other authors. The method of solution (related to the inverse scattering method) is then analyzed within the context of Hamiltonian dynamics where it is shown that the method can be viewed as simply a pair of canonical transformations. The Abel Transformation, which appears here and in the work of other authors, is shown to be a special form of Liouville's transformation to action-angle variables. The construction of closed form solutions of these nonlinear wave equations, via the solution of Jacobi's inversion problem, is surveyed briefly

  13. Nonlinear gravitons and curved twistor theory

    International Nuclear Information System (INIS)

    Penrose, R.

    1976-01-01

    A new approach to the quantization of general relativity is suggested in which a state consisting of just one graviton can be described, but in a way which involves both the curvature and nonlinearities of Einstein's theory. It is felt that this approach can be justified solely on its own merits but it also receives striking encouragement from another direction: a surprising mathematical result enables one to construct the general such nonlinear gravitation state from a curved twistor space, the construction being given in terms of one arbitrary holomorphic function of three complex variables. In this way, the approach fits naturally into the general twistor program for the description of quantized fields. (U.K.)

  14. Nonlinear analysis approximation theory, optimization and applications

    CERN Document Server

    2014-01-01

    Many of our daily-life problems can be written in the form of an optimization problem. Therefore, solution methods are needed to solve such problems. Due to the complexity of the problems, it is not always easy to find the exact solution. However, approximate solutions can be found. The theory of the best approximation is applicable in a variety of problems arising in nonlinear functional analysis and optimization. This book highlights interesting aspects of nonlinear analysis and optimization together with many applications in the areas of physical and social sciences including engineering. It is immensely helpful for young graduates and researchers who are pursuing research in this field, as it provides abundant research resources for researchers and post-doctoral fellows. This will be a valuable addition to the library of anyone who works in the field of applied mathematics, economics and engineering.

  15. Nonlinear dynamic behaviour of a rotor-foundation system coupled through passive magnetic bearings with magnetic anisotropy - Theory and experiment

    DEFF Research Database (Denmark)

    Enemark, Søren; Santos, Ilmar F.

    2016-01-01

    In this work, the nonlinear dynamic behaviour of a vertical rigid rotor interacting with a flexible foundation by means of two passive magnetic bearings is quantified and evaluated. The quantification is based on theoretical and experimental investigation of the non-uniformity (anisotropy......) of the magnetic field and the weak nonlinearity of the magnetic forces. Through mathematical modelling the nonlinear equations of motion are established for describing the shaft and bearing housing lateral dynamics coupled via the nonlinear and non-uniform magnetic forces. The equations of motion are solved...

  16. A new integrability theory for certain nonlinear physical problems

    International Nuclear Information System (INIS)

    Berger, M.S.

    1993-01-01

    A new mathematically sound integrability theory for certain nonlinear problems defined by ordinary or partial differential equations is defined. The new theory works in an arbitrary finite number of space dimensions. Moreover, if a system is integrable in the new sense described here, it has a remarkable stability property that distinguishes if from any previously known integrability ideas. The new theory proceeds by establishing a ''global normal form'' for the problem at hand. This normal form holds subject to canonical coordinate transformations, extending such classical ideas by using new nonlinear methods of infinite dimensional functional analysis. The global normal form in question is related to the mathematical theory of singularities of mappings of H. Whitney and R. Thom extended globally and form finite to infinite dimensions. Thus bifurcation phenomena are naturally included in the new integrability theory. Typical examples include the classically nonintegrable Riccati equation, certain non-Euclidean mean field theories, certain parabolic reaction diffusion equations and the hyperbolic nonlinear telegrapher's equation. (Author)

  17. Nonlinear PDEs a dynamical systems approach

    CERN Document Server

    Schneider, Guido

    2017-01-01

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

  18. Alternative theories of the non-linear negative mass instability

    International Nuclear Information System (INIS)

    Channell, P.J.

    1974-01-01

    A theory non-linear negative mass instability is extended to include resistance. The basic assumption is explained physically and an alternative theory is offered. The two theories are compared computationally. 7 refs., 8 figs

  19. In-Flight Aeroelastic Stability of the Thermal Protection System on the NASA HIAD, Part II: Nonlinear Theory and Extended Aerodynamics

    Science.gov (United States)

    Goldman, Benjamin D.; Dowell, Earl H.; Scott, Robert C.

    2015-01-01

    Conical shell theory and a supersonic potential flow aerodynamic theory are used to study the nonlinear pressure buckling and aeroelastic limit cycle behavior of the thermal protection system for NASA's Hypersonic Inflatable Aerodynamic Decelerator. The structural model of the thermal protection system consists of an orthotropic conical shell of the Donnell type, resting on several circumferential elastic supports. Classical Piston Theory is used initially for the aerodynamic pressure, but was found to be insufficient at low supersonic Mach numbers. Transform methods are applied to the convected wave equation for potential flow, and a time-dependent aerodynamic pressure correction factor is obtained. The Lagrangian of the shell system is formulated in terms of the generalized coordinates for all displacements and the Rayleigh-Ritz method is used to derive the governing differential-algebraic equations of motion. Aeroelastic limit cycle oscillations and buckling deformations are calculated in the time domain using a Runge-Kutta method in MATLAB. Three conical shell geometries were considered in the present analysis: a 3-meter diameter 70 deg. cone, a 3.7-meter 70 deg. cone, and a 6-meter diameter 70 deg. cone. The 6-meter configuration was loaded statically and the results were compared with an experimental load test of a 6-meter HIAD. Though agreement between theoretical and experimental strains was poor, the circumferential wrinkling phenomena observed during the experiments was captured by the theory and axial deformations were qualitatively similar in shape. With Piston Theory aerodynamics, the nonlinear flutter dynamic pressures of the 3-meter configuration were in agreement with the values calculated using linear theory, and the limit cycle amplitudes were generally on the order of the shell thickness. The effect of axial tension was studied for this configuration, and increasing tension was found to decrease the limit cycle amplitudes when the circumferential

  20. Electro-optic chaotic system based on the reverse-time chaos theory and a nonlinear hybrid feedback loop.

    Science.gov (United States)

    Jiang, Xingxing; Cheng, Mengfan; Luo, Fengguang; Deng, Lei; Fu, Songnian; Ke, Changjian; Zhang, Minming; Tang, Ming; Shum, Ping; Liu, Deming

    2016-12-12

    A novel electro-optic chaos source is proposed on the basis of the reverse-time chaos theory and an analog-digital hybrid feedback loop. The analog output of the system can be determined by the numeric states of shift registers, which makes the system robust and easy to control. The dynamical properties as well as the complexity dependence on the feedback parameters are investigated in detail. The correlation characteristics of the system are also studied. Two improving strategies which were established in digital field and analog field are proposed to conceal the time-delay signature. The proposed scheme has the potential to be used in radar and optical secure communication systems.

  1. SEACAS Theory Manuals: Part II. Nonlinear Continuum Mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.

    1998-09-01

    This report summarizes the key continuum mechanics concepts required for the systematic prescription and numerical solution of finite deformation solid mechanics problems. Topics surveyed include measures of deformation appropriate for media undergoing large deformations, stress measures appropriate for such problems, balance laws and their role in nonlinear continuum mechanics, the role of frame indifference in description of large deformation response, and the extension of these theories to encompass two dimensional idealizations, structural idealizations, and rigid body behavior. There are three companion reports that describe the problem formulation, constitutive modeling, and finite element technology for nonlinear continuum mechanics systems.

  2. Properties of some nonlinear Schroedinger equations motivated through information theory

    International Nuclear Information System (INIS)

    Yuan, Liew Ding; Parwani, Rajesh R

    2009-01-01

    We update our understanding of nonlinear Schroedinger equations motivated through information theory. In particular we show that a q-deformation of the basic nonlinear equation leads to a perturbative increase in the energy of a system, thus favouring the simplest q = 1 case. Furthermore the energy minimisation criterion is shown to be equivalent, at leading order, to an uncertainty maximisation argument. The special value η = 1/4 for the interpolation parameter, where leading order energy shifts vanish, implies the preservation of existing supersymmetry in nonlinearised supersymmetric quantum mechanics. Physically, η might be encoding relativistic effects.

  3. Governing Laws of Complex System Predictability under Co-evolving Uncertainty Sources: Theory and Nonlinear Geophysical Applications

    Science.gov (United States)

    Perdigão, R. A. P.

    2017-12-01

    Predictability assessments are traditionally made on a case-by-case basis, often by running the particular model of interest with randomly perturbed initial/boundary conditions and parameters, producing computationally expensive ensembles. These approaches provide a lumped statistical view of uncertainty evolution, without eliciting the fundamental processes and interactions at play in the uncertainty dynamics. In order to address these limitations, we introduce a systematic dynamical framework for predictability assessment and forecast, by analytically deriving governing equations of predictability in terms of the fundamental architecture of dynamical systems, independent of any particular problem under consideration. The framework further relates multiple uncertainty sources along with their coevolutionary interplay, enabling a comprehensive and explicit treatment of uncertainty dynamics along time, without requiring the actual model to be run. In doing so, computational resources are freed and a quick and effective a-priori systematic dynamic evaluation is made of predictability evolution and its challenges, including aspects in the model architecture and intervening variables that may require optimization ahead of initiating any model runs. It further brings out universal dynamic features in the error dynamics elusive to any case specific treatment, ultimately shedding fundamental light on the challenging issue of predictability. The formulated approach, framed with broad mathematical physics generality in mind, is then implemented in dynamic models of nonlinear geophysical systems with various degrees of complexity, in order to evaluate their limitations and provide informed assistance on how to optimize their design and improve their predictability in fundamental dynamical terms.

  4. Waves and Structures in Nonlinear Nondispersive Media General Theory and Applications to Nonlinear Acoustics

    CERN Document Server

    Gurbatov, S N; Saichev, A I

    2012-01-01

    "Waves and Structures in Nonlinear Nondispersive Media: General Theory and Applications to Nonlinear Acoustics” is devoted completely to nonlinear structures. The general theory is given here in parallel with mathematical models. Many concrete examples illustrate the general analysis of Part I. Part II is devoted to applications to nonlinear acoustics, including specific nonlinear models and exact solutions, physical mechanisms of nonlinearity, sawtooth-shaped wave propagation, self-action phenomena, nonlinear resonances and engineering application (medicine, nondestructive testing, geophysics, etc.). This book is designed for graduate and postgraduate students studying the theory of nonlinear waves of various physical nature. It may also be useful as a handbook for engineers and researchers who encounter the necessity of taking nonlinear wave effects into account of their work. Dr. Gurbatov S.N. is the head of Department, and Vice Rector for Research of Nizhny Novgorod State University. Dr. Rudenko O.V. is...

  5. A Survey of Nonlinear Dynamics (Chaos Theory)

    Science.gov (United States)

    1991-04-01

    example of an n = 1 Hamiltonian system does have separatrices. This is the 1D pendulum (Fig. 4.2): 9=p, p=-asin9;H(9,p) =p2 /2- acosO . (4-5) Phase space...method. There is no substitute for the actual labor of applying the nonlinear operator to a sum of normal modes, producing a general Galerkin vector

  6. The theory of dissipative structures of the kinetic system for defects of nonlinear physical system 'metal+loading+irradiation'. Part 3

    International Nuclear Information System (INIS)

    Tarasov, V.A.; Borikov, T.L.; Kryzhanovskaya, T.V.; Chernezhenko, S.A.; Rusov, V.D.

    2007-01-01

    The kinetic system for defects of physical nonlinear system 'metal + load + irradiation' is specified [1, 2, 3]. Developing the approaches offered in [4], where distinctions of mechanisms of radiating creep and areas of their applicability are formalized (depending on external parameters) for fuel and constructional metals, division of kinetic systems for defects of constructional and fuel metals is carrying out. Thus the accent on the autocatalytic features of kinetic system for defects of reactor fuel metals, resulting from the exoenergic autocatalytic character of nuclear fission reactions being the main point defect source is done. In this part of the article the basic attention is given to the kinetic of sink drains for point defects. For kinetic systems of sinks-sources new approaches for the task of boundary conditions are offered. The possible structure of the computer program modelling kinetic system for defects of nonlinear physical system 'metal + load + irradiation' is considered

  7. Two-dimensional nonlinear equations of supersymmetric gauge theories

    International Nuclear Information System (INIS)

    Savel'ev, M.V.

    1985-01-01

    Supersymmetric generalization of two-dimensional nonlinear dynamical equations of gauge theories is presented. The nontrivial dynamics of a physical system in the supersymmetry and supergravity theories for (2+2)-dimensions is described by the integrable embeddings of Vsub(2/2) superspace into the flat enveloping superspace Rsub(N/M), supplied with the structure of a Lie superalgebra. An equation is derived which describes a supersymmetric generalization of the two-dimensional Toda lattice. It contains both super-Liouville and Sinh-Gordon equations

  8. Quantization of a nonlinearly realized supersymmetric theory

    International Nuclear Information System (INIS)

    Shima, K.

    1977-01-01

    The two-dimensional version of the Volkov-Akulov Lagrangian, where the supersymmetry is realized nonlinearly by means of a single Majorana spinor psi (x), is quantized. The equal-time anticommutators for the field are not c numbers but are functions of the field itself. By explicit calculation we shall show that the supersymmetry charges of the model form the supersymmetry algebra (the graded Lie algebra); therefore the Hamiltonian of the system P 0 is written as a bilinear sum of products of supersymmetry charges. We shall also show that the supersymmetry charges exactly generate a constant translation of psi (x) in the spinor space

  9. Theories of quantum dissipation and nonlinear coupling bath descriptors

    Science.gov (United States)

    Xu, Rui-Xue; Liu, Yang; Zhang, Hou-Dao; Yan, YiJing

    2018-03-01

    The quest of an exact and nonperturbative treatment of quantum dissipation in nonlinear coupling environments remains in general an intractable task. In this work, we address the key issues toward the solutions to the lowest nonlinear environment, a harmonic bath coupled both linearly and quadratically with an arbitrary system. To determine the bath coupling descriptors, we propose a physical mapping scheme, together with the prescription reference invariance requirement. We then adopt a recently developed dissipaton equation of motion theory [R. X. Xu et al., Chin. J. Chem. Phys. 30, 395 (2017)], with the underlying statistical quasi-particle ("dissipaton") algebra being extended to the quadratic bath coupling. We report the numerical results on a two-level system dynamics and absorption and emission line shapes.

  10. 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...

  11. Nonlinear solar cycle forecasting: theory and perspectives

    Science.gov (United States)

    Baranovski, A. L.; Clette, F.; Nollau, V.

    2008-02-01

    In this paper we develop a modern approach to solar cycle forecasting, based on the mathematical theory of nonlinear dynamics. We start from the design of a static curve fitting model for the experimental yearly sunspot number series, over a time scale of 306 years, starting from year 1700 and we establish a least-squares optimal pulse shape of a solar cycle. The cycle-to-cycle evolution of the parameters of the cycle shape displays different patterns, such as a Gleissberg cycle and a strong anomaly in the cycle evolution during the Dalton minimum. In a second step, we extract a chaotic mapping for the successive values of one of the key model parameters - the rate of the exponential growth-decrease of the solar activity during the n-th cycle. We examine piece-wise linear techniques for the approximation of the derived mapping and we provide its probabilistic analysis: calculation of the invariant distribution and autocorrelation function. We find analytical relationships for the sunspot maxima and minima, as well as their occurrence times, as functions of chaotic values of the above parameter. Based on a Lyapunov spectrum analysis of the embedded mapping, we finally establish a horizon of predictability for the method, which allows us to give the most probable forecasting of the upcoming solar cycle 24, with an expected peak height of 93±21 occurring in 2011/2012.

  12. Nonlinear solar cycle forecasting: theory and perspectives

    Directory of Open Access Journals (Sweden)

    A. L. Baranovski

    2008-02-01

    Full Text Available In this paper we develop a modern approach to solar cycle forecasting, based on the mathematical theory of nonlinear dynamics. We start from the design of a static curve fitting model for the experimental yearly sunspot number series, over a time scale of 306 years, starting from year 1700 and we establish a least-squares optimal pulse shape of a solar cycle. The cycle-to-cycle evolution of the parameters of the cycle shape displays different patterns, such as a Gleissberg cycle and a strong anomaly in the cycle evolution during the Dalton minimum. In a second step, we extract a chaotic mapping for the successive values of one of the key model parameters – the rate of the exponential growth-decrease of the solar activity during the n-th cycle. We examine piece-wise linear techniques for the approximation of the derived mapping and we provide its probabilistic analysis: calculation of the invariant distribution and autocorrelation function. We find analytical relationships for the sunspot maxima and minima, as well as their occurrence times, as functions of chaotic values of the above parameter. Based on a Lyapunov spectrum analysis of the embedded mapping, we finally establish a horizon of predictability for the method, which allows us to give the most probable forecasting of the upcoming solar cycle 24, with an expected peak height of 93±21 occurring in 2011/2012.

  13. Charges in nonlinear higher-spin theory

    Energy Technology Data Exchange (ETDEWEB)

    Didenko, V.E. [I.E. Tamm Department of Theoretical Physics, Lebedev Physical Institute,Leninsky prospect 53, 119991, Moscow (Russian Federation); Misuna, N.G. [I.E. Tamm Department of Theoretical Physics, Lebedev Physical Institute,Leninsky prospect 53, 119991, Moscow (Russian Federation); Moscow Institute of Physics and Technology,Institutsky lane 9, 141700, Dolgoprudny, Moscow region (Russian Federation); Vasiliev, M.A. [I.E. Tamm Department of Theoretical Physics, Lebedev Physical Institute,Leninsky prospect 53, 119991, Moscow (Russian Federation)

    2017-03-30

    Nonlinear higher-spin equations in four dimensions admit a closed two-form that defines a gauge-invariant global charge as an integral over a two-dimensional cycle. In this paper we argue that this charge gives rise to partitions depending on various lower- and higher-spin chemical potentials identified with modules of topological fields in the theory. The vacuum contribution to the partition is calculated to the first nontrivial order for a solution to higher-spin equations that generalizes AdS{sub 4} Kerr black hole of General Relativity. The resulting partition is non-zero being in parametric agreement with the ADM-like behavior of a rotating source. The linear response of chemical potentials to the partition function is also extracted. The explicit unfolded form of 4d GR black holes is given. An explicit formula relating asymptotic higher-spin charges expressed in terms of the generalized higher-spin Weyl tensor with those expressed in terms of Fronsdal fields is obtained.

  14. Charges in nonlinear higher-spin theory

    International Nuclear Information System (INIS)

    Didenko, V.E.; Misuna, N.G.; Vasiliev, M.A.

    2017-01-01

    Nonlinear higher-spin equations in four dimensions admit a closed two-form that defines a gauge-invariant global charge as an integral over a two-dimensional cycle. In this paper we argue that this charge gives rise to partitions depending on various lower- and higher-spin chemical potentials identified with modules of topological fields in the theory. The vacuum contribution to the partition is calculated to the first nontrivial order for a solution to higher-spin equations that generalizes AdS 4 Kerr black hole of General Relativity. The resulting partition is non-zero being in parametric agreement with the ADM-like behavior of a rotating source. The linear response of chemical potentials to the partition function is also extracted. The explicit unfolded form of 4d GR black holes is given. An explicit formula relating asymptotic higher-spin charges expressed in terms of the generalized higher-spin Weyl tensor with those expressed in terms of Fronsdal fields is obtained.

  15. 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.

  16. Periodicity of a class of nonlinear fuzzy systems with delays

    International Nuclear Information System (INIS)

    Yu Jiali; Yi Zhang; Zhang Lei

    2009-01-01

    The well known Takagi-Sugeno (T-S) model gives an effective method to combine some simple local systems with their linguistic description to represent complex nonlinear dynamic systems. By using the T-S method, a class of local nonlinear systems having nice dynamic properties can be employed to represent some global complex nonlinear systems. This paper proposes to study the periodicity of a class of global nonlinear fuzzy systems with delays by using T-S method. Conditions for guaranteeing periodicity are derived. Examples are employed to illustrate the theory.

  17. 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.

  18. 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

  19. Augmented nonlinear differentiator design and application to nonlinear uncertain systems.

    Science.gov (United States)

    Shao, Xingling; Liu, Jun; Li, Jie; Cao, Huiliang; Shen, Chong; Zhang, Xiaoming

    2017-03-01

    In this paper, an augmented nonlinear differentiator (AND) based on sigmoid function is developed to calculate the noise-less time derivative under noisy measurement condition. The essential philosophy of proposed AND in achieving high attenuation of noise effect is established by expanding the signal dynamics with extra state variable representing the integrated noisy measurement, then with the integral of measurement as input, the augmented differentiator is formulated to improve the estimation quality. The prominent advantages of the present differentiation technique are: (i) better noise suppression ability can be achieved without appreciable delay; (ii) the improved methodology can be readily extended to construct augmented high-order differentiator to obtain multiple derivatives. In addition, the convergence property and robustness performance against noises are investigated via singular perturbation theory and describing function method, respectively. Also, comparison with several classical differentiators is given to illustrate the superiority of AND in noise suppression. Finally, the robust control problems of nonlinear uncertain systems, including a numerical example and a mass spring system, are addressed to demonstrate the effectiveness of AND in precisely estimating the disturbance and providing the unavailable differential estimate to implement output feedback based controller. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

  20. Nonlinear Response of Strong Nonlinear System Arisen in Polymer Cushion

    Directory of Open Access Journals (Sweden)

    Jun Wang

    2013-01-01

    Full Text Available A dynamic model is proposed for a polymer foam-based nonlinear cushioning system. An accurate analytical solution for the nonlinear free vibration of the system is derived by applying He's variational iteration method, and conditions for resonance are obtained, which should be avoided in the cushioning design.

  1. The constructive approach to nonlinear quantum field theory

    International Nuclear Information System (INIS)

    Segal, I.

    1976-01-01

    The general situation in nonlinear quantum field theory is outlined. The author discusses a reversion to the canonical quantization formalism and develops it to the maximal level attainable on the basis of advances in the past decade in nonlinear scattering and functional integration. (B.R.H.)

  2. Nonlinear theory of the free-electron laser

    International Nuclear Information System (INIS)

    Chian, A.C.-L.; Padua Brito Serbeto, A. de.

    1984-01-01

    A theory of Raman free-electron laser using a circularly polarized electromagnetic pump is investigated. Coupled wave equations that describe both linear and nonlinear evolution of stimulated Raman scattering are derived. The dispersion relation and the growth rate for the parametric instability are obtained. Nonlinear processes that may lead to saturation of the free-electron laser are discussed. (Author) [pt

  3. Nonlinear dynamics in biological systems

    CERN Document Server

    Carballido-Landeira, Jorge

    2016-01-01

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

  4. Deterministic nonlinear systems a short course

    CERN Document Server

    Anishchenko, Vadim S; Strelkova, Galina I

    2014-01-01

    This text is a short yet complete course on nonlinear dynamics of deterministic systems. Conceived as a modular set of 15 concise lectures it reflects the many years of teaching experience by the authors. The lectures treat in turn the fundamental aspects of the theory of dynamical systems, aspects of stability and bifurcations, the theory of deterministic chaos and attractor dimensions, as well as the elements of the theory of Poincare recurrences.Particular attention is paid to the analysis of the generation of periodic, quasiperiodic and chaotic self-sustained oscillations and to the issue of synchronization in such systems.  This book is aimed at graduate students and non-specialist researchers with a background in physics, applied mathematics and engineering wishing to enter this exciting field of research.

  5. An introduction to nonlinear analysis and fixed point theory

    CERN Document Server

    Pathak, Hemant Kumar

    2018-01-01

    This book systematically introduces the theory of nonlinear analysis, providing an overview of topics such as geometry of Banach spaces, differential calculus in Banach spaces, monotone operators, and fixed point theorems. It also discusses degree theory, nonlinear matrix equations, control theory, differential and integral equations, and inclusions. The book presents surjectivity theorems, variational inequalities, stochastic game theory and mathematical biology, along with a large number of applications of these theories in various other disciplines. Nonlinear analysis is characterised by its applications in numerous interdisciplinary fields, ranging from engineering to space science, hydromechanics to astrophysics, chemistry to biology, theoretical mechanics to biomechanics and economics to stochastic game theory. Organised into ten chapters, the book shows the elegance of the subject and its deep-rooted concepts and techniques, which provide the tools for developing more realistic and accurate models for ...

  6. Theory of weakly nonlinear self-sustained detonations

    KAUST Repository

    Faria, Luiz; Kasimov, Aslan R.; Rosales, Rodolfo R.

    2015-01-01

    We propose a theory of weakly nonlinear multidimensional self-sustained detonations based on asymptotic analysis of the reactive compressible Navier-Stokes equations. We show that these equations can be reduced to a model consisting of a forced

  7. Frequency response functions for nonlinear convergent systems

    NARCIS (Netherlands)

    Pavlov, A.V.; Wouw, van de N.; Nijmeijer, H.

    2007-01-01

    Convergent systems constitute a practically important class of nonlinear systems that extends the class of asymptotically stable linear time-invariant systems. In this note, we extend frequency response functions defined for linear systems to nonlinear convergent systems. Such nonlinear frequency

  8. Nonlinear transport theory in the metal with tunnel barrier

    Science.gov (United States)

    Zubov, E. E.

    2018-02-01

    Within the framework of the scattering matrix formalism, the nonlinear Kubo theory for electron transport in the metal with a tunnel barrier has been considered. A general expression for the mean electrical current was obtained. It significantly simplifies the calculation of nonlinear contributions to the conductivity of various hybrid structures. In the model of the tunnel Hamiltonian, all linear and nonlinear contributions to a mean electrical current are evaluated. The linear approximation agrees with results of other theories. For effective barrier transmission ?, the ballistic transport is realised with a value of the Landauer conductivity equal to ?.

  9. Theory of Nonlinear Dispersive Waves and Selection of the Ground State

    International Nuclear Information System (INIS)

    Soffer, A.; Weinstein, M.I.

    2005-01-01

    A theory of time-dependent nonlinear dispersive equations of the Schroedinger or Gross-Pitaevskii and Hartree type is developed. The short, intermediate and large time behavior is found, by deriving nonlinear master equations (NLME), governing the evolution of the mode powers, and by a novel multitime scale analysis of these equations. The scattering theory is developed and coherent resonance phenomena and associated lifetimes are derived. Applications include Bose-Einstein condensate large time dynamics and nonlinear optical systems. The theory reveals a nonlinear transition phenomenon, 'selection of the ground state', and NLME predicts the decay of excited state, with half its energy transferred to the ground state and half to radiation modes. Our results predict the recent experimental observations of Mandelik et al. in nonlinear optical waveguides

  10. Spectral decomposition of nonlinear systems with memory

    Science.gov (United States)

    Svenkeson, Adam; Glaz, Bryan; Stanton, Samuel; West, Bruce J.

    2016-02-01

    We present an alternative approach to the analysis of nonlinear systems with long-term memory that is based on the Koopman operator and a Lévy transformation in time. Memory effects are considered to be the result of interactions between a system and its surrounding environment. The analysis leads to the decomposition of a nonlinear system with memory into modes whose temporal behavior is anomalous and lacks a characteristic scale. On average, the time evolution of a mode follows a Mittag-Leffler function, and the system can be described using the fractional calculus. The general theory is demonstrated on the fractional linear harmonic oscillator and the fractional nonlinear logistic equation. When analyzing data from an ill-defined (black-box) system, the spectral decomposition in terms of Mittag-Leffler functions that we propose may uncover inherent memory effects through identification of a small set of dynamically relevant structures that would otherwise be obscured by conventional spectral methods. Consequently, the theoretical concepts we present may be useful for developing more general methods for numerical modeling that are able to determine whether observables of a dynamical system are better represented by memoryless operators, or operators with long-term memory in time, when model details are unknown.

  11. Explicit Nonlinear Model Predictive Control Theory and Applications

    CERN Document Server

    Grancharova, Alexandra

    2012-01-01

    Nonlinear Model Predictive Control (NMPC) has become the accepted methodology to solve complex control problems related to process industries. The main motivation behind explicit NMPC is that an explicit state feedback law avoids the need for executing a numerical optimization algorithm in real time. The benefits of an explicit solution, in addition to the efficient on-line computations, include also verifiability of the implementation and the possibility to design embedded control systems with low software and hardware complexity. This book considers the multi-parametric Nonlinear Programming (mp-NLP) approaches to explicit approximate NMPC of constrained nonlinear systems, developed by the authors, as well as their applications to various NMPC problem formulations and several case studies. The following types of nonlinear systems are considered, resulting in different NMPC problem formulations: Ø  Nonlinear systems described by first-principles models and nonlinear systems described by black-box models; �...

  12. NONLINEAR TIDES IN CLOSE BINARY SYSTEMS

    International Nuclear Information System (INIS)

    Weinberg, Nevin N.; Arras, Phil; Quataert, Eliot; Burkart, Josh

    2012-01-01

    We study the excitation and damping of tides in close binary systems, accounting for the leading-order nonlinear corrections to linear tidal theory. These nonlinear corrections include two distinct physical effects: three-mode nonlinear interactions, i.e., the redistribution of energy among stellar modes of oscillation, and nonlinear excitation of stellar normal modes by the time-varying gravitational potential of the companion. This paper, the first in a series, presents the formalism for studying nonlinear tides and studies the nonlinear stability of the linear tidal flow. Although the formalism we present is applicable to binaries containing stars, planets, and/or compact objects, we focus on non-rotating solar-type stars with stellar or planetary companions. Our primary results include the following: (1) The linear tidal solution almost universally used in studies of binary evolution is unstable over much of the parameter space in which it is employed. More specifically, resonantly excited internal gravity waves in solar-type stars are nonlinearly unstable to parametric resonance for companion masses M' ∼> 10-100 M ⊕ at orbital periods P ≈ 1-10 days. The nearly static 'equilibrium' tidal distortion is, however, stable to parametric resonance except for solar binaries with P ∼ 3 [P/10 days] for a solar-type star) and drives them as a single coherent unit with growth rates that are a factor of ≈N faster than the standard three-wave parametric instability. These are local instabilities viewed through the lens of global analysis; the coherent global growth rate follows local rates in the regions where the shear is strongest. In solar-type stars, the dynamical tide is unstable to this collective version of the parametric instability for even sub-Jupiter companion masses with P ∼< a month. (4) Independent of the parametric instability, the dynamical and equilibrium tides excite a wide range of stellar p-modes and g-modes by nonlinear inhomogeneous forcing

  13. Sensitivity theory for general non-linear algebraic equations with constraints

    International Nuclear Information System (INIS)

    Oblow, E.M.

    1977-04-01

    Sensitivity theory has been developed to a high state of sophistication for applications involving solutions of the linear Boltzmann equation or approximations to it. The success of this theory in the field of radiation transport has prompted study of possible extensions of the method to more general systems of non-linear equations. Initial work in the U.S. and in Europe on the reactor fuel cycle shows that the sensitivity methodology works equally well for those non-linear problems studied to date. The general non-linear theory for algebraic equations is summarized and applied to a class of problems whose solutions are characterized by constrained extrema. Such equations form the basis of much work on energy systems modelling and the econometrics of power production and distribution. It is valuable to have a sensitivity theory available for these problem areas since it is difficult to repeatedly solve complex non-linear equations to find out the effects of alternative input assumptions or the uncertainties associated with predictions of system behavior. The sensitivity theory for a linear system of algebraic equations with constraints which can be solved using linear programming techniques is discussed. The role of the constraints in simplifying the problem so that sensitivity methodology can be applied is highlighted. The general non-linear method is summarized and applied to a non-linear programming problem in particular. Conclusions are drawn in about the applicability of the method for practical problems

  14. Nonlinear time heteronymous damping in nonlinear parametric planetary systems

    Czech Academy of Sciences Publication Activity Database

    Hortel, Milan; Škuderová, Alena

    2014-01-01

    Roč. 225, č. 7 (2014), s. 2059-2073 ISSN 0001-5970 Institutional support: RVO:61388998 Keywords : nonlinear dynamics * planetary systems * heteronymous damping Subject RIV: JT - Propulsion, Motors ; Fuels Impact factor: 1.465, year: 2014

  15. Passivity Based Stabilization of Non-minimum Phase Nonlinear Systems

    Czech Academy of Sciences Publication Activity Database

    Travieso-Torres, J.C.; Duarte-Mermoud, M.A.; Zagalak, Petr

    2009-01-01

    Roč. 45, č. 3 (2009), s. 417-426 ISSN 0023-5954 R&D Projects: GA ČR(CZ) GA102/07/1596 Institutional research plan: CEZ:AV0Z10750506 Keywords : nonlinear systems * stabilisation * passivity * state feedback Subject RIV: BC - Control Systems Theory Impact factor: 0.445, year: 2009 http://library.utia.cas.cz/separaty/2009/AS/zagalak-passivity based stabilization of non-minimum phase nonlinear systems.pdf

  16. Nonlinear theory of localized standing waves

    OpenAIRE

    Denardo, Bruce; Larraza, Andrés; Putterman, Seth; Roberts, Paul

    1992-01-01

    An investigation of the nonlinear dispersive equations of continuum mechanics reveals localized standing-wave solutions that are domain walls between regions of different wave number. These states can appear even when the dispersion law is a single-valued function of the wave number. In addition, we calculate solutions for kinks in cutoff and noncutoff modes, as well as cutoff breather solitons. Division of Engineering and Geophysics of the Office of Basic Energy Science of U.S. DOE for su...

  17. Nonlinear theory of collisionless trapped ion modes

    International Nuclear Information System (INIS)

    Hahm, T.S.; Tang, W.M.

    1996-01-01

    A simplified two field nonlinear model for collisionless trapped-ion-mode turbulence has been derived from nonlinear bounce-averaged drift kinetic equations. The renormalized thermal diffusivity obtained from this analysis exhibits a Bohm-like scaling. A new nonlinearity associated with the neoclassical polarization density is found to introduce an isotope-dependent modification to this Bohm-like diffusivity. The asymptotic balance between the equilibrium variation and the finite banana width induced reduction of the fluctuation potential leads to the result that the radial correlation length decreases with increasing plasma current. Other important conclusions from the present analysis include the predictions that (i) the relative density fluctuation level δn/n 0 is lower than the conventional mixing length estimate, Δr/L n (ii) the ion temperature fluctuation level δT i /T i significantly exceeds the density fluctuation level δn/n 0 ; and (iii) the parallel ion velocity fluctuation level δv iparallel /v Ti is expected to be negligible

  18. An enstrophy-based linear and nonlinear receptivity theory

    Science.gov (United States)

    Sengupta, Aditi; Suman, V. K.; Sengupta, Tapan K.; Bhaumik, Swagata

    2018-05-01

    In the present research, a new theory of instability based on enstrophy is presented for incompressible flows. Explaining instability through enstrophy is counter-intuitive, as it has been usually associated with dissipation for the Navier-Stokes equation (NSE). This developed theory is valid for both linear and nonlinear stages of disturbance growth. A previously developed nonlinear theory of incompressible flow instability based on total mechanical energy described in the work of Sengupta et al. ["Vortex-induced instability of an incompressible wall-bounded shear layer," J. Fluid Mech. 493, 277-286 (2003)] is used to compare with the present enstrophy based theory. The developed equations for disturbance enstrophy and disturbance mechanical energy are derived from NSE without any simplifying assumptions, as compared to other classical linear/nonlinear theories. The theory is tested for bypass transition caused by free stream convecting vortex over a zero pressure gradient boundary layer. We explain the creation of smaller scales in the flow by a cascade of enstrophy, which creates rotationality, in general inhomogeneous flows. Linear and nonlinear versions of the theory help explain the vortex-induced instability problem under consideration.

  19. Nonlinearity of colloid systems oxyhydrate systems

    CERN Document Server

    Sucharev, Yuri I

    2008-01-01

    The present monograph is the first systematic study of the non-linear characteristic of gel oxy-hydrate systems involving d- and f- elements. These are the oxyhydrates of rare-earth elements and oxides - hydroxides of d- elements (zirconium, niobium, titanium, etc.) The non-linearity of these gel systems introduces fundamental peculiarities into their structure and, consequently, their properties. The polymer-conformational diversity of energetically congenial gel fragments, which continu-ously transform under the effect of, for instance, system dissipation heat, is central to the au-thor's hy

  20. An introduction to geometric theory of fully nonlinear parabolic equations

    International Nuclear Information System (INIS)

    Lunardi, A.

    1991-01-01

    We study a class of nonlinear evolution equations in general Banach space being an abstract version of fully nonlinear parabolic equations. In addition to results of existence, uniqueness and continuous dependence on the data, we give some qualitative results about stability of the stationary solutions, existence and stability of the periodic orbits. We apply such results to some parabolic problems arising from combustion theory. (author). 24 refs

  1. Introduction to the theory of nonlinear optimization

    CERN Document Server

    Jahn, Johannes

    2007-01-01

    This book serves as an introductory text to optimization theory in normed spaces. The topics of this book are existence results, various differentiability notions together with optimality conditions, the contingent cone, a generalization of the Lagrange multiplier rule, duality theory, extended semidefinite optimization, and the investigation of linear quadratic and time minimal control problems. This textbook presents fundamentals with particular emphasis on the application to problems in the calculus of variations, approximation and optimal control theory. The reader is expected to have a ba

  2. 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

  3. A non-linear field theory

    International Nuclear Information System (INIS)

    Skyrme, T.H.R.

    1994-01-01

    A unified field theory of mesons and their particle sources is proposed and considered in its classical aspects. The theory has static solutions of a singular nature, but finite energy, characterized by spin directions; the number of such entities is a rigorously conserved constant of motion; they interact with an external meson field through a derivative-type coupling with the spins, akin to the formalism of strong-coupling meson theory. There is a conserved current identifiable with isobaric spin, and another that may be related to hypercharge. The postulates include one constant of the dimensions of length, and another that is conjecture necessarily to have the value (h/2π)c, or perhaps 1/2(h/2π)c, in the quantized theory. (author). 5 refs

  4. Discrete-time inverse optimal control for nonlinear systems

    CERN Document Server

    Sanchez, Edgar N

    2013-01-01

    Discrete-Time Inverse Optimal Control for Nonlinear Systems proposes a novel inverse optimal control scheme for stabilization and trajectory tracking of discrete-time nonlinear systems. This avoids the need to solve the associated Hamilton-Jacobi-Bellman equation and minimizes a cost functional, resulting in a more efficient controller. Design More Efficient Controllers for Stabilization and Trajectory Tracking of Discrete-Time Nonlinear Systems The book presents two approaches for controller synthesis: the first based on passivity theory and the second on a control Lyapunov function (CLF). Th

  5. Applications of equivalent linearization approaches to nonlinear piping systems

    International Nuclear Information System (INIS)

    Park, Y.; Hofmayer, C.; Chokshi, N.

    1997-01-01

    The piping systems in nuclear power plants, even with conventional snubber supports, are highly complex nonlinear structures under severe earthquake loadings mainly due to various mechanical gaps in support structures. Some type of nonlinear analysis is necessary to accurately predict the piping responses under earthquake loadings. The application of equivalent linearization approaches (ELA) to seismic analyses of nonlinear piping systems is presented. Two types of ELA's are studied; i.e., one based on the response spectrum method and the other based on the linear random vibration theory. The test results of main steam and feedwater piping systems supported by snubbers and energy absorbers are used to evaluate the numerical accuracy and limitations

  6. Nonlinear physical systems spectral analysis, stability and bifurcations

    CERN Document Server

    Kirillov, Oleg N

    2013-01-01

    Bringing together 18 chapters written by leading experts in dynamical systems, operator theory, partial differential equations, and solid and fluid mechanics, this book presents state-of-the-art approaches to a wide spectrum of new and challenging stability problems.Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations focuses on problems of spectral analysis, stability and bifurcations arising in the nonlinear partial differential equations of modern physics. Bifurcations and stability of solitary waves, geometrical optics stability analysis in hydro- and magnetohydrodynam

  7. Lie Symmetries and Solitons in Nonlinear Systems with Spatially Inhomogeneous Nonlinearities

    International Nuclear Information System (INIS)

    Belmonte-Beitia, Juan; Perez-Garcia, Victor M.; Vekslerchik, Vadym; Torres, Pedro J.

    2007-01-01

    Using Lie group theory and canonical transformations, we construct explicit solutions of nonlinear Schroedinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to show that localized nonlinearities can support bound states with an arbitrary number solitons, and discuss other applications of interest to the field of nonlinear matter waves

  8. Nonlinear systems techniques for dynamical analysis and control

    CERN Document Server

    Lefeber, Erjen; Arteaga, Ines

    2017-01-01

    This treatment of modern topics related to the control of nonlinear systems is a collection of contributions celebrating the work of Professor Henk Nijmeijer and honoring his 60th birthday. It addresses several topics that have been the core of Professor Nijmeijer’s work, namely: the control of nonlinear systems, geometric control theory, synchronization, coordinated control, convergent systems and the control of underactuated systems. The book presents recent advances in these areas, contributed by leading international researchers in systems and control. In addition to the theoretical questions treated in the text, particular attention is paid to a number of applications including (mobile) robotics, marine vehicles, neural dynamics and mechanical systems generally. This volume provides a broad picture of the analysis and control of nonlinear systems for scientists and engineers with an interest in the interdisciplinary field of systems and control theory. The reader will benefit from the expert participan...

  9. Linear and Nonlinear Theories of Cosmic Ray Transport

    International Nuclear Information System (INIS)

    Shalchi, A.

    2005-01-01

    The transport of charged cosmic rays in plasmawave turbulence is a modern and interesting field of research. We are mainly interested in spatial diffusion parallel and perpendicular to a large scale magnetic field. During the last decades quasilinear theory was the standard tool for the calculation of diffusion coefficients. Through comparison with numerical simulations we found several cases where quasilinear theory is invalid. On could define three major problems of transport theory. I will demonstrate that new nonlinear theories which were proposed recently can solve at least some to these problems

  10. Empirical Differential Balancing for Nonlinear Systems

    NARCIS (Netherlands)

    Kawano, Yu; Scherpen, Jacquelien M.A.; Dochain, Denis; Henrion, Didier; Peaucelle, Dimitri

    In this paper, we consider empirical balancing of nonlinear systems by using its prolonged system, which consists of the original nonlinear system and its variational system. For the prolonged system, we define differential reachability and observability Gramians, which are matrix valued functions

  11. Theory for Nonlinear Spectroscopy of Vibrational Polaritons

    OpenAIRE

    Ribeiro, RF; Dunkelberger, AD; Xiang, B; Xiong, W; Simpkins, BS; Owrutsky, JC; Yuen-Zhou, J

    2017-01-01

    Molecular polaritons have gained considerable attention due to their potential to control nanoscale molecular processes by harnessing electromagnetic coherence. Although recent experiments with liquid-phase vibrational polaritons have shown great promise for exploiting these effects, significant challenges remain in interpreting their spectroscopic signatures. In this letter, we develop a quantum-mechanical theory of pump-probe spectroscopy for this class of polaritons based on the quantum La...

  12. Nonlinear neoclassical theory for toroidal edge plasmas

    International Nuclear Information System (INIS)

    Fueloep, T.; Helander, P.

    2001-01-01

    Edge plasma processes play a critical role for the global confinement of the plasma. In the edge region, where impurity ions are abundant and the temperature and density gradients are large, the assumptions of the standard neoclassical theory break down. We have extended the theory of neoclassical transport in an impure plasma with arbitrary cross section and aspect ratio to allow for steeper pressure and temperature gradients than are usually considered in the conventional theory. The gradients are allowed to be so large that the friction force between the bulk ions and heavy impurities is comparable to the parallel impurity pressure gradient. In this case the impurity ions are found to undergo a spontaneous rearrangement on each flux surface. This reduces their parallel friction with the bulk ions and causes the neoclassical ion flux to become a non-monotonic function of the gradients for plasma parameters typical of the tokamak edge. Thus, the neoclassical confinement is improved in regions where the gradients are large, such as in the edge pedestal. The theoretical predictions are compared with experimental data from several tokamaks. (orig.)

  13. Soliton excitations in a class of nonlinear field theory models

    International Nuclear Information System (INIS)

    Makhan'kov, V.G.; Fedyanin, V.K.

    1985-01-01

    Investigation results of nonlinear models of the field theory with a lagrangian are described. The theory includes models both with zero stable vacuum epsilon=1 and with condensate epsilon=-1 (of disturbed symmetry). Conditions of existence of particle-like solutions (PLS), stability of these solutions are investigated. Soliton dynamics is studied. PLS formfactors are calculated. Statistical mechanics of solitons is built and their dynamic structure factors are calculated

  14. Differential geometric methods in system theory.

    Science.gov (United States)

    Brockett, R. W.

    1971-01-01

    Discussion of certain problems in system theory which have been or might be solved using some basic concepts from differential geometry. The problems considered involve differential equations, controllability, optimal control, qualitative behavior, stochastic processes, and bilinear systems. The main goal is to extend the essentials of linear theory to some nonlinear classes of problems.

  15. Nonlinear H-infinity control, Hamiltonian systems and Hamilton-Jacobi equations

    CERN Document Server

    Aliyu, MDS

    2011-01-01

    A comprehensive overview of nonlinear Haeu control theory for both continuous-time and discrete-time systems, Nonlinear Haeu-Control, Hamiltonian Systems and Hamilton-Jacobi Equations covers topics as diverse as singular nonlinear Haeu-control, nonlinear Haeu -filtering, mixed H2/ Haeu-nonlinear control and filtering, nonlinear Haeu-almost-disturbance-decoupling, and algorithms for solving the ubiquitous Hamilton-Jacobi-Isaacs equations. The link between the subject and analytical mechanics as well as the theory of partial differential equations is also elegantly summarized in a single chapter

  16. de Sitter limit of inflation and nonlinear perturbation theory

    DEFF Research Database (Denmark)

    R. Jarnhus, Philip; Sloth, Martin Snoager

    2007-01-01

    We study the fourth order action of the comoving curvature perturbation in an inflationary universe in order to understand more systematically the de Sitter limit in nonlinear cosmological perturbation theory. We derive the action of the curvature perturbation to fourth order in the comoving gaug...

  17. Non-linear theory of elasticity

    CERN Document Server

    Lurie, AI

    2012-01-01

    This book examines in detail the Theory of Elasticity which is a branch of the mechanics of a deformable solid. Special emphasis is placed on the investigation of the process of deformation within the framework of the generally accepted model of a medium which, in this case, is an elastic body. A comprehensive list of Appendices is included providing a wealth of references for more in depth coverage. The work will provide both a stimulus for future research in this field as well as useful reference material for many years to come.

  18. 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...

  19. Importance theory for lumped-parameter systems

    International Nuclear Information System (INIS)

    Cady, K.B.; Kenton, M.A.; Ward, J.C.; Piepho, M.G.

    1981-01-01

    A general sensitivity theory has been developed for nonlinear lumped parameter system simulations. The point of departure is general perturbation theory for nonlinear systems. Importance theory as developed here allows the calculation of the sensitivity of a response function to any physical or design parameter; importance of any equation or term or physical effect in the system model on the response function; variance of the response function caused by the variances and covariances of all physical parameters; and approximate effect on the response function of missing physical phenomena or incorrect parameters

  20. Analytical filtration model for nonlinear viscoplastic oil in the theory of oil production stimulation and heating of oil reservoir in a dual-well system

    Science.gov (United States)

    Ivanovich Astafev, Vladimir; Igorevich Gubanov, Sergey; Alexandrovna Olkhovskaya, Valeria; Mikhailovna Sylantyeva, Anastasia; Mikhailovich Zinovyev, Alexey

    2018-02-01

    Production of high-viscosity oil and design of field development systems for such oil is one of the most promising directions in the development of world oil industry. The ability of high-viscosity oil to show in filtration process properties typical for non-Newtonian systems is proven by experimental studies. Nonlinear relationship between the pressure gradient and the rate of oil flow is due to interaction of high-molecular substances, in particular, asphaltenes and tars that form a plastic structure in it. The authors of this article have used the analytical model of stationary influx of nonlinear viscoplastic oil to the well bottom in order to provide rationale for the intensifying impact on a reservoir. They also have analyzed the method of periodic heating of productive reservoir by means of dual-wells. The high-temperature source is placed at the bottom of the vertical well, very close to the reservoir; at the same time the side well, located outside the zone of expected rock damage, is used for production. Suggested method of systemic treatment of reservoirs with dual wells can be useful for small fields of high-viscosity oil. The effect is based on the opportunity to control the structural and mechanical properties of high-viscosity oil and to increase depletion of reserves.

  1. Backward stochastic differential equations from linear to fully nonlinear theory

    CERN Document Server

    Zhang, Jianfeng

    2017-01-01

    This book provides a systematic and accessible approach to stochastic differential equations, backward stochastic differential equations, and their connection with partial differential equations, as well as the recent development of the fully nonlinear theory, including nonlinear expectation, second order backward stochastic differential equations, and path dependent partial differential equations. Their main applications and numerical algorithms, as well as many exercises, are included. The book focuses on ideas and clarity, with most results having been solved from scratch and most theories being motivated from applications. It can be considered a starting point for junior researchers in the field, and can serve as a textbook for a two-semester graduate course in probability theory and stochastic analysis. It is also accessible for graduate students majoring in financial engineering.

  2. On Similarity Invariance of Balancing for Nonlinear Systems

    NARCIS (Netherlands)

    Scherpen, Jacquelien M.A.

    1995-01-01

    A previously obtained balancing method for nonlinear systems is investigated on similarity in variance by generalization of the observations on the similarity invariance of the linear balanced realization theory. For linear systems it is well known that the Hankel singular values are similarity

  3. Nonlinear Waves in Complex Systems

    DEFF Research Database (Denmark)

    2007-01-01

    The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations, it is the ......The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations...

  4. Discontinuity and complexity in nonlinear physical systems

    CERN Document Server

    Baleanu, Dumitru; Luo, Albert

    2014-01-01

    This unique book explores recent developments in experimental research in this broad field, organized in four distinct sections. Part I introduces the reader to the fractional dynamics and Lie group analysis for nonlinear partial differential equations. Part II covers chaos and complexity in nonlinear Hamiltonian systems, important to understand the resonance interactions in nonlinear dynamical systems, such as Tsunami waves and wildfire propagations; as well as Lev flights in chaotic trajectories, dynamical system synchronization and DNA information complexity analysis. Part III examines chaos and periodic motions in discontinuous dynamical systems, extensively present in a range of systems, including piecewise linear systems, vibro-impact systems and drilling systems in engineering. And in Part IV, engineering and financial nonlinearity are discussed. The mechanism of shock wave with saddle-node bifurcation and rotating disk stability will be presented, and the financial nonlinear models will be discussed....

  5. Scattering theory of nonlinear thermoelectricity in quantum coherent conductors.

    Science.gov (United States)

    Meair, Jonathan; Jacquod, Philippe

    2013-02-27

    We construct a scattering theory of weakly nonlinear thermoelectric transport through sub-micron scale conductors. The theory incorporates the leading nonlinear contributions in temperature and voltage biases to the charge and heat currents. Because of the finite capacitances of sub-micron scale conducting circuits, fundamental conservation laws such as gauge invariance and current conservation require special care to be preserved. We do this by extending the approach of Christen and Büttiker (1996 Europhys. Lett. 35 523) to coupled charge and heat transport. In this way we write relations connecting nonlinear transport coefficients in a manner similar to Mott's relation between the linear thermopower and the linear conductance. We derive sum rules that nonlinear transport coefficients must satisfy to preserve gauge invariance and current conservation. We illustrate our theory by calculating the efficiency of heat engines and the coefficient of performance of thermoelectric refrigerators based on quantum point contacts and resonant tunneling barriers. We identify, in particular, rectification effects that increase device performance.

  6. Stability analysis of nonlinear systems with slope restricted nonlinearities.

    Science.gov (United States)

    Liu, Xian; Du, Jiajia; Gao, Qing

    2014-01-01

    The problem of absolute stability of Lur'e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP) lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results.

  7. Stability Analysis of Nonlinear Systems with Slope Restricted Nonlinearities

    Directory of Open Access Journals (Sweden)

    Xian Liu

    2014-01-01

    Full Text Available The problem of absolute stability of Lur’e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results.

  8. Non-linearities in Theory-of-Mind Development.

    Science.gov (United States)

    Blijd-Hoogewys, Els M A; van Geert, Paul L C

    2016-01-01

    Research on Theory-of-Mind (ToM) has mainly focused on ages of core ToM development. This article follows a quantitative approach focusing on the level of ToM understanding on a measurement scale, the ToM Storybooks, in 324 typically developing children between 3 and 11 years of age. It deals with the eventual occurrence of developmental non-linearities in ToM functioning, using smoothing techniques, dynamic growth model building and additional indicators, namely moving skewness, moving growth rate changes and moving variability. The ToM sum-scores showed an overall developmental trend that leveled off toward the age of 10 years. Within this overall trend two non-linearities in the group-based change pattern were found: a plateau at the age of around 56 months and a dip at the age of 72-78 months. These temporary regressions in ToM sum-score were accompanied by a decrease in growth rate and variability, and a change in skewness of the ToM data, all suggesting a developmental shift in ToM understanding. The temporary decreases also occurred in the different ToM sub-scores and most clearly so in the core ToM component of beliefs. It was also found that girls had an earlier growth spurt than boys and that the underlying developmental path was more salient in girls than in boys. The consequences of these findings are discussed from various theoretical points of view, with an emphasis on a dynamic systems interpretation of the underlying developmental paths.

  9. Effective-medium theory for nonlinear magneto-optics in magnetic granular alloys: cubic nonlinearity

    International Nuclear Information System (INIS)

    Granovsky, Alexander B.; Kuzmichov, Michail V.; Clerc, J.-P.; Inoue, Mitsuteru

    2003-01-01

    We propose a simple effective-medium approach for calculating the effective dielectric function of a magnetic metal-insulator granular alloy in which there is a weakly nonlinear relation between electric displacement D and electric field E for both constituent materials of the form D i =ε i (0) E i +χ i (3) |E i | 2 E i . We assume that linear ε i (0) and cubic nonlinear χ i (3) dielectric functions are diagonal and linear with magnetization non-diagonal components. For such metal-insulator composite magneto-optical effects depend on a light intensity and the effective cubic dielectric function χ eff (3) can be significantly greater (up to 10 3 times) than that for constituent materials. The calculation scheme is based on the Bergman and Stroud-Hui theory of nonlinear optical properties of granular matter. The giant cubic magneto-optical nonlinearity is found for composites with metallic volume fraction close to the percolation threshold and at a resonance of optical conductivity. It is shown that a composite may exhibit nonlinear magneto-optics even when both constituent materials have no cubic magneto-optical nonlinearity

  10. Effective-medium theory for nonlinear magneto-optics in magnetic granular alloys: cubic nonlinearity

    Energy Technology Data Exchange (ETDEWEB)

    Granovsky, Alexander B. E-mail: granov@magn.ru; Kuzmichov, Michail V.; Clerc, J.-P.; Inoue, Mitsuteru

    2003-03-01

    We propose a simple effective-medium approach for calculating the effective dielectric function of a magnetic metal-insulator granular alloy in which there is a weakly nonlinear relation between electric displacement D and electric field E for both constituent materials of the form D{sub i}={epsilon}{sub i}{sup (0)}E{sub i} +{chi}{sub i}{sup (3)}|E{sub i}|{sup 2}E{sub i}. We assume that linear {epsilon}{sub i}{sup (0)} and cubic nonlinear {chi}{sub i}{sup (3)} dielectric functions are diagonal and linear with magnetization non-diagonal components. For such metal-insulator composite magneto-optical effects depend on a light intensity and the effective cubic dielectric function {chi}{sub eff}{sup (3)} can be significantly greater (up to 10{sup 3} times) than that for constituent materials. The calculation scheme is based on the Bergman and Stroud-Hui theory of nonlinear optical properties of granular matter. The giant cubic magneto-optical nonlinearity is found for composites with metallic volume fraction close to the percolation threshold and at a resonance of optical conductivity. It is shown that a composite may exhibit nonlinear magneto-optics even when both constituent materials have no cubic magneto-optical nonlinearity.

  11. Multiscale System Theory

    Science.gov (United States)

    1990-02-21

    LIDS-P-1953 Multiscale System Theory Albert Benveniste IRISA-INRIA, Campus de Beaulieu 35042 RENNES CEDEX, FRANCE Ramine Nikoukhah INRIA...TITLE AND SUBTITLE Multiscale System Theory 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e...the development of a corresponding system theory and a theory of stochastic processes and their estimation. The research presented in this and several

  12. Simulation of creep effects in framework of a geometrically nonlinear endochronic theory of inelasticity

    Science.gov (United States)

    Zabavnikova, T. A.; Kadashevich, Yu. I.; Pomytkin, S. P.

    2018-05-01

    A geometric non-linear endochronic theory of inelasticity in tensor parametric form is considered. In the framework of this theory, the creep strains are modelled. The effect of various schemes of applying stresses and changing of material properties on the development of creep strains is studied. The constitutive equations of the model are represented by non-linear systems of ordinary differential equations which are solved in MATLAB environment by implicit difference method. Presented results demonstrate a good qualitative agreement of theoretical data and experimental observations including the description of the tertiary creep and pre-fracture of materials.

  13. Nonlinear turbulence theory and simulation of Buneman instability

    International Nuclear Information System (INIS)

    Yoon, P. H.; Umeda, T.

    2010-01-01

    In the present paper, the weak turbulence theory for reactive instabilities, formulated in a companion paper [P. H. Yoon, Phys. Plasmas 17, 112316 (2010)], is applied to the strong electron-ion two-stream (or Buneman) instability. The self-consistent theory involves quasilinear velocity space diffusion equation for the particles and nonlinear wave kinetic equation that includes quasilinear (or induced emission) term as well as nonlinear wave-particle interaction term (or a term that represents an induced scattering off ions). We have also performed one-dimensional electrostatic Vlasov simulation in order to benchmark the theoretical analysis. Under the assumption of self-similar drifting Gaussian distribution function for the electrons it is shown that the current reduction and the accompanying electron heating as well as electric field turbulence generation can be discussed in a self-consistent manner. Upon comparison with the Vlasov simulation result it is found that quasilinear wave kinetic equation alone is insufficient to account for the final saturation amplitude. Upon including the nonlinear scattering term in the wave kinetic equation, however, we find that a qualitative agreement with the simulation is recovered. From this, we conclude that the combined quasilinear particle diffusion plus induced emission and scattering (off ions) processes adequately account for the nonlinear development of the Buneman instability.

  14. Chaos synchronization of a new chaotic system via nonlinear control

    International Nuclear Information System (INIS)

    Zhang Qunjiao; Lu Junan

    2008-01-01

    This paper investigates chaos synchronization of a new chaotic system [Lue J, Chen G, Cheng D. A new chaotic system and beyond: the generalized Lorenz-like system. Int J Bifurcat Chaos 2004;14:1507-37]. Two kinds of novel nonlinear controllers are designed based on the Lyapunov stability theory. It can be viewed as an improvement to the existing results of reference [Park JH. Chaos synchronization of a chaotic system via nonlinear control. Chaos, Solitons and Fractals 2005;25:579-84] because we use less controllers but realize a global and exponential asymptotical synchronization. Numerical simulations are provided to show the effectiveness and advantage of this method

  15. Composite Beam Theory with Material Nonlinearities and Progressive Damage

    Science.gov (United States)

    Jiang, Fang

    Beam has historically found its broad applications. Nowadays, many engineering constructions still rely on this type of structure which could be made of anisotropic and heterogeneous materials. These applications motivate the development of beam theory in which the impact of material nonlinearities and damage on the global constitutive behavior has been a focus in recent years. Reliable predictions of these nonlinear beam responses depend on not only the quality of the material description but also a comprehensively generalized multiscale methodology which fills the theoretical gaps between the scales in an efficient yet high-fidelity manner. The conventional beam modeling methodologies which are built upon ad hoc assumptions are in lack of such reliability in need. Therefore, the focus of this dissertation is to create a reliable yet efficient method and the corresponding tool for composite beam modeling. A nonlinear beam theory is developed based on the Mechanics of Structure Genome (MSG) using the variational asymptotic method (VAM). The three-dimensional (3D) nonlinear continuum problem is rigorously reduced to a one-dimensional (1D) beam model and a two-dimensional (2D) cross-sectional analysis featuring both geometric and material nonlinearities by exploiting the small geometric parameter which is an inherent geometric characteristic of the beam. The 2D nonlinear cross-sectional analysis utilizes the 3D material models to homogenize the beam cross-sectional constitutive responses considering the nonlinear elasticity and progressive damage. The results from such a homogenization are inputs as constitutive laws into the global nonlinear 1D beam analysis. The theoretical foundation is formulated without unnecessary kinematic assumptions. Curvilinear coordinates and vector calculus are utilized to build the 3D deformation gradient tensor, of which the components are formulated in terms of cross-sectional coordinates, generalized beam strains, unknown warping

  16. An approximation theory for nonlinear partial differential equations with applications to identification and control

    Science.gov (United States)

    Banks, H. T.; Kunisch, K.

    1982-01-01

    Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.

  17. The preparation problem in nonlinear extensions of quantum theory

    OpenAIRE

    Cavalcanti, Eric G.; Menicucci, Nicolas C.; Pienaar, Jacques L.

    2012-01-01

    Nonlinear modifications to the laws of quantum mechanics have been proposed as a possible way to consistently describe information processing in the presence of closed timelike curves. These have recently generated controversy due to possible exotic information-theoretic effects, including breaking quantum cryptography and radically speeding up both classical and quantum computers. The physical interpretation of such theories, however, is still unclear. We consider a large class of operationa...

  18. Second quantization of classical nonlinear relativistic field theory. Pt. 2

    International Nuclear Information System (INIS)

    Balaban, T.

    1976-01-01

    The construction of a relativistic interacting local quantum field is given in two steps: first the classical nonlinear relativistic field theory is written down in terms of Poisson brackets, with initial conditions as canonical variables: next a representation of Poisson bracket Lie algebra by means of linear operators in the topological vector space is given and an explicit form of a local interacting relativistic quantum field PHI is obtained. (orig./BJ) [de

  19. Synthesis of robust nonlinear autopilots using differential game theory

    Science.gov (United States)

    Menon, P. K. A.

    1991-01-01

    A synthesis technique for handling unmodeled disturbances in nonlinear control law synthesis was advanced using differential game theory. Two types of modeling inaccuracies can be included in the formulation. The first is a bias-type error, while the second is the scale-factor-type error in the control variables. The disturbances were assumed to satisfy an integral inequality constraint. Additionally, it was assumed that they act in such a way as to maximize a quadratic performance index. Expressions for optimal control and worst-case disturbance were then obtained using optimal control theory.

  20. Development of a nonlinear unsteady transonic flow theory

    Science.gov (United States)

    Stahara, S. S.; Spreiter, J. R.

    1973-01-01

    A nonlinear, unsteady, small-disturbance theory capable of predicting inviscid transonic flows about aerodynamic configurations undergoing both rigid body and elastic oscillations was developed. The theory is based on the concept of dividing the flow into steady and unsteady components and then solving, by method of local linearization, the coupled differential equation for unsteady surface pressure distribution. The equations, valid at all frequencies, were derived for two-dimensional flows, numerical results, were obtained for two classses of airfoils and two types of oscillatory motions.

  1. Microscopic theory of linear and nonlinear terahertz spectroscopy of semiconductors

    Energy Technology Data Exchange (ETDEWEB)

    Steiner, Johannes

    2008-12-09

    This Thesis presents a fully microscopic theory to describe terahertz (THz)-induced processes in optically-excited semiconductors. The formation process of excitons and other quasi-particles after optical excitation has been studied in great detail for a variety of conditions. Here, the formation process is not modelled but a realistic initial many-body state is assumed. In particular, the linear THz response is reviewed and it is demonstrated that correlated quasi-particles such as excitons and plasmons can be unambiguously detected via THz spectroscopy. The focus of the investigations, however, is on situations where the optically-excited many-body state is excited by intense THz fields. While weak pulses detect the many-body state, strong THz pulses control and manipulate the quasi-particles in a way that is not accessible via conventional techniques. The nonlinear THz dynamics of exciton populations is especially interesting because similarities and differences to optics with atomic systems can be studied. (orig.)

  2. Positive real balancing for nonlinear systems

    NARCIS (Netherlands)

    Ionescu, Tudor C.; Scherpen, Jacquelien M.A.; Ciuprina, G; Ioan, D

    2007-01-01

    We extend the positive real balancing procedure for passive linear systems to the nonlinear systems case. We show that, just like in the linear case, model reduction based on this technique preserves passivity.

  3. On Stabilization of Nonautonomous Nonlinear Systems

    International Nuclear Information System (INIS)

    Bogdanov, A. Yu.

    2008-01-01

    The procedures to obtain the sufficient conditions of asymptotic stability for nonlinear nonstationary continuous-time systems are discussed. We consider different types of the following general controlled system: x = X(t,x,u) = F(t,x)+B(t,x)u, x(t 0 ) = x 0 . (*) The basis of investigation is limiting equations, limiting Lyapunov functions, etc. The improved concept of observability of the pair of functional matrices is presented. By these results the problem of synthesis of asymptotically stable control nonlinear nonautonomous systems (with linear parts) involving the quadratic time-dependent Lyapunov functions is solved as well as stabilizing a given unstable system with nonlinear control law.

  4. Fluctuations in Nonlinear Systems: A Short Review

    International Nuclear Information System (INIS)

    Rubia, F.J. de la; Buceta, J.; Cabrera, J.L.; Olarrea, J.; Parrondo, J.M.R.

    2003-01-01

    We review some results that illustrate the constructive role of noise in nonlinear systems. Several phenomena are briefly discussed: optimal localization of orbits in a system with limit cycle behavior and perturbed by colored noise; stochastic branch selection at secondary bifurcations; noise- induced order/disorder transitions and pattern formation in spatially extended systems. In all cases the presence of noise is crucial, and the results reinforce the modern view of the importance of noise in the evolution of nonlinear systems. (author)

  5. 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.

  6. Advances and applications in nonlinear control systems

    CERN Document Server

    Volos, Christos

    2016-01-01

    The book reports on the latest advances and applications of nonlinear control systems. It consists of 30 contributed chapters by subject experts who are specialized in the various topics addressed in this book. The special chapters have been brought out in the broad areas of nonlinear control systems such as robotics, nonlinear circuits, power systems, memristors, underwater vehicles, chemical processes, observer design, output regulation, backstepping control, sliding mode control, time-delayed control, variables structure control, robust adaptive control, fuzzy logic control, chaos, hyperchaos, jerk systems, hyperjerk systems, chaos control, chaos synchronization, etc. Special importance was given to chapters offering practical solutions, modeling and novel control methods for the recent research problems in nonlinear control systems. This book will serve as a reference book for graduate students and researchers with a basic knowledge of electrical and control systems engineering. The resulting design proce...

  7. Method of asymptotic expansions and qualitative analysis of finite-dimensional models in the nonlinear field theory

    International Nuclear Information System (INIS)

    Eleonskij, V.M.; Kulagin, N.E.; Novozhilova, N.S.; Silin, V.P.

    1984-01-01

    The reasons which prevent the existence of periodic in time and self-localised in space solutions of the nonlinear wave equation u=F (u) are determined by the methods of qualitative theory of dynamical systems. The correspondence between the qualitative behaviour of special (separatrix) trajectories in the phase space and asymptotic solutions of the nonlinear wave equation is analysed

  8. Symmetries and semi-invariants in the analysis of nonlinear systems with control applications

    CERN Document Server

    Menini, Laura

    2014-01-01

    This volume details the analysis of continuous- and discrete-time dynamical systems described by differential and difference equations. The theory is developed for general nonlinear systems and specialized for the class of Hamiltonian systems.

  9. A Future of Communication Theory: Systems Theory.

    Science.gov (United States)

    Lindsey, Georg N.

    Concepts of general systems theory, cybernetics and the like may provide the methodology for communication theory to move from a level of technology to a level of pure science. It was the purpose of this paper to (1) demonstrate the necessity of applying systems theory to the construction of communication theory, (2) review relevant systems…

  10. Chaos synchronization of a chaotic system via nonlinear control

    International Nuclear Information System (INIS)

    Park, Ju H.

    2005-01-01

    In this letter, the problem of chaos synchronization of a chaotic system which is proposed by Lue et al. [Int J Bifurcat Chaos 2004;14:1507] is considered. A novel nonlinear controller is designed based on the Lyapunov stability theory. The proposed controller ensures that the states of the controlled chaotic slave system asymptotically synchronizes the states of the master system. A numerical example is given to illuminate the design procedure and advantage of the result derived

  11. On the non-linear scale of cosmological perturbation theory

    CERN Document Server

    Blas, Diego; Konstandin, Thomas

    2013-01-01

    We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.

  12. Nonlinear responses of chiral fluids from kinetic theory

    Science.gov (United States)

    Hidaka, Yoshimasa; Pu, Shi; Yang, Di-Lun

    2018-01-01

    The second-order nonlinear responses of inviscid chiral fluids near local equilibrium are investigated by applying the chiral kinetic theory (CKT) incorporating side-jump effects. It is shown that the local equilibrium distribution function can be nontrivially introduced in a comoving frame with respect to the fluid velocity when the quantum corrections in collisions are involved. For the study of anomalous transport, contributions from both quantum corrections in anomalous hydrodynamic equations of motion and those from the CKT and Wigner functions are considered under the relaxation-time (RT) approximation, which result in anomalous charge Hall currents propagating along the cross product of the background electric field and the temperature (or chemical-potential) gradient and of the temperature and chemical-potential gradients. On the other hand, the nonlinear quantum correction on the charge density vanishes in the classical RT approximation, which in fact satisfies the matching condition given by the anomalous equation obtained from the CKT.

  13. On the non-linear scale of cosmological perturbation theory

    International Nuclear Information System (INIS)

    Blas, Diego; Garny, Mathias; Konstandin, Thomas

    2013-04-01

    We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.

  14. On the non-linear scale of cosmological perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Blas, Diego [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

    2013-04-15

    We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.

  15. 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)

  16. Boundary Controllability of Nonlinear Fractional Integrodifferential Systems

    Directory of Open Access Journals (Sweden)

    Ahmed HamdyM

    2010-01-01

    Full Text Available Sufficient conditions for boundary controllability of nonlinear fractional integrodifferential systems in Banach space are established. The results are obtained by using fixed point theorems. We also give an application for integropartial differential equations of fractional order.

  17. Symmetry properties of some nonlinear field theory models

    International Nuclear Information System (INIS)

    Shvachka, A.B.

    1984-01-01

    Various approaches towards the study of symmetry properties of some nonlinear evolution equations as well as possible ways of their computer implementation using the computer algebra systems langage are discussed. Special attention is paid to the method of pseudopotential investigation of formal integrability and isovector method for the equations of balance

  18. Universal formats for nonlinear ordinary differential systems

    International Nuclear Information System (INIS)

    Kerner, E.H.

    1981-01-01

    It is shown that very general nonlinear ordinary differential systems (embracing all that arise in practice) may, first, be brought down to polynomial systems (where the nonlinearities occur only as polynomials in the dependent variables) by introducing suitable new variables into the original system; second, that polynomial systems are reducible to ''Riccati systems,'' where the nonlinearities are quadratic at most; third, that Riccati systems may be brought to elemental universal formats containing purely quadratic terms with simple arrays of coefficients that are all zero or unity. The elemental systems have representations as novel types of matrix Riccati equations. Different starting systems and their associated Riccati systems differ from one another, at the final elemental level, in order and in initial data, but not in format

  19. 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...

  20. Nonlinear many-body reaction theories from nuclear mean field approximations

    International Nuclear Information System (INIS)

    Griffin, J.J.

    1983-01-01

    Several methods of utilizing nonlinear mean field propagation in time to describe nuclear reaction have been studied. The property of physical asymptoticity is analyzed in this paper, which guarantees that the prediction by a reaction theory for the physical measurement of internal fragment properties shall not depend upon the precise location of the measuring apparatus. The physical asymptoticity is guaranteed in the Schroedinger collision theory of a scuttering system with translationally invariant interaction by the constancy of the S-matrix elements and by the translational invariance of the internal motion for well-separated fragments. Both conditions are necessary for the physical asymptoticity. The channel asymptotic single-determinantal propagation can be described by the Dirac-TDHF (time dependent Hartree-Fock) time evolution. A new asymptotic Hartree-Fock stationary phase (AHFSP) description together with the S-matrix time-dependent Hartree-Fock (TD-S-HF) theory constitute the second example of a physically asymptotic nonlinear many-body reaction theory. A review of nonlinear mean field many-body reaction theories shows that initial value TDHF is non-asymptotic. The TD-S-HF theory is asymptotic by the construction. The gauge invariant periodic quantized solution of the exact Schroedinger problem has been considered to test whether it includes all of the exact eigenfunctions as it ought to. It did, but included as well an infinity of all spurions solutions. (Kato, T.)

  1. Theory of plasmonic effects in nonlinear optics: the case of graphene

    Science.gov (United States)

    Rostami, Habib; Katsnelson, Mikhail I.; Polini, Marco; Mikhail I. Katsnelson Collaboration; Habib Rostami; Marco Polini Collaboration

    The nonlinear optical properties of two-dimensional electronic systems are beginning to attract considerable interest both in the theoretical and experimental sectors. Recent experiments on the nonlinear optical properties of graphene reveal considerably strong third harmonic generation and four-wave mixing of this single-atomic-layer electronic system. We develop a large-N theory of electron-electron interaction corrections to multi-legged Feynman diagrams describing second- and third-order nonlinear response functions. Our theory is completely general and is useful to understand all second- and third-order nonlinear effects, including harmonic generation, wave mixing, and photon drag. We apply our theoretical framework to the case of graphene, by carrying out microscopic calculations of the second- and third-order nonlinear response functions of an interacting two-dimensional gas of massless Dirac fermions. We compare our results with recent measurements, where all-optical launching of graphene plasmons has been achieved. This work was supported by Fondazione Istituto Italiano di Tecnologia, the European Union's Horizon 2020 research and innovation programme under Grant agreement No. 696656 GrapheneCore, and the ERC Advanced Grant 338957 FEMTO/NANO (M.I.K.).

  2. Adaptive PI Controller for a Nonlinear System

    Directory of Open Access Journals (Sweden)

    D. Rathikarani

    2009-10-01

    Full Text Available Most of the industrial processes are inherently nonlinear in their behaviour. Designs of controllers for these nonlinear processes are difficult, as they do not follow superposition theorem. Adaptive controller can change its behaviour in response to changes in the dynamics of the process and disturbances. Hence adaptive controller can be used to control nonlinear processes. Direct Model Reference Adaptive Control is a technique, in which a reference model involving the desired performances is specified. In the present work, a DMRAC is designed and implemented to achieve satisfactory control of a nonlinear system in all its local linear operating regions. The closed loop system is made BIBO stable by proper control techniques. The controller is designed through simulation in Matlab platform and is validated in real time by conducting experiments on the laboratory Air Flow Control System using the dSPACE interface.

  3. Non-linear theory of elasticity and optimal design

    CERN Document Server

    Ratner, LW

    2003-01-01

    In order to select an optimal structure among possible similar structures, one needs to compare the elastic behavior of the structures. A new criterion that describes elastic behavior is the rate of change of deformation. Using this criterion, the safe dimensions of a structure that are required by the stress distributed in a structure can be calculated. The new non-linear theory of elasticity allows one to determine the actual individual limit of elasticity/failure of a structure using a simple non-destructive method of measurement of deformation on the model of a structure while presently it

  4. Maximized gust loads for a nonlinear airplane using matched filter theory and constrained optimization

    Science.gov (United States)

    Scott, Robert C.; Perry, Boyd, III; Pototzky, Anthony S.

    1991-01-01

    This paper describes and illustrates two matched-filter-theory based schemes for obtaining maximized and time-correlated gust-loads for a nonlinear airplane. The first scheme is computationally fast because it uses a simple one-dimensional search procedure to obtain its answers. The second scheme is computationally slow because it uses a more complex multidimensional search procedure to obtain its answers, but it consistently provides slightly higher maximum loads than the first scheme. Both schemes are illustrated with numerical examples involving a nonlinear control system.

  5. Nonlinear electroelasticity: material properties, continuum theory and applications.

    Science.gov (United States)

    Dorfmann, Luis; Ogden, Ray W

    2017-08-01

    In the last few years, it has been recognized that the large deformation capacity of elastomeric materials that are sensitive to electric fields can be harnessed for use in transducer devices such as actuators and sensors. This has led to the reassessment of the mathematical theory that is needed for the description of the electromechanical (in particular, electroelastic) interactions for purposes of material characterization and prediction. After a review of the key experiments concerned with determining the nature of the electromechanical interactions and a discussion of the range of applications to devices, we provide a short account of the history of developments in the nonlinear theory. This is followed by a succinct modern treatment of electroelastic theory, including the governing equations and constitutive laws needed for both material characterization and the analysis of general electroelastic coupling problems. For illustration, the theory is then applied to two simple representative boundary-value problems that are relevant to the geometries of activation devices; in particular, (a) a rectangular plate and (b) a circular cylindrical tube, in each case with compliant electrodes on the major surfaces and a potential difference between them. In (a), an electric field is generated normal to the major surfaces and in (b), a radial electric field is present. This is followed by a short section in which other problems addressed on the basis of the general theory are described briefly.

  6. Nonlinear electroelasticity: material properties, continuum theory and applications

    Science.gov (United States)

    Dorfmann, Luis; Ogden, Ray W.

    2017-08-01

    In the last few years, it has been recognized that the large deformation capacity of elastomeric materials that are sensitive to electric fields can be harnessed for use in transducer devices such as actuators and sensors. This has led to the reassessment of the mathematical theory that is needed for the description of the electromechanical (in particular, electroelastic) interactions for purposes of material characterization and prediction. After a review of the key experiments concerned with determining the nature of the electromechanical interactions and a discussion of the range of applications to devices, we provide a short account of the history of developments in the nonlinear theory. This is followed by a succinct modern treatment of electroelastic theory, including the governing equations and constitutive laws needed for both material characterization and the analysis of general electroelastic coupling problems. For illustration, the theory is then applied to two simple representative boundary-value problems that are relevant to the geometries of activation devices; in particular, (a) a rectangular plate and (b) a circular cylindrical tube, in each case with compliant electrodes on the major surfaces and a potential difference between them. In (a), an electric field is generated normal to the major surfaces and in (b), a radial electric field is present. This is followed by a short section in which other problems addressed on the basis of the general theory are described briefly.

  7. Nonlinear dynamical system approaches towards neural prosthesis

    International Nuclear Information System (INIS)

    Torikai, Hiroyuki; Hashimoto, Sho

    2011-01-01

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

  8. Analysis and control of nonlinear systems a flatness-based approach

    CERN Document Server

    Levine, Jean

    2009-01-01

    This book examines control of nonlinear systems. Coverage ranges from mathematical system theory to practical industrial control applications. The author offers web-based videos illustrating some dynamical aspects and case studies in simulation.

  9. Nonlinear theory of diffusive acceleration of particles by shock waves

    Energy Technology Data Exchange (ETDEWEB)

    Malkov, M.A. [University of California at San Diego, La Jolla, CA (United States)]. E-mail: mmalkov@ucsd.edu; Drury, L. O' C. [Dublin Institute for Advanced Studies, 5 Merrion Square, Dublin 2 (Ireland)

    2001-04-01

    Among the various acceleration mechanisms which have been suggested as responsible for the nonthermal particle spectra and associated radiation observed in many astrophysical and space physics environments, diffusive shock acceleration appears to be the most successful. We review the current theoretical understanding of this process, from the basic ideas of how a shock energizes a few reactionless particles to the advanced nonlinear approaches treating the shock and accelerated particles as a symbiotic self-organizing system. By means of direct solution of the nonlinear problem we set the limit to the test-particle approximation and demonstrate the fundamental role of nonlinearity in shocks of astrophysical size and lifetime. We study the bifurcation of this system, proceeding from the hydrodynamic to kinetic description under a realistic condition of Bohm diffusivity. We emphasize the importance of collective plasma phenomena for the global flow structure and acceleration efficiency by considering the injection process, an initial stage of acceleration and, the related aspects of the physics of collisionless shocks. We calculate the injection rate for different shock parameters and different species. This, together with differential acceleration resulting from nonlinear large-scale modification, determines the chemical composition of accelerated particles. The review concentrates on theoretical and analytical aspects but our strategic goal is to link the fundamental theoretical ideas with the rapidly growing wealth of observational data. (author)

  10. Analytic theory of the nonlinear M = 1 tearing mode

    International Nuclear Information System (INIS)

    Hazeltine, R.D.; Meiss, J.D.; Morrison, P.J.

    1985-09-01

    Numerical studies show that the m = 1 tearing mode continues to grow exponentially well into the nonlinear regime, in contrast with the slow, ''Rutherford,'' growth of m > 1 modes. We present a single helicity calculation which generalizes that of Rutherford to the case when the constant-psi approximation is invalid. As in that theory, the parallel current becomes an approximate flux function when the island size, W, exceeds the linear tearing layer width. However for the m = 1 mode, W becomes proportional to deltaB, rather than (deltaB)/sup 1/2/ above this critical amplitude. This implies that the convective nonlinearity in Ohm's law, which couples the m = 0 component to the m = 1 component, dominates the resistive diffusion term. The balance between the inductive electric field and this convective nonlinearity results in exponential growth. Assuming the form of the perturbed fields to be like that of the linear mode, we find that the growth occurs at 71% of the linear rate

  11. Strongly nonlinear theory of rapid solidification near absolute stability

    Science.gov (United States)

    Kowal, Katarzyna N.; Altieri, Anthony L.; Davis, Stephen H.

    2017-10-01

    We investigate the nonlinear evolution of the morphological deformation of a solid-liquid interface of a binary melt under rapid solidification conditions near two absolute stability limits. The first of these involves the complete stabilization of the system to cellular instabilities as a result of large enough surface energy. We derive nonlinear evolution equations in several limits in this scenario and investigate the effect of interfacial disequilibrium on the nonlinear deformations that arise. In contrast to the morphological stability problem in equilibrium, in which only cellular instabilities appear and only one absolute stability boundary exists, in disequilibrium the system is prone to oscillatory instabilities and a second absolute stability boundary involving attachment kinetics arises. Large enough attachment kinetics stabilize the oscillatory instabilities. We derive a nonlinear evolution equation to describe the nonlinear development of the solid-liquid interface near this oscillatory absolute stability limit. We find that strong asymmetries develop with time. For uniform oscillations, the evolution equation for the interface reduces to the simple form f''+(βf')2+f =0 , where β is the disequilibrium parameter. Lastly, we investigate a distinguished limit near both absolute stability limits in which the system is prone to both cellular and oscillatory instabilities and derive a nonlinear evolution equation that captures the nonlinear deformations in this limit. Common to all these scenarios is the emergence of larger asymmetries in the resulting shapes of the solid-liquid interface with greater departures from equilibrium and larger morphological numbers. The disturbances additionally sharpen near the oscillatory absolute stability boundary, where the interface becomes deep-rooted. The oscillations are time-periodic only for small-enough initial amplitudes and their frequency depends on a single combination of physical parameters, including the

  12. Nonlinear mean field theory for nuclear matter and surface properties

    International Nuclear Information System (INIS)

    Boguta, J.; Moszkowski, S.A.

    1983-01-01

    Nuclear matter properties are studied in a nonlinear relativistic mean field theory. We determine the parameters of the model from bulk properties of symmetric nuclear matter and a reasonable value of the effective mass. In this work, we stress the nonrelativistic limit of the theory which is essentially equivalent to a Skyrme hamiltonian, and we show that most of the results can be obtained, to a good approximation, analytically. The strength of the required parameters is determined from the binding energy and density of nuclear matter and the effective nucleon mass. For realistic values of the parameters, the nonrelativistic approximation turns out to be quite satisfactory. Using reasonable values of the parameters, we can account for other key properties of nuclei, such as the spin-orbit coupling, surface energy, and diffuseness of the nuclear surface. Also the energy dependence of the nucleon-nucleus optical model is accounted for reasonably well except near the Fermi surface. It is found, in agreement with empirical results, that the Landau parameter F 0 is quite small in normal nuclear matter. Both density dependence and momentum dependence of the NN interaction, but especially the former, are important for nuclear saturation. The required scalar and vector coupling constants agree fairly well with those obtained from analyses of NN scattering phase shifts with one-boson-exchange models. The mean field theory provides a semiquantitative justification for the weak Skyrme interaction in odd states. The strength of the required nonlinear term is roughly consistent with that derived using a new version of the chiral mean field theory in which the vector mass as well as the nucleon mass is generated by the sigma-field. (orig.)

  13. Feedback System Theory

    Science.gov (United States)

    1978-11-01

    R 2. GOVT A $ SION NO. 3 RIEqLPýIVT’S.;TALOG NUMBER r/ 4. TITLE (and wbiFflT, -L M4 1 , FEEDBACK SYSTEM THEORY ~r Inter in- 6. PERFORMING ORG. REPORT...ANNUAL REPORT FEEDBACK SYSTEM THEORY AFOSR GRANT NO. 76-2946B Air Force Office of Scientific Research for year ending October 31, 1978 79 02 08 L|I...re less stringent than in other synthesis techniques which cannot handle significant parameter uncertainty. _I FEEDBACK SYSTEM THEORY 1. Introduction

  14. A non-linear theory of strong interactions

    International Nuclear Information System (INIS)

    Skyrme, T.H.R.

    1994-01-01

    A non-linear theory of mesons, nucleons and hyperons is proposed. The three independent fields of the usual symmetrical pseudo-scalar pion field are replaced by the three directions of a four-component field vector of constant length, conceived in an Euclidean four-dimensional isotopic spin space. This length provides the universal scaling factor, all other constants being dimensionless; the mass of the meson field is generated by a φ 4 term; this destroys the continuous rotation group in the iso-space, leaving a 'cubic' symmetry group. Classification of states by this group introduces quantum numbers corresponding to isotopic spin and to 'strangeness'; one consequences is that, at least in elementary interactions, charge is only conserved module 4. Furthermore, particle states have not a well-defined parity, but parity is effectively conserved for meson-nucleon interactions. A simplified model, using only two dimensions of space and iso-space, is considered further; the non-linear meson field has solutions with particle character, and an indication is given of the way in which the particle field variables might be introduced as collective co-ordinates describing the dynamics of these particular solutions of the meson field equations, suggesting a unified theory based on the meson field alone. (author). 7 refs

  15. Application of H∞ control theory to power control of a nonlinear reactor model

    International Nuclear Information System (INIS)

    Suzuki, Katsuo; Shimazaki, Junya; Shinohara, Yoshikuni

    1993-01-01

    The H∞ control theory is applied to the compensator design of a nonlinear nuclear reactor model, and the results are compared with standard linear quadratic Gaussian (LQG) control. The reactor model is assumed to be provided with a control rod drive system having the compensation of rod position feedback. The nonlinearity of the reactor model exerts a great influence on the stability of the control system, and hence, it is desirable for a power control system of a nuclear reactor to achieve robust stability and to improve the sensitivity of the feedback control system. A computer simulation based on a power control system synthesized by LQG control was performed revealing that the control system has some stationary offset and less stability. Therefore, here, attention is given to the development of a methodology for robust control that can withstand exogenous disturbances and nonlinearity in view of system parameter changes. The developed methodology adopts H∞ control theory in the feedback system and shows interesting features of robustness. The results of the computer simulation indicate that the feedback control system constructed by the developed H∞ compensator possesses sufficient robustness of control on the stability and disturbance attenuation, which are essential for the safe operation of a nuclear reactor

  16. Inverse operator theory method mathematics-mechanization for the solutions of nonlinear equations and some typical applications in nonlinear physics

    International Nuclear Information System (INIS)

    Fang Jinqing; Yao Weiguang

    1992-12-01

    Inverse operator theory method (IOTM) has developed rapidly in the last few years. It is an effective and useful procedure for quantitative solution of nonlinear or stochastic continuous dynamical systems. Solutions are obtained in series form for deterministic equations, and in the case of stochastic equation it gives statistic measures of the solution process. A very important advantage of the IOTM is to eliminate a number of restrictive and assumption on the nature of stochastic processes. Therefore, it provides more realistic solutions. The IOTM and its mathematics-mechanization (MM) are briefly introduced. They are used successfully to study the chaotic behaviors of the nonlinear dynamical systems for the first time in the world. As typical examples, the Lorentz equation, generalized Duffing equation, two coupled generalized Duffing equations are investigated by the use of the IOTM and the MM. The results are in good agreement with ones by the Runge-Kutta method (RKM). It has higher accuracy and faster convergence. So the IOTM realized by the MM is of potential application valuable in nonlinear science

  17. Controller Design of Complex System Based on Nonlinear Strength

    Directory of Open Access Journals (Sweden)

    Rongjun Mu

    2015-01-01

    Full Text Available This paper presents a new idea of controller design for complex systems. The nonlinearity index method was first developed for error propagation of nonlinear system. The nonlinearity indices access the boundary between the strong and the weak nonlinearities of the system model. The algorithm of nonlinearity index according to engineering application is first proposed in this paper. Applying this method on nonlinear systems is an effective way to measure the nonlinear strength of dynamics model over the full flight envelope. The nonlinearity indices access the boundary between the strong and the weak nonlinearities of system model. According to the different nonlinear strength of dynamical model, the control system is designed. The simulation time of dynamical complex system is selected by the maximum value of dynamic nonlinearity indices. Take a missile as example; dynamical system and control characteristic of missile are simulated. The simulation results show that the method is correct and appropriate.

  18. Algorithms of estimation for nonlinear systems a differential and algebraic viewpoint

    CERN Document Server

    Martínez-Guerra, Rafael

    2017-01-01

    This book acquaints readers with recent developments in dynamical systems theory and its applications, with a strong focus on the control and estimation of nonlinear systems. Several algorithms are proposed and worked out for a set of model systems, in particular so-called input-affine or bilinear systems, which can serve to approximate a wide class of nonlinear control systems. These can either take the form of state space models or be represented by an input-output equation. The approach taken here further highlights the role of modern mathematical and conceptual tools, including differential algebraic theory, observer design for nonlinear systems and generalized canonical forms.

  19. 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.

  20. A study of discrete nonlinear systems

    International Nuclear Information System (INIS)

    Dhillon, H.S.

    2001-04-01

    An investigation of various spatially discrete time-independent nonlinear models was undertaken. These models are generically applicable to many different physical systems including electron-phonon interactions in solids, magnetic multilayers, layered superconductors and classical lattice systems. To characterise the possible magnetic structures created on magnetic multilayers a model has been formulated and studied. The Euler-Lagrange equation for this model is a discrete version of the Sine-Gordon equation. Solutions of this equation are generated by applying the methods of Chaotic Dynamics - treating the space variable associated with the layer number as a discrete time variable. The states found indicate periodic, quasiperiodic and chaotic structures. Analytic solutions to the discrete nonlinear Schroedinger Equation (DNSE) with cubic nonlinearity are presented in the strong coupling limit. Using these as a starting point, a procedure is developed to determine the wave function and the energy eigenvalue for moderate coupling. The energy eigenvalues of the different structures of the wave function are found to be in excellent agreement with the exact strong coupling result. The solutions to the DNSE indicate commensurate and incommensurate spatial structures associated with different localisation patterns of the wave function. The states which arise may be fractal, periodic, quasiperiodic or chaotic. This work is then extended to solve a first order discrete nonlinear equation. The exact solutions for both the first and second order discrete nonlinear equations with cubic nonlinearity suggests that this method of studying discrete nonlinear equations may be applied to solve discrete equations with any order difference and cubic nonlinearity. (author)

  1. Nonlinear polarization of ionic liquids: theory, simulations, experiments

    Science.gov (United States)

    Kornyshev, Alexei

    2010-03-01

    Room temperature ionic liquids (RTILs) composed of large, often asymmetric, organic cations and simple or complex inorganic or organic anions do not freeze at ambient temperatures. Their rediscovery some 15 years ago is widely accepted as a ``green revolution'' in chemistry, offering an unlimited number of ``designer'' solvents for chemical and photochemical reactions, homogeneous catalysis, lubrication, and solvent-free electrolytes for energy generation and storage. As electrolytes they are non-volatile, some can sustain without decomposition up to 6 times higher voltages than aqueous electrolytes, and many are environmentally friendly. The studies of RTILs and their applications have reached a critical stage. So many of them can be synthesized - about a thousand are known already - their mixtures can further provide ``unlimited'' number of combinations! Thus, establishing some general laws that could direct the best choice of a RTIL for a given application became crucial; guidance is expected from theory and modelling. But for a physical theory, RTILs comprise a peculiar and complex class of media, the description of which lies at the frontier line of condensed matter theoretical physics: dense room temperature ionic plasmas with ``super-strong'' Coulomb correlations, which behave like glasses at short time-scale, but like viscous liquids at long-time scale. This talk will introduce RTILs to physicists and overview the current understanding of the nonlinear response of RTILs to electric field. It will focus on the theory, simulations, and experimental characterisation of the structure and nonlinear capacitance of the electrical double layer at a charged electrode. It will also discuss pros and contras of supercapacitor applications of RTILs.

  2. Resonant driving of a nonlinear Hamiltonian system

    International Nuclear Information System (INIS)

    Palmisano, Carlo; Gervino, Gianpiero; Balma, Massimo; Devona, Dorina; Wimberger, Sandro

    2013-01-01

    As a proof of principle, we show how a classical nonlinear Hamiltonian system can be driven resonantly over reasonably long times by appropriately shaped pulses. To keep the parameter space reasonably small, we limit ourselves to a driving force which consists of periodic pulses additionally modulated by a sinusoidal function. The main observables are the average increase of kinetic energy and of the action variable (of the non-driven system) with time. Applications of our scheme aim for driving high frequencies of a nonlinear system with a fixed modulation signal.

  3. Globally Asymptotic Stability of Stochastic Nonlinear Systems with Time-Varying Delays via Output Feedback Control

    Directory of Open Access Journals (Sweden)

    Mingzhu Song

    2016-01-01

    Full Text Available We address the problem of globally asymptotic stability for a class of stochastic nonlinear systems with time-varying delays. By the backstepping method and Lyapunov theory, we design a linear output feedback controller recursively based on the observable linearization for a class of stochastic nonlinear systems with time-varying delays to guarantee that the closed-loop system is globally asymptotically stable in probability. In particular, we extend the deterministic nonlinear system to stochastic nonlinear systems with time-varying delays. Finally, an example and its simulations are given to illustrate the theoretical results.

  4. Approximate Stream Function wavemaker theory for highly non-linear waves in wave flumes

    DEFF Research Database (Denmark)

    Zhang, H.W.; Schäffer, Hemming Andreas

    2007-01-01

    An approximate Stream Function wavemaker theory for highly non-linear regular waves in flumes is presented. This theory is based on an ad hoe unified wave-generation method that combines linear fully dispersive wavemaker theory and wave generation for non-linear shallow water waves. This is done...... by applying a dispersion correction to the paddle position obtained for non-linear long waves. The method is validated by a number of wave flume experiments while comparing with results of linear wavemaker theory, second-order wavemaker theory and Cnoidal wavemaker theory within its range of application....

  5. Controlling chaotic systems via nonlinear feedback control

    International Nuclear Information System (INIS)

    Park, Ju H.

    2005-01-01

    In this article, a new method to control chaotic systems is proposed. Using Lyapunov method, we design a nonlinear feedback controller to make the controlled system be stabilized. A numerical example is given to illuminate the design procedure and advantage of the result derived

  6. A hierarchy of systems of nonlinear equations

    International Nuclear Information System (INIS)

    Falkensteiner, P.; Grosse, H.

    1985-01-01

    Imposing isospectral invariance for the one-dimensional Dirac operator yields an infinite hierarchy of systems of chiral invariant nonlinear partial differential equations. The same system is obtained through a Lax pair construction and finally a formulation in terms of Kac-Moody generators is given. (Author)

  7. Fault detection for nonlinear systems - A standard problem approach

    DEFF Research Database (Denmark)

    Stoustrup, Jakob; Niemann, Hans Henrik

    1998-01-01

    The paper describes a general method for designing (nonlinear) fault detection and isolation (FDI) systems for nonlinear processes. For a rich class of nonlinear systems, a nonlinear FDI system can be designed using convex optimization procedures. The proposed method is a natural extension...

  8. Comment on the consistency of truncated nonlinear integral equation based theories of freezing

    International Nuclear Information System (INIS)

    Cerjan, C.; Bagchi, B.; Rice, S.A.

    1985-01-01

    We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim--Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions

  9. Network science, nonlinear science and infrastructure systems

    CERN Document Server

    2007-01-01

    Network Science, Nonlinear Science and Infrastructure Systems has been written by leading scholars in these areas. Its express purpose is to develop common theoretical underpinnings to better solve modern infrastructural problems. It is felt by many who work in these fields that many modern communication problems, ranging from transportation networks to telecommunications, Internet, supply chains, etc., are fundamentally infrastructure problems. Moreover, these infrastructure problems would benefit greatly from a confluence of theoretical and methodological work done with the areas of Network Science, Dynamical Systems and Nonlinear Science. This book is dedicated to the formulation of infrastructural tools that will better solve these types of infrastructural problems. .

  10. Theory of weakly nonlinear self-sustained detonations

    KAUST Repository

    Faria, Luiz

    2015-11-03

    We propose a theory of weakly nonlinear multidimensional self-sustained detonations based on asymptotic analysis of the reactive compressible Navier-Stokes equations. We show that these equations can be reduced to a model consisting of a forced unsteady small-disturbance transonic equation and a rate equation for the heat release. In one spatial dimension, the model simplifies to a forced Burgers equation. Through analysis, numerical calculations and comparison with the reactive Euler equations, the model is demonstrated to capture such essential dynamical characteristics of detonations as the steady-state structure, the linear stability spectrum, the period-doubling sequence of bifurcations and chaos in one-dimensional detonations and cellular structures in multidimensional detonations.

  11. Nonlinear problems of the theory of heterogeneous slightly curved shells

    Science.gov (United States)

    Kantor, B. Y.

    1973-01-01

    An account if given of the variational method of the solution of physically and geometrically nonlinear problems of the theory of heterogeneous slightly curved shells. Examined are the bending and supercritical behavior of plates and conical and spherical cupolas of variable thickness in a temperature field, taking into account the dependence of the elastic parameters on temperature. The bending, stability in general and load-bearing capacity of flexible isotropic elastic-plastic shells with different criteria of plasticity, taking into account compressibility and hardening. The effect of the plastic heterogeneity caused by heat treatment, surface work hardening and irradiation by fast neutron flux is investigated. Some problems of the dynamic behavior of flexible shells are solved. Calculations are performed in high approximations. Considerable attention is given to the construction of a machine algorithm and to the checking of the convergence of iterative processes.

  12. History of nonlinear oscillations theory in France (1880-1940)

    CERN Document Server

    Ginoux, Jean-Marc

    2017-01-01

    This book reveals the French scientific contribution to the mathematical theory of nonlinear oscillations and its development. The work offers a critical examination of sources with a focus on the twentieth century, especially the period between the wars. Readers will see that, contrary to what is often written, France's role has been significant. Important contributions were made through both the work of French scholars from within diverse disciplines (mathematicians, physicists, engineers), and through the geographical crossroads that France provided to scientific communication at the time. This study includes an examination of the period before the First World War which is vital to understanding the work of the later period. By examining literature sources such as periodicals on the topic of electricity from that era, the author has unearthed a very important text by Henri Poincaré, dating from 1908. In this work Poincaré applied the concept of limit cycle (which he had introduced in 1882 through his own...

  13. Linear system theory

    Science.gov (United States)

    Callier, Frank M.; Desoer, Charles A.

    1991-01-01

    The aim of this book is to provide a systematic and rigorous access to the main topics of linear state-space system theory in both the continuous-time case and the discrete-time case; and the I/O description of linear systems. The main thrusts of the work are the analysis of system descriptions and derivations of their properties, LQ-optimal control, state feedback and state estimation, and MIMO unity-feedback systems.

  14. Aeroelastic oscillations of a cantilever with structural nonlinearities: theory and numerical simulation.

    Energy Technology Data Exchange (ETDEWEB)

    Robinson, Brandon [Carleton Univ., Ottawa, ON (Canada). Dept. of Civil and Environmental Engineering; Rocha da Costa, Leandro Jose [Carleton Univ., Ottawa, ON (Canada). Dept. of Civil and Environmental Engineering; Poirel, Dominique [Royal Military College of Canada, Kingston (Canada). Dept. of Mechanical and Aerospace Engineering; Pettit, Chris [US Naval Academy, Annapolis, MD (United States). Dept. of Mechanical and Aerospace Engineering; Khalil, Mohammad [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Sarkar, Abhijit [Carleton Univ., Ottawa, ON (Canada). Dept. of Civil and Environmental Engineering

    2017-09-01

    Our study details the derivation of the nonlinear equations of motion for the axial, biaxial bending and torsional vibrations of an aeroelastic cantilever undergoing rigid body (pitch) rotation at the base. The primary attenstion is focussed on the geometric nonlinearities of the system, whereby the aeroelastic load is modeled by the theory of linear quasisteady aerodynamics. This modelling effort is intended to mimic the wind-tunnel experimental setup at the Royal Military College of Canada. While the derivation closely follows the work of Hodges and Dowell [1] for rotor blades, this aeroelastic system contains new inertial terms which stem from the fundamentally different kinematics than those exhibited by helicopter or wind turbine blades. Using the Hamilton’s principle, a set of coupled nonlinear partial differential equations (PDEs) and an ordinary differential equation (ODE) are derived which describes the coupled axial-bending-bending-torsion-pitch motion of the aeroelastic cantilever with the pitch rotation. The finite dimensional approximation of the coupled system of PDEs are obtained using the Galerkin projection, leading to a coupled system of ODEs. Subsequently, these nonlinear ODEs are solved numerically using the built-in MATLAB implicit ODE solver and the associated numerical results are compared with those obtained using Houbolt’s method. It is demonstrated that the system undergoes coalescence flutter, leading to a limit cycle oscillation (LCO) due to coupling between the rigid body pitching mode and teh flexible mode arising from the flapwise bending motion.

  15. Controllability of non-linear systems: generic singularities and their stability

    International Nuclear Information System (INIS)

    Davydov, Alexey A; Zakalyukin, Vladimir M

    2012-01-01

    This paper presents an overview of the state of the art in applications of singularity theory to the analysis of generic singularities of controllability of non-linear systems on manifolds. Bibliography: 40 titles.

  16. 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.

  17. A general theory of two-wave mixing in nonlinear media

    DEFF Research Database (Denmark)

    Chi, Mingjun; Huignard, Jean-Pierre; Petersen, Paul Michael

    2009-01-01

    A general theory of two-wave mixing in nonlinear media is presented. Assuming a gain (or absorption) grating and a refractive index grating are generated because of the nonlinear process in a nonlinear medium, the coupled-wave equations of two-wave mixing are derived based on the Maxwell’s wave e...

  18. Nonlinear theory of the collisional Rayleigh-Taylor instability in equatorial spread F

    International Nuclear Information System (INIS)

    Chaturvedi, P.K.; Ossakow, S.L.

    1977-01-01

    The nonlinear behavior of the collisional Rayleigh-Taylor instability is studied in equatorial Spread F by including a dominant two-dimensional nonlinearity. It is found that on account of this nonlinearity the instability saturates by generating damped higher spatial harmonics. The saturated power spectrum for the density fluctuations is discussed. A comparison between experimental observations and theory is presented

  19. Systems Theory in Immunology

    CERN Document Server

    Doria, Gino; Koch, Giorgio; Strom, Roberto

    1979-01-01

    This volume collects the contributions presented at the "Working Conference on System Theory in Immunology", held in Rome, May 1978. The aim of the Conference was to bring together immunologists on one side and experts in system theory and applied mathematics on the other, in order to identify problems of common interest and to establish a network of joint effort toward their solution. The methodologies of system theory for processing experimental data and for describing dynamical phenomena could indeed contribute significantly to the under­ standing of basic immunological facts. Conversely, the complexity of experimental results and of interpretative models should stimulate mathematicians to formulate new problems and to design appropriate procedures of analysis. The multitude of scientific publications in theoretical biology, appeared in recent years, confirms this trend and calls for extensive interaction between mat- matics and immunology. The material of this volume is divided into five sections, along ...

  20. Phase Control in Nonlinear Systems

    Science.gov (United States)

    Zambrano, Samuel; Seoane, Jesús M.; Mariño, Inés P.; Sanjuán, Miguel A. F.; Meucci, Riccardo

    The following sections are included: * Introduction * Phase Control of Chaos * Description of the model * Numerical exploration of phase control of chaos * Experimental evidence of phase control of chaos * Phase Control of Intermittency in Dynamical Systems * Crisis-induced intermittency and its control * Experimental setup and implementation of the phase control scheme * Phase control of the laser in the pre-crisis regime * Phase control of the intermittency after the crisis * Phase control of the intermittency in the quadratic map * Phase Control of Escapes in Open Dynamical Systems * Control of open dynamical systems * Model description * Numerical simulations and heuristic arguments * Experimental implementation in an electronic circuit * Conclusions and Discussions * Acknowledgments * References

  1. Workshop on Nonlinear Phenomena in Complex Systems

    CERN Document Server

    1989-01-01

    This book contains a thorough treatment of neural networks, cellular-automata and synergetics, in an attempt to provide three different approaches to nonlinear phenomena in complex systems. These topics are of major interest to physicists active in the fields of statistical mechanics and dynamical systems. They have been developed with a high degree of sophistication and include the refinements necessary to work with the complexity of real systems as well as the more recent research developments in these areas.

  2. Periodic Solutions for Highly Nonlinear Oscillation Systems

    DEFF Research Database (Denmark)

    Ghadimi, M; Barari, Amin; Kaliji, H.D

    2012-01-01

    In this paper, Frequency-Amplitude Formulation is used to analyze the periodic behavior of tapered beam as well as two complex nonlinear systems. Many engineering structures, such as offshore foundations, oil platform supports, tower structures and moving arms, are modeled as tapered beams...

  3. Exploring Nonlinearities in Financial Systemic Risk

    NARCIS (Netherlands)

    Wolski, M.

    2013-01-01

    We propose a new methodology of assessing the effects of individual institution's risk on the others and on the system as a whole. We build upon the Conditional Value-at-Risk approach, however, we introduce the explicit Granger causal linkages and we account for possible nonlinearities in the

  4. Experimental chaos in nonlinear vibration isolation system

    International Nuclear Information System (INIS)

    Lou Jingjun; Zhu Shijian; He Lin; He Qiwei

    2009-01-01

    The chaotic vibration isolation method was studied thoroughly from an experimental perspective. The nonlinear load-deflection characteristic of the conical coil spring used in the experiment was surveyed. Chaos and subharmonic responses including period-2 and period-6 motions were observed. The line spectrum reduction and the drop of the acceleration vibration level in chaotic state and that in non-chaotic state were compared, respectively. It was concluded from the experiment that the nonlinear vibration isolation system in chaotic state has strong ability in line spectrum reduction.

  5. Nonlinear distortion in wireless systems modeling and simulation with Matlab

    CERN Document Server

    Gharaibeh, Khaled M

    2011-01-01

    This book covers the principles of modeling and simulation of nonlinear distortion in wireless communication systems with MATLAB simulations and techniques In this book, the author describes the principles of modeling and simulation of nonlinear distortion in single and multichannel wireless communication systems using both deterministic and stochastic signals. Models and simulation methods of nonlinear amplifiers explain in detail how to analyze and evaluate the performance of data communication links under nonlinear amplification. The book addresses the analysis of nonlinear systems

  6. Applied multidimensional systems theory

    CERN Document Server

    Bose, Nirmal K

    2017-01-01

    Revised and updated, this concise new edition of the pioneering book on multidimensional signal processing is ideal for a new generation of students. Multidimensional systems or m-D systems are the necessary mathematical background for modern digital image processing with applications in biomedicine, X-ray technology and satellite communications. Serving as a firm basis for graduate engineering students and researchers seeking applications in mathematical theories, this edition eschews detailed mathematical theory not useful to students. Presentation of the theory has been revised to make it more readable for students, and introduce some new topics that are emerging as multidimensional DSP topics in the interdisciplinary fields of image processing. New topics include Groebner bases, wavelets, and filter banks.

  7. 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

  8. Analysis of nonlinear systems using ARMA [autoregressive moving average] models

    International Nuclear Information System (INIS)

    Hunter, N.F. Jr.

    1990-01-01

    While many vibration systems exhibit primarily linear behavior, a significant percentage of the systems encountered in vibration and model testing are mildly to severely nonlinear. Analysis methods for such nonlinear systems are not yet well developed and the response of such systems is not accurately predicted by linear models. Nonlinear ARMA (autoregressive moving average) models are one method for the analysis and response prediction of nonlinear vibratory systems. In this paper we review the background of linear and nonlinear ARMA models, and illustrate the application of these models to nonlinear vibration systems. We conclude by summarizing the advantages and disadvantages of ARMA models and emphasizing prospects for future development. 14 refs., 11 figs

  9. Indirect learning control for nonlinear dynamical systems

    Science.gov (United States)

    Ryu, Yeong Soon; Longman, Richard W.

    1993-01-01

    In a previous paper, learning control algorithms were developed based on adaptive control ideas for linear time variant systems. The learning control methods were shown to have certain advantages over their adaptive control counterparts, such as the ability to produce zero tracking error in time varying systems, and the ability to eliminate repetitive disturbances. In recent years, certain adaptive control algorithms have been developed for multi-body dynamic systems such as robots, with global guaranteed convergence to zero tracking error for the nonlinear system euations. In this paper we study the relationship between such adaptive control methods designed for this specific class of nonlinear systems, and the learning control problem for such systems, seeking to converge to zero tracking error in following a specific command repeatedly, starting from the same initial conditions each time. The extension of these methods from the adaptive control problem to the learning control problem is seen to be trivial. The advantages and disadvantages of using learning control based on such adaptive control concepts for nonlinear systems, and the use of other currently available learning control algorithms are discussed.

  10. Janus field theories from non-linear BF theories for multiple M2-branes

    International Nuclear Information System (INIS)

    Ryang, Shijong

    2009-01-01

    We integrate the nonpropagating B μ gauge field for the non-linear BF Lagrangian describing N M2-branes which includes terms with even number of the totally antisymmetric tensor M IJK in arXiv:0808.2473 and for the two-types of non-linear BF Lagrangians which include terms with odd number of M IJK as well in arXiv:0809:0985. For the former Lagrangian we derive directly the DBI-type Lagrangian expressed by the SU(N) dynamical A μ gauge field with a spacetime dependent coupling constant, while for the low-energy expansions of the latter Lagrangians the B μ integration is iteratively performed. The derived Janus field theory Lagrangians are compared.

  11. Stochastic Control Theory, Nonlinear Structural Mechanics and Applied Combinatorics

    Science.gov (United States)

    1989-05-12

    More specifically: (") x 3 PAS and Steiner triple systems; (") x 4 PAS and Steiner triple systems which can be nested; and (’) x 5 PAS and Steiner ...am Rudolf Wille CONCEPTUAL SCALING Technische Hochschule Darmstadt Abstract: Scaling of empirical data uses formal patterns to lead to a better...of Arizona Jan 18 - 22 Wille, Rudolf Technische Hochschule Darmstadt Jan 17 - 23 21 APPLICATIONS OF COMBINATORICS AND GRAPH THEORY TO THE BIOLOGICAL

  12. Nonlinear transport properties of non-ideal systems

    International Nuclear Information System (INIS)

    Pavlov, G A

    2009-01-01

    The theory of nonlinear transport is elaborated to determine the Burnett transport properties of non-ideal multi-element plasma and neutral systems. The procedure for the comparison of the phenomenological conservation equations of a continuous dense medium and the microscopic equations for dynamical variable operators is used for the definition of these properties. The Mori algorithm is developed to derive the equations of motion of dynamical value operators of a non-ideal system in the form of the generalized nonlinear Langevin equations. In consequence, the microscopic expressions of transport coefficients corresponding to second-order thermal disturbances (temperature, mass velocity, etc) have been found in the long wavelength and low frequency limits

  13. Transient response of nonlinear polymer networks: A kinetic theory

    Science.gov (United States)

    Vernerey, Franck J.

    2018-06-01

    Dynamic networks are found in a majority of natural materials, but also in engineering materials, such as entangled polymers and physically cross-linked gels. Owing to their transient bond dynamics, these networks display a rich class of behaviors, from elasticity, rheology, self-healing, or growth. Although classical theories in rheology and mechanics have enabled us to characterize these materials, there is still a gap in our understanding on how individuals (i.e., the mechanics of each building blocks and its connection with others) affect the emerging response of the network. In this work, we introduce an alternative way to think about these networks from a statistical point of view. More specifically, a network is seen as a collection of individual polymer chains connected by weak bonds that can associate and dissociate over time. From the knowledge of these individual chains (elasticity, transient attachment, and detachment events), we construct a statistical description of the population and derive an evolution equation of their distribution based on applied deformation and their local interactions. We specifically concentrate on nonlinear elastic response that follows from the strain stiffening response of individual chains of finite size. Upon appropriate averaging operations and using a mean field approximation, we show that the distribution can be replaced by a so-called chain distribution tensor that is used to determine important macroscopic measures such as stress, energy storage and dissipation in the network. Prediction of the kinetic theory are then explored against known experimental measurement of polymer responses under uniaxial loading. It is found that even under the simplest assumptions of force-independent chain kinetics, the model is able to reproduce complex time-dependent behaviors of rubber and self-healing supramolecular polymers.

  14. 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.

  15. Quantum theory of a one-dimensional laser with output coupling. 2. Nonlinear theory

    International Nuclear Information System (INIS)

    Penaforte, J.C.; Baseia, B.

    1984-01-01

    A previous paper describing the quantum theory of a laser in linear approximation is here extended to the nonlinear case. Instead of the approach of conventional theory - which deals with discrete 'cavity-modes' and includes artificial mechanisms to simulates radiation field losses due to beam extraction - a more realistic model of optical cavity having output coupling is used that works entirely within the continuous spectrum, allowing one to obtain the equations for the field both inside and outside the laser cavity. Besides the quantum noise due to spontaneous emission, a noise term of classical nature due to transmission losses automatically emerges from the present treatment. For single-collective-mode operation the equations for laser field are solved exactly, yielding the transient and steady-state solutions. Inside the laser cavity, the results of nonlinear analysis agree with those found in conventional theory once the conventional 'mode-amplitude' is reinterpreted as a collective variable. Outside the cavity - unaccessible region in the conventional treatment - the solution for the laser field is also exhibited. Further considerations as concerning the role played by the noise terms in the field buildup are discussed. (Author) [pt

  16. Model reduction of systems with localized nonlinearities.

    Energy Technology Data Exchange (ETDEWEB)

    Segalman, Daniel Joseph

    2006-03-01

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

  17. Controllability of nonlinear delay oscillating systems

    Directory of Open Access Journals (Sweden)

    Chengbin Liang

    2017-05-01

    Full Text Available In this paper, we study the controllability of a system governed by second order delay differential equations. We introduce a delay Gramian matrix involving the delayed matrix sine, which is used to establish sufficient and necessary conditions of controllability for the linear problem. In addition, we also construct a specific control function for controllability. For the nonlinear problem, we construct a control function and transfer the controllability problem to a fixed point problem for a suitable operator. We give a sufficient condition to guarantee the nonlinear delay system is controllable. Two examples are given to illustrate our theoretical results by calculating a specific control function and inverse of a delay Gramian matrix.

  18. Theory for stationary nonlinear wave propagation in complex magnetic geometry

    International Nuclear Information System (INIS)

    Watanabe, T.; Hojo, H.; Nishikawa, Kyoji.

    1977-08-01

    We present our recent efforts to derive a systematic calculation scheme for nonlinear wave propagation in the self-consistent plasma profile in complex magnetic-field geometry. Basic assumptions and/or approximations are i) use of the collisionless two-fluid model with an equation of state; ii) restriction to a steady state propagation and iii) existence of modified magnetic surface, modification due to Coriolis' force. We discuss four situations: i) weak-field propagation without static flow, ii) arbitrary field strength with flow in axisymmetric system, iii) weak field limit of case ii) and iv) arbitrary field strength in nonaxisymmetric torus. Except for case iii), we derive a simple variation principle, similar to that of Seligar and Whitham, by introducing appropriate coordinates. In cases i) and iii), we derive explicit results for quasilinear profile modification. (auth.)

  19. 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.

  20. Global chaos synchronization of new chaotic systems via nonlinear control

    International Nuclear Information System (INIS)

    Chen, H.-K.

    2005-01-01

    Nonlinear control is an effective method for making two identical chaotic systems or two different chaotic systems be synchronized. However, this method assumes that the Lyapunov function of error dynamic (e) of synchronization is always formed as V (e) = 1/2e T e. In this paper, modification based on Lyapunov stability theory to design a controller is proposed in order to overcome this limitation. The method has been applied successfully to make two identical new systems and two different chaotic systems (new system and Lorenz system) globally asymptotically synchronized. Since the Lyapunov exponents are not required for the calculation, this method is effective and convenient to synchronize two identical systems and two different chaotic systems. Numerical simulations are also given to validate the proposed synchronization approach

  1. Fractional-Order Nonlinear Systems Modeling, Analysis and Simulation

    CERN Document Server

    Petráš, Ivo

    2011-01-01

    "Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation" presents a study of fractional-order chaotic systems accompanied by Matlab programs for simulating their state space trajectories, which are shown in the illustrations in the book. Description of the chaotic systems is clearly presented and their analysis and numerical solution are done in an easy-to-follow manner. Simulink models for the selected fractional-order systems are also presented. The readers will understand the fundamentals of the fractional calculus, how real dynamical systems can be described using fractional derivatives and fractional differential equations, how such equations can be solved, and how to simulate and explore chaotic systems of fractional order. The book addresses to mathematicians, physicists, engineers, and other scientists interested in chaos phenomena or in fractional-order systems. It can be used in courses on dynamical systems, control theory, and applied mathematics at graduate or postgraduate level. ...

  2. One-dimensional nonlinear theory for rectangular helix traveling-wave tube

    Energy Technology Data Exchange (ETDEWEB)

    Fu, Chengfang, E-mail: fchffchf@126.com; Zhao, Bo; Yang, Yudong; Ju, Yongfeng [Faculty of Electronic Information Engineering, Huaiyin Institute of Technology, Huai' an 223003 (China); Wei, Yanyu [School of Physical Electronics, University of Electronic and Technology of China, Chengdu 610054 (China)

    2016-08-15

    A 1-D nonlinear theory of a rectangular helix traveling-wave tube (TWT) interacting with a ribbon beam is presented in this paper. The RF field is modeled by a transmission line equivalent circuit, the ribbon beam is divided into a sequence of thin rectangular electron discs with the same cross section as the beam, and the charges are assumed to be uniformly distributed over these discs. Then a method of computing the space-charge field by solving Green's Function in the Cartesian Coordinate-system is fully described. Nonlinear partial differential equations for field amplitudes and Lorentz force equations for particles are solved numerically using the fourth-order Runge-Kutta technique. The tube's gain, output power, and efficiency of the above TWT are computed. The results show that increasing the cross section of the ribbon beam will improve a rectangular helix TWT's efficiency and reduce the saturated length.

  3. 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.

  4. Applied systems theory

    CERN Document Server

    Dekkers, Rob

    2017-01-01

    Offering an up-to-date account of systems theories and its applications, this book provides a different way of resolving problems and addressing challenges in a swift and practical way, without losing overview and grip on the details. From this perspective, it offers a different way of thinking in order to incorporate different perspectives and to consider multiple aspects of any given problem. Drawing examples from a wide range of disciplines, it also presents worked cases to illustrate the principles. The multidisciplinary perspective and the formal approach to modelling of systems and processes of ‘Applied Systems Theory’ makes it suitable for managers, engineers, students, researchers, academics and professionals from a wide range of disciplines; they can use this ‘toolbox’ for describing, analysing and designing biological, engineering and organisational systems as well as getting a better understanding of societal problems. This revised, updated and expanded second edition includes coverage of a...

  5. Simplified non-linear time-history analysis based on the Theory of Plasticity

    DEFF Research Database (Denmark)

    Costa, Joao Domingues

    2005-01-01

    This paper aims at giving a contribution to the problem of developing simplified non-linear time-history (NLTH) analysis of structures which dynamical response is mainly governed by plastic deformations, able to provide designers with sufficiently accurate results. The method to be presented...... is based on the Theory of Plasticity. Firstly, the formulation and the computational procedure to perform time-history analysis of a rigid-plastic single degree of freedom (SDOF) system are presented. The necessary conditions for the method to incorporate pinching as well as strength degradation...

  6. Solution of linear and nonlinear matrix systems. Application to a nonlinear diffusion equation

    International Nuclear Information System (INIS)

    Bonnet, M.; Meurant, G.

    1978-01-01

    Different methods of solution of linear and nonlinear algebraic systems are applied to the nonlinear system obtained by discretizing a nonlinear diffusion equation. For linear systems, methods in general use of alternating directions type or Gauss Seidel's methods are compared to more recent ones of the type of generalized conjugate gradient; the superiority of the latter is shown by numerical examples. For nonlinear systems, a method on nonlinear conjugate gradient is studied as also Newton's method and some of its variants. It should be noted, however that Newton's method is found to be more efficient when coupled with a good method for solution of the linear system. To conclude, such methods are used to solve a nonlinear diffusion problem and the numerical results obtained are to be compared [fr

  7. Solution of linear and nonlinear matrix systems. Application to a nonlinear diffusion equation

    International Nuclear Information System (INIS)

    Bonnet, M.; Meurant, G.

    1978-01-01

    The object of this study is to compare different methods of solving linear and nonlinear algebraic systems and to apply them to the nonlinear system obtained by discretizing a nonlinear diffusion equation. For linear systems the conventional methods of alternating direction type or Gauss Seidel's methods are compared to more recent ones of the type of generalized conjugate gradient; the superiority of the latter is shown by numerical examples. For nonlinear systems, a method of nonlinear conjugate gradient is studied together with Newton's method and some of its variants. It should be noted, however, that Newton's method is found to be more efficient when coupled with a good method for solving the linear system. As a conclusion, these methods are used to solve a nonlinear diffusion problem and the numerical results obtained are compared [fr

  8. Topological equivalence of nonlinear autonomous dynamical systems

    International Nuclear Information System (INIS)

    Nguyen Huynh Phan; Tran Van Nhung

    1995-12-01

    We show in this paper that the autonomous nonlinear dynamical system Σ(A,B,F): x' = Ax+Bu+F(x) is topologically equivalent to the linear dynamical system Σ(A,B,O): x' = Ax+Bu if the projection of A on the complement in R n of the controllable vectorial subspace is hyperbolic and if lipschitz constant of F is sufficiently small ( * ) and F(x) = 0 when parallel x parallel is sufficiently large ( ** ). In particular, if Σ(A,B,O) is controllable, it is topologically equivalent to Σ(A,B,F) when it is only that F satisfy ( ** ). (author). 18 refs

  9. Tracking Control for Switched Cascade Nonlinear Systems

    Directory of Open Access Journals (Sweden)

    Xiaoxiao Dong

    2015-01-01

    Full Text Available The issue of H∞ output tracking for switched cascade nonlinear systems is discussed in this paper, where not all the linear parts of subsystems are stabilizable. The conditions of the solvability for the issue are given by virtue of the structural characteristics of the systems and the average dwell time method, in which the total activation time for stabilizable subsystems is longer than that for the unstabilizable subsystems. At last, a simulation example is used to demonstrate the validity and advantages of the proposed approach.

  10. Nonlinear theory of scattering by localized potentials in metals

    Energy Technology Data Exchange (ETDEWEB)

    Howard, I A [Department of Physics, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp (Belgium); March, N H [Department of Physics, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp (Belgium); Oxford University, Oxford (United Kingdom); Echenique, P M [Donostia International Physics Center (DIPC), 20018 San Sebastian, Basque Country (Spain); Departamento de Fisica de Materiales and Centro Mixto CSIC-UPV/EHU, Facultad de Quimicas, UPV/EHU, Apartado 1072, 20080, San Sebastian (Spain)

    2003-11-14

    In early work, March and Murray gave a perturbation theory of the Dirac density matrix {gamma}(r, r') generated by a localized potential V(r) embedded in an initially uniform Fermi gas to all orders in V(r). For potentials sufficiently slowly varying in space, they summed the resulting series for r' = r to regain the Thomas-Fermi density {rho}(r) {proportional_to} [{mu} - V(r)]{sup 3/2}, with {mu} the chemical potential of the Fermi gas. For an admittedly simplistic repulsive central potential V(r) = vertical bar A vertical bar exp(-cr), it is first shown here that what amounts to the sum of the March-Murray series for the s-wave (only) contribution to the density, namely {rho}{sub s}(r, {mu}), can be obtained in closed form. Furthermore, for specific numerical values of A and c in this exponential potential, the long-range behaviour of {rho}{sub s}(r, {mu}) is related to the zero-potential form of March and Murray, which merely suffers a {mu}-dependent phase shift. This result is interpreted in relation to the recent high density screening theorem of Zaremba, Nagy and Echenique. A brief discussion of excess electrical resistivity caused by nonlinear scattering in a Fermi gas is added; this now involves an off-diagonal local density of states. Finally, for periodic lattices, contact is made with the quantum-mechanical defect centre models of Koster and Slater (1954 Phys. Rev. 96 1208) and of Beeby (1967 Proc. R. Soc. A 302 113), and also with the semiclassical approximation of Friedel (1954 Adv. Phys. 3 446). In appendices, solvable low-dimensional models are briefly summarized.

  11. Robust methods and asymptotic theory in nonlinear econometrics

    CERN Document Server

    Bierens, Herman J

    1981-01-01

    This Lecture Note deals with asymptotic properties, i.e. weak and strong consistency and asymptotic normality, of parameter estimators of nonlinear regression models and nonlinear structural equations under various assumptions on the distribution of the data. The estimation methods involved are nonlinear least squares estimation (NLLSE), nonlinear robust M-estimation (NLRME) and non­ linear weighted robust M-estimation (NLWRME) for the regression case and nonlinear two-stage least squares estimation (NL2SLSE) and a new method called minimum information estimation (MIE) for the case of structural equations. The asymptotic properties of the NLLSE and the two robust M-estimation methods are derived from further elaborations of results of Jennrich. Special attention is payed to the comparison of the asymptotic efficiency of NLLSE and NLRME. It is shown that if the tails of the error distribution are fatter than those of the normal distribution NLRME is more efficient than NLLSE. The NLWRME method is appropriate ...

  12. Dynamics of Nonlinear Time-Delay Systems

    CERN Document Server

    Lakshmanan, Muthusamy

    2010-01-01

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

  13. Control of self-organizing nonlinear systems

    CERN Document Server

    Klapp, Sabine; Hövel, Philipp

    2016-01-01

    The book summarizes the state-of-the-art of research on control of self-organizing nonlinear systems with contributions from leading international experts in the field. The first focus concerns recent methodological developments including control of networks and of noisy and time-delayed systems. As a second focus, the book features emerging concepts of application including control of quantum systems, soft condensed matter, and biological systems. Special topics reflecting the active research in the field are the analysis and control of chimera states in classical networks and in quantum systems, the mathematical treatment of multiscale systems, the control of colloidal and quantum transport, the control of epidemics and of neural network dynamics.

  14. 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

  15. 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.

  16. Applied systems theory

    CERN Document Server

    Dekkers, Rob

    2014-01-01

    Offering an up-to-date account of systems theories and its applications, this book provides a different way of resolving problems and addressing challenges in a swift and practical way, without losing overview and not having a grip on the details. From this perspective, it offers a different way of thinking in order to incorporate different perspectives and to consider multiple aspects of any given problem. Drawing examples from a wide range of disciplines, it also presents worked cases to illustrate the principles. The multidisciplinary perspective and the formal approach to modelling of syst

  17. Origin of soft limits from nonlinear supersymmetry in Volkov-Akulov theory

    Energy Technology Data Exchange (ETDEWEB)

    Kallosh, Renata; Karlsson, Anna; Murli, Divyanshu [Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, Stanford, CA 94305 (United States)

    2017-03-15

    We apply the background field technique, recently developed for a general class of nonlinear symmetries, at tree level, to the Volkov-Akulov theory with spontaneously broken N=1 supersymmetry. We find that the background field expansion in terms of the free fields to the lowest order reproduces the nonlinear supersymmetry transformation rules. The double soft limit of the background field is, in agreement with the new general identities, defined by the algebra of the nonlinear symmetries.

  18. Exactly and completely integrable nonlinear dynamical systems

    International Nuclear Information System (INIS)

    Leznov, A.N.; Savel'ev, M.V.

    1987-01-01

    The survey is devoted to a consitent exposition of the group-algebraic methods for the integration of systems of nonlinear partial differential equations possessing a nontrivial internal symmetry algebra. Samples of exactly and completely integrable wave and evolution equations are considered in detail, including generalized (periodic and finite nonperiodic Toda lattice, nonlinear Schroedinger, Korteweg-de Vries, Lotka-Volterra equations, etc.) For exactly integrable systems the general solutions of the Cauchy and Goursat problems are given in an explicit form, while for completely integrable systems an effective method for the construction of their soliton solutions is developed. Application of the developed methods to a differential geometry problem of classification of the integrable manifolds embeddings is discussed. For exactly integrable systems the supersymmetric extensions are constructed. By the example of the generalized Toda lattice a quantization scheme is developed. It includes an explicit derivation of the corresponding Heisenberg operators and their desription in terms of the quantum algebras of the Hopf type. Among multidimensional systems the four-dimensional self-dual Yang-Mills equations are investigated most attentively with a goal of constructing their general solutions

  19. Geometrical phases from global gauge invariance of nonlinear classical field theories

    International Nuclear Information System (INIS)

    Garrison, J.C.; Chiao, R.Y.

    1988-01-01

    We show that the geometrical phases recently discovered in quantum mechanics also occur naturally in the theory of any classical complex multicomponent field satisfying nonlinear equations derived from a Lagrangean with is invariant under gauge transformations of the first kind. Some examples are the paraxial wave equation for nonlinear optics, and Ginzburg-Landau equations for complex order parameters in condensed-matter physics

  20. Kinetic theory of nonlinear transport phenomena in complex plasmas

    International Nuclear Information System (INIS)

    Mishra, S. K.; Sodha, M. S.

    2013-01-01

    In contrast to the prevalent use of the phenomenological theory of transport phenomena, a number of transport properties of complex plasmas have been evaluated by using appropriate expressions, available from the kinetic theory, which are based on Boltzmann's transfer equation; in particular, the energy dependence of the electron collision frequency has been taken into account. Following the recent trend, the number and energy balance of all the constituents of the complex plasma and the charge balance on the particles is accounted for; the Ohmic loss has also been included in the energy balance of the electrons. The charging kinetics for the complex plasma comprising of uniformly dispersed dust particles, characterized by (i) uniform size and (ii) the Mathis, Rumpl, and Nordsieck power law of size distribution has been developed. Using appropriate expressions for the transport parameters based on the kinetic theory, the system of equations has been solved to investigate the parametric dependence of the complex plasma transport properties on the applied electric field and other plasma parameters; the results are graphically illustrated.

  1. Non-linear electrodynamics in Kaluza-Klein theory

    International Nuclear Information System (INIS)

    Kerner, R.

    1987-01-01

    The most general variational principle based on the invariants of the Riemann tensor and leading to the second order differential equations should contain, in dimensions higher than four, the invariants of the Gauss-Bonnet type. In five dimensions the lagrangian should be a linear combination of the scalar curvature and the second-order invariant. The equations of the electromagnetic field are derived in the absence of scalar and gravitational fields of the Kaluza-Klein model. They yield the unique extension of Maxwell's system in the Kaluza-Klein theory. Some properties of eventual solutions are discussed [fr

  2. Finding a nonlinear lattice with improved integrability using Lie transform perturbation theory

    International Nuclear Information System (INIS)

    Sonnad, Kiran G.; Cary, John R.

    2004-01-01

    A condition for improved dynamic aperture for nonlinear, alternating gradient transport systems is derived using Lie transform perturbation theory. The Lie transform perturbation method is used here to perform averaging over fast oscillations by canonically transforming to slowly oscillating variables. This is first demonstrated for a linear sinusoidal focusing system. This method is then employed to average the dynamics over a lattice period for a nonlinear focusing system, provided by the use of higher order poles such as sextupoles and octupoles along with alternate gradient quadrupoles. Unlike the traditional approach, the higher order focusing is not treated as a perturbation. The Lie transform method is particularly advantageous for such a system where the form of the Hamiltonian is complex. This is because the method exploits the property of canonical invariance of Poisson brackets so that the change of variables is accomplished by just replacing the old ones with the new. The analysis shows the existence of a condition in which the system is azimuthally symmetric in the transformed, slowly oscillating frame. Such a symmetry in the time averaged frame renders the system nearly integrable in the laboratory frame. This condition leads to reduced chaos and improved confinement when compared to a system that is not close to integrability. Numerical calculations of single-particle trajectories and phase space projections of the dynamic aperture performed for a lattice with quadrupoles and sextupoles confirm that this is indeed the case

  3. Perturbation methods and closure approximations in nonlinear systems

    International Nuclear Information System (INIS)

    Dubin, D.H.E.

    1984-01-01

    In the first section of this thesis, Hamiltonian theories of guiding center and gyro-center motion are developed using modern symplectic methods and Lie transformations. Littlejohn's techniques, combined with the theory of resonant interaction and island overlap, are used to explore the problem of adiabatic invariance and onset of stochasticity. As an example, the breakdown of invariance due to resonance between drift motion and gyromotion in a tokamak is considered. A Hamiltonian is developed for motion in a straight magnetic field with electrostatic perturbations in the gyrokinetic ordering, from which nonlinear gyrokinetic equations are constructed which have the property of phase-space preservation, useful for computer simulation. Energy invariants are found and various limits of the equations are considered. In the second section, statistical closure theories are applied to simple dynamical systems. The logistic map is used as an example because of its universal properties and simple quadratic nonlinearity. The first closure considered is the direct interaction approximation of Kraichnan, which is found to fail when applied to the logistic map because it cannot approximate the bounded support of the map's equilibrium distribution. By imposing a periodically constraint on a Langevin form of the DIA a new stable closure is developed

  4. Seismic analysis of a nonlinear airlock system

    International Nuclear Information System (INIS)

    Huang, S.N.

    1983-01-01

    The containment equipment airlock door of the Fast Flux Test Facility utilizes screw-type actuators as a push-pull mechanism for closing and opening operations. Special design features were used to protect these actuators from pressure differential loading. These made the door behave as a nonlinear system during a seismic event. Seismic analyses, utilizing the time history method, were conducted to determine the seismic loads on these scew-type actuators. Several sizes of actuators were examined. Procedures for determining the final optimum design are discussed in detail

  5. An efficient control algorithm for nonlinear systems

    International Nuclear Information System (INIS)

    Sinha, S.

    1990-12-01

    We suggest a scheme to step up the efficiency of a recently proposed adaptive control algorithm, which is remarkably effective for regulating nonlinear systems. The technique involves monitoring of the ''stiffness of control'' to get maximum gain while maintaining a predetermined accuracy. The success of the procedure is demonstrated for the case of the logistic map, where we show that the improvement in performance is often factors of tens, and for small control stiffness, even factors of hundreds. (author). 4 refs, 1 fig., 1 tab

  6. Neural networks for feedback feedforward nonlinear control systems.

    Science.gov (United States)

    Parisini, T; Zoppoli, R

    1994-01-01

    This paper deals with the problem of designing feedback feedforward control strategies to drive the state of a dynamic system (in general, nonlinear) so as to track any desired trajectory joining the points of given compact sets, while minimizing a certain cost function (in general, nonquadratic). Due to the generality of the problem, conventional methods are difficult to apply. Thus, an approximate solution is sought by constraining control strategies to take on the structure of multilayer feedforward neural networks. After discussing the approximation properties of neural control strategies, a particular neural architecture is presented, which is based on what has been called the "linear-structure preserving principle". The original functional problem is then reduced to a nonlinear programming one, and backpropagation is applied to derive the optimal values of the synaptic weights. Recursive equations to compute the gradient components are presented, which generalize the classical adjoint system equations of N-stage optimal control theory. Simulation results related to nonlinear nonquadratic problems show the effectiveness of the proposed method.

  7. Nonlinear Hamiltonian mechanics applied to molecular dynamics theory and computational methods for understanding molecular spectroscopy and chemical reactions

    CERN Document Server

    Farantos, Stavros C

    2014-01-01

    This brief presents numerical methods for describing and calculating invariant phase space structures, as well as solving the classical and quantum equations of motion for polyatomic molecules. Examples covered include simple model systems to realistic cases of molecules spectroscopically studied. Vibrationally excited and reacting molecules are nonlinear dynamical systems, and thus, nonlinear mechanics is the proper theory to elucidate molecular dynamics by investigating invariant structures in phase space. Intramolecular energy transfer, and the breaking and forming of a chemical bond have now found a rigorous explanation by studying phase space structures.

  8. The Volterra's integral equation theory for accelerator single-freedom nonlinear components

    International Nuclear Information System (INIS)

    Wang Sheng; Xie Xi

    1996-01-01

    The Volterra's integral equation equivalent to the dynamic equation of accelerator single-freedom nonlinear components is given, starting from which the transport operator of accelerator single-freedom nonlinear components and its inverse transport operator are obtained. Therefore, another algorithm for the expert system of the beam transport operator of accelerator single-freedom nonlinear components is developed

  9. Computer Simulation of Hydraulic Systems with Typical Nonlinear Characteristics

    Directory of Open Access Journals (Sweden)

    D. N. Popov

    2017-01-01

    Full Text Available The task was to synthesise an adjustable hydraulic system structure, the mathematical model of which takes into account its inherent nonlinearity. Its solution suggests using a successive computer simulations starting with a structure of the linearized stable hydraulic system, which is then complicated by including the essentially non-linear elements. The hydraulic system thus obtained may be unable to meet the Lyapunov stability criterion and be unstable. This can be eliminated through correcting elements. Control of correction results is provided according to the form of transition processes due to stepwise variation of the control signal.Computer simulation of a throttle-controlled electrohydraulic servo drive with the rotary output element illustrates the proposed method application. A constant pressure power source provides fluid feed for the drive under pressure.For drive simulation the following models were involved: the linear model, the model taking into consideration a non-linearity of the flow-dynamic characteristics of a spool-type valve, and the non-linear models that take into account the dry friction in the spool-type valve, the backlash in the steering angle sensor of the motor shaft.The paper shows possibility of damping oscillation caused by variable hydrodynamic forces through introducing a correction device.The list of references attached contains 16 sources, which were used to justify and explain certain factors of the automatic control theory and the fluid mechanics of unsteady flows.The article presents 6 block-diagrams of the electrohydraulic servo drive and their appropriate transition processes, which have been studied.

  10. Impulse position control algorithms for nonlinear systems

    Energy Technology Data Exchange (ETDEWEB)

    Sesekin, A. N., E-mail: sesekin@list.ru [Ural Federal University, 19 S. Mira, Ekaterinburg, 620002 (Russian Federation); Institute of Mathematics and Mechanics, Ural Division of Russian Academy of Sciences, 16 S. Kovalevskaya, Ekaterinburg, 620990 (Russian Federation); Nepp, A. N., E-mail: anepp@urfu.ru [Ural Federal University, 19 S. Mira, Ekaterinburg, 620002 (Russian Federation)

    2015-11-30

    The article is devoted to the formalization and description of impulse-sliding regime in nonlinear dynamical systems that arise in the application of impulse position controls of a special kind. The concept of trajectory impulse-sliding regime formalized as some limiting network element Euler polygons generated by a discrete approximation of the impulse position control This paper differs from the previously published papers in that it uses a definition of solutions of systems with impulse controls, it based on the closure of the set of smooth solutions in the space of functions of bounded variation. The need for the study of such regimes is the fact that they often arise when parry disturbances acting on technical or economic control system.

  11. Impulse position control algorithms for nonlinear systems

    Science.gov (United States)

    Sesekin, A. N.; Nepp, A. N.

    2015-11-01

    The article is devoted to the formalization and description of impulse-sliding regime in nonlinear dynamical systems that arise in the application of impulse position controls of a special kind. The concept of trajectory impulse-sliding regime formalized as some limiting network element Euler polygons generated by a discrete approximation of the impulse position control This paper differs from the previously published papers in that it uses a definition of solutions of systems with impulse controls, it based on the closure of the set of smooth solutions in the space of functions of bounded variation. The need for the study of such regimes is the fact that they often arise when parry disturbances acting on technical or economic control system.

  12. MPPT for Photovoltaic System Using Nonlinear Controller

    Directory of Open Access Journals (Sweden)

    Ramsha Iftikhar

    2018-01-01

    Full Text Available Photovoltaic (PV system generates energy that varies with the variation in environmental conditions such as temperature and solar radiation. To cope up with the ever increasing demand of energy, the PV system must operate at maximum power point (MPP, which changes with load as well as weather conditions. This paper proposes a nonlinear backstepping controller to harvest maximum power from a PV array using DC-DC buck converter. A regression plane is formulated after collecting the data of the PV array from its characteristic curves to provide the reference voltage to track MPP. Asymptotic stability of the system is proved using Lyapunov stability criteria. The simulation results validate the rapid tracking and efficient performance of the controller. For further validation of the results, it also provides a comparison of the proposed controller with conventional perturb and observe (P&O and fuzzy logic-based controller (FLBC under abrupt changes in environmental conditions.

  13. 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.

  14. Information Dynamics of a Nonlinear Stochastic Nanopore System

    Directory of Open Access Journals (Sweden)

    Claire Gilpin

    2018-03-01

    Full Text Available Nanopores have become a subject of interest in the scientific community due to their potential uses in nanometer-scale laboratory and research applications, including infectious disease diagnostics and DNA sequencing. Additionally, they display behavioral similarity to molecular and cellular scale physiological processes. Recent advances in information theory have made it possible to probe the information dynamics of nonlinear stochastic dynamical systems, such as autonomously fluctuating nanopore systems, which has enhanced our understanding of the physical systems they model. We present the results of local (LER and specific entropy rate (SER computations from a simulation study of an autonomously fluctuating nanopore system. We learn that both metrics show increases that correspond to fluctuations in the nanopore current, indicating fundamental changes in information generation surrounding these fluctuations.

  15. 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.

  16. An Asymptotic Derivation of Weakly Nonlinear Ray Theory

    Indian Academy of Sciences (India)

    The transport equation for the amplitude has been deduced with an error (2) where is the small parameter appearing in the high frequency approximation. On a length scale over which Choquet–Bruhat's theory is valid, this theory reduces to the former. The theory is valid on a much larger length scale and the leading ...

  17. Fuzzy Stabilization for Nonlinear Discrete Ship Steering Stochastic Systems Subject to State Variance and Passivity Constraints

    Directory of Open Access Journals (Sweden)

    Wen-Jer Chang

    2014-01-01

    Full Text Available For nonlinear discrete-time stochastic systems, a fuzzy controller design methodology is developed in this paper subject to state variance constraint and passivity constraint. According to fuzzy model based control technique, the nonlinear discrete-time stochastic systems considered in this paper are represented by the discrete-time Takagi-Sugeno fuzzy models with multiplicative noise. Employing Lyapunov stability theory, upper bound covariance control theory, and passivity theory, some sufficient conditions are derived to find parallel distributed compensation based fuzzy controllers. In order to solve these sufficient conditions, an iterative linear matrix inequality algorithm is applied based on the linear matrix inequality technique. Finally, the fuzzy stabilization problem for nonlinear discrete ship steering stochastic systems is investigated in the numerical example to illustrate the feasibility and validity of proposed fuzzy controller design method.

  18. Euclidean null controllability of nonlinear infinite delay systems with ...

    African Journals Online (AJOL)

    Sufficient conditions for the Euclidean null controllability of non-linear delay systems with time varying multiple delays in the control and implicit derivative are derived. If the uncontrolled system is uniformly asymptotically stable and if the control system is controllable, then the non-linear infinite delay system is Euclidean null ...

  19. Non-linear σ-models and string theories

    International Nuclear Information System (INIS)

    Sen, A.

    1986-10-01

    The connection between σ-models and string theories is discussed, as well as how the σ-models can be used as tools to prove various results in string theories. Closed bosonic string theory in the light cone gauge is very briefly introduced. Then, closed bosonic string theory in the presence of massless background fields is discussed. The light cone gauge is used, and it is shown that in order to obtain a Lorentz invariant theory, the string theory in the presence of background fields must be described by a two-dimensional conformally invariant theory. The resulting constraints on the background fields are found to be the equations of motion of the string theory. The analysis is extended to the case of the heterotic string theory and the superstring theory in the presence of the massless background fields. It is then shown how to use these results to obtain nontrivial solutions to the string field equations. Another application of these results is shown, namely to prove that the effective cosmological constant after compactification vanishes as a consequence of the classical equations of motion of the string theory. 34 refs

  20. Model-based nonlinear control of hydraulic servo systems: Challenges, developments and perspectives

    Science.gov (United States)

    Yao, Jianyong

    2018-06-01

    Hydraulic servo system plays a significant role in industries, and usually acts as a core point in control and power transmission. Although linear theory-based control methods have been well established, advanced controller design methods for hydraulic servo system to achieve high performance is still an unending pursuit along with the development of modern industry. Essential nonlinearity is a unique feature and makes model-based nonlinear control more attractive, due to benefit from prior knowledge of the servo valve controlled hydraulic system. In this paper, a discussion for challenges in model-based nonlinear control, latest developments and brief perspectives of hydraulic servo systems are presented: Modelling uncertainty in hydraulic system is a major challenge, which includes parametric uncertainty and time-varying disturbance; some specific requirements also arise ad hoc difficulties such as nonlinear friction during low velocity tracking, severe disturbance, periodic disturbance, etc.; to handle various challenges, nonlinear solutions including parameter adaptation, nonlinear robust control, state and disturbance observation, backstepping design and so on, are proposed and integrated, theoretical analysis and lots of applications reveal their powerful capability to solve pertinent problems; and at the end, some perspectives and associated research topics (measurement noise, constraints, inner valve dynamics, input nonlinearity, etc.) in nonlinear hydraulic servo control are briefly explored and discussed.

  1. Information systems theory

    CERN Document Server

    Dwivedi, Yogesh K; Schneberger, Scott L

    2011-01-01

    The overall mission of this book is to provide a comprehensive understanding and coverage of the various theories and models used in IS research. Specifically, it aims to focus on the following key objectives: To describe the various theories and models applicable to studying IS/IT management issues. To outline and describe, for each of the various theories and models, independent and dependent constructs, reference discipline/originating area, originating author(s), seminal articles, level of analysis (i.e. firm, individual, industry) and links with other theories. To provide a critical revie

  2. Expert system for accelerator single-freedom nonlinear components

    International Nuclear Information System (INIS)

    Wang Sheng; Xie Xi; Liu Chunliang

    1995-01-01

    An expert system by Arity Prolog is developed for accelerator single-freedom nonlinear components. It automatically yields any order approximate analytical solutions for various accelerator single-freedom nonlinear components. As an example, the eighth order approximate analytical solution is derived by this expert system for a general accelerator single-freedom nonlinear component, showing that the design of the expert system is successful

  3. Complexity, Chaos, and Nonlinear Dynamics: A New Perspective on Career Development Theory

    Science.gov (United States)

    Bloch, Deborah P.

    2005-01-01

    The author presents a theory of career development drawing on nonlinear dynamics and chaos and complexity theories. Career is presented as a complex adaptive entity, a fractal of the human entity. Characteristics of complex adaptive entities, including (a) autopiesis, or self-regeneration; (b) open exchange; (c) participation in networks; (d)…

  4. Non-Linear Wave Loads and Ship responses by a time-domain Strip Theory

    DEFF Research Database (Denmark)

    Xia, Jinzhu; Wang, Zhaohui; Jensen, Jørgen Juncher

    1998-01-01

    . Based on this time-domain strip theory, an efficient non-linear hyroelastic method of wave- and slamming-induced vertical motions and structural responses of ships is developed, where the structure is represented by the Timoshenko beam theory. Numerical calculations are presented for the S175...

  5. A nonlinear theory for elastic plates with application to characterizing paper properties

    Science.gov (United States)

    M. W. Johnson; Thomas J. Urbanik

    1984-03-01

    A theory of thin plates which is physically as well as kinematically nonlinear is, developed and used to characterize elastic material behavior for arbitrary stretching and bending deformations. It is developed from a few clearly defined assumptions and uses a unique treatment of strain energy. An effective strain concept is introduced to simplify the theory to a...

  6. Distributed Fault Detection for a Class of Nonlinear Stochastic Systems

    Directory of Open Access Journals (Sweden)

    Bingyong Yan

    2014-01-01

    Full Text Available A novel distributed fault detection strategy for a class of nonlinear stochastic systems is presented. Different from the existing design procedures for fault detection, a novel fault detection observer, which consists of a nonlinear fault detection filter and a consensus filter, is proposed to detect the nonlinear stochastic systems faults. Firstly, the outputs of the nonlinear stochastic systems act as inputs of a consensus filter. Secondly, a nonlinear fault detection filter is constructed to provide estimation of unmeasurable system states and residual signals using outputs of the consensus filter. Stability analysis of the consensus filter is rigorously investigated. Meanwhile, the design procedures of the nonlinear fault detection filter are given in terms of linear matrix inequalities (LMIs. Taking the influence of the system stochastic noises into consideration, an outstanding feature of the proposed scheme is that false alarms can be reduced dramatically. Finally, simulation results are provided to show the feasibility and effectiveness of the proposed fault detection approach.

  7. An overview of adaptive model theory: solving the problems of redundancy, resources, and nonlinear interactions in human movement control.

    Science.gov (United States)

    Neilson, Peter D; Neilson, Megan D

    2005-09-01

    Adaptive model theory (AMT) is a computational theory that addresses the difficult control problem posed by the musculoskeletal system in interaction with the environment. It proposes that the nervous system creates motor maps and task-dependent synergies to solve the problems of redundancy and limited central resources. These lead to the adaptive formation of task-dependent feedback/feedforward controllers able to generate stable, noninteractive control and render nonlinear interactions unobservable in sensory-motor relationships. AMT offers a unified account of how the nervous system might achieve these solutions by forming internal models. This is presented as the design of a simulator consisting of neural adaptive filters based on cerebellar circuitry. It incorporates a new network module that adaptively models (in real time) nonlinear relationships between inputs with changing and uncertain spectral and amplitude probability density functions as is the case for sensory and motor signals.

  8. Computational Models for Nonlinear Aeroelastic Systems, Phase II

    Data.gov (United States)

    National Aeronautics and Space Administration — Clear Science Corp. and Duke University propose to develop and demonstrate new and efficient computational methods of modeling nonlinear aeroelastic systems. The...

  9. Model Updating Nonlinear System Identification Toolbox, Phase II

    Data.gov (United States)

    National Aeronautics and Space Administration — ZONA Technology (ZONA) proposes to develop an enhanced model updating nonlinear system identification (MUNSID) methodology that utilizes flight data with...

  10. Bifurcations and Patterns in Nonlinear Dissipative Systems

    Energy Technology Data Exchange (ETDEWEB)

    Guenter Ahlers

    2005-05-27

    This project consists of experimental investigations of heat transport, pattern formation, and bifurcation phenomena in non-linear non-equilibrium fluid-mechanical systems. These issues are studies in Rayleigh-B\\'enard convection, using both pure and multicomponent fluids. They are of fundamental scientific interest, but also play an important role in engineering, materials science, ecology, meteorology, geophysics, and astrophysics. For instance, various forms of convection are important in such diverse phenomena as crystal growth from a melt with or without impurities, energy production in solar ponds, flow in the earth's mantle and outer core, geo-thermal stratifications, and various oceanographic and atmospheric phenomena. Our work utilizes computer-enhanced shadowgraph imaging of flow patterns, sophisticated digital image analysis, and high-resolution heat transport measurements.

  11. Adaptive H∞ synchronization of chaotic systems via linear and nonlinear feedback control

    International Nuclear Information System (INIS)

    Fu Shi-Hui; Lu Qi-Shao; Du Ying

    2012-01-01

    Adaptive H ∞ synchronization of chaotic systems via linear and nonlinear feedback control is investigated. The chaotic systems are redesigned by using the generalized Hamiltonian systems and observer approach. Based on Lyapunov's stability theory, linear and nonlinear feedback control of adaptive H ∞ synchronization is established in order to not only guarantee stable synchronization of both master and slave systems but also reduce the effect of external disturbance on an H ∞ -norm constraint. Adaptive H ∞ synchronization of chaotic systems via three kinds of control is investigated with applications to Lorenz and Chen systems. Numerical simulations are also given to identify the effectiveness of the theoretical analysis. (general)

  12. Nonlinear observer design for a nonlinear string/cable FEM model using contraction theory

    DEFF Research Database (Denmark)

    Turkyilmaz, Yilmaz; Jouffroy, Jerome; Egeland, Olav

    model is presented in the form of partial differential equations (PDE). Galerkin's method is then applied to obtain a set of ordinary differential equations such that the cable model is approximated by a FEM model. Based on the FEM model, a nonlinear observer is designed to estimate the cable...

  13. Nonlinear decentralized robust governor control for hydroturbine-generator sets in multi-machine power systems

    Energy Technology Data Exchange (ETDEWEB)

    Qiang Lu; Yusong Sun; Yuanzhang Sun [Tsinghua University, Beijing (China). Dept. of Electrical Engineering; Felix F Wu; Yixin Ni [University of Hong Kong (China). Dept. of Electrical and Electronic Engineering; Yokoyama, Akihiko [University of Tokyo (Japan). Dept. of Electrical Engineering; Goto, Masuo; Konishi, Hiroo [Hitachi Ltd., Tokyo (Japan). Power System Div.

    2004-06-01

    A novel nonlinear decentralized robust governor control for hydroturbine-generator sets in multi-machine power systems is suggested in this paper. The nonelastic water hammer effect and disturbances are considered in the modeling. The advanced differential geometry theory, nonlinear robust control theory and the dynamic feedback method are combined to solve the problem. The nonlinear decentralized robust control law for the speed governor of hydroturbine-generators has been derived. The input signals to the proposed controller are all local measurements and independent to the system parameters. The derived control law guarantees the integrated system stability with disturbance attenuation, which is significant to the real power system application. Computer tests on an 8-machine, 36-bus power system show clearly the effectiveness of the new control strategy in transient stability enhancement and disturbance attenuation. The computer test results based on the suggested controller are compared favorably with those based on the conventional linear governor control. (author)

  14. Nonlinear analysis of a reaction-diffusion system: Amplitude equations

    Energy Technology Data Exchange (ETDEWEB)

    Zemskov, E. P., E-mail: zemskov@ccas.ru [Russian Academy of Sciences, Dorodnicyn Computing Center (Russian Federation)

    2012-10-15

    A reaction-diffusion system with a nonlinear diffusion term is considered. Based on nonlinear analysis, the amplitude equations are obtained in the cases of the Hopf and Turing instabilities in the system. Turing pattern-forming regions in the parameter space are determined for supercritical and subcritical instabilities in a two-component reaction-diffusion system.

  15. Adaptive projective synchronization of different chaotic systems with nonlinearity inputs

    International Nuclear Information System (INIS)

    Niu Yu-Jun; Pei Bing-Nan; Wang Xing-Yuan

    2012-01-01

    We investigate the projective synchronization of different chaotic systems with nonlinearity inputs. Based on the adaptive technique, sliding mode control method and pole assignment technique, a novel adaptive projective synchronization scheme is proposed to ensure the drive system and the response system with nonlinearity inputs can be rapidly synchronized up to the given scaling factor. (general)

  16. A new active absorption system and its performance to linear and non-linear waves

    DEFF Research Database (Denmark)

    Andersen, Thomas Lykke; Clavero, M.; Frigaard, Peter Bak

    2016-01-01

    Highlights •An active absorption system for wavemakers has been developed. •The theory for flush mounted gauges has been extended to cover also small gaps. •The new system has been validated in a wave flume with wavemakers in both ends. •A generation and absorption procedure for highly non-linear...

  17. Global output feedback stabilisation of stochastic high-order feedforward nonlinear systems with time-delay

    Science.gov (United States)

    Zhang, Kemei; Zhao, Cong-Ran; Xie, Xue-Jun

    2015-12-01

    This paper considers the problem of output feedback stabilisation for stochastic high-order feedforward nonlinear systems with time-varying delay. By using the homogeneous domination theory and solving several troublesome obstacles in the design and analysis, an output feedback controller is constructed to drive the closed-loop system globally asymptotically stable in probability.

  18. Nonlinear Disturbance Attenuation Controller for Turbo-Generators in Power Systems via Recursive Design

    NARCIS (Netherlands)

    Cao, M.; Shen, T.L.; Song, Y.H.; Mei, S.W.

    2002-01-01

    The paper proposes a nonlinear robust controller for steam governor control in power systems. Based on dissipation theory, an innovative recursive design method is presented to construct the storage function of single machine infinite bus (SMIB) and multi-machine power systems. Furthermore, the

  19. Right-invertibility for a class of nonlinear control systems: A geometric approach

    NARCIS (Netherlands)

    Nijmeijer, Henk

    1986-01-01

    In recent years it has become evident that various synthesis problems known from linear system theory can also be solved for nonlinear control systems by using differential geometric methods. The purpose of this paper is to use this mathematical framework for giving a preliminary account on the

  20. Application of the comparison principle to analysis of nonlinear systems. [using Lipschitz condition and differential equations

    Science.gov (United States)

    Gunderson, R. W.

    1975-01-01

    A comparison principle based on a Kamke theorem and Lipschitz conditions is presented along with its possible applications and modifications. It is shown that the comparison lemma can be used in the study of such areas as classical stability theory, higher order trajectory derivatives, Liapunov functions, boundary value problems, approximate dynamic systems, linear and nonlinear systems, and bifurcation analysis.

  1. Nonlinear feedback synchronisation control between fractional-order and integer-order chaotic systems

    International Nuclear Information System (INIS)

    Jia Li-Xin; Dai Hao; Hui Meng

    2010-01-01

    This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems. Based on Lyapunov stability theory and numerical differentiation, a nonlinear feedback controller is obtained to achieve the synchronisation between fractional-order and integer-order chaotic systems. Numerical simulation results are presented to illustrate the effectiveness of this method

  2. 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)

  3. Spatial nonlinearities: Cascading effects in the earth system

    Science.gov (United States)

    Peters, Debra P.C.; Pielke, R.A.; Bestelmeyer, B.T.; Allen, Craig D.; Munson-McGee, Stuart; Havstad, K. M.; Canadell, Josep G.; Pataki, Diane E.; Pitelka, Louis F.

    2006-01-01

    Nonlinear behavior is prevalent in all aspects of the Earth System, including ecological responses to global change (Gallagher and Appenzeller 1999; Steffen et al. 2004). Nonlinear behavior refers to a large, discontinuous change in response to a small change in a driving variable (Rial et al. 2004). In contrast to linear systems where responses are smooth, well-behaved, continuous functions, nonlinear systems often undergo sharp or discontinuous transitions resulting from the crossing of thresholds. These nonlinear responses can result in surprising behavior that makes forecasting difficult (Kaplan and Glass 1995). Given that many system dynamics are nonlinear, it is imperative that conceptual and quantitative tools be developed to increase our understanding of the processes leading to nonlinear behavior in order to determine if forecasting can be improved under future environmental changes (Clark et al. 2001).

  4. New solutions of a nonlinear classical field theory

    International Nuclear Information System (INIS)

    Marques, G.C.; Ventura, I.

    1975-01-01

    New solutions of a relativistic, classical, field theoretical model having logarithmic nonlinearities are obtained. Some of these solutions correspond to field not bounded in time but having finite energy and charge. There are no bounded solutions (bound states and resonances in particular) if the charge exceeds a certain value. This effect is due to the existance of a 'charge barrier' in this field theoretical model. All calculations are performed in a number of spatial dimensions [pt

  5. Nonlinear time series theory, methods and applications with R examples

    CERN Document Server

    Douc, Randal; Stoffer, David

    2014-01-01

    FOUNDATIONSLinear ModelsStochastic Processes The Covariance World Linear Processes The Multivariate Cases Numerical Examples ExercisesLinear Gaussian State Space Models Model Basics Filtering, Smoothing, and Forecasting Maximum Likelihood Estimation Smoothing Splines and the Kalman Smoother Asymptotic Distribution of the MLE Missing Data Modifications Structural Component Models State-Space Models with Correlated Errors Exercises Beyond Linear ModelsNonlinear Non-Gaussian Data Volterra Series Expansion Cumulants and Higher-Order Spectra Bilinear Models Conditionally Heteroscedastic Models Thre

  6. Practical application of equivalent linearization approaches to nonlinear piping systems

    International Nuclear Information System (INIS)

    Park, Y.J.; Hofmayer, C.H.

    1995-01-01

    The use of mechanical energy absorbers as an alternative to conventional hydraulic and mechanical snubbers for piping supports has attracted a wide interest among researchers and practitioners in the nuclear industry. The basic design concept of energy absorbers (EA) is to dissipate the vibration energy of piping systems through nonlinear hysteretic actions of EA exclamation point s under design seismic loads. Therefore, some type of nonlinear analysis needs to be performed in the seismic design of piping systems with EA supports. The equivalent linearization approach (ELA) can be a practical analysis tool for this purpose, particularly when the response approach (RSA) is also incorporated in the analysis formulations. In this paper, the following ELA/RSA methods are presented and compared to each other regarding their practice and numerical accuracy: Response approach using the square root of sum of squares (SRSS) approximation (denoted RS in this paper). Classical ELA based on modal combinations and linear random vibration theory (denoted CELA in this paper). Stochastic ELA based on direct solution of response covariance matrix (denoted SELA in this paper). New algorithms to convert response spectra to the equivalent power spectral density (PSD) functions are presented for both the above CELA and SELA methods. The numerical accuracy of the three EL are studied through a parametric error analysis. Finally, the practicality of the presented analysis is demonstrated in two application examples for piping systems with EA supports

  7. Data-Driven H∞ Control for Nonlinear Distributed Parameter Systems.

    Science.gov (United States)

    Luo, Biao; Huang, Tingwen; Wu, Huai-Ning; Yang, Xiong

    2015-11-01

    The data-driven H∞ control problem of nonlinear distributed parameter systems is considered in this paper. An off-policy learning method is developed to learn the H∞ control policy from real system data rather than the mathematical model. First, Karhunen-Loève decomposition is used to compute the empirical eigenfunctions, which are then employed to derive a reduced-order model (ROM) of slow subsystem based on the singular perturbation theory. The H∞ control problem is reformulated based on the ROM, which can be transformed to solve the Hamilton-Jacobi-Isaacs (HJI) equation, theoretically. To learn the solution of the HJI equation from real system data, a data-driven off-policy learning approach is proposed based on the simultaneous policy update algorithm and its convergence is proved. For implementation purpose, a neural network (NN)- based action-critic structure is developed, where a critic NN and two action NNs are employed to approximate the value function, control, and disturbance policies, respectively. Subsequently, a least-square NN weight-tuning rule is derived with the method of weighted residuals. Finally, the developed data-driven off-policy learning approach is applied to a nonlinear diffusion-reaction process, and the obtained results demonstrate its effectiveness.

  8. Thermal conductivity in one-dimensional nonlinear systems

    Science.gov (United States)

    Politi, Antonio; Giardinà, Cristian; Livi, Roberto; Vassalli, Massimo

    2000-03-01

    Thermal conducitivity of one-dimensional nonlinear systems typically diverges in the thermodynamic limit, whenever the momentum is conserved (i.e. in the absence of interactions with an external substrate). Evidence comes from detailed studies of Fermi-Pasta-Ulam and diatomic Toda chains. Here, we discuss the first example of a one-dimensional system obeying Fourier law : a chain of coupled rotators. Numerical estimates of the thermal conductivity obtained by simulating a chain in contact with two thermal baths at different temperatures are found to be consistent with those ones based on linear response theory. The dynamics of the Fourier modes provides direct evidence of energy diffusion. The finiteness of the conductivity is traced back to the occurrence of phase-jumps. Our conclusions are confirmed by the analysis of two variants of the rotator model.

  9. From Hamiltonian chaos to complex systems a nonlinear physics approach

    CERN Document Server

    Leonetti, Marc

    2013-01-01

    From Hamiltonian Chaos to Complex Systems: A Nonlinear Physics Approach collects contributions on recent developments in non-linear dynamics and statistical physics with an emphasis on complex systems. This book provides a wide range of state-of-the-art research in these fields. The unifying aspect of this book is a demonstration of how similar tools coming from dynamical systems, nonlinear physics, and statistical dynamics can lead to a large panorama of  research in various fields of physics and beyond, most notably with the perspective of application in complex systems. This book also: Illustrates the broad research influence of tools coming from dynamical systems, nonlinear physics, and statistical dynamics Adopts a pedagogic approach to facilitate understanding by non-specialists and students Presents applications in complex systems Includes 150 illustrations From Hamiltonian Chaos to Complex Systems: A Nonlinear Physics Approach is an ideal book for graduate students and researchers working in applied...

  10. Frequency domain performance analysis of nonlinearly controlled motion systems

    NARCIS (Netherlands)

    Pavlov, A.V.; Wouw, van de N.; Pogromski, A.Y.; Heertjes, M.F.; Nijmeijer, H.

    2007-01-01

    At the heart of the performance analysis of linear motion control systems lie essential frequency domain characteristics such as sensitivity and complementary sensitivity functions. For a class of nonlinear motion control systems called convergent systems, generalized versions of these sensitivity

  11. Information theory of molecular systems

    CERN Document Server

    Nalewajski, Roman F

    2006-01-01

    As well as providing a unified outlook on physics, Information Theory (IT) has numerous applications in chemistry and biology owing to its ability to provide a measure of the entropy/information contained within probability distributions and criteria of their information ""distance"" (similarity) and independence. Information Theory of Molecular Systems applies standard IT to classical problems in the theory of electronic structure and chemical reactivity. The book starts by introducing the basic concepts of modern electronic structure/reactivity theory based upon the Density Functional Theory

  12. Quantization of a non-linearly realized supersymmetric theory

    International Nuclear Information System (INIS)

    Shima, Kazunari

    1976-01-01

    The two-dimensional version of the Volkov-Akulov's Lagrngian, where the super-symmetry is realized non-linearly by means of a single Majorana spinor psi(x), is quantized. The equal time anti-commutators for the field are not c-numbers but functions of the field itself. By the explicite calculation we shall show that supersymmetry charges of the model form the supersymmetry algebra(the graded Lie algebra) and the supersymmetry charges exactly generate a constant translation of psi(x) in the spinor space. In this work we restrict our investigation to the two-dimensional space-time for the sake of simplicity. (auth.)

  13. Nonlinear Theory of Nonparaxial Laser Pulse Propagation in Plasma Channels

    International Nuclear Information System (INIS)

    Esarey, E.; Schroeder, C. B.; Shadwick, B. A.; Wurtele, J. S.; Leemans, W. P.

    2000-01-01

    Nonparaxial propagation of ultrashort, high-power laser pulses in plasma channels is examined. In the adiabatic limit, pulse energy conservation, nonlinear group velocity, damped betatron oscillations, self-steepening, self-phase modulation, and shock formation are analyzed. In the nonadiabatic limit, the coupling of forward Raman scattering (FRS) and the self-modulation instability (SMI) is analyzed and growth rates are derived, including regimes of reduced growth. The SMI is found to dominate FRS in most regimes of interest. (c) 2000 The American Physical Society

  14. Nonlinear theory of transverse-multimode plasma accelerators

    International Nuclear Information System (INIS)

    Kuzelev, M.V.; Panin, V.A.; Plotnikov, A.P.

    1991-01-01

    The excitation of the higher transverse modes in a plasma-filled waveguide by a high-power electron beam is considered. General nonlinear equations are obtained which treat the excitation of the higher transverse plasma waves by a high-current relativistic beam. Results are presented of the numerical solutions of these equations. In the case of ultrarelativistic beams analytical expressions are found for the maximum amplitudes of the excited modes and the Q of the amplification. Numerical estimates are presented for realistic parameters

  15. Beyond the SM with nonlinearly realized gauge theories

    International Nuclear Information System (INIS)

    ERRARI, R.

    2014-01-01

    A Stuckelberg Mass Term (SMT) is introduced in a SU(2) non-abelian gauge theory as an alternative to the Higgs mechanism. A lattice model is used in order to investigate the mass spectrum of the theory, in particular the presence of Higgs-like bound states. Simulations indicate the presence of neutral bound states. Further investigations are needed in order to compare the model with experiments.

  16. Nonlinear modulation near the Lighthill instability threshold in 2+1 Whitham theory

    Science.gov (United States)

    Bridges, Thomas J.; Ratliff, Daniel J.

    2018-04-01

    The dispersionless Whitham modulation equations in 2+1 (two space dimensions and time) are reviewed and the instabilities identified. The modulation theory is then reformulated, near the Lighthill instability threshold, with a slow phase, moving frame and different scalings. The resulting nonlinear phase modulation equation near the Lighthill surfaces is a geometric form of the 2+1 two-way Boussinesq equation. This equation is universal in the same sense as Whitham theory. Moreover, it is dispersive, and it has a wide range of interesting multi-periodic, quasi-periodic and multi-pulse localized solutions. For illustration the theory is applied to a complex nonlinear 2+1 Klein-Gordon equation which has two Lighthill surfaces in the manifold of periodic travelling waves. This article is part of the theme issue `Stability of nonlinear waves and patterns and related topics'.

  17. Noninteracting control of nonlinear systems based on relaxed control

    NARCIS (Netherlands)

    Jayawardhana, B.

    2010-01-01

    In this paper, we propose methodology to solve noninteracting control problem for general nonlinear systems based on the relaxed control technique proposed by Artstein. For a class of nonlinear systems which cannot be stabilized by smooth feedback, a state-feedback relaxed control can be designed to

  18. New developments in state estimation for Nonlinear Systems

    DEFF Research Database (Denmark)

    Nørgård, Peter Magnus; Poulsen, Niels Kjølstad; Ravn, Ole

    2000-01-01

    Based on an interpolation formula, accurate state estimators for nonlinear systems can be derived. The estimators do not require derivative information which makes them simple to implement.; State estimators for nonlinear systems are derived based on polynomial approximations obtained with a mult......-known estimators, such as the extended Kalman filter (EKF) and its higher-order relatives, in most practical applications....

  19. Model reduction of nonlinear systems subject to input disturbances

    KAUST Repository

    Ndoye, Ibrahima; Laleg-Kirati, Taous-Meriem

    2017-01-01

    The method of convex optimization is used as a tool for model reduction of a class of nonlinear systems in the presence of disturbances. It is shown that under some conditions the nonlinear disturbed system can be approximated by a reduced order

  20. Considering "Nonlinearity" Across the Continuum in Medical Education Assessment: Supporting Theory, Practice, and Future Research Directions.

    Science.gov (United States)

    Durning, Steven J; Lubarsky, Stuart; Torre, Dario; Dory, Valérie; Holmboe, Eric

    2015-01-01

    The purpose of this article is to propose new approaches to assessment that are grounded in educational theory and the concept of "nonlinearity." The new approaches take into account related phenomena such as "uncertainty," "ambiguity," and "chaos." To illustrate these approaches, we will use the example of assessment of clinical reasoning, although the principles we outline may apply equally well to assessment of other constructs in medical education. Theoretical perspectives include a discussion of script theory, assimilation theory, self-regulated learning theory, and situated cognition. Assessment examples to include script concordance testing, concept maps, self-regulated learning microanalytic technique, and work-based assessment, which parallel the above-stated theories, respectively, are also highlighted. We conclude with some practical suggestions for approaching nonlinearity. © 2015 The Alliance for Continuing Education in the Health Professions, the Society for Academic Continuing Medical Education, and the Council on Continuing Medical Education, Association for Hospital Medical Education.

  1. Nonlinear Science

    CERN Document Server

    Yoshida, Zensho

    2010-01-01

    This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy, "nonlinear science" is explained as a challenge of deconstruction of the modern sciences. This book is not a technical guide to teach mathematical tools of nonlinear analysis, nor a zoology of so-called nonlinear phenomena. By critically analyzing the structure of linear theories, and cl

  2. Stabilization and regulation of nonlinear systems a robust and adaptive approach

    CERN Document Server

    Chen, Zhiyong

    2015-01-01

    The core of this textbook is a systematic and self-contained treatment of the nonlinear stabilization and output regulation problems. Its coverage embraces both fundamental concepts and advanced research outcomes and includes many numerical and practical examples. Several classes of important uncertain nonlinear systems are discussed. The state-of-the art solution presented uses robust and adaptive control design ideas in an integrated approach which demonstrates connections between global stabilization and global output regulation allowing both to be treated as stabilization problems. Stabilization and Regulation of Nonlinear Systems takes advantage of rich new results to give students up-to-date instruction in the central design problems of nonlinear control, problems which are a driving force behind the furtherance of modern control theory and its application. The diversity of systems in which stabilization and output regulation become significant concerns in the mathematical formulation of practical contr...

  3. 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.

  4. Nonlinear spectral mixing theory to model multispectral signatures

    Energy Technology Data Exchange (ETDEWEB)

    Borel, C.C. [Los Alamos National Lab., NM (United States). Astrophysics and Radiation Measurements Group

    1996-02-01

    Nonlinear spectral mixing occurs due to multiple reflections and transmissions between discrete surfaces, e.g. leaves or facets of a rough surface. The radiosity method is an energy conserving computational method used in thermal engineering and it models nonlinear spectral mixing realistically and accurately. In contrast to the radiative transfer method the radiosity method takes into account the discreteness of the scattering surfaces (e.g. exact location, orientation and shape) such as leaves and includes mutual shading between them. An analytic radiosity-based scattering model for vegetation was developed and used to compute vegetation indices for various configurations. The leaf reflectance and transmittance was modeled using the PROSPECT model for various amounts of water, chlorophyll and variable leaf structure. The soil background was modeled using SOILSPEC with a linear mixture of reflectances of sand, clay and peat. A neural network and a geometry based retrieval scheme were used to retrieve leaf area index and chlorophyll concentration for dense canopies. Only simulated canopy reflectances in the 6 visible through short wave IR Landsat TM channels were used. The authors used an empirical function to compute the signal-to-noise ratio of a retrieved quantity.

  5. Model reduction of nonlinear systems subject to input disturbances

    KAUST Repository

    Ndoye, Ibrahima

    2017-07-10

    The method of convex optimization is used as a tool for model reduction of a class of nonlinear systems in the presence of disturbances. It is shown that under some conditions the nonlinear disturbed system can be approximated by a reduced order nonlinear system with similar disturbance-output properties to the original plant. The proposed model reduction strategy preserves the nonlinearity and the input disturbance nature of the model. It guarantees a sufficiently small error between the outputs of the original and the reduced-order systems, and also maintains the properties of input-to-state stability. The matrices of the reduced order system are given in terms of a set of linear matrix inequalities (LMIs). The paper concludes with a demonstration of the proposed approach on model reduction of a nonlinear electronic circuit with additive disturbances.

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

    Directory of Open Access Journals (Sweden)

    Adailton S. Borges

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

  7. Tail estimates for stochastic fixed point equations via nonlinear renewal theory

    DEFF Research Database (Denmark)

    Collamore, Jeffrey F.; Vidyashankar, Anand N.

    2013-01-01

    estimate P(V>u)~Cu^{-r} as u tends to infinity, and also present a corresponding Lundberg-type upper bound. To this end, we introduce a novel dual change of measure on a random time interval and analyze the path properties, using nonlinear renewal theory, of the Markov chain resulting from the forward...... iteration of the given stochastic fixed point equation. In the process, we establish several new results in the realm of nonlinear renewal theory for these processes. As a consequence of our techniques, we also establish a new characterization of the extremal index. Finally, we provide some extensions...... of our methods to Markov-driven processes....

  8. Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality

    Science.gov (United States)

    Acikmese, Ahmet Behcet; Corless, Martin

    2004-01-01

    We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.

  9. Nonlinear Dynamics, Chaotic and Complex Systems

    Science.gov (United States)

    Infeld, E.; Zelazny, R.; Galkowski, A.

    2011-04-01

    Part I. Dynamic Systems Bifurcation Theory and Chaos: 1. Chaos in random dynamical systems V. M. Gunldach; 2. Controlling chaos using embedded unstable periodic orbits: the problem of optimal periodic orbits B. R. Hunt and E. Ott; 3. Chaotic tracer dynamics in open hydrodynamical flows G. Karolyi, A. Pentek, T. Tel and Z. Toroczkai; 4. Homoclinic chaos L. P. Shilnikov; Part II. Spatially Extended Systems: 5. Hydrodynamics of relativistic probability flows I. Bialynicki-Birula; 6. Waves in ionic reaction-diffusion-migration systems P. Hasal, V. Nevoral, I. Schreiber, H. Sevcikova, D. Snita, and M. Marek; 7. Anomalous scaling in turbulence: a field theoretical approach V. Lvov and I. Procaccia; 8. Abelian sandpile cellular automata M. Markosova; 9. Transport in an incompletely chaotic magnetic field F. Spineanu; Part III. Dynamical Chaos Quantum Physics and Foundations Of Statistical Mechanics: 10. Non-equilibrium statistical mechanics and ergodic theory L. A. Bunimovich; 11. Pseudochaos in statistical physics B. Chirikov; 12. Foundations of non-equilibrium statistical mechanics J. P. Dougherty; 13. Thermomechanical particle simulations W. G. Hoover, H. A. Posch, C. H. Dellago, O. Kum, C. G. Hoover, A. J. De Groot and B. L. Holian; 14. Quantum dynamics on a Markov background and irreversibility B. Pavlov; 15. Time chaos and the laws of nature I. Prigogine and D. J. Driebe; 16. Evolutionary Q and cognitive systems: dynamic entropies and predictability of evolutionary processes W. Ebeling; 17. Spatiotemporal chaos information processing in neural networks H. Szu; 18. Phase transitions and learning in neural networks C. Van den Broeck; 19. Synthesis of chaos A. Vanecek and S. Celikovsky; 20. Computational complexity of continuous problems H. Wozniakowski; Part IV. Complex Systems As An Interface Between Natural Sciences and Environmental Social and Economic Sciences: 21. Stochastic differential geometry in finance studies V. G. Makhankov; Part V. Conference Banquet

  10. Robust Control Design for Uncertain Nonlinear Dynamic Systems

    Science.gov (United States)

    Kenny, Sean P.; Crespo, Luis G.; Andrews, Lindsey; Giesy, Daniel P.

    2012-01-01

    Robustness to parametric uncertainty is fundamental to successful control system design and as such it has been at the core of many design methods developed over the decades. Despite its prominence, most of the work on robust control design has focused on linear models and uncertainties that are non-probabilistic in nature. Recently, researchers have acknowledged this disparity and have been developing theory to address a broader class of uncertainties. This paper presents an experimental application of robust control design for a hybrid class of probabilistic and non-probabilistic parametric uncertainties. The experimental apparatus is based upon the classic inverted pendulum on a cart. The physical uncertainty is realized by a known additional lumped mass at an unknown location on the pendulum. This unknown location has the effect of substantially altering the nominal frequency and controllability of the nonlinear system, and in the limit has the capability to make the system neutrally stable and uncontrollable. Another uncertainty to be considered is a direct current motor parameter. The control design objective is to design a controller that satisfies stability, tracking error, control power, and transient behavior requirements for the largest range of parametric uncertainties. This paper presents an overview of the theory behind the robust control design methodology and the experimental results.

  11. Geometrical theory of nonlinear phase distortion of intense laser beams

    International Nuclear Information System (INIS)

    Glaze, J.A.; Hunt, J.T.; Speck, D.R.

    1975-01-01

    Phase distortion arising from whole beam self-focusing of intense laser pulses with arbitrary spatial profiles is treated in the limit of geometrical optics. The constant shape approximation is used to obtain the phase and angular distribution of the geometrical rays in the near field. Conditions for the validity of this approximation are discussed. Geometrical focusing of the aberrated beam is treated for the special case of a beam with axial symmetry. Equations are derived that show both the shift of the focus and the distortion of the intensity distribution that are caused by the nonlinear index of refraction of the optical medium. An illustrative example treats the case of beam distortion in a Nd:Glass amplifier

  12. Linear and nonlinear theory study of Alpha Virginis

    International Nuclear Information System (INIS)

    Cox, A.N.; Hodson, S.W.; Clancy, S.P.

    1981-01-01

    Nonlinear radiation hydrodynamic calculations using a model for α Virginis, a β Cephei star, have been made to see if the cause of the recurrent radial pulsation epochs can be discovered. The basic observed characteristics of β Cephei variables are presented. A review of the various proposals to make these stars pulsate concludes that the excitation mechanism must be in the central convective core or variable composition regions. The envelope damps radial fundamental mode pulsations in 4 years and in even shorter periods for radial overtones. It is proposed here that the mixing of envelope hydrogen into the hydrogen depleted (or even exhausted) core can produce periodic pressure pulses which drive the pulsation amplitude up to the observed value. During the decay of the pulsations, evolution toward higher luminosities enables further episodes of mixing and driving to occur. We predict rapid amplitude increases when mixing occurs and a slow decay of radial (and nonradial modes for other β Cephei variables) between mixing episodes

  13. Nonlinear aeroelastic modelling for wind turbine blades based on blade element momentum theory and geometrically exact beam theory

    International Nuclear Information System (INIS)

    Wang, Lin; Liu, Xiongwei; Renevier, Nathalie; Stables, Matthew; Hall, George M.

    2014-01-01

    Due to the increasing size and flexibility of large wind turbine blades, accurate and reliable aeroelastic modelling is playing an important role for the design of large wind turbines. Most existing aeroelastic models are linear models based on assumption of small blade deflections. This assumption is not valid anymore for very flexible blade design because such blades often experience large deflections. In this paper, a novel nonlinear aeroelastic model for large wind turbine blades has been developed by combining BEM (blade element momentum) theory and mixed-form formulation of GEBT (geometrically exact beam theory). The nonlinear aeroelastic model takes account of large blade deflections and thus greatly improves the accuracy of aeroelastic analysis of wind turbine blades. The nonlinear aeroelastic model is implemented in COMSOL Multiphysics and validated with a series of benchmark calculation tests. The results show that good agreement is achieved when compared with experimental data, and its capability of handling large deflections is demonstrated. Finally the nonlinear aeroelastic model is applied to aeroelastic modelling of the parked WindPACT 1.5 MW baseline wind turbine, and reduced flapwise deflection from the nonlinear aeroelastic model is observed compared to the linear aeroelastic code FAST (Fatigue, Aerodynamics, Structures, and Turbulence). - Highlights: • A novel nonlinear aeroelastic model for wind turbine blades is developed. • The model takes account of large blade deflections and geometric nonlinearities. • The model is reliable and efficient for aeroelastic modelling of wind turbine blades. • The accuracy of the model is verified by a series of benchmark calculation tests. • The model provides more realistic aeroelastic modelling than FAST (Fatigue, Aerodynamics, Structures, and Turbulence)

  14. Nonlinear stochastic systems with incomplete information filtering and control

    CERN Document Server

    Shen, Bo; Shu, Huisheng

    2013-01-01

    Nonlinear Stochastic Processes addresses the frequently-encountered problem of incomplete information. The causes of this problem considered here include: missing measurements; sensor delays and saturation; quantization effects; and signal sampling. Divided into three parts, the text begins with a focus on H∞ filtering and control problems associated with general classes of nonlinear stochastic discrete-time systems. Filtering problems are considered in the second part, and in the third the theory and techniques previously developed are applied to the solution of issues arising in complex networks with the design of sampled-data-based controllers and filters. Among its highlights, the text provides: ·         a unified framework for handling filtering and control problems in complex communication networks with limited bandwidth; ·         new concepts such as random sensor and signal saturations for more realistic modeling; and ·         demonstration of the use of techniques such...

  15. Investigation on the Nonlinear Control System of High-Pressure Common Rail (HPCR) System in a Diesel Engine

    Science.gov (United States)

    Cai, Le; Mao, Xiaobing; Ma, Zhexuan

    2018-02-01

    This study first constructed the nonlinear mathematical model of the high-pressure common rail (HPCR) system in the diesel engine. Then, the nonlinear state transformation was performed using the flow’s calculation and the standard state space equation was acquired. Based on sliding-mode variable structure control (SMVSC) theory, a sliding-mode controller for nonlinear systems was designed for achieving the control of common rail pressure and the diesel engine’s rotational speed. Finally, on the simulation platform of MATLAB, the designed nonlinear HPCR system was simulated. The simulation results demonstrate that sliding-mode variable structure control algorithm shows favorable control performances and overcome the shortcomings of traditional PID control in overshoot, parameter adjustment, system precision, adjustment time and ascending time.

  16. Non-linear second-order periodic systems with non-smooth potential

    Indian Academy of Sciences (India)

    In this paper we study second order non-linear periodic systems driven by the ordinary vector -Laplacian with a non-smooth, locally Lipschitz potential function. Our approach is variational and it is based on the non-smooth critical point theory. We prove existence and multiplicity results under general growth conditions on ...

  17. Non-linear second-order periodic systems with non-smooth potential

    Indian Academy of Sciences (India)

    R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

    Abstract. In this paper we study second order non-linear periodic systems driven by the ordinary vector p-Laplacian with a non-smooth, locally Lipschitz potential function. Our approach is variational and it is based on the non-smooth critical point theory. We prove existence and multiplicity results under general growth ...

  18. Poincaré-MacMillan Equations of Motion for a Nonlinear Nonholonomic Dynamical System

    Science.gov (United States)

    Amjad, Hussain; Syed Tauseef, Mohyud-Din; Ahmet, Yildirim

    2012-03-01

    MacMillan's equations are extended to Poincaré's formalism, and MacMillan's equations for nonlinear nonholonomic systems are obtained in terms of Poincaré parameters. The equivalence of the results obtained here with other forms of equations of motion is demonstrated. An illustrative example of the theory is provided as well.

  19. Introductive backgrounds of modern quantum mathematics with application to nonlinear dynamical systems

    International Nuclear Information System (INIS)

    Prykarpatsky, A.K.; Bogoliubov, N.N. Jr.; Golenia, J.; Taneri, U.

    2007-09-01

    Introductive backgrounds of a new mathematical physics discipline - Quantum Mathematics - are discussed and analyzed both from historical and analytical points of view. The magic properties of the second quantization method, invented by V. Fock in 1934, are demonstrated, and an impressive application to the nonlinear dynamical systems theory is considered. (author)

  20. Useful tools for non-linear systems: Several non-linear integral inequalities

    Czech Academy of Sciences Publication Activity Database

    Agahi, H.; Mohammadpour, A.; Mesiar, Radko; Vaezpour, M. S.

    2013-01-01

    Roč. 49, č. 1 (2013), s. 73-80 ISSN 0950-7051 R&D Projects: GA ČR GAP402/11/0378 Institutional support: RVO:67985556 Keywords : Monotone measure * Comonotone functions * Integral inequalities * Universal integral Subject RIV: BA - General Mathematics Impact factor: 3.058, year: 2013 http://library.utia.cas.cz/separaty/2013/E/mesiar-useful tools for non-linear systems several non-linear integral inequalities.pdf

  1. Adaptive Neural Control of Nonaffine Nonlinear Systems without Differential Condition for Nonaffine Function

    Directory of Open Access Journals (Sweden)

    Chaojiao Sun

    2016-01-01

    Full Text Available An adaptive neural control scheme is proposed for nonaffine nonlinear system without using the implicit function theorem or mean value theorem. The differential conditions on nonaffine nonlinear functions are removed. The control-gain function is modeled with the nonaffine function probably being indifferentiable. Furthermore, only a semibounded condition for nonaffine nonlinear function is required in the proposed method, and the basic idea of invariant set theory is then constructively introduced to cope with the difficulty in the control design for nonaffine nonlinear systems. It is rigorously proved that all the closed-loop signals are bounded and the tracking error converges to a small residual set asymptotically. Finally, simulation examples are provided to demonstrate the effectiveness of the designed method.

  2. Optimization theory for large systems

    CERN Document Server

    Lasdon, Leon S

    2002-01-01

    Important text examines most significant algorithms for optimizing large systems and clarifying relations between optimization procedures. Much data appear as charts and graphs and will be highly valuable to readers in selecting a method and estimating computer time and cost in problem-solving. Initial chapter on linear and nonlinear programming presents all necessary background for subjects covered in rest of book. Second chapter illustrates how large-scale mathematical programs arise from real-world problems. Appendixes. List of Symbols.

  3. Advanced nonlinear theory: Long-term stability at the SSC

    International Nuclear Information System (INIS)

    Heifets, S.

    1987-01-01

    This paper discussed the long-term stability of the particle beams in the Superconducting Super Collider. In particular the dynamics of a single particle beam is considered in depth. The topics of this paper include: the Hamiltonian of this particle approach, perturbation theory, canonical transformations, interaction of the resonances, structure of the phase space, synchro-Betatron oscillations, modulation diffusion and noise-resonance interaction. 36 refs

  4. Nonlinear von Neumann equations for quantum dissipative systems

    International Nuclear Information System (INIS)

    Messer, J.; Baumgartner, B.

    1978-01-01

    For pure states nonlinear Schroedinger equations, the so-called Schroedinger-Langevin equations are well-known to model quantum dissipative systems of the Langevin type. For mixtures it is shown that these wave equations do not extend to master equations, but to corresponding nonlinear von Neumann equations. Solutions for the damped harmonic oscillator are discussed. (Auth.)

  5. Nonlinear von Neumann equations for quantum dissipative systems

    International Nuclear Information System (INIS)

    Messer, J.; Baumgartner, B.

    For pure states nonlinear Schroedinger equations, the so-called Schroedinger-Langevin equations are well-known to model quantum dissipative systems of the Langevin type. For mixtures it is shown that these wave equations do not extend to master equations, but to corresponding nonlinear von Neumann equations. Solutions for the damped harmonic oscillator are discussed. (Author)

  6. 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.

  7. Nucleon-nucleon scattering in the functional quantum theory of the nonlinear spinor field

    International Nuclear Information System (INIS)

    Haegele, G.

    1979-01-01

    The author calculates the S matrix for the elastic nucleon-nucleon scattering in the lowest approximation using the quantum theory of nonlinear spinor fields with special emphasis to the ghost configuration of this theory. Introducing a general scalar product a new functional channel calculus is considered. From the results the R and T matrix elements and the differential and integral cross sections are derived. (HSI)

  8. Imaging theory of nonlinear second harmonic and third harmonic generations in confocal microscopy

    Institute of Scientific and Technical Information of China (English)

    TANG Zhilie; XING Da; LIU Songhao

    2004-01-01

    The imaging theory of nonlinear second harmonic generation (SHG) and third harmonic generation (THG) in confocal microscopy is presented in this paper. The nonlinear effect of SHG and THG on the imaging properties of confocal microscopy has been analyzed in detail by the imaging theory. It is proved that the imaging process of SHG and THG in confocal microscopy, which is different from conventional coherent imaging or incoherent imaging, can be divided into two different processes of coherent imaging. The three-dimensional point spread functions (3D-PSF) of SHG and THG confocal microscopy are derived based on the nonlinear principles of SHG and THG. The imaging properties of SHG and THG confocal microscopy are discussed in detail according to its 3D-PSF. It is shown that the resolution of SHG and THG confocal microscopy is higher than that of single-and two-photon confocal microscopy.

  9. General systems theory mathematical foundations

    CERN Document Server

    Mesarovic, Mihajlo D

    1975-01-01

    In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank mat

  10. Ergodic theory and dynamical systems

    CERN Document Server

    Coudène, Yves

    2016-01-01

    This textbook is a self-contained and easy-to-read introduction to ergodic theory and the theory of dynamical systems, with a particular emphasis on chaotic dynamics. This book contains a broad selection of topics and explores the fundamental ideas of the subject. Starting with basic notions such as ergodicity, mixing, and isomorphisms of dynamical systems, the book then focuses on several chaotic transformations with hyperbolic dynamics, before moving on to topics such as entropy, information theory, ergodic decomposition and measurable partitions. Detailed explanations are accompanied by numerous examples, including interval maps, Bernoulli shifts, toral endomorphisms, geodesic flow on negatively curved manifolds, Morse-Smale systems, rational maps on the Riemann sphere and strange attractors. Ergodic Theory and Dynamical Systems will appeal to graduate students as well as researchers looking for an introduction to the subject. While gentle on the beginning student, the book also contains a number of commen...

  11. Stochastic Finite Element Analysis of Non-Linear Structures Modelled by Plasticity Theory

    DEFF Research Database (Denmark)

    Frier, Christian; Sørensen, John Dalsgaard

    2003-01-01

    A Finite Element Reliability Method (FERM) is introduced to perform reliability analyses on two-dimensional structures in plane stress, modeled by non-linear plasticity theory. FERM is a coupling between the First Order Reliability Method (FORM) and the Finite Element Method (FEM). FERM can be us...

  12. Chaos Theory as a Model for Life Transitions Counseling: Nonlinear Dynamics and Life's Changes

    Science.gov (United States)

    Bussolari, Cori J.; Goodell, Judith A.

    2009-01-01

    Chaos theory is presented for counselors working with clients experiencing life transitions. It is proposed as a model that considers disorder, unpredictability, and lack of control as normal parts of transition processes. Nonlinear constructs from physics are adapted for use in counseling. The model provides a method clients can use to…

  13. Non-linear wave loads and ship responses by a time-domain strip theory

    DEFF Research Database (Denmark)

    Xia, Jinzhu; Wang, Zhaohui; Jensen, Jørgen Juncher

    1998-01-01

    . Based on this time-domain strip theory, an efficient non-linear hydroelastic method of wave- and slamming-induced vertical motions and structural responses of ships is developed, where the structure is represented as a Timoshenko beam. Numerical calculations are presented for the S175 Containership...

  14. White noise theory of robust nonlinear filtering with correlated state and observation noises

    NARCIS (Netherlands)

    Bagchi, Arunabha; Karandikar, Rajeeva

    1992-01-01

    In the direct white noise theory of nonlinear filtering, the state process is still modeled as a Markov process satisfying an Ito stochastic differential equation, while a finitely additive white noise is used to model the observation noise. In the present work, this asymmetry is removed by modeling

  15. White noise theory of robust nonlinear filtering with correlated state and observation noises

    NARCIS (Netherlands)

    Bagchi, Arunabha; Karandikar, Rajeeva

    1994-01-01

    In the existing `direct¿ white noise theory of nonlinear filtering, the state process is still modelled as a Markov process satisfying an Itô stochastic differential equation, while a `finitely additive¿ white noise is used to model the observation noise. We remove this asymmetry by modelling the

  16. Advances in nonlinear optics

    CERN Document Server

    Chen, Xianfeng; Zeng, Heping; Guo, Qi; She, Weilong

    2015-01-01

    This book presents an overview of the state of the art of nonlinear optics from weak light nonlinear optics, ultrafast nonlinear optics to electro-optical theory and applications. Topics range from the fundamental studies of the interaction between matter and radiation to the development of devices, components, and systems of tremendous commercial interest for widespread applications in optical telecommunications, medicine, and biotechnology.

  17. Advanced nonlinear engine speed control systems

    DEFF Research Database (Denmark)

    Vesterholm, Thomas; Hendricks, Elbert

    1994-01-01

    Several subsidiary control problems have turned out to be important for improving driveability and fuel consumption in modern spark ignition (SI) engine cars. Among these are idle speed control and cruise control. In this paper the idle speed and cruise control problems will be treated as one......: accurately tracking of a desired engine speed in the presence of model uncertainties and severe load disturbances. This is accomplished by using advanced nonlinear control techniques such as input/output-linearization and sliding mode control. These techniques take advantage of a nonlinear model...... of the engine dynamics, a mean value engine model....

  18. Analytical Evaluation of the Nonlinear Vibration of Coupled Oscillator Systems

    DEFF Research Database (Denmark)

    Bayat, M.; Shahidi, M.; Barari, Amin

    2011-01-01

    approximations to the achieved nonlinear differential oscillation equations where the displacement of the two-mass system can be obtained directly from the linear second-order differential equation using the first order of the current approach. Compared with exact solutions, just one iteration leads us to high......We consider periodic solutions for nonlinear free vibration of conservative, coupled mass-spring systems with linear and nonlinear stiffnesses. Two practical cases of these systems are explained and introduced. An analytical technique called energy balance method (EBM) was applied to calculate...

  19. Analysis and design of robust decentralized controllers for nonlinear systems

    Energy Technology Data Exchange (ETDEWEB)

    Schoenwald, D.A.

    1993-07-01

    Decentralized control strategies for nonlinear systems are achieved via feedback linearization techniques. New results on optimization and parameter robustness of non-linear systems are also developed. In addition, parametric uncertainty in large-scale systems is handled by sensitivity analysis and optimal control methods in a completely decentralized framework. This idea is applied to alleviate uncertainty in friction parameters for the gimbal joints on Space Station Freedom. As an example of decentralized nonlinear control, singular perturbation methods and distributed vibration damping are merged into a control strategy for a two-link flexible manipulator.

  20. Hadron–Quark Combustion as a Nonlinear, Dynamical System

    Directory of Open Access Journals (Sweden)

    Amir Ouyed

    2018-03-01

    Full Text Available The hadron–quark combustion front is a system that couples various processes, such as chemical reactions, hydrodynamics, diffusion, and neutrino transport. Previous numerical work has shown that this system is very nonlinear, and can be very sensitive to some of these processes. In these proceedings, we contextualize the hadron–quark combustion as a nonlinear system, subject to dramatic feedback triggered by leptonic weak decays and neutrino transport.

  1. Hadron–Quark Combustion as a Nonlinear, Dynamical System

    Science.gov (United States)

    Ouyed, Amir; Ouyed, Rachid; Jaikumar, Prashanth

    2018-03-01

    The hadron-quark combustion front is a system that couples various processes, such as chemical reactions, hydrodynamics, diffusion, and neutrino transport. Previous numerical work has shown that this system is very nonlinear, and can be very sensitive to some of these processes. In these proceedings, we contextualize the hadron-quark combustion as a nonlinear system, subject to dramatic feedback triggered by leptonic weak decays and neutrino transport.

  2. Nonlinear adaptive robust back stepping force control of hydraulic load simulator: Theory and experiments

    International Nuclear Information System (INIS)

    Yao, Jianyong; Jiao, Zongxia; Yao, Bin

    2014-01-01

    High performance robust force control of hydraulic load simulator with constant but unknown hydraulic parameters is considered. In contrast to the linear control based on hydraulic linearization equations, hydraulic inherent nonlinear properties and uncertainties make the conventional feedback proportional-integral-derivative (PID) control not yield to high performance requirements. Furthermore, the hydraulic system may be subjected to non-smooth and discontinuous nonlinearities due to the directional change of valve opening. In this paper, based on a nonlinear system model of hydraulic load simulator, a discontinuous projection-based nonlinear adaptive robust back stepping controller is developed with servo valve dynamics. The proposed controller constructs a novel stable adaptive controller and adaptation laws with additional pressure dynamic related unknown parameters, which can compensate for the system nonlinearities and uncertain parameters, meanwhile a well-designed robust controller is also synthesized to dominate the model uncertainties coming from both parametric uncertainties and uncertain nonlinearities including unmodeled and ignored system dynamics. The controller theoretically guarantee a prescribed transient performance and final tracking accuracy in presence of both parametric uncertainties and uncertain nonlinearities; while achieving asymptotic output tracking in the absence of unstructured uncertainties. The implementation issues are also discussed for controller simplification. Some comparative results are obtained to verify the high-performance nature of the proposed controller.

  3. Nonlinear adaptive robust back stepping force control of hydraulic load simulator: Theory and experiments

    Energy Technology Data Exchange (ETDEWEB)

    Yao, Jianyong [Nanjing University of Science and Technology, Nanjing (China); Jiao, Zongxia [Beihang University, Beijing (China); Yao, Bin [Purdue University, West Lafayette (United States)

    2014-04-15

    High performance robust force control of hydraulic load simulator with constant but unknown hydraulic parameters is considered. In contrast to the linear control based on hydraulic linearization equations, hydraulic inherent nonlinear properties and uncertainties make the conventional feedback proportional-integral-derivative (PID) control not yield to high performance requirements. Furthermore, the hydraulic system may be subjected to non-smooth and discontinuous nonlinearities due to the directional change of valve opening. In this paper, based on a nonlinear system model of hydraulic load simulator, a discontinuous projection-based nonlinear adaptive robust back stepping controller is developed with servo valve dynamics. The proposed controller constructs a novel stable adaptive controller and adaptation laws with additional pressure dynamic related unknown parameters, which can compensate for the system nonlinearities and uncertain parameters, meanwhile a well-designed robust controller is also synthesized to dominate the model uncertainties coming from both parametric uncertainties and uncertain nonlinearities including unmodeled and ignored system dynamics. The controller theoretically guarantee a prescribed transient performance and final tracking accuracy in presence of both parametric uncertainties and uncertain nonlinearities; while achieving asymptotic output tracking in the absence of unstructured uncertainties. The implementation issues are also discussed for controller simplification. Some comparative results are obtained to verify the high-performance nature of the proposed controller.

  4. A Unified Approach to Adaptive Neural Control for Nonlinear Discrete-Time Systems With Nonlinear Dead-Zone Input.

    Science.gov (United States)

    Liu, Yan-Jun; Gao, Ying; Tong, Shaocheng; Chen, C L Philip

    2016-01-01

    In this paper, an effective adaptive control approach is constructed to stabilize a class of nonlinear discrete-time systems, which contain unknown functions, unknown dead-zone input, and unknown control direction. Different from linear dead zone, the dead zone, in this paper, is a kind of nonlinear dead zone. To overcome the noncausal problem, which leads to the control scheme infeasible, the systems can be transformed into a m -step-ahead predictor. Due to nonlinear dead-zone appearance, the transformed predictor still contains the nonaffine function. In addition, it is assumed that the gain function of dead-zone input and the control direction are unknown. These conditions bring about the difficulties and the complicacy in the controller design. Thus, the implicit function theorem is applied to deal with nonaffine dead-zone appearance, the problem caused by the unknown control direction can be resolved through applying the discrete Nussbaum gain, and the neural networks are used to approximate the unknown function. Based on the Lyapunov theory, all the signals of the resulting closed-loop system are proved to be semiglobal uniformly ultimately bounded. Moreover, the tracking error is proved to be regulated to a small neighborhood around zero. The feasibility of the proposed approach is demonstrated by a simulation example.

  5. Nonlinear propagation in fusion laser systems

    International Nuclear Information System (INIS)

    Bliss, E.S.; Glass, A.J.; Glaze, J.A.

    1977-11-01

    This report was assembled to provide a brief review of the historical development of the study of self-focusing and nonlinear light propagation and its impact on the design of large, Nd-glass lasers for fusion research. No claim to completeness is made, but we feel that the enclosed summary does not miss many of the major developments in the field

  6. H∞ control of Lur'e systems with sector and slope restricted nonlinearities

    International Nuclear Information System (INIS)

    Park, Ju H.; Ji, D.H.; Won, S.C.; Lee, S.M.; Choi, S.J.

    2009-01-01

    This Letter considers H ∞ controller design scheme for Lur'e systems with sector/slope restrictions and external disturbance. Based on Lyapunov theory and linear matrix inequality (LMI) formulation, a state feedback controller is designed to not only guarantee stability of systems but also reduce the effect of external disturbance to an H ∞ norm constraint. The nonlinearities are expressed as convex combinations of sector and slope bounds so that equality constraints are converted into inequality constraints using convex properties of the nonlinear function. Then, the stabilizing feedback gain matrix is derived through LMI formulation. Finally, a numerical example shows the effectiveness of the proposed method.

  7. Application of Contraction Mappings to the Control of Nonlinear Systems. Ph.D. Thesis

    Science.gov (United States)

    Killingsworth, W. R., Jr.

    1972-01-01

    The theoretical and applied aspects of successive approximation techniques are considered for the determination of controls for nonlinear dynamical systems. Particular emphasis is placed upon the methods of contraction mappings and modified contraction mappings. It is shown that application of the Pontryagin principle to the optimal nonlinear regulator problem results in necessary conditions for optimality in the form of a two point boundary value problem (TPBVP). The TPBVP is represented by an operator equation and functional analytic results on the iterative solution of operator equations are applied. The general convergence theorems are translated and applied to those operators arising from the optimal regulation of nonlinear systems. It is shown that simply structured matrices and similarity transformations may be used to facilitate the calculation of the matrix Green functions and the evaluation of the convergence criteria. A controllability theory based on the integral representation of TPBVP's, the implicit function theorem, and contraction mappings is developed for nonlinear dynamical systems. Contraction mappings are theoretically and practically applied to a nonlinear control problem with bounded input control and the Lipschitz norm is used to prove convergence for the nondifferentiable operator. A dynamic model representing community drug usage is developed and the contraction mappings method is used to study the optimal regulation of the nonlinear system.

  8. Relativistic mean-field theory for unstable nuclei with non-linear σ and ω terms

    International Nuclear Information System (INIS)

    Sugahara, Y.; Toki, H.

    1994-01-01

    We search for a new parameter set for the description of stable as well as unstable nuclei in the wide mass range within the relativistic mean-field theory. We include a non-linear ω self-coupling term in addition to the non-linear σ self-coupling terms, the necessity of which is suggested by the relativistic Brueckner-Hartree-Fock (RBHF) theory of nuclear matter. We find two parameter sets, one of which is for nuclei above Z=20 and the other for nuclei below that. The calculated results agree very well with the existing data for finite nuclei. The parameter set for the heavy nuclei provides the equation of state of nuclear matter similar to the one of the RBHF theory. ((orig.))

  9. Chaos synchronization of uncertain chaotic systems using composite nonlinear feedback based integral sliding mode control.

    Science.gov (United States)

    Mobayen, Saleh

    2018-06-01

    This paper proposes a combination of composite nonlinear feedback and integral sliding mode techniques for fast and accurate chaos synchronization of uncertain chaotic systems with Lipschitz nonlinear functions, time-varying delays and disturbances. The composite nonlinear feedback method allows accurate following of the master chaotic system and the integral sliding mode control provides invariance property which rejects the perturbations and preserves the stability of the closed-loop system. Based on the Lyapunov- Krasovskii stability theory and linear matrix inequalities, a novel sufficient condition is offered for the chaos synchronization of uncertain chaotic systems. This method not only guarantees the robustness against perturbations and time-delays, but also eliminates reaching phase and avoids chattering problem. Simulation results demonstrate that the suggested procedure leads to a great control performance. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

  10. Methods for Fault Diagnosability Analysis of a Class of Affine Nonlinear Systems

    Directory of Open Access Journals (Sweden)

    Xiafu Peng

    2015-01-01

    Full Text Available The fault diagnosability analysis for a given model, before developing a diagnosis algorithm, can be used to answer questions like “can the fault fi be detected by observed states?” and “can it separate fault fi from fault fj by observed states?” If not, we should redesign the sensor placement. This paper deals with the problem of the evaluation of detectability and separability for the diagnosability analysis of affine nonlinear system. First, we used differential geometry theory to analyze the nonlinear system and proposed new detectability criterion and separability criterion. Second, the related matrix between the faults and outputs of the system and the fault separable matrix are designed for quantitative fault diagnosability calculation and fault separability calculation, respectively. Finally, we illustrate our approach to exemplify how to analyze diagnosability by a certain nonlinear system example, and the experiment results indicate the effectiveness of the fault evaluation methods.

  11. Point source identification in nonlinear advection–diffusion–reaction systems

    International Nuclear Information System (INIS)

    Mamonov, A V; Tsai, Y-H R

    2013-01-01

    We consider a problem of identification of point sources in time-dependent advection–diffusion systems with a nonlinear reaction term. The linear counterpart of the problem in question can be reduced to solving a system of nonlinear algebraic equations via the use of adjoint equations. We extend this approach by constructing an algorithm that solves the problem iteratively to account for the nonlinearity of the reaction term. We study the question of improving the quality of source identification by adding more measurements adaptively using the solution obtained previously with a smaller number of measurements. (paper)

  12. Model Updating Nonlinear System Identification Toolbox, Phase I

    Data.gov (United States)

    National Aeronautics and Space Administration — ZONA Technology proposes to develop an enhanced model updating nonlinear system identification (MUNSID) methodology by adopting the flight data with state-of-the-art...

  13. Stabilization and Control Models of Systems With Hysteresis Nonlinearities

    Directory of Open Access Journals (Sweden)

    Mihail E. Semenov

    2012-05-01

    Full Text Available Mechanical and economic systems with hysteresis nonlinearities are studied in article. Dissipativity condition of inverted pendulum under the hysteresis control is obtained. The solution of the optimal production strategy problem was found where price has hysteresis behaviour.

  14. Computational Models for Nonlinear Aeroelastic Systems, Phase I

    Data.gov (United States)

    National Aeronautics and Space Administration — Clear Science Corp. and Duke University propose to develop and demonstrate a new and efficient computational method of modeling nonlinear aeroelastic systems. The...

  15. Distributed Adaptive Neural Control for Stochastic Nonlinear Multiagent Systems.

    Science.gov (United States)

    Wang, Fang; Chen, Bing; Lin, Chong; Li, Xuehua

    2016-11-14

    In this paper, a consensus tracking problem of nonlinear multiagent systems is investigated under a directed communication topology. All the followers are modeled by stochastic nonlinear systems in nonstrict feedback form, where nonlinearities and stochastic disturbance terms are totally unknown. Based on the structural characteristic of neural networks (in Lemma 4), a novel distributed adaptive neural control scheme is put forward. The raised control method not only effectively handles unknown nonlinearities in nonstrict feedback systems, but also copes with the interactions among agents and coupling terms. Based on the stochastic Lyapunov functional method, it is indicated that all the signals of the closed-loop system are bounded in probability and all followers' outputs are convergent to a neighborhood of the output of leader. At last, the efficiency of the control method is testified by a numerical example.

  16. Self-sustained solitons in systems with nonlinear damping

    International Nuclear Information System (INIS)

    Gonzalez, J.A.

    1993-05-01

    The existence and stability of kinks in systems with nonlinear damping are investigated. We discuss the mechanism of a bifurcation after which the kink becomes a non-stationary state. (author). 9 refs

  17. Optimal beamforming in MIMO systems with HPA nonlinearity

    KAUST Repository

    Qi, Jian

    2010-09-01

    In this paper, multiple-input multiple-output (MIMO) transmit beamforming (TB) systems under the consideration of nonlinear high-power amplifiers (HPAs) are investigated. The optimal beamforming scheme, with the optimal beamforming weight vector and combining vector, is proposed for MIMO systems with HPA nonlinearity. The performance of the proposed MIMO beamforming scheme in the presence of HPA nonlinearity is evaluated in terms of average symbol error probability (SEP), outage probability and system capacity, considering transmission over uncorrelated quasi-static frequency-flat Rayleigh fading channels. Numerical results are provided and show the effects of several system parameters, namely, parameters of nonlinear HPA, numbers of transmit and receive antennas, and modulation order of phase-shift keying (PSK), on performance. ©2010 IEEE.

  18. Robust receding horizon control for networked and distributed nonlinear systems

    CERN Document Server

    Li, Huiping

    2017-01-01

    This book offers a comprehensive, easy-to-understand overview of receding-horizon control for nonlinear networks. It presents novel general strategies that can simultaneously handle general nonlinear dynamics, system constraints, and disturbances arising in networked and large-scale systems and which can be widely applied. These receding-horizon-control-based strategies can achieve sub-optimal control performance while ensuring closed-loop stability: a feature attractive to engineers. The authors address the problems of networked and distributed control step-by-step, gradually increasing the level of challenge presented. The book first introduces the state-feedback control problems of nonlinear networked systems and then studies output feedback control problems. For large-scale nonlinear systems, disturbance is considered first, then communication delay separately, and lastly the simultaneous combination of delays and disturbances. Each chapter of this easy-to-follow book not only proposes and analyzes novel ...

  19. Optimal beamforming in MIMO systems with HPA nonlinearity

    KAUST Repository

    Qi, Jian; Aissa, Sonia

    2010-01-01

    In this paper, multiple-input multiple-output (MIMO) transmit beamforming (TB) systems under the consideration of nonlinear high-power amplifiers (HPAs) are investigated. The optimal beamforming scheme, with the optimal beamforming weight vector and combining vector, is proposed for MIMO systems with HPA nonlinearity. The performance of the proposed MIMO beamforming scheme in the presence of HPA nonlinearity is evaluated in terms of average symbol error probability (SEP), outage probability and system capacity, considering transmission over uncorrelated quasi-static frequency-flat Rayleigh fading channels. Numerical results are provided and show the effects of several system parameters, namely, parameters of nonlinear HPA, numbers of transmit and receive antennas, and modulation order of phase-shift keying (PSK), on performance. ©2010 IEEE.

  20. 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)

  1. Development of ultrasound transducer diffractive field theory for nonlinear propagation-based imaging

    Science.gov (United States)

    Kharin, Nikolay A.

    2000-04-01

    In nonlinear ultrasound imaging the images are formed using the second harmonic energy generated due to the nonlinear nature of finite amplitude propagation. This propagation can be modeled using the KZK wave equation. This paper presents further development of nonlinear diffractive field theory based on the KZK equation and its solution by means of the slowly changing profile method for moderate nonlinearity. The analytical expression for amplitudes and phases of sum frequency wave are obtained in addition to the second harmonic wave. Also, the analytical expression for the relative curvature of the wave fronts of fundamental and second harmonic signals are derived. The media with different nonlinear properties and absorption coefficients were investigated to characterize the diffractive field of the transducer at medical frequencies. All expressions demonstrate good agreement with experimental results. The expressions are novel and provide an easy way for prediction of amplitude and phase structure of nonlinearly distorted field of a transducer. The sum frequency signal technique could be implemented as well as second harmonic technique to improve the quality of biomedical images. The results obtained are of importance for medical diagnostic ultrasound equipment design.

  2. Application of inertia-induced excitation theory for nonlinear acoustic ...

    Indian Academy of Sciences (India)

    estimated. By these calculations, a generalized statement is reported that all possible sound ..... we carry out order-by-order analysis of eqs (9)–(13) in a stretched coordinate system ..... The financial support by the CSIR received through.

  3. Robust stabilization of nonlinear systems: The LMI approach

    Directory of Open Access Journals (Sweden)

    Šiljak D. D.

    2000-01-01

    Full Text Available This paper presents a new approach to robust quadratic stabilization of nonlinear systems within the framework of Linear Matrix Inequalities (LMI. The systems are composed of a linear constant part perturbed by an additive nonlinearity which depends discontinuously on both time and state. The only information about the nonlinearity is that it satisfies a quadratic constraint. Our major objective is to show how linear constant feedback laws can be formulated to stabilize this type of systems and, at the same time, maximize the bounds on the nonlinearity which the system can tolerate without going unstable. We shall broaden the new setting to include design of decentralized control laws for robust stabilization of interconnected systems. Again, the LMI methods will be used to maximize the class of uncertain interconnections which leave the overall system connectively stable. It is useful to learn that the proposed LMI formulation “recognizes” the matching conditions by returning a feedback gain matrix for any prescribed bound on the interconnection terms. More importantly, the new formulation provides a suitable setting for robust stabilization of nonlinear systems where the nonlinear perturbations satisfy the generalized matching conditions.

  4. Theory and Simulations of Solar System Plasmas

    Science.gov (United States)

    Goldstein, Melvyn L.

    2011-01-01

    "Theory and simulations of solar system plasmas" aims to highlight results from microscopic to global scales, achieved by theoretical investigations and numerical simulations of the plasma dynamics in the solar system. The theoretical approach must allow evidencing the universality of the phenomena being considered, whatever the region is where their role is studied; at the Sun, in the solar corona, in the interplanetary space or in planetary magnetospheres. All possible theoretical issues concerning plasma dynamics are welcome, especially those using numerical models and simulations, since these tools are mandatory whenever analytical treatments fail, in particular when complex nonlinear phenomena are at work. Comparative studies for ongoing missions like Cassini, Cluster, Demeter, Stereo, Wind, SDO, Hinode, as well as those preparing future missions and proposals, like, e.g., MMS and Solar Orbiter, are especially encouraged.

  5. Microscopic nonlinear relativistic quantum theory of absorption of powerful x-ray radiation in plasma.

    Science.gov (United States)

    Avetissian, H K; Ghazaryan, A G; Matevosyan, H H; Mkrtchian, G F

    2015-10-01

    The microscopic quantum theory of plasma nonlinear interaction with the coherent shortwave electromagnetic radiation of arbitrary intensity is developed. The Liouville-von Neumann equation for the density matrix is solved analytically considering a wave field exactly and a scattering potential of plasma ions as a perturbation. With the help of this solution we calculate the nonlinear inverse-bremsstrahlung absorption rate for a grand canonical ensemble of electrons. The latter is studied in Maxwellian, as well as in degenerate quantum plasma for x-ray lasers at superhigh intensities and it is shown that one can achieve the efficient absorption coefficient in these cases.

  6. 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

  7. On Restructurable Control System Theory

    Science.gov (United States)

    Athans, M.

    1983-01-01

    The state of stochastic system and control theory as it impacts restructurable control issues is addressed. The multivariable characteristics of the control problem are addressed. The failure detection/identification problem is discussed as a multi-hypothesis testing problem. Control strategy reconfiguration, static multivariable controls, static failure hypothesis testing, dynamic multivariable controls, fault-tolerant control theory, dynamic hypothesis testing, generalized likelihood ratio (GLR) methods, and adaptive control are discussed.

  8. Nonlinear State Space Modeling and System Identification for Electrohydraulic Control

    Directory of Open Access Journals (Sweden)

    Jun Yan

    2013-01-01

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

  9. MINPACK-1, Subroutine Library for Nonlinear Equation System

    International Nuclear Information System (INIS)

    Garbow, Burton S.

    1984-01-01

    1 - Description of problem or function: MINPACK1 is a package of FORTRAN subprograms for the numerical solution of systems of non- linear equations and nonlinear least-squares problems. The individual programs are: Identification/Description: - CHKDER: Check gradients for consistency with functions, - DOGLEG: Determine combination of Gauss-Newton and gradient directions, - DPMPAR: Provide double precision machine parameters, - ENORM: Calculate Euclidean norm of vector, - FDJAC1: Calculate difference approximation to Jacobian (nonlinear equations), - FDJAC2: Calculate difference approximation to Jacobian (least squares), - HYBRD: Solve system of nonlinear equations (approximate Jacobian), - HYBRD1: Easy-to-use driver for HYBRD, - HYBRJ: Solve system of nonlinear equations (analytic Jacobian), - HYBRJ1: Easy-to-use driver for HYBRJ, - LMDER: Solve nonlinear least squares problem (analytic Jacobian), - LMDER1: Easy-to-use driver for LMDER, - LMDIF: Solve nonlinear least squares problem (approximate Jacobian), - LMDIF1: Easy-to-use driver for LMDIF, - LMPAR: Determine Levenberg-Marquardt parameter - LMSTR: Solve nonlinear least squares problem (analytic Jacobian, storage conserving), - LMSTR1: Easy-to-use driver for LMSTR, - QFORM: Accumulate orthogonal matrix from QR factorization QRFAC Compute QR factorization of rectangular matrix, - QRSOLV: Complete solution of least squares problem, - RWUPDT: Update QR factorization after row addition, - R1MPYQ: Apply orthogonal transformations from QR factorization, - R1UPDT: Update QR factorization after rank-1 addition, - SPMPAR: Provide single precision machine parameters. 4. Method of solution - MINPACK1 uses the modified Powell hybrid method and the Levenberg-Marquardt algorithm

  10. A deep belief network with PLSR for nonlinear system modeling.

    Science.gov (United States)

    Qiao, Junfei; Wang, Gongming; Li, Wenjing; Li, Xiaoli

    2017-10-31

    Nonlinear system modeling plays an important role in practical engineering, and deep learning-based deep belief network (DBN) is now popular in nonlinear system modeling and identification because of the strong learning ability. However, the existing weights optimization for DBN is based on gradient, which always leads to a local optimum and a poor training result. In this paper, a DBN with partial least square regression (PLSR-DBN) is proposed for nonlinear system modeling, which focuses on the problem of weights optimization for DBN using PLSR. Firstly, unsupervised contrastive divergence (CD) algorithm is used in weights initialization. Secondly, initial weights derived from CD algorithm are optimized through layer-by-layer PLSR modeling from top layer to bottom layer. Instead of gradient method, PLSR-DBN can determine the optimal weights using several PLSR models, so that a better performance of PLSR-DBN is achieved. Then, the analysis of convergence is theoretically given to guarantee the effectiveness of the proposed PLSR-DBN model. Finally, the proposed PLSR-DBN is tested on two benchmark nonlinear systems and an actual wastewater treatment system as well as a handwritten digit recognition (nonlinear mapping and modeling) with high-dimension input data. The experiment results show that the proposed PLSR-DBN has better performances of time and accuracy on nonlinear system modeling than that of other methods. Copyright © 2017 Elsevier Ltd. All rights reserved.

  11. Excitation power quantities in phase resonance testing of nonlinear systems with phase-locked-loop excitation

    Science.gov (United States)

    Peter, Simon; Leine, Remco I.

    2017-11-01

    Phase resonance testing is one method for the experimental extraction of nonlinear normal modes. This paper proposes a novel method for nonlinear phase resonance testing. Firstly, the issue of appropriate excitation is approached on the basis of excitation power considerations. Therefore, power quantities known from nonlinear systems theory in electrical engineering are transferred to nonlinear structural dynamics applications. A new power-based nonlinear mode indicator function is derived, which is generally applicable, reliable and easy to implement in experiments. Secondly, the tuning of the excitation phase is automated by the use of a Phase-Locked-Loop controller. This method provides a very user-friendly and fast way for obtaining the backbone curve. Furthermore, the method allows to exploit specific advantages of phase control such as the robustness for lightly damped systems and the stabilization of unstable branches of the frequency response. The reduced tuning time for the excitation makes the commonly used free-decay measurements for the extraction of backbone curves unnecessary. Instead, steady-state measurements for every point of the curve are obtained. In conjunction with the new mode indicator function, the correlation of every measured point with the associated nonlinear normal mode of the underlying conservative system can be evaluated. Moreover, it is shown that the analysis of the excitation power helps to locate sources of inaccuracies in the force appropriation process. The method is illustrated by a numerical example and its functionality in experiments is demonstrated on a benchmark beam structure.

  12. 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.

  13. Theory of nonlinear interaction of particles and waves in an inverse plasma maser. Part 1

    International Nuclear Information System (INIS)

    Krivitsky, V.S.; Vladimirov, S.V.

    1991-01-01

    An expression is obtained for the collision integral describing the simultaneous interaction of plasma particles with resonant and non-resonant waves. It is shown that this collision integral is determined by two processes: a 'direct' nonlinear interaction of particles and waves, and the influence of the non-stationary of the system. The expression for the nonlinear collision integral is found to be quite different from the expression for a quasi-linear collision integral; in particular, the nonlinear integral contains higher-order derivatives of the distribution function with respect to momentum than the quasi-linear one. (author)

  14. ℋ- adaptive observer design and parameter identification for a class of nonlinear fractional-order systems

    KAUST Repository

    Ndoye, Ibrahima; Voos, Holger; Laleg-Kirati, Taous-Meriem; Darouach, Mohamed

    2014-01-01

    In this paper, an adaptive observer design with parameter identification for a nonlinear system with external perturbations and unknown parameters is proposed. The states of the nonlinear system are estimated by a nonlinear observer and the unknown

  15. A Modified Lindstedt–Poincaré Method for a Strongly Nonlinear System with Quadratic and Cubic Nonlinearities

    Directory of Open Access Journals (Sweden)

    S.H. Chen

    1996-01-01

    Full Text Available A modified Lindstedt–Poincaré method is presented for extending the range of the validity of perturbation expansion to strongly nonlinear oscillations of a system with quadratic and cubic nonlinearities. Different parameter transformations are introduced to deal with equations with different nonlinear characteristics. All examples show that the efficiency and accuracy of the present method are very good.

  16. Improved Polynomial Fuzzy Modeling and Controller with Stability Analysis for Nonlinear Dynamical Systems

    Directory of Open Access Journals (Sweden)

    Hamed Kharrati

    2012-01-01

    Full Text Available This study presents an improved model and controller for nonlinear plants using polynomial fuzzy model-based (FMB systems. To minimize mismatch between the polynomial fuzzy model and nonlinear plant, the suitable parameters of membership functions are determined in a systematic way. Defining an appropriate fitness function and utilizing Taylor series expansion, a genetic algorithm (GA is used to form the shape of membership functions in polynomial forms, which are afterwards used in fuzzy modeling. To validate the model, a controller based on proposed polynomial fuzzy systems is designed and then applied to both original nonlinear plant and fuzzy model for comparison. Additionally, stability analysis for the proposed polynomial FMB control system is investigated employing Lyapunov theory and a sum of squares (SOS approach. Moreover, the form of the membership functions is considered in stability analysis. The SOS-based stability conditions are attained using SOSTOOLS. Simulation results are also given to demonstrate the effectiveness of the proposed method.

  17. Generalized projective chaos synchronization of gyroscope systems subjected to dead-zone nonlinear inputs

    International Nuclear Information System (INIS)

    Yau, H.-T.

    2008-01-01

    This Letter presents a robust control scheme to generalized projective synchronization between two identical two-degrees-of-freedom heavy symmetric gyroscopes with dead zone nonlinear inputs. Because of the nonlinear terms of the gyroscope system, the system exhibits complex and chaotic motions. By the Lyapunov stability theory with control terms, two suitable sliding surfaces are proposed to ensure the stability of the controlled closed-loop system in sliding mode. Then, two sliding mode controllers (SMC) are designed to guarantee the hitting of the sliding surfaces even when the control inputs contain dead-zone nonlinearity. This method allows us to arbitrarily direct the scaling factor onto a desired value. Numerical simulations show that this method works very well for the proposed controller

  18. Nonlinear signal processing using neural networks: Prediction and system modelling

    Energy Technology Data Exchange (ETDEWEB)

    Lapedes, A.; Farber, R.

    1987-06-01

    The backpropagation learning algorithm for neural networks is developed into a formalism for nonlinear signal processing. We illustrate the method by selecting two common topics in signal processing, prediction and system modelling, and show that nonlinear applications can be handled extremely well by using neural networks. The formalism is a natural, nonlinear extension of the linear Least Mean Squares algorithm commonly used in adaptive signal processing. Simulations are presented that document the additional performance achieved by using nonlinear neural networks. First, we demonstrate that the formalism may be used to predict points in a highly chaotic time series with orders of magnitude increase in accuracy over conventional methods including the Linear Predictive Method and the Gabor-Volterra-Weiner Polynomial Method. Deterministic chaos is thought to be involved in many physical situations including the onset of turbulence in fluids, chemical reactions and plasma physics. Secondly, we demonstrate the use of the formalism in nonlinear system modelling by providing a graphic example in which it is clear that the neural network has accurately modelled the nonlinear transfer function. It is interesting to note that the formalism provides explicit, analytic, global, approximations to the nonlinear maps underlying the various time series. Furthermore, the neural net seems to be extremely parsimonious in its requirements for data points from the time series. We show that the neural net is able to perform well because it globally approximates the relevant maps by performing a kind of generalized mode decomposition of the maps. 24 refs., 13 figs.

  19. 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.

  20. Nonlinear Predictive Sliding Mode Control for Active Suspension System

    Directory of Open Access Journals (Sweden)

    Dazhuang Wang

    2018-01-01

    Full Text Available An active suspension system is important in meeting the requirements of the ride comfort and handling stability for vehicles. In this work, a nonlinear model of active suspension system and a corresponding nonlinear robust predictive sliding mode control are established for the control problem of active suspension. Firstly, a seven-degree-of-freedom active suspension model is established considering the nonlinear effects of springs and dampers; and secondly, the dynamic model is expanded in the time domain, and the corresponding predictive sliding mode control is established. The uncertainties in the controller are approximated by the fuzzy logic system, and the adaptive controller reduces the approximation error to increase the robustness of the control system. Finally, the simulation results show that the ride comfort and handling stability performance of the active suspension system is better than that of the passive suspension system and the Skyhook active suspension. Thus, the system can obviously improve the shock absorption performance of vehicles.

  1. Nonlinear theory for the parametric instability with comparable electron and ion temperatures

    International Nuclear Information System (INIS)

    Oberman, C.

    1972-01-01

    The basic linear theory of the parametric instability driven by a pump E 0 sin ω 0 t oscillating near the electron plasma frequency is reviewed. An expression is derived for the temporal nonlinear development of the fluctuation spectrum of the excited waves. For plasma with comparable electron and ion temperatures nonlinear Landau damping of electron plasma waves on ions provides the dominant nonlinearity. The steady state solutions are examined both analytically and numerically in the limit when the spontaneous emission term is small. The characteristics of the plasma wave spectrum agrees well with the general features of ionospheric observations. The enhanced dissipation rate of the pump due to the presence of the fluctuations agrees with laboratory observations. (U.S.)

  2. Theory of nonlinear acoustic forces acting on fluids and particles in microsystems

    DEFF Research Database (Denmark)

    Karlsen, Jonas Tobias

    fundamentally new capabilities in chemical, biomedical, or clinical studies of single cells and bioparticles. This thesis, entitled Theory of nonlinear acoustic forces acting on fluids and particles in microsystems, advances the fundamental understanding of acoustofluidics by addressing the origin...... of the nonlinear acoustic forces acting on fluids and particles. Classical results in nonlinear acoustics for the non-dissipative acoustic radiation force acting on a particle or an interface, as well as the dissipative acoustic force densities driving acoustic streaming, are derived and discussed in terms...... in the continuous fluid parameters of density and compressibility, e.g., due to a solute concentration field, the thesis presents novel analytical results on the acoustic force density acting on inhomogeneous fluids in acoustic fields. This inhomogeneity-induced acoustic force density is non-dissipative in origin...

  3. Quantum theory from a nonlinear perspective Riccati equations in fundamental physics

    CERN Document Server

    Schuch, Dieter

    2018-01-01

    This book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics. Quantum mechanics is supposedly linear, invariant under time-reversal, conserving energy and, in contrast to classical theories, essentially based on the use of complex quantities. However, on a macroscopic level, processes apparently obey nonlinear irreversible evolution equations and dissipate energy. The Riccati equation, a nonlinear equation that can be linearized, has the potential to link these two worlds when applied to complex quantities. The nonlinearity can provide information about the phase-amplitude correlations of the complex quantities that cannot be obtained from the linearized form. As revealed in this wide ranging treatment, Riccati equations can also be found in many diverse fields of physics from Bose-Einstein-condensates to cosmology. The book will appeal to graduate students and theoretical physicists interested in ...

  4. Nonlinear scattering from a plasma column. I - Theory. II Special cases

    Science.gov (United States)

    Crawford, F. W.; Harker, K. J.

    1983-01-01

    The scattered signal excited by nonlinear mixing of two plane waves normally incident on an infinitely long column of plasma is investigated. A general solution is obtained for the polarization in which the electric field vectors of the waves are perpendicular to the column axis and the column is assumed to be radically inhomogeneous. This general theory is then applied to the special cases of the inhomogeneous column in the long-wavelength limit, and the homogeneous column both for the general case and in the long-wavelength limit. It is determined that dipole and quadrupole components should predominate in the polar radiation pattern for the long-wavelength case. The special case of second harmonic generation due to a single incident wave is analyzed in detail. Nonlinear scattering coefficients are computed, and the corresponding polar radiation patterns are determined. The findings of this study are employed to evaluate the feasibility of observing nonlinear scattering from meteor trails.

  5. A new extended H∞ filter for discrete nonlinear systems

    Institute of Scientific and Technical Information of China (English)

    张永安; 周荻; 段广仁

    2004-01-01

    Nonlinear estimation problem is investigated in this paper. By extension of a linear H∞ estimation with corrector-predictor form to nonlinear cases, a new extended H∞ filter is proposed for time-varying discretetime nonlinear systems. The new filter has a simple observer structure based on a local linearization model, and can be viewed as a general case of the extended Kalman filter (EKF). An example demonstrates that the new filter with a suitable-chosen prescribed H∞ bound performs better than the EKF.

  6. Integrability of a system of two nonlinear Schroedinger equations

    International Nuclear Information System (INIS)

    Zhukhunashvili, V.Z.

    1989-01-01

    In recent years the inverse scattering method has achieved significant successes in the integration of nonlinear models that arise in different branches of physics. However, its region of applicability is still restricted, i.e., not all nonlinear models can be integrated. In view of the great mathematical difficulties that arise in integration, it is clearly worth testing a model for integrability before turning to integration. Such a possibility is provided by the Zakharov-Schulman method. The question of the integrability of a system of two nonlinear Schroedinger equations is resolved. It is shown that the previously known cases exhaust all integrable variants

  7. Stability properties of nonlinear dynamical systems and evolutionary stable states

    Energy Technology Data Exchange (ETDEWEB)

    Gleria, Iram, E-mail: iram@fis.ufal.br [Instituto de Física, Universidade Federal de Alagoas, 57072-970 Maceió-AL (Brazil); Brenig, Leon [Faculté des Sciences, Université Libre de Bruxelles, 1050 Brussels (Belgium); Rocha Filho, Tarcísio M.; Figueiredo, Annibal [Instituto de Física and International Center for Condensed Matter Physics, Universidade de Brasília, 70919-970 Brasília-DF (Brazil)

    2017-03-18

    Highlights: • We address the problem of equilibrium stability in a general class of non-linear systems. • We link Evolutionary Stable States (ESS) to stable fixed points of square quasi-polynomial (QP) systems. • We show that an interior ES point may be related to stable interior fixed points of QP systems. - Abstract: In this paper we address the problem of stability in a general class of non-linear systems. We establish a link between the concepts of asymptotic stable interior fixed points of square Quasi-Polynomial systems and evolutionary stable states, a property of some payoff matrices arising from evolutionary games.

  8. Stability Analysis of Fractional-Order Nonlinear Systems with Delay

    Directory of Open Access Journals (Sweden)

    Yu Wang

    2014-01-01

    Full Text Available Stability analysis of fractional-order nonlinear systems with delay is studied. We propose the definition of Mittag-Leffler stability of time-delay system and introduce the fractional Lyapunov direct method by using properties of Mittag-Leffler function and Laplace transform. Then some new sufficient conditions ensuring asymptotical stability of fractional-order nonlinear system with delay are proposed firstly. And the application of Riemann-Liouville fractional-order systems is extended by the fractional comparison principle and the Caputo fractional-order systems. Numerical simulations of an example demonstrate the universality and the effectiveness of the proposed method.

  9. 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.

  10. General Systems Theory and Instructional Systems Design.

    Science.gov (United States)

    Salisbury, David F.

    1990-01-01

    Describes basic concepts in the field of general systems theory (GST) and identifies commonalities that exist between GST and instructional systems design (ISD). Models and diagrams that depict system elements in ISD are presented, and two matrices that show how GST has been used in ISD literature are included. (11 references) (LRW)

  11. Dynamic pull-in instability of geometrically nonlinear actuated micro-beams based on the modified couple stress theory

    Directory of Open Access Journals (Sweden)

    Hamid M. Sedighi

    Full Text Available This paper investigates the dynamic pull-in instability of vibrating micro-beams undergoing large deflection under electrosatically actuation. The governing equation of motion is derived based on the modified couple stress theory. Homotopy Perturbation Method is employed to produce the high accuracy approximate solution as well as the second-order frequency- amplitude relationship. The nonlinear governing equation of micro beam vibrations predeformed by an electric field includes both even and odd nonlinearities. The influences of basic non-dimensional parameters on the pull-in instability as well as the natural frequency are studied. It is demonstrated that two terms in series expansions are sufficient to produce high accuracy solution of the micro-structure. The accuracy of proposed asymptotic approach is validated via numerical results. The phase portrait of the system exhibits periodic and homoclinic orbits.

  12. Fault detection and fault-tolerant control for nonlinear systems

    CERN Document Server

    Li, Linlin

    2016-01-01

    Linlin Li addresses the analysis and design issues of observer-based FD and FTC for nonlinear systems. The author analyses the existence conditions for the nonlinear observer-based FD systems to gain a deeper insight into the construction of FD systems. Aided by the T-S fuzzy technique, she recommends different design schemes, among them the L_inf/L_2 type of FD systems. The derived FD and FTC approaches are verified by two benchmark processes. Contents Overview of FD and FTC Technology Configuration of Nonlinear Observer-Based FD Systems Design of L2 nonlinear Observer-Based FD Systems Design of Weighted Fuzzy Observer-Based FD Systems FTC Configurations for Nonlinear Systems< Application to Benchmark Processes Target Groups Researchers and students in the field of engineering with a focus on fault diagnosis and fault-tolerant control fields The Author Dr. Linlin Li completed her dissertation under the supervision of Prof. Steven X. Ding at the Faculty of Engineering, University of Duisburg-Essen, Germany...

  13. 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.

  14. Nonlinear Vibroimpact Characteristics of a Planetary Gear Transmission System

    Directory of Open Access Journals (Sweden)

    Jianxing Zhou

    2016-01-01

    Full Text Available In order to research the vibroimpact characteristics of a planetary gear transmission system under high speed and lightly loaded conditions, a new modeling method is proposed. In the modeling process, linear spring was used to simulate gear mesh elasticity under heavy load cases, and Hertz contact theory was used to calculate the contact force of gear pair under light load cases. Then, effects of the working conditions on the system vibroimpact characteristics are analyzed. The results show that, with input speed growing, the mesh force produced obvious fluctuations on the resonance frequencies of the sun gear and carrier torsion vibration, ring gear’s transverse vibration under the heavy load. Under light load condition, the collision vibration occurs in the gear pair; the changing trend of the contact force shows strongly nonlinear characteristics. The time of mesh-apart in gears pair decreases gradually as the load is increased; until it reaches collision vibration threshold value, the gear pair is no longer mesh-apart. With increasing of the input speed, the time of mesh-apart is decreased gradually; the fluctuation amplitude of contact force shows a linearly increasing trend. The study provides useful theoretical guideline for planetary gear transmission low-noise design.

  15. Frequency domain analysis and design of nonlinear systems based on Volterra series expansion a parametric characteristic approach

    CERN Document Server

    Jing, Xingjian

    2015-01-01

    This book is a systematic summary of some new advances in the area of nonlinear analysis and design in the frequency domain, focusing on the application oriented theory and methods based on the GFRF concept, which is mainly done by the author in the past 8 years. The main results are formulated uniformly with a parametric characteristic approach, which provides a convenient and novel insight into nonlinear influence on system output response in terms of characteristic parameters and thus facilitate nonlinear analysis and design in the frequency domain.  The book starts with a brief introduction to the background of nonlinear analysis in the frequency domain, followed by recursive algorithms for computation of GFRFs for different parametric models, and nonlinear output frequency properties. Thereafter the parametric characteristic analysis method is introduced, which leads to the new understanding and formulation of the GFRFs, and nonlinear characteristic output spectrum (nCOS) and the nCOS based analysis a...

  16. Dynamic Output Feedback Control for Nonlinear Networked Control Systems with Random Packet Dropout and Random Delay

    Directory of Open Access Journals (Sweden)

    Shuiqing Yu

    2013-01-01

    Full Text Available This paper investigates the dynamic output feedback control for nonlinear networked control systems with both random packet dropout and random delay. Random packet dropout and random delay are modeled as two independent random variables. An observer-based dynamic output feedback controller is designed based upon the Lyapunov theory. The quantitative relationship of the dropout rate, transition probability matrix, and nonlinear level is derived by solving a set of linear matrix inequalities. Finally, an example is presented to illustrate the effectiveness of the proposed method.

  17. Control and synchronization of chaos in nonlinear systems and prospects for application. Pt.1

    International Nuclear Information System (INIS)

    Fang Jinqing

    1996-01-01

    Main progress in one challenging subject of nonlinear science--control and synchronization of chaos in nonlinear systems are reviewed systematically, including recent advance in controlling and synchronizing hyperchaos. Current methods and principles of schemes of chaos control and synchronization are classified and summarized in detail. Potential prospects for application are commented both in theory and experiment. The whole review is divided into two parts. In the first one, subject on the mechanism and method of chaos control are analyzed and discussed extensively. In the second one, the synchronization of non-chaos, chaos, hyperchaos and their control and application are described. Main trends for development of the subject is mentioned. (101 refs.)

  18. Non-linear feedback control of the p53 protein-mdm2 inhibitor system using the derivative-free non-linear Kalman filter.

    Science.gov (United States)

    Rigatos, Gerasimos G

    2016-06-01

    It is proven that the model of the p53-mdm2 protein synthesis loop is a differentially flat one and using a diffeomorphism (change of state variables) that is proposed by differential flatness theory it is shown that the protein synthesis model can be transformed into the canonical (Brunovsky) form. This enables the design of a feedback control law that maintains the concentration of the p53 protein at the desirable levels. To estimate the non-measurable elements of the state vector describing the p53-mdm2 system dynamics, the derivative-free non-linear Kalman filter is used. Moreover, to compensate for modelling uncertainties and external disturbances that affect the p53-mdm2 system, the derivative-free non-linear Kalman filter is re-designed as a disturbance observer. The derivative-free non-linear Kalman filter consists of the Kalman filter recursion applied on the linearised equivalent of the protein synthesis model together with an inverse transformation based on differential flatness theory that enables to retrieve estimates for the state variables of the initial non-linear model. The proposed non-linear feedback control and perturbations compensation method for the p53-mdm2 system can result in more efficient chemotherapy schemes where the infusion of medication will be better administered.

  19. Nonlinear transport behavior of low dimensional electron systems

    Science.gov (United States)

    Zhang, Jingqiao

    The nonlinear behavior of low-dimensional electron systems attracts a great deal of attention for its fundamental interest as well as for potentially important applications in nanoelectronics. In response to microwave radiation and dc bias, strongly nonlinear electron transport that gives rise to unusual electron states has been reported in two-dimensional systems of electrons in high magnetic fields. There has also been great interest in the nonlinear response of quantum ballistic constrictions, where the effects of quantum interference, spatial dispersion and electron-electron interactions play crucial roles. In this thesis, experimental results of the research of low dimensional electron gas systems are presented. The first nonlinear phenomena were observed in samples of highly mobile two dimensional electrons in GaAs heavily doped quantum wells at different magnitudes of DC and AC (10 KHz to 20 GHz) excitations. We found that in the DC excitation regime the differential resistance oscillates with the DC current and external magnetic field, similar behavior was observed earlier in AlGaAs/GaAs heterostructures [C.L. Yang et al. ]. At external AC excitations the resistance is found to be also oscillating as a function of the magnetic field. However the form of the oscillations is considerably different from the DC case. We show that at frequencies below 100 KHz the difference is a result of a specific average of the DC differential resistance during the period of the external AC excitations. Secondly, in similar samples, strong suppression of the resistance by the electric field is observed in magnetic fields at which the Landau quantization of electron motion occurs. The phenomenon survives at high temperatures at which the Shubnikov de Haas oscillations are absent. The scale of the electric fields essential for the effect, is found to be proportional to temperature in the low temperature limit. We suggest that the strong reduction of the longitudinal resistance

  20. Continuous and distributed systems theory and applications

    CERN Document Server

    Sadovnichiy, Victor

    2014-01-01

    In this volume, the authors close the gap between abstract mathematical approaches, such as abstract algebra, number theory, nonlinear functional analysis, partial differential equations, methods of nonlinear and multi-valued analysis, on the one hand, and practical applications in nonlinear mechanics, decision making theory and control theory on the other. Readers will also benefit from the presentation of modern mathematical modeling methods for the numerical solution of complicated engineering problems in hydromechanics, geophysics and mechanics of continua. This compilation will be of interest to mathematicians and engineers working at the interface of these field. It presents selected works of the open seminar series of Lomonosov Moscow State University and the National Technical University of Ukraine “Kyiv Polytechnic Institute”. The authors come from Germany, Italy, Spain, Russia, Ukraine, and the USA.

  1. Enhanced aeroelastic energy harvesting by exploiting combined nonlinearities: theory and experiment

    International Nuclear Information System (INIS)

    Sousa, V C; De M Anicézio, M; De Marqui Jr, C; Erturk, A

    2011-01-01

    Converting aeroelastic vibrations into electricity for low power generation has received growing attention over the past few years. In addition to potential applications for aerospace structures, the goal is to develop alternative and scalable configurations for wind energy harvesting to use in wireless electronic systems. This paper presents modeling and experiments of aeroelastic energy harvesting using piezoelectric transduction with a focus on exploiting combined nonlinearities. An airfoil with plunge and pitch degrees of freedom (DOF) is investigated. Piezoelectric coupling is introduced to the plunge DOF while nonlinearities are introduced through the pitch DOF. A state-space model is presented and employed for the simulations of the piezoaeroelastic generator. A two-state approximation to Theodorsen aerodynamics is used in order to determine the unsteady aerodynamic loads. Three case studies are presented. First the interaction between piezoelectric power generation and linear aeroelastic behavior of a typical section is investigated for a set of resistive loads. Model predictions are compared to experimental data obtained from the wind tunnel tests at the flutter boundary. In the second case study, free play nonlinearity is added to the pitch DOF and it is shown that nonlinear limit-cycle oscillations can be obtained not only above but also below the linear flutter speed. The experimental results are successfully predicted by the model simulations. Finally, the combination of cubic hardening stiffness and free play nonlinearities is considered in the pitch DOF. The nonlinear piezoaeroelastic response is investigated for different values of the nonlinear-to-linear stiffness ratio. The free play nonlinearity reduces the cut-in speed while the hardening stiffness helps in obtaining persistent oscillations of acceptable amplitude over a wider range of airflow speeds. Such nonlinearities can be introduced to aeroelastic energy harvesters (exploiting

  2. On the theory of weak turbulence for the nonlinear Schrödinger equation

    CERN Document Server

    Escobedo, M

    2015-01-01

    The authors study the Cauchy problem for a kinetic equation arising in the weak turbulence theory for the cubic nonlinear Schrödinger equation. They define suitable concepts of weak and mild solutions and prove local and global well posedness results. Several qualitative properties of the solutions, including long time asymptotics, blow up results and condensation in finite time are obtained. The authors also prove the existence of a family of solutions that exhibit pulsating behavior.

  3. Robust Nonlinear Control with Compensation Operator for a Peltier System

    Directory of Open Access Journals (Sweden)

    Sheng-Jun Wen

    2014-01-01

    Full Text Available Robust nonlinear control with compensation operator is presented for a Peltier actuated system, where the compensation operator is designed by using a predictive model on heat radiation. For the Peltier system, the heat radiation is related to the fourth power of temperature. So, the heat radiation is affected evidently by the temperature when it is high and temperature difference between the system and environment is large. A new nonlinear model with the heat radiation is set up for the system according to some thermal conduction laws. To ensure robust stability of the nonlinear system, operator based robust right coprime factorization design is considered. Also, a compensation operator based on a predictive model is proposed to cancel effect of the heat radiation, where the predictive model is set up by using radial basis kernel function based SVM (support vector machine method. Finally, simulation results are given to show the effectiveness of the proposed scheme.

  4. Nonlinear control for a class of hydraulic servo system.

    Science.gov (United States)

    Yu, Hong; Feng, Zheng-jin; Wang, Xu-yong

    2004-11-01

    The dynamics of hydraulic systems are highly nonlinear and the system may be subjected to non-smooth and discontinuous nonlinearities due to directional change of valve opening, friction, etc. Aside from the nonlinear nature of hydraulic dynamics, hydraulic servo systems also have large extent of model uncertainties. To address these challenging issues, a robust state-feedback controller is designed by employing backstepping design technique such that the system output tracks a given signal arbitrarily well, and all signals in the closed-loop system remain bounded. Moreover, a relevant disturbance attenuation inequality is satisfied by the closed-loop signals. Compared with previously proposed robust controllers, this paper's robust controller based on backstepping recursive design method is easier to design, and is more suitable for implementation.

  5. Rigorous Verification for the Solution of Nonlinear Interval System ...

    African Journals Online (AJOL)

    We survey a general method for solving nonlinear interval systems of equations. In particular, we paid special attention to the computational aspects of linear interval systems since the bulk of computations are done during the stage of computing outer estimation of the including linear interval systems. The height of our ...

  6. Synchronization of two different chaotic systems via nonlinear ...

    African Journals Online (AJOL)

    ADOWIE PERE

    ABSTRACT: This work reports the synchronization of a pair of four chaotic systems via nonlinear control technique. This method has been found to be easy to implement and effective especially on two different chaotic systems. We paired four chaotic systems out of which one is new and we have six possible pairs.

  7. Systems Theory and Systems Approach to Leadership

    Directory of Open Access Journals (Sweden)

    Dr.Sc. Berim Ramosaj

    2014-06-01

    Full Text Available Systems theory is product of the efforts of many researchers to create an intermediate field of coexistence of all sciences. If not for anything else, because of the magnitude that the use of systemic thinking and systemic approach has taken, it has become undisputed among the theories. Systems theory not only provides a glossary of terms with which researchers from different fields can be understood, but provides a framework for the presentation and interpretation of phenomena and realities. This paper addresses a systematic approach to leadership, as an attempt to dredge leadership and systems theory literature to find the meeting point. Systems approach is not an approach to leadership in terms of a manner of leader’s work, but it’s the leader's determination to factorize in his leadership the external environment and relationships with and among elements. Leader without followers is unable to exercise his leadership and to ensure their conviction he should provide a system, a structure, a purpose, despite the alternative chaos. Systems approach clarifies the thought on the complexity and dynamism of the environment and provides a framework for building ideas. If the general system theory is the skeleton of science (Boulding: 1956, this article aims to replenish it with leadership muscles by prominent authors who have written on systems theory and leadership, as well as through original ideas. In this work analytical methods were used (by analyzing approaches individually as well as synthetic methods (by assaying individual approaches in context of entirety. The work is a critical review of literature as well as a deductive analysis mingled with models proposed by authors through inductive analysis. Meta-analysis has been used to dissect the interaction and interdependence between leadership approaches.

  8. Nonlinear analysis of the cooperation of strategic alliances through stochastic catastrophe theory

    Science.gov (United States)

    Xu, Yan; Hu, Bin; Wu, Jiang; Zhang, Jianhua

    2014-04-01

    The excitation intervention of strategic alliance may change with the changes in the parameters of circumstance (e.g., external alliance tasks). As a result, the stable cooperation between members may suffer a complete unplanned betrayal at last. However, current perspectives on strategic alliances cannot adequately explain this transition mechanism. This study is a first attempt to analyze this nonlinear phenomenon through stochastic catastrophe theory (SCT). A stochastic dynamics model is constructed based on the cooperation of strategic alliance from the perspective of evolutionary game theory. SCT explains the discontinuous changes caused by the changes in environmental parameters. Theoretically, we identify conditions where catastrophe can occur in the cooperation of alliance members.

  9. T.I.Tech./K.E.S. Conference on Nonlinear and Convex Analysis in Economic Theory

    CERN Document Server

    Takahashi, Wataru

    1995-01-01

    The papers collected in this volume are contributions to T.I.Tech./K.E.S. Conference on Nonlinear and Convex Analysis in Economic Theory, which was held at Keio University, July 2-4, 1993. The conference was organized by Tokyo Institute of Technology (T. I. Tech.) and the Keio Economic Society (K. E. S.) , and supported by Nihon Keizai Shimbun Inc .. A lot of economic problems can be formulated as constrained optimiza­ tions and equilibrations of their solutions. Nonlinear-convex analysis has been supplying economists with indispensable mathematical machineries for these problems arising in economic theory. Conversely, mathematicians working in this discipline of analysis have been stimulated by various mathematical difficulties raised by economic the­ ories. Although our special emphasis was laid upon "nonlinearity" and "con­ vexity" in relation with economic theories, we also incorporated stochastic aspects of financial economics in our project taking account of the remark­ able rapid growth of this dis...

  10. A nonlinear theory of relativistic klystrons connected to a coaxial waveguide

    International Nuclear Information System (INIS)

    Uhm, H.S.; Hendricks, K.J.; Arman, M.J.; Bowers, L.; Hackett, K.E.; Spencer, T.A.; Coleman, P.D.; Lemke, R.W.

    1997-01-01

    A self-consistent nonlinear theory of current modulation in an electron beam propagating through relativistic klystrons connected to a coaxial waveguide is developed. A theoretical model of the beam-energy increase Δγ near the extraction cavity is also developed, based on the self-potential depression. The potential depression κ can be significantly reduced in the vicinity of the extraction cavity from its value at the injection point. In appropriate system parameters, the kinetic-energy increase can easily be more than 50 keV, thereby eliminating the possibility of virtual cathode in the extraction cavity. Properties of the current modulation in a klystron are also investigated, assuming that a regular cylindrical waveguide is connected to a coaxial waveguide at the propagation distance z=z 1 . Due to proximity of a grounded conductor, the beam close-quote s potential depression κ in the coaxial region is considerably less than that in the regular region. It is shown in the present analysis that amplitude of the current modulation increases drastically as the coaxial inner-conductor approaches the driving cavity. Moreover, the amplitude of the current modulation in the coaxial region changes slowly in comparison with that in the regular region

  11. Transients of the electromagnetically-induced-transparency-enhanced refractive Kerr nonlinearity: Theory

    International Nuclear Information System (INIS)

    Pack, M. V.; Camacho, R. M.; Howell, J. C.

    2006-01-01

    We present a theory describing the transients and rise times of the refractive Kerr nonlinearity which is enhanced using electromagnetically induced transparency (EIT). We restrict our analysis to the case of a pulsed signal field with continuous-wave EIT fields, and all fields are well below saturation. These restrictions enable the reduction of an EIT Kerr, four-level, density-matrix equation to a two-level Bloch-vector equation which has a simple and physically intuitive algebraic solution. The physically intuitive picture of a two-level Bloch vector provides insights that are easily generalized to more complex and experimentally realistic models. We consider generalization to the cases of Doppler broadening, many-level EIT systems (we consider the D1 line of 87 Rb), and optically thick media. For the case of optically thick media we find that the rise time of the refractive EIT Kerr effect is proportional to the optical thickness. The rise time of the refractive EIT Kerr effect sets important limitations for potential few-photon applications

  12. Gestalt Therapy and General System Theory.

    Science.gov (United States)

    Whitner, Phillip A.

    While General Systems Theory (GST) concepts appear to be applicable in explaining some of the phenomena that occur in a Gestalt Therapy group, research is needed to support this assumption. General Systems Theory may not be a group theory per se. Instead, GST may be a theory about groups. A meta-theory exists where its value and usefulness is…

  13. Dichotomy of nonlinear systems: Application to chaos control of nonlinear electronic circuit

    International Nuclear Information System (INIS)

    Wang Jinzhi; Duan Zhisheng; Huang Lin

    2006-01-01

    In this Letter a new method of chaos control for Chua's circuit and the modified canonical Chua's electrical circuit is proposed by using the results of dichotomy in nonlinear systems. A linear feedback control based on linear matrix inequality (LMI) is given such that chaos oscillation or hyperchaos phenomenon of circuit systems injected control signal disappear. Numerical simulations are presented to illustrate the efficiency of the proposed method

  14. Switching control for a class of nonlinear SISO systems with an application to post-harvest food storage

    NARCIS (Netherlands)

    van Mourik, S.; Zwart, Heiko J.; Keesman, K.J.

    2007-01-01

    For a class of scalar nonlinear systems with switching input a controller is designed using design theory for linear systems. A stability criterion is derived that contains all the physical system parameters, allowing a stability analysis without the need for numerical simulation. The results are

  15. System Theory and Physiological Processes.

    Science.gov (United States)

    Jones, R W

    1963-05-03

    Engineers and physiologists working together in experimental and theoretical studies predict that the application of system analysis to biological processes will increase understanding of these processes and broaden the base of system theory. Richard W. Jones, professor of electrical engineering at Northwestern University, Evanston, Illinois, and John S. Gray, professor of physiology at Northwestern's Medical School, discuss these developments. Their articles are adapted from addresses delivered in Chicago in November 1962 at the 15th Annual Conference on Engineering in Medicine and Biology.

  16. A nonlinear complementarity approach for the national energy modeling system

    International Nuclear Information System (INIS)

    Gabriel, S.A.; Kydes, A.S.

    1995-01-01

    The National Energy Modeling System (NEMS) is a large-scale mathematical model that computes equilibrium fuel prices and quantities in the U.S. energy sector. At present, to generate these equilibrium values, NEMS sequentially solves a collection of linear programs and nonlinear equations. The NEMS solution procedure then incorporates the solutions of these linear programs and nonlinear equations in a nonlinear Gauss-Seidel approach. The authors describe how the current version of NEMS can be formulated as a particular nonlinear complementarity problem (NCP), thereby possibly avoiding current convergence problems. In addition, they show that the NCP format is equally valid for a more general form of NEMS. They also describe several promising approaches for solving the NCP form of NEMS based on recent Newton type methods for general NCPs. These approaches share the feature of needing to solve their direction-finding subproblems only approximately. Hence, they can effectively exploit the sparsity inherent in the NEMS NCP

  17. Trends in modern system theory

    Science.gov (United States)

    Athans, M.

    1976-01-01

    The topics considered are related to linear control system design, adaptive control, failure detection, control under failure, system reliability, and large-scale systems and decentralized control. It is pointed out that the design of a linear feedback control system which regulates a process about a desirable set point or steady-state condition in the presence of disturbances is a very important problem. The linearized dynamics of the process are used for design purposes. The typical linear-quadratic design involving the solution of the optimal control problem of a linear time-invariant system with respect to a quadratic performance criterion is considered along with gain reduction theorems and the multivariable phase margin theorem. The stumbling block in many adaptive design methodologies is associated with the amount of real time computation which is necessary. Attention is also given to the desperate need to develop good theories for large-scale systems, the beginning of a microprocessor revolution, the translation of the Wiener-Hopf theory into the time domain, and advances made in dynamic team theory, dynamic stochastic games, and finite memory stochastic control.

  18. Nonlinear dynamic analysis of 2-DOF nonlinear vibration isolation floating raft systems with feedback control

    International Nuclear Information System (INIS)

    Li Yingli; Xu Daolin; Fu Yiming; Zhou Jiaxi

    2012-01-01

    In this paper, the average method is adopted to analysis dynamic characteristics of nonlinear vibration isolation floating raft system with feedback control. The analytic results show that the purposes of reducing amplitude of oscillation and complicating the motion can be achieved by adjusting properly the system parameters, exciting frequency and control gain. The conclusions can provide some available evidences for the design and improvement of both the passive and active control of the vibration isolation systems. By altering the exciting frequency and control gain, complex motion of the system can be obtained. Numerical simulations show the system exhibits period vibration, double period vibration and quasi-period motion.

  19. Incremental passivity and output regulation for switched nonlinear systems

    Science.gov (United States)

    Pang, Hongbo; Zhao, Jun

    2017-10-01

    This paper studies incremental passivity and global output regulation for switched nonlinear systems, whose subsystems are not required to be incrementally passive. A concept of incremental passivity for switched systems is put forward. First, a switched system is rendered incrementally passive by the design of a state-dependent switching law. Second, the feedback incremental passification is achieved by the design of a state-dependent switching law and a set of state feedback controllers. Finally, we show that once the incremental passivity for switched nonlinear systems is assured, the output regulation problem is solved by the design of global nonlinear regulator controllers comprising two components: the steady-state control and the linear output feedback stabilising controllers, even though the problem for none of subsystems is solvable. Two examples are presented to illustrate the effectiveness of the proposed approach.

  20. Decreasing the LHC impedance with a nonlinear collimation system

    CERN Document Server

    Resta-López, J; Zimmermann, F

    2007-01-01

    A two-stage nonlinear collimation system based on a pair of skew sextupoles is presented for the LHC.We show the details of the optics design and study the halo cleaning efficiency of such a system. This nonlinear collimation system would allow opening up collimator gaps, and thereby reduce the collimator impedance, which presently limits the LHC beam intensity. Assuming the nominal LHC beam at 7 TeV, the transverse coherent tune shifts of rigid-dipole coupled-bunch modes are computed for both the baseline linear collimation system and the proposed nonlinear one. In either case, the tune shifts of the most unstable modes are compared with the stability diagrams for Landau damping.

  1. 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.

  2. Nonlinear optimization

    CERN Document Server

    Ruszczynski, Andrzej

    2011-01-01

    Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates the theory and the methods of nonlinear optimization in a unified, clear, and mathematically rigorous fashion, with detailed and easy-to-follow proofs illustrated by numerous examples and figures. The book covers convex analysis, the theory of optimality conditions, duality theory, and numerical methods for solving unconstrained and constrained optimization problems. It addresses not only classical material but also modern top...

  3. Fault prediction for nonlinear stochastic system with incipient faults based on particle filter and nonlinear regression.

    Science.gov (United States)

    Ding, Bo; Fang, Huajing

    2017-05-01

    This paper is concerned with the fault prediction for the nonlinear stochastic system with incipient faults. Based on the particle filter and the reasonable assumption about the incipient faults, the modified fault estimation algorithm is proposed, and the system state is estimated simultaneously. According to the modified fault estimation, an intuitive fault detection strategy is introduced. Once each of the incipient fault is detected, the parameters of which are identified by a nonlinear regression method. Then, based on the estimated parameters, the future fault signal can be predicted. Finally, the effectiveness of the proposed method is verified by the simulations of the Three-tank system. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

  4. Nonlinear theory of magnetohydrodynamic flows of a compressible fluid in the shallow water approximation

    Energy Technology Data Exchange (ETDEWEB)

    Klimachkov, D. A., E-mail: klimchakovdmitry@gmail.com; Petrosyan, A. S., E-mail: apetrosy@iki.rssi.ru [Russian Academy of Sciences, Space Research Institute (Russian Federation)

    2016-09-15

    Shallow water magnetohydrodynamic (MHD) theory describing incompressible flows of plasma is generalized to the case of compressible flows. A system of MHD equations is obtained that describes the flow of a thin layer of compressible rotating plasma in a gravitational field in the shallow water approximation. The system of quasilinear hyperbolic equations obtained admits a complete simple wave analysis and a solution to the initial discontinuity decay problem in the simplest version of nonrotating flows. In the new equations, sound waves are filtered out, and the dependence of density on pressure on large scales is taken into account that describes static compressibility phenomena. In the equations obtained, the mass conservation law is formulated for a variable that nontrivially depends on the shape of the lower boundary, the characteristic vertical scale of the flow, and the scale of heights at which the variation of density becomes significant. A simple wave theory is developed for the system of equations obtained. All self-similar discontinuous solutions and all continuous centered self-similar solutions of the system are obtained. The initial discontinuity decay problem is solved explicitly for compressible MHD equations in the shallow water approximation. It is shown that there exist five different configurations that provide a solution to the initial discontinuity decay problem. For each configuration, conditions are found that are necessary and sufficient for its implementation. Differences between incompressible and compressible cases are analyzed. In spite of the formal similarity between the solutions in the classical case of MHD flows of an incompressible and compressible fluids, the nonlinear dynamics described by the solutions are essentially different due to the difference in the expressions for the squared propagation velocity of weak perturbations. In addition, the solutions obtained describe new physical phenomena related to the dependence of the

  5. Seismic testing and analysis of a prototypic nonlinear piping system

    International Nuclear Information System (INIS)

    Barta, D.A.; Anderson, M.J.; Severud, L.K.

    1982-11-01

    A series of seismic tests and analyses of a nonlinear Fast Flux Test Facility (FFTF) prototypic piping system are described, and measured responses are compared with analytical predictions. The test loop was representative of a typical LMFBR insulated small bore piping system and it was supported from a rigid test frame by prototypic dead weight supports, mechanical snubbers and pipe clamps. Various piping support configurations were tested and analyzed to evaluate the effects of free play and other nonlinear stiffness characteristics on the piping system response

  6. Stability properties of a general class of nonlinear dynamical systems

    Science.gov (United States)

    Gléria, I. M.; Figueiredo, A.; Rocha Filho, T. M.

    2001-05-01

    We establish sufficient conditions for the boundedness of the trajectories and the stability of the fixed points in a class of general nonlinear systems, the so-called quasi-polynomial vector fields, with the help of a natural embedding of such systems in a family of generalized Lotka-Volterra (LV) equations. A purely algebraic procedure is developed to determine such conditions. We apply our method to obtain new results for LV systems, by a reparametrization in time variable, and to study general nonlinear vector fields, originally far from the LV format.

  7. Stability properties of a general class of nonlinear dynamical systems

    Energy Technology Data Exchange (ETDEWEB)

    Gleria, I.M. [Filho Instituto de Fisica, Universidade de Brasilia, Campus Universitario Darcy Ribeiro, Brasilia (Brazil). E-mail: iram@ucb.br; Figueiredo, A. [Filho Instituto de Fisica, Universidade de Brasilia, Campus Universitario Darcy Ribeiro, Brasilia (Brazil). E-mail: annibal@helium.fis.unb.br; Rocha, T.M. [Filho Instituto de Fisica, Universidade de Brasilia, Campus Universitario Darcy Ribeiro, Brasilia (Brazil). E-mail: marciano@helium.fis.unb.br

    2001-05-04

    We establish sufficient conditions for the boundedness of the trajectories and the stability of the fixed points in a class of general nonlinear systems, the so-called quasi-polynomial vector fields, with the help of a natural embedding of such systems in a family of generalized Lotka-Volterra (LV) equations. A purely algebraic procedure is developed to determine such conditions. We apply our method to obtain new results for LV systems, by a reparametrization in time variable, and to study general nonlinear vector fields, originally far from the LV format. (author)

  8. Partial regularity of weak solutions to a PDE system with cubic nonlinearity

    Science.gov (United States)

    Liu, Jian-Guo; Xu, Xiangsheng

    2018-04-01

    In this paper we investigate regularity properties of weak solutions to a PDE system that arises in the study of biological transport networks. The system consists of a possibly singular elliptic equation for the scalar pressure of the underlying biological network coupled to a diffusion equation for the conductance vector of the network. There are several different types of nonlinearities in the system. Of particular mathematical interest is a term that is a polynomial function of solutions and their partial derivatives and this polynomial function has degree three. That is, the system contains a cubic nonlinearity. Only weak solutions to the system have been shown to exist. The regularity theory for the system remains fundamentally incomplete. In particular, it is not known whether or not weak solutions develop singularities. In this paper we obtain a partial regularity theorem, which gives an estimate for the parabolic Hausdorff dimension of the set of possible singular points.

  9. Nonlinear Analysis of Rotors Supported by Air Foil Journal Bearings – Theory and Experiments

    DEFF Research Database (Denmark)

    Larsen, Jon Steffen

    with a good margin of rotordynamical stable operation. To ensure this, good mathematical models, capable of accurately predicting the dynamic behaviour of the rotor-bearing system, are required at the design stage. This thesis focuses on developing and improving existing mathematical models for predicting...... mechanical behaviour of the bump foils was carefully examined. A mathematical model capable of predicting this nonlinear behaviour was developed and compared to the experimental results with good agreement. With the second test rig, the overall nonlinear behaviour of the rotor-bearing system was investigated...

  10. Measurement Model Nonlinearity in Estimation of Dynamical Systems

    Science.gov (United States)

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

    2012-06-01

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

  11. Model Reduction of Nonlinear Aeroelastic Systems Experiencing Hopf Bifurcation

    KAUST Repository

    Abdelkefi, Abdessattar

    2013-06-18

    In this paper, we employ the normal form to derive a reduced - order model that reproduces nonlinear dynamical behavior of aeroelastic systems that undergo Hopf bifurcation. As an example, we consider a rigid two - dimensional airfoil that is supported by nonlinear springs in the pitch and plunge directions and subjected to nonlinear aerodynamic loads. We apply the center manifold theorem on the governing equations to derive its normal form that constitutes a simplified representation of the aeroelastic sys tem near flutter onset (manifestation of Hopf bifurcation). Then, we use the normal form to identify a self - excited oscillator governed by a time - delay ordinary differential equation that approximates the dynamical behavior while reducing the dimension of the original system. Results obtained from this oscillator show a great capability to predict properly limit cycle oscillations that take place beyond and above flutter as compared with the original aeroelastic system.

  12. Distributed control design for nonlinear output agreement in convergent systems

    NARCIS (Netherlands)

    Weitenberg, Erik; De Persis, Claudio

    2015-01-01

    This work studies the problem of output agreement in homogeneous networks of nonlinear dynamical systems under time-varying disturbances using controllers placed at the nodes of the networks. For the class of contractive systems, necessary and sufficient conditions for output agreement are derived,

  13. Linear time heteronymous damping in nonlinear parametric systems

    Czech Academy of Sciences Publication Activity Database

    Hortel, Milan; Škuderová, Alena; Houfek, Martin

    2016-01-01

    Roč. 40, 23-24 (2016), s. 10038-10051 ISSN 0307-904X Institutional support: RVO:61388998 Keywords : nonlinear dynamics of systems * parametric systems * time heteronymous damping * gears Subject RIV: JT - Propulsion, Motors ; Fuels Impact factor: 2.350, year: 2016

  14. Nonlinear observer based phase synchronization of chaotic systems

    International Nuclear Information System (INIS)

    Meng Juan; Wang Xingyuan

    2007-01-01

    This Letter analyzes the phase synchronization problem of autonomous chaotic systems. Based on the nonlinear state observer algorithm and the pole placement technique, a phase synchronization scheme is designed. The phase synchronization of a new chaotic system is achieved by using this observer controller. Numerical simulations further demonstrate the effectiveness of the proposed phase synchronization scheme

  15. Medium Theory and Social Systems

    DEFF Research Database (Denmark)

    Tække, Jesper

      the  possibility  for  observation both of a social micro and a social macro level from a medium perspective. In the next  section  the paper  frames  the macro  level by  a  tentative  synthesis of  the medium  theory  and  the  sociological systems theory briefly describing a socio......-evolutionary process where new media alter  the societal capacity to handle complexity  in  time and space.  In  this section it becomes probable  that  by  means  of  different  media,  social  systems  give  different  possibilities  for  actual  social  performance.  In a way,  social  systems  themselves can be......  seen as medium  for  formation. Finally  the  paper  takes  the micro  level  perspective  by  applying  the  theory  to  newsgroups,  interpreting  them as self-organizing interactive systems giving a differentiated and diversified scope for social  inclusion.  ...

  16. Contraction theory based adaptive synchronization of chaotic systems

    International Nuclear Information System (INIS)

    Sharma, B.B.; Kar, I.N.

    2009-01-01

    Contraction theory based stability analysis exploits the incremental behavior of trajectories of a system with respect to each other. Application of contraction theory provides an alternative way for stability analysis of nonlinear systems. This paper considers the design of a control law for synchronization of certain class of chaotic systems based on backstepping technique. The controller is selected so as to make the error dynamics between the two systems contracting. Synchronization problem with and without uncertainty in system parameters is discussed and necessary stability proofs are worked out using contraction theory. Suitable adaptation laws for unknown parameters are proposed based on the contraction principle. The numerical simulations verify the synchronization of the chaotic systems. Also parameter estimates converge to their true values with the proposed adaptation laws.

  17. Nonlinear dynamics and complexity

    CERN Document Server

    Luo, Albert; Fu, Xilin

    2014-01-01

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

  18. φq-field theory for portfolio optimization: “fat tails” and nonlinear correlations

    Science.gov (United States)

    Sornette, D.; Simonetti, P.; Andersen, J. V.

    2000-08-01

    Physics and finance are both fundamentally based on the theory of random walks (and their generalizations to higher dimensions) and on the collective behavior of large numbers of correlated variables. The archetype examplifying this situation in finance is the portfolio optimization problem in which one desires to diversify on a set of possibly dependent assets to optimize the return and minimize the risks. The standard mean-variance solution introduced by Markovitz and its subsequent developments is basically a mean-field Gaussian solution. It has severe limitations for practical applications due to the strongly non-Gaussian structure of distributions and the nonlinear dependence between assets. Here, we present in details a general analytical characterization of the distribution of returns for a portfolio constituted of assets whose returns are described by an arbitrary joint multivariate distribution. In this goal, we introduce a non-linear transformation that maps the returns onto Gaussian variables whose covariance matrix provides a new measure of dependence between the non-normal returns, generalizing the covariance matrix into a nonlinear covariance matrix. This nonlinear covariance matrix is chiseled to the specific fat tail structure of the underlying marginal distributions, thus ensuring stability and good conditioning. The portfolio distribution is then obtained as the solution of a mapping to a so-called φq field theory in particle physics, of which we offer an extensive treatment using Feynman diagrammatic techniques and large deviation theory, that we illustrate in details for multivariate Weibull distributions. The interaction (non-mean field) structure in this field theory is a direct consequence of the non-Gaussian nature of the distribution of asset price returns. We find that minimizing the portfolio variance (i.e. the relatively “small” risks) may often increase the large risks, as measured by higher normalized cumulants. Extensive

  19. Stochastic theory of polarized light in nonlinear birefringent media: An application to optical rotation

    Science.gov (United States)

    Tsuchida, Satoshi; Kuratsuji, Hiroshi

    2018-05-01

    A stochastic theory is developed for the light transmitting the optical media exhibiting linear and nonlinear birefringence. The starting point is the two-component nonlinear Schrödinger equation (NLSE). On the basis of the ansatz of “soliton” solution for the NLSE, the evolution equation for the Stokes parameters is derived, which turns out to be the Langevin equation by taking account of randomness and dissipation inherent in the birefringent media. The Langevin equation is converted to the Fokker-Planck (FP) equation for the probability distribution by employing the technique of functional integral on the assumption of the Gaussian white noise for the random fluctuation. The specific application is considered for the optical rotation, which is described by the ellipticity (third component of the Stokes parameters) alone: (i) The asymptotic analysis is given for the functional integral, which leads to the transition rate on the Poincaré sphere. (ii) The FP equation is analyzed in the strong coupling approximation, by which the diffusive behavior is obtained for the linear and nonlinear birefringence. These would provide with a basis of statistical analysis for the polarization phenomena in nonlinear birefringent media.

  20. Nonlinear vibration of rectangular atomic force microscope cantilevers by considering the Hertzian contact theory

    Energy Technology Data Exchange (ETDEWEB)

    Sadeghi, A., E-mail: a_sadeghi@srbiau.ac.ir [Islamic Azad Univ., Dept. of Mechanical and Aerospace Engineering, Science and Research Branch, Tehran (Iran, Islamic Republic of); Zohoor, H. [Sharif Univ. of Technology, Center of Excellence in Design, Robotics and Automation, Tehran (Iran, Islamic Republic of); The Academy of Sciences if I.R. Iran (Iran, Islamic Republic of)

    2010-05-15

    The nonlinear flexural vibration for a rectangular atomic force microscope cantilever is investigated by using Timoshenko beam theory. In this paper, the normal and tangential tip-sample interaction forces are found from a Hertzian contact model and the effects of the contact position, normal and lateral contact stiffness, tip height, thickness of the beam, and the angle between the cantilever and the sample surface on the nonlinear frequency to linear frequency ratio are studied. The differential quadrature method is employed to solve the nonlinear differential equations of motion. The results show that softening behavior is seen for most cases and by increasing the normal contact stiffness, the frequency ratio increases for the first mode, but for the second mode, the situation is reversed. The nonlinear-frequency to linear-frequency ratio increases by increasing the Timoshenko beam parameter, but decreases by increasing the contact position for constant amplitude for the first and second modes. For the first mode, the frequency ratio decreases by increasing both of the lateral contact stiffness and the tip height, but increases by increasing the angle α between the cantilever and sample surface. (author)

  1. Systemic Thinking in Career Development Theory: Contributions of the Systems Theory Framework

    Science.gov (United States)

    McMahon, Mary; Patton, Wendy

    2018-01-01

    This article considers systemic thinking in relation to the Systems Theory Framework (STF) and to career theory. An overview of systems theory and its applications is followed by a discussion of career theory to provide a context for the subsequent description of STF. The contributions of STF to career theory and to theory integration are…

  2. Adaptive Fuzzy Output-Constrained Fault-Tolerant Control of Nonlinear Stochastic Large-Scale Systems With Actuator Faults.

    Science.gov (United States)

    Li, Yongming; Ma, Zhiyao; Tong, Shaocheng

    2017-09-01

    The problem of adaptive fuzzy output-constrained tracking fault-tolerant control (FTC) is investigated for the large-scale stochastic nonlinear systems of pure-feedback form. The nonlinear systems considered in this paper possess the unstructured uncertainties, unknown interconnected terms and unknown nonaffine nonlinear faults. The fuzzy logic systems are employed to identify the unknown lumped nonlinear functions so that the problems of structured uncertainties can be solved. An adaptive fuzzy state observer is designed to solve the nonmeasurable state problem. By combining the barrier Lyapunov function theory, adaptive decentralized and stochastic control principles, a novel fuzzy adaptive output-constrained FTC approach is constructed. All the signals in the closed-loop system are proved to be bounded in probability and the system outputs are constrained in a given compact set. Finally, the applicability of the proposed controller is well carried out by a simulation example.

  3. Linear and nonlinear instability theory of a noble gas MHD generator

    International Nuclear Information System (INIS)

    Mesland, A.J.

    1982-01-01

    This thesis deals with the stability of the working medium of a seeded noble gas magnetohydrodynamic generator. The aim of the study is to determine the instability mechanism which is most likely to occur in experimental MHD generators and to describe its behaviour with linear and nonlinear theories. In chapter I a general introduction is given. The pertinent macroscopic basic equations are derived in chapter II, viz. the continuity, the momentum and the energy equation for the electrons and the heavy gas particles, consisting of the seed particles and the noble gas atoms. Chapter III deals with the linear plane wave analysis of small disturbances of a homogeneous steady state. The steady state is discussed in chapter IV. The values for the steady state parameters used for the calculations both for the linear analysis as for the nonlinear analysis are made plausible with the experimental values. Based on the results of the linear plane wave theory a nonlinear plane wave model of the electrothermal instability is introduced in chapter V. (Auth.)

  4. Networked Predictive Control for Nonlinear Systems With Arbitrary Region Quantizers.

    Science.gov (United States)

    Yang, Hongjiu; Xu, Yang; Xia, Yuanqing; Zhang, Jinhui

    2017-04-06

    In this paper, networked predictive control is investigated for planar nonlinear systems with quantization by an extended state observer (ESO). The ESO is used not only to deal with nonlinear terms but also to generate predictive states for dealing with network-induced delays. Two arbitrary region quantizers are applied to take effective values of signals in forward channel and feedback channel, respectively. Based on a "zoom" strategy, sufficient conditions are given to guarantee stabilization of the closed-loop networked control system with quantization. A simulation example is proposed to exhibit advantages and availability of the results.

  5. Convergence criteria for systems of nonlinear elliptic partial differential equations

    International Nuclear Information System (INIS)

    Sharma, R.K.

    1986-01-01

    This thesis deals with convergence criteria for a special system of nonlinear elliptic partial differential equations. A fixed-point algorithm is used, which iteratively solves one linearized elliptic partial differential equation at a time. Conditions are established that help foresee the convergence of the algorithm. Under reasonable hypotheses it is proved that the algorithm converges for such nonlinear elliptic systems. Extensive experimental results are reported and they show the algorithm converges in a wide variety of cases and the convergence is well correlated with the theoretical conditions introduced in this thesis

  6. Nonlinear Aeroelastic Analysis of the HIAD TPS Coupon in the NASA 8' High Temperature Tunnel: Theory and Experiment

    Science.gov (United States)

    Goldman, Benjamin D.; Scott, Robert C,; Dowell, Earl H.

    2014-01-01

    The purpose of this work is to develop a set of theoretical and experimental techniques to characterize the aeroelasticity of the thermal protection system (TPS) on the NASA Hypersonic Inflatable Aerodynamic Decelerator (HIAD). A square TPS coupon experiences trailing edge oscillatory behavior during experimental testing in the 8' High Temperature Tunnel (HTT), which may indicate the presence of aeroelastic flutter. Several theoretical aeroelastic models have been developed, each corresponding to a different experimental test configuration. Von Karman large deflection theory is used for the plate-like components of the TPS, along with piston theory for the aerodynamics. The constraints between the individual TPS layers and the presence of a unidirectional foundation at the back of the coupon are included by developing the necessary energy expressions and using the Rayleigh Ritz method to derive the nonlinear equations of motion. Free vibrations and limit cycle oscillations are computed and the frequencies and amplitudes are compared with accelerometer and photogrammetry data from the experiments.

  7. A universal nonlinear relation among boundary states in closed string field theory

    International Nuclear Information System (INIS)

    Kishimoto, Isao; Matsuo, Yutaka; Watanabe, Eitoku

    2004-01-01

    We show that the boundary states satisfy a nonlinear relation (the idempotency equation) with respect to the star product of closed string field theory. This relation is universal in the sense that various D-branes, including the infinitesimally deformed ones, satisfy the same equation, including the coefficient. This paper generalizes our analysis [hep-th/0306189] in the following senses. (1) We present a background-independent formulation based on conformal field theory. It illuminates the geometric nature of the relation and allows us to more systematically analyze the variations around the D-brane background. (2) We show that the Witten-type star product satisfies a similar relation but with a more divergent coefficient. (3) We determine the coefficient of the relation analytically. The result shows that the α parameter can be formally factored out, and the relation becomes universal. We present a conjecture on vacuum theory based on this computation. (author)

  8. Nonlocal Symmetries to Systems of Nonlinear Diffusion Equations

    International Nuclear Information System (INIS)

    Qu Changzheng; Kang Jing

    2008-01-01

    In this paper, we study potential symmetries to certain systems of nonlinear diffusion equations. Those systems have physical applications in soil science, mathematical biology, and invariant curve flows in R 3 . Lie point symmetries of the potential system, which cannot be projected to vector fields of the given dependent and independent variables, yield potential symmetries. The class of the system that admits potential symmetries is expanded.

  9. Chaos synchronizations of chaotic systems via active nonlinear control

    International Nuclear Information System (INIS)

    Huang, J; Xiao, T J

    2008-01-01

    This paper not only investigates the chaos synchronization between two LCC chaotic systems, but also discusses the chaos synchronization between LCC system and Genesio system. Some novel active nonlinear controllers are designed to achieve synchronizations between drive and response systems effectively. Moreover, the sufficient conditions of synchronizations are derived by using Lyapunov stability theorem. Numerical simulations are presented to verify the theoretical analysis, which shows that the synchronization schemes are global effective

  10. Accelerator-feasible N-body nonlinear integrable system

    Directory of Open Access Journals (Sweden)

    V. Danilov

    2014-12-01

    Full Text Available Nonlinear N-body integrable Hamiltonian systems, where N is an arbitrary number, have attracted the attention of mathematical physicists for the last several decades, following the discovery of some number of these systems. This paper presents a new integrable system, which can be realized in facilities such as particle accelerators. This feature makes it more attractive than many of the previous such systems with singular or unphysical forces.

  11. Dynamical systems V bifurcation theory and catastrophe theory

    CERN Document Server

    1994-01-01

    Bifurcation theory and catastrophe theory are two of the best known areas within the field of dynamical systems. Both are studies of smooth systems, focusing on properties that seem to be manifestly non-smooth. Bifurcation theory is concerned with the sudden changes that occur in a system when one or more parameters are varied. Examples of such are familiar to students of differential equations, from phase portraits. Moreover, understanding the bifurcations of the differential equations that describe real physical systems provides important information about the behavior of the systems. Catastrophe theory became quite famous during the 1970's, mostly because of the sensation caused by the usually less than rigorous applications of its principal ideas to "hot topics", such as the characterization of personalities and the difference between a "genius" and a "maniac". Catastrophe theory is accurately described as singularity theory and its (genuine) applications. The authors of this book, the first printing of w...

  12. Asymptotic stabilization of nonlinear systems using state feedback

    International Nuclear Information System (INIS)

    D'Attellis, Carlos

    1990-01-01

    This paper studies the design of state-feedback controllers for the stabilization of single-input single-output nonlinear systems x = f(x) + g(x)u, y = h(x). Two approaches for the stabilization problem are given; the asymptotic stability is achieved by means of: a) nonlinear state feedback: two nonlinear feedbacks are used; the first separates the system in a controllable linear part and in the zeros-dynamic part. The second feedback generates an asymptotically stable equilibrium on the manifold where this dynamics evolves; b) nonlinear dynamic feedback: conditions are established under which the system can follow the output of a completely controllable bilinear system which uses bounded controls. This fact enables the system to reach, using bounded controls too, a desired output value in finite time. As this value corresponds to a state that lays in the attraction basin of a stable equilibrium with the same output, the system evolves to that point. The two methods are illustrated by examples. (Author) [es

  13. Jump resonant frequency islands in nonlinear feedback control systems

    Science.gov (United States)

    Koenigsberg, W. D.; Dunn, J. C.

    1975-01-01

    A new type of jump resonance is predicted and observed in certain nonlinear feedback control systems. The new jump resonance characteristic is described as a 'frequency island' due to the fact that a portion of the input-output transfer characteristic is disjoint from the main body. The presence of such frequency islands was predicted by using a sinusoidal describing function characterization of the dynamics of an inertial gyro employing nonlinear ternary rebalance logic. While the general conditions under which such islands are possible has not been examined, a numerical approach is presented which can aid in establishing their presence. The existence of the frequency islands predicted for the ternary rebalanced gyro was confirmed by simulating the nonlinear system and measuring the transfer function.

  14. Methodology for global nonlinear analysis of nuclear systems

    International Nuclear Information System (INIS)

    Cacuci, D.G.; Cacuci, G.L.

    1987-01-01

    This paper outlines a general method for globally computing the crucial features of nonlinear problems: bifurcations, limit points, saddle points, extrema (maxima and minima); our method also yields the local sensitivities (i.e., first order derivatives) of the system's state variables (e.g., fluxes, power, temperatures, flows) at any point in the system's phase space. We also present an application of this method to the nonlinear BWR model discussed in Refs. 8 and 11. The most significant novel feature of our method is the recasting of a general mathematical problem comprising three aspects: (1) nonlinear constrained optimization, (2) sensitivity analysis, into a fixed point problem of the form F[u(s), λ(s)] = 0 whose global zeros and singular points are related to the special features (i.e., extrema, bifurcations, etc.) of the original problem

  15. Exact solutions for a system of nonlinear plasma fluid equations

    International Nuclear Information System (INIS)

    Prahovic, M.G.; Hazeltine, R.D.; Morrison, P.J.

    1991-04-01

    A method is presented for constructing exact solutions to a system of nonlinear plasma fluid equations that combines the physics of reduced magnetohydrodynamics and the electrostatic drift-wave description of the Charney-Hasegawa-Mima equation. The system has nonlinearities that take the form of Poisson brackets involving the fluid field variables. The method relies on modifying a class of simple equilibrium solutions, but no approximations are made. A distinguishing feature is that the original nonlinear problem is reduced to the solution of two linear partial differential equations, one fourth-order and the other first-order. The first-order equation has Hamiltonian characteristics and is easily integrated, supplying information about the general structure of solutions. 6 refs

  16. Non-linear gauge transformations in D=10 SYM theory and the BCJ duality

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Seungjin [Max-Planck-Institut für Gravitationsphysik Albert-Einstein-Institut,14476 Potsdam (Germany); Mafra, Carlos R. [Institute for Advanced Study, School of Natural Sciences,Einstein Drive, Princeton, NJ 08540 (United States); DAMTP, University of Cambridge,Wilberforce Road, Cambridge, CB3 0WA (United Kingdom); Schlotterer, Oliver [Max-Planck-Institut für Gravitationsphysik Albert-Einstein-Institut,14476 Potsdam (Germany)

    2016-03-14

    Recent progress on scattering amplitudes in super Yang-Mills and superstring theory benefitted from the use of multiparticle superfields. They universally capture tree-level subdiagrams, and their generating series solve the non-linear equations of ten-dimensional super Yang-Mills. We provide simplified recursions for multiparticle superfields and relate them to earlier representations through non-linear gauge transformations of their generating series. Moreover, we discuss the gauge transformations which enforce their Lie symmetries as suggested by the Bern-Carrasco-Johansson duality between color and kinematics. Another gauge transformation due to Harnad and Shnider is shown to streamline the theta-expansion of multiparticle superfields, bypassing the need to use their recursion relations beyond the lowest components. The findings of this work tremendously simplify the component extraction from kinematic factors in pure spinor superspace.

  17. Influence of magnetic flutter on tearing growth in linear and nonlinear theory

    Science.gov (United States)

    Kreifels, L.; Hornsby, W. A.; Weikl, A.; Peeters, A. G.

    2018-06-01

    Recent simulations of tearing modes in turbulent regimes show an unexpected enhancement in the growth rate. In this paper the effect is investigated analytically. The enhancement is linked to the influence of turbulent magnetic flutter, which is modelled by diffusion terms in magnetohydrodynamics (MHD) momentum balance and Ohm’s law. Expressions for the linear growth rate as well as the island width in nonlinear theory for small amplitudes are derived. The results indicate an enhanced linear growth rate and a larger linear layer width compared with resistive MHD. Also the island width in the nonlinear regime grows faster in the diffusive model. These observations correspond well to simulations in which the effect of turbulence on the magnetic island width and tearing mode growth is analyzed.

  18. Nonlinear theory of trapped electron temperature gradient driven turbulence in flat density H-mode plasmas

    International Nuclear Information System (INIS)

    Hahm, T.S.

    1990-12-01

    Ion temperature gradient turbulence based transport models have difficulties reconciling the recent DIII-D H-mode results where the density profile is flat, but χ e > χ i in the core region. In this work, a nonlinear theory is developed for recently discovered ion temperature gradient trapped electron modes propagating in the electron diamagnetic direction. This instability is predicted to be linearly unstable for L Ti /R approx-lt κ θ ρ s approx-lt (L Ti /R) 1/4 . They are also found to be strongly dispersive even at these long wavelengths, thereby suggesting the importance of the wave-particle-wave interactions in the nonlinear saturation phase. The fluctuation spectrum and anomalous fluxes are calculated. In accordance with the trends observed in DIII-D, the predicted electron thermal diffusivity can be larger than the ion thermal diffusivity. 17 refs., 3 figs

  19. Nonlinear theory for axisymmetric self-similar two-dimensional oscillations of electrons in cold plasma with constant proton background

    Science.gov (United States)

    Osherovich, V. A.; Fainberg, J.

    2018-01-01

    We consider simultaneous oscillations of electrons moving both along the axis of symmetry and also in the direction perpendicular to the axis. We derive a system of three nonlinear ordinary differential equations which describe self-similar oscillations of cold electrons in a constant proton density background (np = n0 = constant). These three equations represent an exact class of solutions. For weak nonlinear conditions, the frequency spectra of electric field oscillations exhibit split frequency behavior at the Langmuir frequency ωp0 and its harmonics, as well as presence of difference frequencies at low spectral values. For strong nonlinear conditions, the spectra contain peaks at frequencies with values ωp0(n +m √{2 }) , where n and m are integer numbers (positive and negative). We predict that both spectral types (weak and strong) should be observed in plasmas where axial symmetry may exist. To illustrate possible applications of our theory, we present a spectrum of electric field oscillations observed in situ in the solar wind by the WAVES experiment on the Wind spacecraft during the passage of a type III solar radio burst.

  20. Adaptive Output Tracking Control for Nonlinear Systems with Failed Actuators and Aircraft Flight System Applications

    Directory of Open Access Journals (Sweden)

    Chuanjing Hou

    2015-01-01

    Full Text Available An adaptive failure compensation scheme using output feedback is proposed for a class of nonlinear systems with nonlinearities depending on the unmeasured states of systems. Adaptive high-gain K-filters are presented to suppress the nonlinearities while the proposed backstepping adaptive high-gain controller guarantees the stability of the closed-loop system and small tracking errors. Simulation results verify that the adaptive failure compensation scheme is effective.

  1. Adaptive Output Tracking Control for Nonlinear Systems with Failed Actuators and Aircraft Flight System Applications

    OpenAIRE

    Hou, Chuanjing; Hu, Lisheng; Zhang, Yingwei

    2015-01-01

    An adaptive failure compensation scheme using output feedback is proposed for a class of nonlinear systems with nonlinearities depending on the unmeasured states of systems. Adaptive high-gain K-filters are presented to suppress the nonlinearities while the proposed backstepping adaptive high-gain controller guarantees the stability of the closed-loop system and small tracking errors. Simulation results verify that the adaptive failure compensation scheme is effective.

  2. Nonlinear analysis of 0-3 polarized PLZT microplate based on the new modified couple stress theory

    Science.gov (United States)

    Wang, Liming; Zheng, Shijie

    2018-02-01

    In this study, based on the new modified couple stress theory, the size- dependent model for nonlinear bending analysis of a pure 0-3 polarized PLZT plate is developed for the first time. The equilibrium equations are derived from a variational formulation based on the potential energy principle and the new modified couple stress theory. The Galerkin method is adopted to derive the nonlinear algebraic equations from governing differential equations. And then the nonlinear algebraic equations are solved by using Newton-Raphson method. After simplification, the new model includes only a material length scale parameter. In addition, numerical examples are carried out to study the effect of material length scale parameter on the nonlinear bending of a simply supported pure 0-3 polarized PLZT plate subjected to light illumination and uniform distributed load. The results indicate the new model is able to capture the size effect and geometric nonlinearity.

  3. Finite Time Control for Fractional Order Nonlinear Hydroturbine Governing System via Frequency Distributed Model

    Directory of Open Access Journals (Sweden)

    Bin Wang

    2016-01-01

    Full Text Available This paper studies the application of frequency distributed model for finite time control of a fractional order nonlinear hydroturbine governing system (HGS. Firstly, the mathematical model of HGS with external random disturbances is introduced. Secondly, a novel terminal sliding surface is proposed and its stability to origin is proved based on the frequency distributed model and Lyapunov stability theory. Furthermore, based on finite time stability and sliding mode control theory, a robust control law to ensure the occurrence of the sliding motion in a finite time is designed for stabilization of the fractional order HGS. Finally, simulation results show the effectiveness and robustness of the proposed scheme.

  4. 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.

  5. Nonlinear optical response in condensed phases : A microscopic theory using the multipolar Hamiltonian

    NARCIS (Netherlands)

    Knoester, Jasper; Mukamel, Shaul

    1990-01-01

    A general scheme is presented for calculating the nonlinear optical response in condensed phases that provides a unified picture of excitons, polaritons, retardation, and local-field effects in crystals and in disordered systems. A fully microscopic starting point is taken by considering the

  6. Kinetic theory of nonlinear viscous flow in two and three dimensions

    NARCIS (Netherlands)

    Ernst, M.H.; Cichocki, B.; Dorfman, J.R.; Sharma, J.; Beijeren, H. van

    1978-01-01

    On the basis of a nonlinear kinetic equation for a moderately dense system of hard spheres and disks it is shown that shear and normal stresses in a steady-state, uniform shear flow contain singular contributions of the form ¦X¦3/2 for hard spheres, or ¦X¦ log ¦X¦ for hard disks. HereX is

  7. Existence of solutions to second-order nonlinear coupled systems with nonlinear coupled boundary conditions

    Directory of Open Access Journals (Sweden)

    Imran Talib

    2015-12-01

    Full Text Available In this article, study the existence of solutions for the second-order nonlinear coupled system of ordinary differential equations $$\\displaylines{ u''(t=f(t,v(t,\\quad t\\in [0,1],\\cr v''(t=g(t,u(t,\\quad t\\in [0,1], }$$ with nonlinear coupled boundary conditions $$\\displaylines{ \\phi(u(0,v(0,u(1,v(1,u'(0,v'(0=(0,0, \\cr \\psi(u(0,v(0,u(1,v(1,u'(1,v'(1=(0,0, }$$ where $f,g:[0,1]\\times \\mathbb{R}\\to \\mathbb{R}$ and $\\phi,\\psi:\\mathbb{R}^6\\to \\mathbb{R}^2$ are continuous functions. Our main tools are coupled lower and upper solutions, Arzela-Ascoli theorem, and Schauder's fixed point theorem.

  8. Nonlinear evolution of the matter power spectrum in modified theories of gravity

    International Nuclear Information System (INIS)

    Koyama, Kazuya; Taruya, Atsushi; Hiramatsu, Takashi

    2009-01-01

    We present a formalism to calculate the nonlinear matter power spectrum in modified gravity models that explain the late-time acceleration of the Universe without dark energy. Any successful modified gravity models should contain a mechanism to recover general relativity (GR) on small scales in order to avoid the stringent constrains on deviations from GR at solar system scales. Based on our formalism, the quasi-nonlinear power spectrum in the Dvali-Gabadadze-Porratti braneworld models and f(R) gravity models are derived by taking into account the mechanism to recover GR properly. We also extrapolate our predictions to fully nonlinear scales using the parametrized post-Friedmann framework. In the Dvali-Gabadadze-Porratti and f(R) gravity models, the predicted nonlinear power spectrum is shown to reproduce N-body results. We find that the mechanism to recover GR suppresses the difference between the modified gravity models and dark energy models with the same expansion history, but the difference remains large at the weakly nonlinear regime in these models. Our formalism is applicable to a wide variety of modified gravity models and it is ready to use once consistent models for modified gravity are developed.

  9. Recurrent fuzzy neural network backstepping control for the prescribed output tracking performance of nonlinear dynamic systems.

    Science.gov (United States)

    Han, Seong-Ik; Lee, Jang-Myung

    2014-01-01

    This paper proposes a backstepping control system that uses a tracking error constraint and recurrent fuzzy neural networks (RFNNs) to achieve a prescribed tracking performance for a strict-feedback nonlinear dynamic system. A new constraint variable was defined to generate the virtual control that forces the tracking error to fall within prescribed boundaries. An adaptive RFNN was also used to obtain the required improvement on the approximation performances in order to avoid calculating the explosive number of terms generated by the recursive steps of traditional backstepping control. The boundedness and convergence of the closed-loop system was confirmed based on the Lyapunov stability theory. The prescribed performance of the proposed control scheme was validated by using it to control the prescribed error of a nonlinear system and a robot manipulator. © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

  10. Tracking Control of Nonlinear Mechanical Systems

    NARCIS (Netherlands)

    Lefeber, A.A.J.

    2000-01-01

    The subject of this thesis is the design of tracking controllers for certain classes of mechanical systems. The thesis consists of two parts. In the first part an accurate mathematical model of the mechanical system under consideration is assumed to be given. The goal is to follow a certain

  11. IMMANUEL WALLERSTEIN'S WORLD SYSTEM THEORY

    Directory of Open Access Journals (Sweden)

    Cosma Sorinel

    2010-12-01

    Full Text Available World-systems analysis is not a theory, but an approach to social analysis and social change developed, among others by the Immanuel Wallerstein. Professor Wallerstein writes in three domains of world-systems analysis: the historical development of the modern world-system; the contemporary crisis of the capitalist world-economy; the structures of knowledge. The American anlyst rejects the notion of a "Third World", claiming there is only one world connected by a complex network of economic exchange relationship. Our world system is characterized by mechanisms which bring about a redistribution of resources from the periphery to the core. His analytical approach has made a significant impact and established an institutional base devoted to the general approach.

  12. Stabilization of switched nonlinear systems with unstable modes

    CERN Document Server

    Yang, Hao; Cocquempot, Vincent

    2014-01-01

    This book provides its reader with a good understanding of the stabilization of switched nonlinear systems (SNS), systems that are of practical use in diverse situations: design of fault-tolerant systems in space- and aircraft; traffic control; and heat propagation control of semiconductor power chips. The practical background is emphasized throughout the book; interesting practical examples frequently illustrate the theoretical results with aircraft and spacecraft given particular prominence. Stabilization of Switched Nonlinear Systems with Unstable Modes treats several different subclasses of SNS according to the characteristics of the individual system (time-varying and distributed parameters, for example), the state composition of individual modes and the degree and distribution of instability in its various modes. Achievement and maintenance of stability across the system as a whole is bolstered by trading off between individual modes which may be either stable or unstable, or by exploiting areas of part...

  13. Linearly and nonlinearly bidirectionally coupled synchronization of hyperchaotic systems

    International Nuclear Information System (INIS)

    Zhou Jin; Lu Junan; Wu Xiaoqun

    2007-01-01

    To date, there have been many results about unidirectionally coupled synchronization of chaotic systems. However, much less work is reported on bidirectionally-coupled synchronization. In this paper, we investigate the synchronization of two bidirectionally coupled Chen hyperchaotic systems, which are coupled linearly and nonlinearly respectively. Firstly, linearly coupled synchronization of two hyperchaotic Chen systems is investigated, and a theorem on how to choose the coupling coefficients are developed to guarantee the global asymptotical synchronization of two coupled hyperchaotic systems. Analysis shows that the choice of the coupling coefficients relies on the bound of the chaotic system. Secondly, the nonlinearly coupled synchronization is studied; a sufficient condition for the locally asymptotical synchronization is derived, which is independent of the bound of the hyperchaotic system. Finally, numerical simulations are included to verify the effectiveness and feasibility of the developed theorems

  14. A self-consistent nonlinear theory of resistive-wall instability in a relativistic electron beam

    International Nuclear Information System (INIS)

    Uhm, H.S.

    1994-01-01

    A self-consistent nonlinear theory of resistive-wall instability is developed for a relativistic electron beam propagating through a grounded cylindrical resistive tube. The theory is based on the assumption that the frequency of the resistive-wall instability is lower than the cutoff frequency of the waveguide. The theory is concentrated on study of the beam current modulation directly related to the resistive-wall klystron, in which a relativistic electron beam is modulated at the first cavity and propagates downstream through the resistive wall. Because of the self-excitation of the space charge waves by the resistive-wall instability, a highly nonlinear current modulation of the electron beam is accomplished as the beam propagates downstream. A partial integrodifferential equation is obtained in terms of the initial energy modulation (ε), the self-field effects (h), and the resistive-wall effects (κ). Analytically investigating the partial integrodifferential equation, a scaling law of the propagation distance z m at which the maximum current modulation occurs is obtained. It is found in general that the self-field effects dominate over the resistive-wall effects at the beginning of the propagation. As the beam propagates farther downstream, the resistive-wall effects dominate. Because of a relatively large growth rate of the instability, the required tube length of the klystron is short for most applications

  15. 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

  16. PWL approximation of nonlinear dynamical systems, part I: structural stability

    International Nuclear Information System (INIS)

    Storace, M; De Feo, O

    2005-01-01

    This paper and its companion address the problem of the approximation/identification of nonlinear dynamical systems depending on parameters, with a view to their circuit implementation. The proposed method is based on a piecewise-linear approximation technique. In particular, this paper describes the approximation method and applies it to some particularly significant dynamical systems (topological normal forms). The structural stability of the PWL approximations of such systems is investigated through a bifurcation analysis (via continuation methods)

  17. Reproduction of Economic Interests as a Nonlinear Dynamical System

    OpenAIRE

    Smiesova Viktoria L.

    2017-01-01

    The aim of the article is to define the system characteristics of reproduction of economic interests of actors, substantiate the possibility of its evolutionary and revolutionary development and the nonlinearity of its development in dynamics. The article justifies the main characteristics of the system of reproduction of economic interests. It is proved that in this system stability and variability are complementarily combined as integrated mechanisms of its development in statics and dynami...

  18. Integrable systems with quadratic nonlinearity in Fourier space

    International Nuclear Information System (INIS)

    Marikhin, V.G.

    2003-01-01

    The Lax pair representation in Fourier space is used to obtain a list of integrable scalar evolutionary equations with quadratic nonlinearity. The known systems of this type such as KdV, intermediate long-wave equation (ILW), Camassa-Holm and Degasperis-Procesi systems are represented in this list. Some new systems are obtained as well. Two-dimensional and discrete generalizations are discussed

  19. Nonlinear control system analysis and design with Maple

    NARCIS (Netherlands)

    Jager, de A.G.; Houstis, E.N.; Rice, J.R.

    1992-01-01

    For the analysis and design of nonlinear control systems non-numerical methods are available. The required analytical computations are mostly too tedious to be done error free in a reasonable time by hand, so the use of symbolic computation programs can be of advantage. To show that the symbolic

  20. Relative controllability of nonlinear systems with delays in state and ...

    African Journals Online (AJOL)

    In this work, sufficient conditions are developed for the relative controllability of perturbed nonlinear systems with time varying multiple delays in control with the perturbation function having implicit derivative with delays depending on both state and control variable, using Darbo's fixed points theorem. Journal of the Nigerian ...