Modulational stability and dark solitons in periodic quadratic nonlinear media
DEFF Research Database (Denmark)
Corney, Joel Frederick; Bang, Ole
2000-01-01
We show that stable dark solitons exist in quadratic nonlinear media with periodic linear and nonlinear susceptibilities. We investigate the modulational stability of plane waves in such systems, a necessary condition for stable dark solitons....
Spectral and modulational stability of periodic wavetrains for the nonlinear Klein-Gordon equation
Jones, Christopher K. R. T.; Marangell, Robert; Miller, Peter D.; Plaza, Ramón G.
2014-12-01
This paper is a detailed and self-contained study of the stability properties of periodic traveling wave solutions of the nonlinear Klein-Gordon equation utt-uxx+V‧(u)=0, where u is a scalar-valued function of x and t, and the potential V(u) is of class C2 and periodic. Stability is considered both from the point of view of spectral analysis of the linearized problem (spectral stability analysis) and from the point of view of wave modulation theory (the strongly nonlinear theory due to Whitham as well as the weakly nonlinear theory of wave packets). The aim is to develop and present new spectral stability results for periodic traveling waves, and to make a solid connection between these results and predictions of the (formal) modulation theory, which has been developed by others but which we review for completeness.
Barker, Blake; Noble, Pascal; Rodrigues, L Miguel; Zumbrun, Kevin
2012-01-01
In this paper we consider the spectral and nonlinear stability of periodic traveling wave solutions of a generalized Kuramoto-Sivashinsky equation. In particular, we resolve the long-standing question of nonlinear modulational stability by demonstrating that spectrally stable waves are nonlinearly stable when subject to small localized (integrable) perturbations. Our analysis is based upon detailed estimates of the linearized solution operator, which are complicated by the fact that the (necessarily essential) spectrum of the associated linearization intersects the imaginary axis at the origin. We carry out a numerical Evans function study of the spectral problem and find bands of spectrally stable periodic traveling waves, in close agreement with previous numerical studies of Frisch-She-Thual, Bar-Nepomnyashchy, Chang-Demekhin-Kopelevich, and others carried out by other techniques. We also compare predictions of the associated Whitham modulation equations, which formally describe the dynamics of weak large s...
Tian, Qing; Wu, Lei; Zhang, Jie-Fang; Malomed, Boris A; Mihalache, D; Liu, W M
2011-01-01
We put forward a generic transformation which helps to find exact soliton solutions of the nonlinear Schrödinger equation with a spatiotemporal modulation of the nonlinearity and external potentials. As an example, we construct exact solitons for the defocusing nonlinearity and harmonic potential. When the soliton's eigenvalue is fixed, the number of exact solutions is determined by energy levels of the linear harmonic oscillator. In addition to the stable fundamental solitons, stable higher-order modes, describing array of dark solitons nested in a finite-width background, are constructed too. We also show how to control the instability domain of the nonstationary solitons.
NONLINEAR STABILITY FOR EADY'S MODEL
Institute of Scientific and Technical Information of China (English)
LIU Yong-ming; QIU Ling-cun
2005-01-01
Poincaré type integral inequality plays an important role in the study of nonlinear stability ( in the sense of Arnold's second theorem) for three-dimensional quasigeostophic flow. The nonlinear stability of Eady's model is one of the most important cases in the application of the method. But the best nonlinear stability criterion obtained so far and the linear stability criterion are not coincident. The two criteria coincide only when the period of the channel is infinite.additional conservation law of momentum and by rigorous estimate of integral inequality. So the new nonlinear stability criterion was obtained, which shows that for Eady 's model in the periodic channel, the linear stable implies the nonlinear stable.
Practical stability of nonlinear systems
Lakshmikantham, Vangipuram; Martynyuk, Anatolii Andreevich
1990-01-01
This is the first book that deals with practical stability and its development. It presents a systematic study of the theory of practical stability in terms of two different measures and arbitrary sets and demonstrates the manifestations of general Lyapunov's method by showing how this effective technique can be adapted to investigate various apparently diverse nonlinear problems including control systems and multivalued differential equations.
Stability analysis of nonlinear systems
Lakshmikantham, Vangipuram; Martynyuk, Anatoly A
2015-01-01
The book investigates stability theory in terms of two different measure, exhibiting the advantage of employing families of Lyapunov functions and treats the theory of a variety of inequalities, clearly bringing out the underlying theme. It also demonstrates manifestations of the general Lyapunov method, showing how this technique can be adapted to various apparently diverse nonlinear problems. Furthermore it discusses the application of theoretical results to several different models chosen from real world phenomena, furnishing data that is particularly relevant for practitioners. Stability Analysis of Nonlinear Systems is an invaluable single-sourse reference for industrial and applied mathematicians, statisticians, engineers, researchers in the applied sciences, and graduate students studying differential equations.
Modulational instability in nonlocal nonlinear Kerr media
DEFF Research Database (Denmark)
Krolikowski, Wieslaw; Bang, Ole; Juul Rasmussen, Jens
2001-01-01
We study modulational instability (MI) of plane waves in nonlocal nonlinear Kerr media. For a focusing nonlinearity we show that, although the nonlocality tends to suppress MI, it can never remove it completely, irrespective of the particular profile of the nonlocal response function....... For a defocusing nonlinearity the stability properties depend sensitively on the response function profile: for a smooth profile (e.g., a Gaussian) plane waves are always stable, but MI may occur for a rectangular response. We also find that the reduced model for a weak nonlocality predicts MI in defocusing media...... for arbitrary response profiles, as long as the intensity exceeds a certain critical value. However, it appears that this regime of MI is beyond the validity of the reduced model, if it is to represent the weakly nonlocal limit of a general nonlocal nonlinearity, as in optics and the theory of Bose...
A nonlinear variable structure stabilizer for power system stability
Energy Technology Data Exchange (ETDEWEB)
Cao, Y.; Jiang, L.; Cheng, S.; Chen, D. (Huazhong Univ. of Science and Technology, Wuhan (China). Dept. of Electrical Power Engineering); Malik, O.P.; Hope, G.S. (Univ. of Calgary, Alberta (Canada). Dept. of Electrical and Computer Engineering)
1994-09-01
A nonlinear variable structure stabilizer is proposed in this paper. Design of this stabilizer involves the nonlinear transformation technique, the variable structure control technique and the linear system theory. Performance of the proposed nonlinear variable structure controller in a single machine connected to an infinite bus power and a multi-machine system with multi-mode oscillations is simulated. The responses of the system with the proposed stabilizer are compared with those obtained with some other kinds of stabilizers when the system is subjected to a variety of disturbances. Simulation results show that the nonlinear variable structure stabilizer gives satisfactory dynamic performance and good robustness.
Stability of fractional positive nonlinear systems
Directory of Open Access Journals (Sweden)
Kaczorek Tadeusz
2015-12-01
Full Text Available The conditions for positivity and stability of a class of fractional nonlinear continuous-time systems are established. It is assumed that the nonlinear vector function is continuous, satisfies the Lipschitz condition and the linear part is described by a Metzler matrix. The stability conditions are established by the use of an extension of the Lyapunov method to fractional positive nonlinear systems.
Nonlinear Resonance Islands and Modulational Effects in a Proton Synchrotron
Energy Technology Data Exchange (ETDEWEB)
Satogata, Todd Jeffrey [Northwestern Univ., Evanston, IL (United States)
1993-01-01
We examine both one-dimensional and two-dimensional nonlinear resonance islands created in the transverse phase space of a proton synchrotron by nonlinear magnets. We also examine application of the theoretical framework constructed to the phenomenon of modulational diffusion in a collider model of the Fermilab Tevatron. For the one-dimensional resonance island system, we examine the effects of two types of modulational perturbations on the stability of these resonance islands: tune modulation and beta function modulation. Hamiltonian models are presented which predict stability boundaries that depend on only three paramders: the strength and frequency of the modulation and the frequency of small oscillations inside the resonance island. These. models are compared to particle tracking with excellent agreement. The tune modulation model is also successfully tested in experiment, where frequency domain analysis coupled with tune modulation is demonstrated to be useful in measuring the strength of a nonlinear resonance. Nonlinear resonance islands are also examined in two transverse dimensions in the presence of coupling and linearly independent crossing resonances. We present a first-order Hamiltonian model which predicts fixed point locations, but does not reproduce small oscillation frequencies seen in tracking; therefore in this circumstance such a model is inadequate. Particle tracking is presented which shows evidence of two-dimensional persistent signals, and we make suggestions on methods for observing such signals in future experiment.
An analysis of nonlinear behavior in delta-sigma modulators
Ardalan, Sasan H.; Paulos, John J.
1987-06-01
The paper introduces a new method of analysis for delta-sigma modulators based on modeling the nonlinear quantizer with a linearized gain, obtained by minimizing a mean-square-error criterion, followed by an additive noise source representing distortion components. In the paper, input signal amplitude dependencies of delta-sigma modulator stability and signal-to-noise ratio are analyzed. It is shown that due to the nonlinearity of the quantizer, the signal-to-noise ratio of the modulator may decrease as the input amplitude increases prior to saturation. Also, a stable third-order delta-sigma modulator may become unstable by increasing the input amplitude beyond a certain threshold. Both of these phenomena are explained by the nonlinear analysis of this paper. The analysis is carried out for both dc and sinusoidal excitations.
Nonlinear Boundary Stabilization of Nonuniform Timoshenko Beam
Institute of Scientific and Technical Information of China (English)
Qing-xu Yan; Hui-chao Zou; De-xing Feng
2003-01-01
In this paper, the stabilization problem of nonuniform Timoshenko beam by some nonlinear boundary feedback controls is considered. By virtue of nonlinear semigroup theory, energy-perturbed approach and exponential multiplier method, it is shown that the vibration of the beam under the proposed control action decays exponentially or in negative power of time t as t →∞.
Qualitative stability of nonlinear networked systems
Angulo, Marco Tulio; Slotine, Jean-Jacques
2016-01-01
In many large systems, such as those encountered in biology or economics, the dynamics are nonlinear and are only known very coarsely. It is often the case, however, that the signs (excitation or inhibition) of individual interactions are known. This paper extends to nonlinear systems the classical criteria of linear sign stability introduced in the 70's, yielding simple sufficient conditions to determine stability using only the sign patterns of the interactions.
Nonlinear approximation in alpha-modulation spaces
DEFF Research Database (Denmark)
Borup, Lasse; Nielsen, Morten
2006-01-01
The α-modulation spaces are a family of spaces that contain the Besov and modulation spaces as special cases. In this paper we prove that brushlet bases can be constructed to form unconditional and even greedy bases for the α-modulation spaces. We study m -term nonlinear approximation with brushlet...... bases, and give complete characterizations of the associated approximation spaces in terms of α-modulation spaces....
Modulational instability in periodic quadratic nonlinear materials
DEFF Research Database (Denmark)
Corney, Joel Frederick; Bang, Ole
2001-01-01
We investigate the modulational instability of plane waves in quadratic nonlinear materials with linear and nonlinear quasi-phase-matching gratings. Exact Floquet calculations, confirmed by numerical simulations, show that the periodicity can drastically alter the gain spectrum but never complete...
A Stability Theory in Nonlinear Programming
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
We propose a new method for finding the local optimal points ofthe constrained nonlinear programming by Ordinary Differential Equations (ODE), and prove asymptotic stability of the singular points of partial variables in this paper. The condition of overall uniform, asymptotic stability is also given.
Adaptive stabilization for cascade nonlinear systems
Institute of Scientific and Technical Information of China (English)
陈岚萍; 王洪元; 吴波
2004-01-01
An adaptive controller of full state feedback for certain cascade nonlinear systems achieving input-to-state stability with respect to unknown bounded disturbance is designed using backstepping and control Lyapunov function (CLF)techniques. We show that unknown bounded disturbance can be estimated by update laws, which requires less information on unknown disturbance, as a part of stabilizing control. The design method achieves the desired property: global robust stability. Our contribution is illustrated with the example of a disturbed pendulum.
Stability analysis of nonlinear systems with slope restricted nonlinearities.
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.
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.
Nonlinear ion trap stability analysis
Energy Technology Data Exchange (ETDEWEB)
Mihalcea, Bogdan M; Visan, Gina G, E-mail: bmihal@infim.r [Institute for Laser, Plasma and Radiation Physics (INFLPR), Atomistilor Str. Nr. 409, 077125 Magurele-Bucharest, Jud. Ilfov (Romania)
2010-09-01
This paper investigates the dynamics of an ion confined in a nonlinear Paul trap. The equation of motion for the ion is shown to be consistent with the equation describing a damped, forced Duffing oscillator. All perturbing factors are taken into consideration in the approach. Moreover, the ion is considered to undergo interaction with an external electromagnetic field. The method is based on numerical integration of the equation of motion, as the system under investigation is highly nonlinear. Phase portraits and Poincare sections show that chaos is present in the associated dynamics. The system of interest exhibits fractal properties and strange attractors. The bifurcation diagrams emphasize qualitative changes of the dynamics and the onset of chaos.
Quadratic stabilization of switched nonlinear systems
Institute of Scientific and Technical Information of China (English)
DONG YaLi; FAN JiaoJiao; MEI ShengWei
2009-01-01
In this paper, the problem of quadratic stabilization of multi-input multi-output switched nonlinear systems under an arbitrary switching law is investigated. When switched nonlinear systems have uniform normal form and the zero dynamics of uniform normal form is asymptotically stable under an arbitrary switching law, state feedbacks are designed and a common quadratic Lyapunov function of all the closed-loop subsystems is constructed to realize quadratic stabilizability of the class of switched nonlinear systems under an arbitrary switching law. The results of this paper are also applied to switched linear systems.
Nonlinear evolution of whistler wave modulational instability
DEFF Research Database (Denmark)
Karpman, V.I.; Lynov, Jens-Peter; Michelsen, Poul;
1995-01-01
The nonlinear evolution of the modulational instability of whistler waves coupled to fast magnetosonic waves (FMS) and to slow magnetosonic waves (SMS) is investigated. Results from direct numerical solutions in two spatial dimensions agree with simplified results from a set of ordinary different......The nonlinear evolution of the modulational instability of whistler waves coupled to fast magnetosonic waves (FMS) and to slow magnetosonic waves (SMS) is investigated. Results from direct numerical solutions in two spatial dimensions agree with simplified results from a set of ordinary...
Symmetry, phase modulation and nonlinear waves
Bridges, Thomas J
2017-01-01
Nonlinear waves are pervasive in nature, but are often elusive when they are modelled and analysed. This book develops a natural approach to the problem based on phase modulation. It is both an elaboration of the use of phase modulation for the study of nonlinear waves and a compendium of background results in mathematics, such as Hamiltonian systems, symplectic geometry, conservation laws, Noether theory, Lagrangian field theory and analysis, all of which combine to generate the new theory of phase modulation. While the build-up of theory can be intensive, the resulting emergent partial differential equations are relatively simple. A key outcome of the theory is that the coefficients in the emergent modulation equations are universal and easy to calculate. This book gives several examples of the implications in the theory of fluid mechanics and points to a wide range of new applications.
Grid-connected of photovoltaic module using nonlinear control
DEFF Research Database (Denmark)
El Fadil, H.; Giri, F.; Guerrero, Josep M.
2012-01-01
The problem of controlling single-phase grid connected photovoltaic (PV) system is considered. The control objective is fourfold: (i) asymptotic stability of the closed loop system, (ii) maximum power point tracking (MPPT) of PV module (iii) tight regulation of the DC bus voltage, and (iv) unity......, for the nonlinear characteristic of PV panel. It is formally shown, through theoretical analysis and simulation results, that the proposed controller does achieve its objectives....
On stability of randomly switched nonlinear systems
Chatterjee, Debasish
2007-01-01
This article is concerned with stability analysis and stabilization of randomly switched nonlinear systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic process which is independent of the state of the system, and between two consecutive switching instants the dynamics are deterministic. Our results provide sufficient conditions for almost sure global asymptotic stability using Lyapunov-based methods when individual subsystems are stable and a certain ``slow switching'' condition holds. This slow switching condition takes the form of an asymptotic upper bound on the probability mass function of the number of switches that occur between the initial and current time instants. This condition is shown to hold for switching signals coming from the states of finite-dimensional continuous-time Markov chains; our results therefore hold for Markov jump systems in particular. For systems with control inputs we provide explicit control s...
Beam stability & nonlinear dynamics. Formal report
Energy Technology Data Exchange (ETDEWEB)
Parsa, Z. [ed.
1996-12-31
his Report includes copies of transparencies and notes from the presentations made at the Symposium on Beam Stability and Nonlinear Dynamics, December 3-5, 1996 at the Institute for Theoretical Physics, University of California, Santa Barbara California, that was made available by the authors. Editing, reduction and changes to the authors contributions were made only to fulfill the printing and publication requirements. We would like to take this opportunity and thank the speakers for their informative presentations and for providing copies of their transparencies and notes for inclusion in this Report.
Stability of Nonlinear Stochastic Discrete-Time Systems
2013-01-01
This paper studies the stability for nonlinear stochastic discrete-time systems. First of all, several definitions on stability are introduced, such as stability, asymptotical stability, and pth moment exponential stability. Moreover, using the method of the Lyapunov functionals, some efficient criteria for stochastic stability are obtained. Some examples are presented to illustrate the effectiveness of the proposed theoretical results.
Stability Analysis of Continuous Waves in Nonlocal Random Nonlinear Media
Directory of Open Access Journals (Sweden)
Maxim A. Molchan
2007-08-01
Full Text Available On the basis of the competing cubic-quintic nonlinearity model, stability (instability of continuous waves in nonlocal random non-Kerr nonlinear media is studied analytically and numerically. Fluctuating media parameters are modeled by the Gaussian white noise. It is shown that for different response functions of a medium nonlocality suppresses, as a rule, both the growth rate peak and bandwidth of instability caused by random parameters. At the same time, for a special form of the response functions there can be an ''anomalous'' subjection of nonlocality to the instability development which leads to further increase of the growth rate. Along with the second-order moments of the modulational amplitude, higher-order moments are taken into account.
Nonlinear physical systems spectral analysis, stability and bifurcations
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
New results in global stabilization for stochastic nonlinear systems
Institute of Scientific and Technical Information of China (English)
Tao BIAN; Zhong-Ping JIANG
2016-01-01
This paper presents new results on the robust global stabilization and the gain assignment problems for stochastic nonlinear systems. Three stochastic nonlinear control design schemes are developed. Furthermore, a new stochastic gain assignment method is developed for a class of uncertain interconnected stochastic nonlinear systems. This method can be combined with the nonlinear small-gain theorem to design partial-state feedback controllers for stochastic nonlinear systems. Two numerical examples are given to illustrate the effectiveness of the proposed methodology.
Organosilicon Polymeric Nonlinear Optical Materials for Optical Switching and Modulation
1994-02-28
Organosilicon Polymeric Nonlinear Optical Materials for Optical C: F49620-93-C-0039 Switching and Modulation 6. AUTHOR(S) Mr. Sandip K. Sengupta, Dr...D FINAL REPORT for Organosilicon Polymeric Nonlinear Optical Materials for Optical Switching and Modulation Prepared for: USAF, AFMC (AFOSR) Air Force...34Organosilicon Polymeric Nonlinear Optical Materials for Optical Switching and Modulation," contract number F49620-93-C-0039. The work has been performed by Dr
Bifurcation and stability for a nonlinear parabolic partial differential equation
Chafee, N.
1973-01-01
Theorems are developed to support bifurcation and stability of nonlinear parabolic partial differential equations in the solution of the asymptotic behavior of functions with certain specified properties.
Robust stabilization of general nonlinear systems with structural uncertainty
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
This paper deals with the robust stabilization and passivity of general nonlinear systems with structural uncertainty. By using Lyapunov function, it verifies that under some conditions the robust passivity implies the zero-state detectability, Furthermore, it also implies the robust stabilization for such nonlinear systems. We then establish a stabilization method for the nonlinear systems with structural uncertainty. The smooth state feedback law can be constructed with the solution of an equation. Finally, it is worth noting that the main contribution of the paper establishes the relation between robust passivity and feedback stabilization for the general nonlinear systems with structural uncertainty. The simulation shows the effectiveness of the method.
Nonlinearity and disorder: Classification and stability of nonlinear impurity modes
DEFF Research Database (Denmark)
Sukhorukov, Andrey A.; Kivshar, Yuri S.; Bang, Ole
2001-01-01
We study the effects produced by competition of two physical mechanisms of energy localization in inhomogeneous nonlinear systems. As an example, we analyze spatially localized modes supported by a nonlinear impurity in the generalized nonlinear Schrödinger equation and describe three types of no...
Nonlinear vibrations and stability of aerostatic bearing
Directory of Open Access Journals (Sweden)
Kozánek J.
2008-12-01
Full Text Available Bearings based on aerostatic principle belong to the new machine elements advantageous for low- and high-speed applications, but their dynamic and stability properties are not yet sufficiently known. This paper presents a new elaborated method and gained results of theoretical investigation of dynamic properties of aerostatic bearing in general dimensionless form. It is aimed also as a supporting tool for diagnostic and identification methods used at developing of new bearings proposed by TECHLAB, Prague for industrial applications. Mathematical model expresses nonlinear and evolutive properties in the entire area of bearing clearance, contains sufficient number of free parameters in functions of restoring and damping forces and can therefore describe all types of motions occurring in gas bearings as periodic, quasi-periodic, including beats and instability, which can leads to chaotic and self-excited vibrations. The influence of non-diagonal elements of stiffness and damping matrices of linearized model on the spectral properties and the stability of system is investigated, too.
Stability analysis of embedded nonlinear predictor neural generalized predictive controller
Directory of Open Access Journals (Sweden)
Hesham F. Abdel Ghaffar
2014-03-01
Full Text Available Nonlinear Predictor-Neural Generalized Predictive Controller (NGPC is one of the most advanced control techniques that are used with severe nonlinear processes. In this paper, a hybrid solution from NGPC and Internal Model Principle (IMP is implemented to stabilize nonlinear, non-minimum phase, variable dead time processes under high disturbance values over wide range of operation. Also, the superiority of NGPC over linear predictive controllers, like GPC, is proved for severe nonlinear processes over wide range of operation. The necessary conditions required to stabilize NGPC is derived using Lyapunov stability analysis for nonlinear processes. The NGPC stability conditions and improvement in disturbance suppression are verified by both simulation using Duffing’s nonlinear equation and real-time using continuous stirred tank reactor. Up to our knowledge, the paper offers the first hardware embedded Neural GPC which has been utilized to verify NGPC–IMP improvement in realtime.
Stability Analysis for Class of Switched Nonlinear Systems
DEFF Research Database (Denmark)
Shaker, Hamid Reza; How, Jonathan P.
2010-01-01
Stability analysis for a class of switched nonlinear systems is addressed in this paper. Two linear matrix inequality (LMI) based sufficient conditions for asymptotic stability are proposed for switched nonlinear systems. These conditions are analogous counterparts for switched linear systems which...
ABSOLUTE STABILITY OF GENERAL LURIE DISCRETE NONLINEAR CONTROL SYSTEMS
Institute of Scientific and Technical Information of China (English)
GAN Zuoxin; HAN Jingqing; ZHAO Suxia; WU Yongxian
2002-01-01
In the present paper, the absolute stability of general Lurie discrete nonlinear control systems has been discussed by Lyapunov function approach. A sufficient condition of absolute stability for the general Lurie discrete nonlinear control systems is derived, and some necessary and sufficient conditions are obtained in special cases. Meanwhile, we give a simple example to illustrate the effectiveness of the results.
Asymptotical Stability of Nonlinear Fractional Differential System with Caputo Derivative
2011-01-01
This paper deals with the stability of nonlinear fractional differential systems equipped with the Caputo derivative. At first, a sufficient condition on asymptotical stability is established by using a Lyapunov-like function. Then, the fractional differential inequalities and comparison method are applied to the analysis of the stability of fractional differential systems. In addition, some other sufficient conditions on stability are also presented.
Stability Analysis and Design for Nonlinear Singular Systems
Yang, Chunyu; Zhou, Linna
2013-01-01
Singular systems which are also referred to as descriptor systems, semi-state systems, differential- algebraic systems or generalized state-space systems have attracted much attention because of their extensive applications in the Leontief dynamic model, electrical and mechanical models, etc. This monograph presented up-to-date research developments and references on stability analysis and design of nonlinear singular systems. It investigated the problems of practical stability, strongly absolute stability, input-state stability and observer design for nonlinear singular systems and the problems of absolute stability and multi-objective control for nonlinear singularly perturbed systems by using Lyapunov stability theory, comparison principle, S-procedure and linear matrix inequality (LMI), etc. Practical stability, being quite different from stability in the sense of Lyapunov, is a significant performance specification from an engineering point of view. The basic concepts and results on practical stability f...
The K-Stability of Nonlinear Delay Systems
Institute of Scientific and Technical Information of China (English)
章毅; 张毅; 王联
1994-01-01
In this paper,we study the K-stability theory of nonlinear delay systems.In the more general case,we establish two nonlinear delay differential inequalities.Therefore,to study the X-stability,a powerful method is provided.By making use of the foregoing inequalities,we analyse and investigate some K-stabiiity conditions of nonlinear delay systems.Finally,some examples are given to illustrate our theory.
Contribution to stability analysis of nonlinear control systems
Directory of Open Access Journals (Sweden)
varc Ivan
2003-12-01
Full Text Available The Popov criterion for the stability of nonlinear control systems is considered. The Popov criterion gives sufficient conditions for stability of nonlinear systems in the frequency domain. It has a direct graphical interpretation and is convenient for both design and analysis. In the article presented, a table of transfer functions of linear parts of nonlinear systems is constructed. The table includes frequency response functions and offers solutions to the stability of the given systems. The table makes a direct stability analysis of selected nonlinear systems possible. The stability analysis is solved analytically and graphically.Then it is easy to find out if the nonlinear system is or is not stable; the task that usually ranks among the difficult task in engineering practice.
Stabilization of a class of switched nonlinear systems
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The stabilization of a class of switched nonlinear systems is investigated in the paper. The systems concerned are of (generalized) switched Byrnes-Isidori canonical form, which has all switched models in (generalized) ByrnesIsidori canonical form. First, a stability result of switched systems is obtained. Then it is used to solve the stabilization problem of the switched nonlinear control systems. In addition, necessary and sufficient conditions are obtained for a switched affine nonlinear system to be feedback equivalent to (generalized) switched Byrnes-Isidori canonical systems are presented.Finally, as an application the stability of switched lorenz systems is investigated.
W-Stability of Multistable Nonlinear Discrete-Time Systems
Directory of Open Access Journals (Sweden)
Zhishuai Ding
2012-01-01
Full Text Available Motivated by the importance and application of discrete dynamical systems, this paper presents a new Lyapunov characterization which is an extension of conventional Lyapunov characterization for multistable discrete-time nonlinear systems. Based on a new type stability notion of W-stability introduced by D. Efimov, the estimates of solution and the Lyapunov stability theorem and converse theorem are proposed for multi-stable discrete-time nonlinear systems.
The structure and stability of persistence modules
Chazal, Frédéric; Glisse, Marc; Oudot, Steve
2016-01-01
This book is a comprehensive treatment of the theory of persistence modules over the real line. It presents a set of mathematical tools to analyse the structure and to establish the stability of such modules, providing a sound mathematical framework for the study of persistence diagrams. Completely self-contained, this brief introduces the notion of persistence measure and makes extensive use of a new calculus of quiver representations to facilitate explicit computations. Appealing to both beginners and experts in the subject, The Structure and Stability of Persistence Modules provides a purely algebraic presentation of persistence, and thus complements the existing literature, which focuses mainly on topological and algorithmic aspects.
Robust stabilization for a class of nonlinear networked control systems
Institute of Scientific and Technical Information of China (English)
Jinfeng GAO; Hongye SU; Xiaofu JI; Jian CHU
2008-01-01
The problem of robust stabilization for a class of uncertain networked control systems(NCSs)with nonlinearities satisfying a given sector condition is investigated in this paper.By introducing a new model of NCSs with parameter uncertainty,network.induced delay,nonlinearity and data packet dropout in the transmission,a strict linear matrix inequality(LMI)criterion is proposed for robust stabilization of the uncenmn nonlinear NCSs based on the Lyapunov stability theory.The maximum allowable transfer interval(MATI)can be derived by solving the feasibility problem of the corresponding LMI.Some numerical examples are provided to demonstrate the applicability of the proposed algorithm.
MATLAB Stability and Control Toolbox Trim and Static Stability Module
Kenny, Sean P.; Crespo, Luis
2012-01-01
MATLAB Stability and Control Toolbox (MASCOT) utilizes geometric, aerodynamic, and inertial inputs to calculate air vehicle stability in a variety of critical flight conditions. The code is based on fundamental, non-linear equations of motion and is able to translate results into a qualitative, graphical scale useful to the non-expert. MASCOT was created to provide the conceptual aircraft designer accurate predictions of air vehicle stability and control characteristics. The code takes as input mass property data in the form of an inertia tensor, aerodynamic loading data, and propulsion (i.e. thrust) loading data. Using fundamental nonlinear equations of motion, MASCOT then calculates vehicle trim and static stability data for the desired flight condition(s). Available flight conditions include six horizontal and six landing rotation conditions with varying options for engine out, crosswind, and sideslip, plus three take-off rotation conditions. Results are displayed through a unique graphical interface developed to provide the non-stability and control expert conceptual design engineer a qualitative scale indicating whether the vehicle has acceptable, marginal, or unacceptable static stability characteristics. If desired, the user can also examine the detailed, quantitative results.
Stabilization of nonlinear excitations by disorder
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Gaididei, Yuri Borisovich; Johansson, M.
1998-01-01
Using analytical and numerical techniques we analyze the static and dynamical properties of solitonlike excitations in the presence of parametric disorder in the one-dimensional nonlinear Schrodinger equation with a homogeneous power nonlinearity. Both the continuum and the discrete problem are i...
Stability of Nonlinear Force-Free Magnetic Fields
Institute of Scientific and Technical Information of China (English)
胡友秋
2001-01-01
Based on the magnetohydrodynamic energy principle, it is proved that Gold-Hoyle's nonlinear force-free magnetic field is unstable. This disproves the sufficient criterion for stability of nonlinear force-free magnetic fields given by Kriiger that a nonlinear force-free field is stable if the maximum absolute value of the force-free factor is smaller than the lowest eigenvalue associated with the domain of interest.
Weakly nonlinear stability of ultra-thin slipping films
Institute of Scientific and Technical Information of China (English)
HU Guohui
2005-01-01
A weakly nonlinear theory is presented to study the effects of slippage on the stability of the ultra-thin polymer films.The nonlinear mathematical model is constructed for perturbations of small finite amplitude based on hydrodynamic equations with the long wave approximation. Results reveal that the nonlinearity always accelerates the rupture of the films. The influences of the slip length, film thickness, and initial amplitude of perturbations on the rupture of the films are investigated.
On absolute stability of nonlinear systems with small delays
Directory of Open Access Journals (Sweden)
M. I. Gil
1998-01-01
Full Text Available Nonlinear nonautonomous retarded systems with separated autonomous linear parts and continuous nonlinear ones are considered. It is assumed that deviations of the argument are sufficiently small. Absolute stability conditions are derived. They are formulated in terms of eigenvalues of auxiliary matrices.
Asymptotic stability and stabilizability of nonlinear systems with delay.
Srinivasan, V; Sukavanam, N
2016-11-01
This paper is concerned with asymptotic stability and stabilizability of a class of nonlinear dynamical systems with fixed delay in state variable. New sufficient conditions are established in terms of the system parameters such as the eigenvalues of the linear operator, delay parameter, and bounds on the nonlinear parts. Finally, examples are given to testify the effectiveness of the proposed theory.
Uniform Stability of Damped Nonlinear Vibrations of an Elastic String
Indian Academy of Sciences (India)
Ganesh C Gorain; Sujit K Bose
2003-11-01
Here we are concerned about uniform stability of damped nonlinear transverse vibrations of an elastic string fixed at its two ends. The vibrations governed by nonlinear integro-differential equation of Kirchoff type, is shown to possess energy uniformly bounded by exponentially decaying function of time. The result is achieved by considering an energy-like Lyapunov functional for the system.
Asymptotical Stability of Nonlinear Fractional Differential System with Caputo Derivative
Directory of Open Access Journals (Sweden)
Fengrong Zhang
2011-01-01
Full Text Available This paper deals with the stability of nonlinear fractional differential systems equipped with the Caputo derivative. At first, a sufficient condition on asymptotical stability is established by using a Lyapunov-like function. Then, the fractional differential inequalities and comparison method are applied to the analysis of the stability of fractional differential systems. In addition, some other sufficient conditions on stability are also presented.
Global stabilization of nonlinear systems with uncertain structure
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
The global stabilization problem of nonlinear systems with uncertain structure is dealt with. Based on control Lyapunov function (CLF), a sufficient and necessary condition for Lyapunov stabilization is given. From the condition,several simply sufficient conditions for the globally asymptotical stability are deduced. A state feedback control law is designed to globally asymptotically stabilize the equilibrium of the closed system. Last, a simulation shows the effectiveness of the method.
Solitons supported by singular spatial modulation of the Kerr nonlinearity
Borovkova, Olga V; Malomed, Boris A
2012-01-01
We introduce a setting based on the one-dimensional (1D) nonlinear Schroedinger equation (NLSE) with the self-focusing (SF) cubic term modulated by a singular function of the coordinate, |x|^{-a}. It may be additionally combined with the uniform self-defocusing (SDF) nonlinear background, and with a similar singular repulsive linear potential. The setting, which can be implemented in optics and BEC, aims to extend the general analysis of the existence and stability of solitons in NLSEs. Results for fundamental solitons are obtained analytically and verified numerically. The solitons feature a quasi-cuspon shape, with the second derivative diverging at the center, and are stable in the entire existence range, which is 0 < a < 1. Dipole (odd) solitons are found too. They are unstable in the infinite domain, but stable in the semi-infinite one. In the presence of the SDF background, there are two subfamilies of fundamental solitons, one stable and one unstable, which exist together above a threshold value ...
Stabilization of vortex beams in Kerr media by nonlinear absorption
Porras, Miguel A.; Carvalho, Márcio; Leblond, Hervé; Malomed, Boris A.
2016-11-01
We elaborate a solution for the problem of stable propagation of transversely localized vortex beams in homogeneous optical media with self-focusing Kerr nonlinearity. Stationary nonlinear Bessel-vortex states are stabilized against azimuthal breakup and collapse by multiphoton absorption, while the respective power loss is offset by the radial influx of the power from an intrinsic reservoir. A linear stability analysis and direct numerical simulations reveal a region of stability of these vortices. Beams with multiple vorticities have their stability regions too. These beams can then form robust tubular filaments in transparent dielectrics as common as air, water, and optical glasses at sufficiently high intensities. We also show that the tubular, rotating, and specklelike filamentation regimes, previously observed in experiments with axicon-generated Bessel beams, can be explained as manifestations of the stability or instability of a specific nonlinear Bessel-vortex state, which is fully identified.
Stabilization of vortex beams in Kerr media by nonlinear absorption
Porras, Miguel A; Leblond, Hervé; Malomed, Boris A
2016-01-01
We elaborate a new solution for the problem of stable propagation of transversely localized vortex beams in homogeneous optical media with self-focusing Kerr nonlinearity. Stationary nonlinear Bessel-vortex states are stabilized against azimuthal breakup and collapse by multiphoton absorption, while the respective power loss is offset by the radial influx of the power from an intrinsic reservoir. A linear stability analysis and direct numerical simulations reveal a region of stability of these vortices. Beams with multiple vorticities have their stability regions too. These beams can then form robust tubular filaments in transparent dielectrics as common as air, water and optical glasses at sufficiently high intensities. We also show that the tubular, rotating and speckle-like filamentation regimes, previously observed in experiments with axicon-generated Bessel beams, can be explained as manifestations of the stability or instability of a specific nonlinear Bessel-vortex state, which is fully identified.
Remarks on the relationship between ℒp stability and internal stability of nonlinear systems
Wang, Xu; Grip, H°avard Fjær; Saberi, Ali A.; Stoorvogel, Anton A.; Saberi, Ingmar
2013-01-01
In this paper, we investigate the relationship between ℒp stability and internal stability of nonlinear systems. It is shown that under certain conditions, ℒp stability without finite gain implies attractivity of the equilibrium, and that local ℒp stability with finite gain implies local asymptotic
Remarks on the relationship between ℒp stability and internal stability of nonlinear systems
Wang, Xu; Grip, H°avard Fjær; Saberi, Ali; Stoorvogel, Anton A.; Saberi, Ingmar
2011-01-01
In this paper, we investigate the relationship between ℒp stability and internal stability of nonlinear systems. It is shown that under certain conditions, ℒp stability without finite gain implies attractivity of the equilibrium, and that local ℒp stability with finite gain implies local asymptotic
Matlab Stability and Control Toolbox: Trim and Static Stability Module
Crespo, Luis G.; Kenny, Sean P.
2006-01-01
This paper presents the technical background of the Trim and Static module of the Matlab Stability and Control Toolbox. This module performs a low-fidelity stability and control assessment of an aircraft model for a set of flight critical conditions. This is attained by determining if the control authority available for trim is sufficient and if the static stability characteristics are adequate. These conditions can be selected from a prescribed set or can be specified to meet particular requirements. The prescribed set of conditions includes horizontal flight, take-off rotation, landing flare, steady roll, steady turn and pull-up/ push-over flight, for which several operating conditions can be specified. A mathematical model was developed allowing for six-dimensional trim, adjustable inertial properties, asymmetric vehicle layouts, arbitrary number of engines, multi-axial thrust vectoring, engine(s)-out conditions, crosswind and gyroscopic effects.
ASYMPTOTIC STABILITY OF SINGULAR NONLINEAR DIFFERENTIAL SYSTEMS WITH UNBOUNDED DELAYS
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
In this paper,the asymptotic stability of singular nonlinear differential systems with unbounded delays is considered.The stability criteria are derived based on a kind of Lyapunov-functional and some technique of matrix inequalities.The criteria are described as matrix equation and matrix inequalities,which are computationally flexible and efficient.Two examples are given to illustrate the results.
Control Lyapunov Stabilization of Nonlinear Systems with Structural Uncertainty
Institute of Scientific and Technical Information of China (English)
CAI Xiu-shan; HAN Zheng-zhi; TANG Hou-jun
2005-01-01
This paper deals with global stabilization problem for the nonlinear systems with structural uncertainty.Based on control Lyapunov function, a sufficient and necessary condition for the globally and asymptotically stabilizing the equailibrium of the closed system is given. Moreovery, an almost smooth state feedback control law is constructed. The simulation shows the effectiveness of the method.
Stochastic Stability Analysis for Markovian Jump Neutral Nonlinear Systems
Directory of Open Access Journals (Sweden)
Bo Wang
2012-10-01
Full Text Available In this paper, the stability problem is studied for a class of Markovian jump neutral nonlinear systems with time-varying delay. By Lyapunov-Krasovskii function approach, a novel mean-square exponential stability criterion is derived for the situations that the system's transition rates are completely accessible, partially accessible and non-accessible, respectively. Moreover, the developed stability criterion is extended to the systems with different bounded sector nonlinear constraints. Finally, some numerical examples are provided to illustrate the effectiveness of the proposed methods.
ON NONLINEAR STABILITY IN NONPARALLEL BOUNDARY LAYER FLOW
Institute of Scientific and Technical Information of China (English)
TANG Deng-bin; WANG Wei-zhi
2004-01-01
The nonlinear stability problem in nonparallel boundary layer flow for two-dimensional disturbances was studied by using a newly presented method called Parabolic Stability Equations (PSE). A series of new modes generated by the nonlinear interaction of disturbance waves were tabulately analyzed, and the Mean Flow Distortion (MFD) was numerically given. The computational techniques developed, including the higher-order spectral method and the more effective algebraic mapping, increased greatly the numerical accuracy and the rate of convergence. With the predictor-corrector approach in the marching procedure, the normalization condition was satisfied, and the stability of numerical calculation could be ensured. With different initial amplitudes, the nonlinear stability of disturbance wave was studied. The results of examples show good agreement with the data given by the DNS using the full Navier-Stokes equations.
Robust Stabilization of a Class of passive Nonlinear Systems
Joshi, Suresh M.; Kelkar, Atul G.
1996-01-01
The problem of feedback stabilization is considered for a class of nonlinear, finite dimensional, time invariant passive systems that are affine in control. Using extensions of the Kalman-Yakubovch lemma, it is shown that such systems can be stabilized by a class of finite demensional, linear, time-invariant controllers which are strictly positive real in the weak or marginal sense. The stability holds regardless of model uncertainties, and is therefore, robust.
Nonlinear stability of cosmological solutions in massive gravity
De Felice, Antonio; Lin, Chunshan; Mukohyama, Shinji
2013-01-01
We investigate nonlinear stability of two classes of cosmological solutions in massive gravity: isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW) solutions and anisotropic FLRW solutions. For this purpose we construct the linear cosmological perturbation theory around axisymmetric Bianchi type--I backgrounds. We then expand the background around the two classes of solutions, which are fixed points of the background evolution equation, and analyze linear perturbations on top of it. This provides a consistent truncation of nonlinear perturbations around these fixed point solutions and allows us to analyze nonlinear stability in a simple way. In particular, it is shown that isotropic FLRW solutions exhibit nonlinear ghost instability. On the other hand, anisotropic FLRW solutions are shown to be ghost-free for a range of parameters and initial conditions.
Robust laser frequency stabilization by serrodyne modulation
Kohlhaas, Ralf; Bernon, Simon; Bertoldi, Andrea; Landragin, Arnaud; Bouyer, Philippe
2011-01-01
We report the frequency stabilization of a distributed feedback erbium-doped fiber laser on an optical cavity by serrodyne frequency shifting. A correction bandwidth of 2.4 MHz and a dynamic range of 220 MHz are achieved, which leads to a strong robustness against large disturbances up to high frequencies. Serrodyne frequency shifting allows to use an electro-optical modulator as a fast external transducer with a correction range which exceeds the one of acousto-optical modulators by at least one order of magnitude.
On the non-linear stability of scalar field cosmologies
Energy Technology Data Exchange (ETDEWEB)
Alho, Artur; Mena, Filipe C [Centro de Matematica, Universidade do Minho, 4710-057 Braga (Portugal); Kroon, Juan A Valiente, E-mail: aalho@math.uminho.pt, E-mail: fmena@math.uminho.pt, E-mail: jav@maths.qmul.ac.uk [School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS (United Kingdom)
2011-09-22
We review recent work on the stability of flat spatially homogeneous and isotropic backgrounds with a self-interacting scalar field. We derive a first order quasi-linear symmetric hyperbolic system for the Einstein-nonlinear-scalar field system. Then, using the linearized system, we show how to obtain necessary and sufficient conditions which ensure the exponential decay to zero of small non-linear perturbations.
Modulational development of nonlinear gravity-wave groups
Chereskin, T. K.; Mollo-Christensen, E.
1985-01-01
Observations of the development of nonlinear surface gravity-wave groups are presented, and the amplitude and phase modulations are calculated using Hilbert-transform techniques. With increasing propagation distance and wave steepness, the phase modulation develops local phase reversals whose locations correspond to amplitude minima or nodes. The concomitant frequency modulation develops jumps or discontinuities. The observations are compared with recent similar results for wavetrains. The observations are modelled numerically using the cubic nonlinear Schroedinger equation. The motivation is twofold: to examine quantitatively the evolution of phase as well as amplitude modulation, and to test the inviscid predictions for the asymptotic behavior of groups versus long-time observations. Although dissipation rules out the recurrence, there is a long-time coherence of the groups. The phase modulation is found to distinguish between dispersive and soliton behavior.
Nonlinear Langmuir Wave Modulation in Weakly Magnetized Plasmas
DEFF Research Database (Denmark)
Dysthe, K. B.; Pécseli, Hans
1978-01-01
influence on the modulation stability of plane Langmuir waves. As in the unmagnetized case, kinetic results were found to deviate considerably from those obtained by using a fluid description for the ion dynamics. With particular attention to ionospheric phenomena, the effect is included of the spatially...... varying electron heating in the amplitude modulated Langmuir wave. For modulations travelling almost perpendicular to the magnetic field, this effect has a profound influence on a modulational instability...
An Improved Nonlinear Five-Point Model for Photovoltaic Modules
Directory of Open Access Journals (Sweden)
Sakaros Bogning Dongue
2013-01-01
Full Text Available This paper presents an improved nonlinear five-point model capable of analytically describing the electrical behaviors of a photovoltaic module for each generic operating condition of temperature and solar irradiance. The models used to replicate the electrical behaviors of operating PV modules are usually based on some simplified assumptions which provide convenient mathematical model which can be used in conventional simulation tools. Unfortunately, these assumptions cause some inaccuracies, and hence unrealistic economic returns are predicted. As an alternative, we used the advantages of a nonlinear analytical five-point model to take into account the nonideal diode effects and nonlinear effects generally ignored, which PV modules operation depends on. To verify the capability of our method to fit PV panel characteristics, the procedure was tested on three different panels. Results were compared with the data issued by manufacturers and with the results obtained using the five-parameter model proposed by other authors.
Nonlinear stabilization of tokamak microturbulence by fast ions
Citrin, J; Garcia, J; Haverkort, J W; Hogeweij, G M D; Jenko, F; Johnson, T; Mantica, P; Pueschel, M J; Told, D; contributors, JET-EFDA
2013-01-01
Nonlinear electromagnetic stabilization by suprathermal pressure gradients found in specific regimes is shown to be a key factor in reducing tokamak microturbulence, augmenting significantly the thermal pressure electromagnetic stabilization. Based on nonlinear gyrokinetic simulations investigating a set of ion heat transport experiments on the JET tokamak, described by Mantica et al. [Phys. Rev. Lett. 107 135004 (2011)], this result explains the experimentally observed ion heat flux and stiffness reduction. These findings are expected to improve the extrapolation of advanced tokamak scenarios to reactor relevant regimes.
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.
Stabilization of nonlinear systems based on robust control Lyapunov function
Institute of Scientific and Technical Information of China (English)
CAI Xiu-shan; HAN Zheng-zhi; LU Gan-yun
2007-01-01
This paper deals with the robust stabilization problem for a class of nonlinear systems with structural uncertainty. Based on robust control Lyapunov function, a sufficient and necessary condition for a function to be a robust control Lyapunov function is given. From this condition, simply sufficient condition for the robust stabilization (robust practical stabilization) is deduced. Moreover, if the equilibrium of the closed-loop system is unique, the existence of such a robust control Lyapunov function will also imply robustly globally asymptotical stabilization. Then a continuous state feedback law can be constructed explicitly. The simulation shows the effectiveness of the method.
Stabilization of a Nonlinear Delay System
Directory of Open Access Journals (Sweden)
Walid Arouri
2012-01-01
Full Text Available Problem statement: The analysis and control of delayed systems are becoming more and more research topics in progress. This is mainly due to the fact that the delay is frequently encountered in technological systems. This can affect their significantly operations. Most control command laws are based on current digital computers and delays are intrinsic to the process or in the control loop caused by the transmission time control sequences, or computing time. The delay may affect one or more states of the considered system. It may also affect the establishment of the command. Several studies have investigated the stability of delay systems under the assumption that the delay is a variable phenomenon; such variation is considered to be bounded or limited to facilitate analysis of the system. In this study we propose a modelling of delayed system by using the multimodels and switched system theory. The analysis of stability is based on the use of second Lyapunov method. The issued stability conditions are expressed as Bilinear Matrix Inequalities impossible to resolve. Thats why we propose the same original relaxations to come over this difficulty, an example of induction machine is given to illustrate over approach. Approach: We propose to use the control theory developed for switched systems to synthesis a control laws for the stabilisation of delays system. Results: We stabilize the induction machine around many operating points despite the non linearities. Conclusion: The developed method is less conservative and less pessimistic than the used classical methods.
Compositional Finite-Time Stability analysis of nonlinear systems
DEFF Research Database (Denmark)
Tabatabaeipour, Mojtaba; Blanke, Mogens
2014-01-01
for the system but with bounded disturbance. Sufficient conditions for finite-time stability and finite-time boundedness of nonlinear systems as well as a computational method based on sum of squares programming to check the conditions are given. The problem of finite-time stability for a system that consists......This paper, investigates finite-time stability and finite-time boundedness for nonlinear systems with polynomial vector fields. Finite-time stability requires the states of the system to remain a given bounded set in a finite-time interval and finite-time boundedness considers the same problem...... of an interconnection of subsystems is also considered and we show how to decompose the problem into subproblems for each subsystem with coupling constraints. A solution to the problem using sum of squares programming and dual decomposition is presented. The method is demonstrated through some examples....
Non-Linear Aeroelastic Stability of Wind Turbines
DEFF Research Database (Denmark)
Zhang, Zili; Sichani, Mahdi Teimouri; Li, Jie;
2013-01-01
As wind turbines increase in magnitude without a proportional increase in stiffness, the risk of dynamic instability is believed to increase. Wind turbines are time dependent systems due to the coupling between degrees of freedom defined in the fixed and moving frames of reference, which may...... trigger off internal resonances. Further, the rotational speed of the rotor is not constant due to the stochastic turbulence, which may also influence the stability. In this paper, a robust measure of the dynamic stability of wind turbines is suggested, which takes the collective blade pitch control...... and non-linear aero-elasticity into consideration. The stability of the wind turbine is determined by the maximum Lyapunov exponent of the system, which is operated directly on the non-linear state vector differential equations. Numerical examples show that this approach is promising for stability...
Stabilization of nonlinear systems by similarity transformations
Directory of Open Access Journals (Sweden)
Irina E. Zuber
1998-01-01
Full Text Available For a system x˙=A(x+b(xu, u(x=s∗(xx, x∈ℝn, where the pair (A(x,b(x is given, we obtain the feedback vector s(x to stabilize the corresponding closed loop system. For an arbitrarily chosen constant vector g, a sufficient condition of the existence and an explicit form of a similarity transformation T(A(x,b(x,g is established. The latter transforms matrix A(x into the Frobenius matrix, vector b(x into g, and an unknown feedback vector s(x into the first unit vector. The boundaries of A˜(y,g are determined by the boundaries of {∂kA(x∂xk,∂kb(x∂xk}, k=0,n−1¯. The stabilization of the transformed system is subject to the choice of the constant vector g.
Nonlinear evolution of the modulational instability under weak forcing and damping
Directory of Open Access Journals (Sweden)
J. Touboul
2010-12-01
Full Text Available The evolution of modulational instability, or Benjamin-Feir instability is investigated within the framework of the two-dimensional fully nonlinear potential equations, modified to include wind forcing and viscous dissipation. The wind model corresponds to the Miles' theory. The introduction of dissipation in the equations is briefly discussed. Evolution of this instability in the presence of damping was considered by Segur et al. (2005a and Wu et al. (2006. Their results were extended theoretically by Kharif et al. (2010 who considered wind forcing and viscous dissipation within the framework of a forced and damped nonlinear Schrödinger equation. The marginal stability curve derived from the fully nonlinear numerical simulations coincides with the curve obtained by Kharif et al. (2010 from a linear stability analysis. Furthermore, it is found that the presence of wind forcing promotes the occurrence of a permanent frequency-downshifting without invoking damping due to breaking wave phenomenon.
Relationship between the magnitude of singular value and nonlinear stability
Institute of Scientific and Technical Information of China (English)
穆穆; 郭欢; 王佳峰; 李勇
2001-01-01
The relationship between the magnitude of singular value and nonlinear stability or instability of the basic flow is investigated. The results show that there is a good corresponding relationship between them. The magnitude of singular value decreases as the stability (or instability) of the basic flow increases (or decreases). In the stable case, the magnitude of the maximum singular value is much smaller than in the unstable case.
Asymptotic Stability of Uniformly Bounded Nonlinear Switched Systems
Jouan, Philippe; Naciri, Said
2012-01-01
We study the asymptotic stability properties of nonlinear switched systems under the assumption of the existence of a common weak Lyapunov function. We consider the class of nonchaotic inputs, which generalize the different notions of inputs with dwell-time, and the class of general ones. For each of them we provide some sufficient conditions for asymptotic stability in terms of the geometry of certain sets. The results, which extend those of Balde, Jouan about linear systems, are illustrated...
Stabilization of discrete nonlinear systems based on control Lyapunov functions
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
The stabilization of discrete nonlinear systems is studied.Based on control Lyapunov functions,asufficient and necessary condition for a quadratic function to be a control Lyapunov function is given.From this condition,a continuous state feedback law is constructed explicitly.It can globally asymptotically stabilize the equilibrium of the closed-loop system.A simulation example shows the effectiveness of the proposed method.
Nonlinear evolution of the modulational instability of whistler waves
DEFF Research Database (Denmark)
Karpman, V.I.; Hansen, F.R.; Huld, T.
1990-01-01
The nonlinear evolution of the modulational instability of whistler waves coupled to fast magnetosonic waves is investigated in two spatial dimensions by numerical simulations. The long time evolution of the modulational instability shows a quasirecurrent behavior with a slow spreading...... of the energy, originally confined to the lowest wave numbers, to larger and larger wave numbers resulting in an apparently chaotic or random wave field. © 1990 The American Physical Society...
The linear and nonlinear stability of thread-annular flow.
Walton, Andrew G
2005-05-15
The surgical technique of thread injection of medical implants is modelled by the axial pressure-gradient-driven flow between concentric cylinders with a moving core. The linear stability of the flow to both axisymmetric and asymmetric perturbations is analysed asymptotically at large Reynolds number, and computationally at finite Reynolds number. The existence of multiple regions of instability is predicted and their dependence upon radius ratio and thread velocity is determined. A discrepancy in critical Reynolds numbers and cut-off velocity is found to exist between experimental results and the predictions of the linear theory. In order to account for this discrepancy, the high Reynolds number, nonlinear stability properties of the flow are analysed and a nonlinear, equilibrium critical layer structure is found, which leads to an enhanced correction to the basic flow. The predictions of the nonlinear theory are found to be in good agreement with the experimental data.
The Local Stability of Solutions for a Nonlinear Equation
Directory of Open Access Journals (Sweden)
Haibo Yan
2014-01-01
Full Text Available The approach of Kruzkov’s device of doubling the variables is applied to establish the local stability of strong solutions for a nonlinear partial differential equation in the space L1(R by assuming that the initial value only lies in the space L1(R∩L∞(R.
Discontinuous stabilization of nonlinear systems : Quantized and switching controls
Ceragioli, Francesca; De Persis, Claudio
2007-01-01
In this paper we consider the classical problem of stabilizing nonlinear systems in the case the control laws take values in a discrete set. First, we present a robust control approach to the problem. Then, we focus on the class of dissipative systems and rephrase classical results available for thi
Asymptotic Stability of Interconnected Passive Non-Linear Systems
Isidori, A.; Joshi, S. M.; Kelkar, A. G.
1999-01-01
This paper addresses the problem of stabilization of a class of internally passive non-linear time-invariant dynamic systems. A class of non-linear marginally strictly passive (MSP) systems is defined, which is less restrictive than input-strictly passive systems. It is shown that the interconnection of a non-linear passive system and a non-linear MSP system is globally asymptotically stable. The result generalizes and weakens the conditions of the passivity theorem, which requires one of the systems to be input-strictly passive. In the case of linear time-invariant systems, it is shown that the MSP property is equivalent to the marginally strictly positive real (MSPR) property, which is much simpler to check.
Deterministic aspects of nonlinear modulation instability
van Groesen, E; Karjanto, N
2011-01-01
Different from statistical considerations on stochastic wave fields, this paper aims to contribute to the understanding of (some of) the underlying physical phenomena that may give rise to the occurrence of extreme, rogue, waves. To that end a specific deterministic wavefield is investigated that develops extreme waves from a uniform background. For this explicitly described nonlinear extension of the Benjamin-Feir instability, the soliton on finite background of the NLS equation, the global down-stream evolving distortions, the time signal of the extreme waves, and the local evolution near the extreme position are investigated. As part of the search for conditions to obtain extreme waves, we show that the extreme wave has a specific optimization property for the physical energy, and comment on the possible validity for more realistic situations.
Reyna, Albert S
2014-01-01
We present a procedure for nonlinearity management of metal-dielectric composites. Varying the volume fraction occupied by silver nanoparticles suspended in acetone we could cancel the refractive index related to the third-order susceptibility, $\\chi_{eff}^{(3)}$, and the nonlinear refraction behavior was due to the fifth-order susceptibility, $\\chi_{eff}^{(5)}$. Hence, in a cross-phase modulation experiment, we demonstrated for the first time the effect of spatial-modulation- instability due to $\\chi_{eff}^{(5)}$. The results are corroborated with numerical calculations based on a generalized Maxwell-Garnet model.
NONLINEAR THEORY OF DYNAMIC STABILITY FOR LAMINATED COMPOSITE CYLINDRICAL SHELLS
Institute of Scientific and Technical Information of China (English)
周承倜; 王列东
2001-01-01
Hamilton Principle was uaed to derive the general governing equations of nonlinear dynamic stability for laminated cylindrical shells in which, factors of nonlinear large deflection, transverse shear and longitudinal inertia force were concluded. Equations were solved by variational method. Analysis reveals that under the action of dynamic load,laminated cylindrical shells will fall into a state of parametric resonance and enter into the dynamic unstable region that causes dynamic instability of shells. Laminated shells of three typical composites were computed: i.e. T300/5 208 graphite epoxy E-glass epoxy, and ARALL shells. Results show that all factors will induce important influence for dynamic stability of laminated shells. So, in research of dynamic stability for laminated shells, to consider these factors is important.
Exponential Stability of Stochastic Nonlinear Dynamical Price System with Delay
Directory of Open Access Journals (Sweden)
Wenli Zhu
2013-01-01
Full Text Available Based on Lyapunov stability theory, Itô formula, stochastic analysis, and matrix theory, we study the exponential stability of the stochastic nonlinear dynamical price system. Using Taylor's theorem, the stochastic nonlinear system with delay is reduced to an n-dimensional semilinear stochastic differential equation with delay. Some sufficient conditions of exponential stability and corollaries for such price system are established by virtue of Lyapunov function. The time delay upper limit is solved by using our theoretical results when the system is exponentially stable. Our theoretical results show that if the classical price Rayleigh equation is exponentially stable, so is its perturbed system with delay provided that both the time delay and the intensity of perturbations are small enough. Two examples are presented to illustrate our results.
Stability of gyro with harmonic nonlinearity in spinning vehicle
Singh, S. N.
1983-03-01
The stability analysis of a rate gyro mounted in a vehicle which is spinning with uncertain angular velocity about the spin axis of the gyro is presented. The complete nonlinear equation of the motion of the gimbal is considered, retaining the fundamental and second harmonic nonlinear terms which are functions of the angular velocity of the vehicle about the spin axis of the gyro. Using the circle criterion for the case of time-varying angular momentum and the Lyapunov approach for the case of uncertain constant angular velocity, conditions for asymptotic stability and global asymptotic stability are obtained. Stable regions in parameter space of the gyro and state space are obtained, and analytical relations for the selection of gyro parameters are derived.
Stabilization of switched nonlinear systems with unstable modes
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...
ANALYSIS OF NONLINEAR DYNAMIC STABILITY OF LIQUID-CONVEYING PIPES
Institute of Scientific and Technical Information of China (English)
张立翔; 黄文虎
2002-01-01
Nonlinearly dynamic stability of flexible liquid-conveying pipe in fluid structure interaction was analyzed by using modal disassembling technique. The effects of Poisson,Junction and Friction couplings in the wave-flowing-vibration system on the pipe dynamic stability were included in the analytical model constituted by four nonlinear differential equations. An analyzing example of cantilevered pipe was done to illustrate the dynamic stability characteristics of the pipe in the full coupling mechanisms, and the phase curves related to the first four modal motions were drawn. The results show that the dynamic stable characteristics of the pipe are very complicated in the complete coupling mechanisms, and the kinds of the singularity points corresponding to the various modal motions are different.
Higher-order modulation instability in nonlinear fiber optics.
Erkintalo, Miro; Hammani, Kamal; Kibler, Bertrand; Finot, Christophe; Akhmediev, Nail; Dudley, John M; Genty, Goëry
2011-12-16
We report theoretical, numerical, and experimental studies of higher-order modulation instability in the focusing nonlinear Schrödinger equation. This higher-order instability arises from the nonlinear superposition of elementary instabilities, associated with initial single breather evolution followed by a regime of complex, yet deterministic, pulse splitting. We analytically describe the process using the Darboux transformation and compare with experiments in optical fiber. We show how a suitably low frequency modulation on a continuous wave field induces higher-order modulation instability splitting with the pulse characteristics at different phases of evolution related by a simple scaling relationship. We anticipate that similar processes are likely to be observed in many other systems including plasmas, Bose-Einstein condensates, and deep water waves.
Extension to nonlinear stability theory of the circular Couette flow
Yau, Pun Wong; Wang, Shixiao; Rusak, Zvi
2016-11-01
A nonlinear stability analysis of the viscous circular Couette flow to axisymmetric perturbations under axial periodic boundary conditions is developed. The analysis is based on investigating the properties of a reduced Arnol'd energy-Casimir function Ard of Wang (2009). We show that all the inviscid flow effects as well as all the viscous-dependent terms related to the flow boundaries vanish. The evolution of ΔArd depends solely on the viscous effects of the perturbation's dynamics inside the flow domain. The requirement for the temporal decay of ΔArd leads to novel sufficient conditions for the nonlinear stability of the circular Couette flow in response to axisymmetric perturbations. Comparisons with historical studies show that our results shed light on the experimental measurements of Wendt (1933) and significantly extend the classical nonlinear stability results of Serrin (1959) and Joseph & Hung (1971). When the flow is nonlinearly stable and evolves axisymmetrically for all time, then it always decays asymptotically in time to the circular Couette flow determined uniquely by the setup of the rotating cylinders. This study provides new physical insights into a classical flow problem that was studied for decades.
Stabilizing model predictive control for constrained nonlinear distributed delay systems.
Mahboobi Esfanjani, R; Nikravesh, S K Y
2011-04-01
In this paper, a model predictive control scheme with guaranteed closed-loop asymptotic stability is proposed for a class of constrained nonlinear time-delay systems with discrete and distributed delays. A suitable terminal cost functional and also an appropriate terminal region are utilized to achieve asymptotic stability. To determine the terminal cost, a locally asymptotically stabilizing controller is designed and an appropriate Lyapunov-Krasoskii functional of the locally stabilized system is employed as the terminal cost. Furthermore, an invariant set for locally stabilized system which is established by using the Razumikhin Theorem is used as the terminal region. Simple conditions are derived to obtain terminal cost and terminal region in terms of Bilinear Matrix Inequalities. The method is illustrated by a numerical example.
Modulation instability of broad optical beams in nonlinear media with general nonlinearity
Institute of Scientific and Technical Information of China (English)
Hongcheng Wang; Weilong She
2006-01-01
@@ The modulation instability of quasi-plane-wave optical beams is investigated in the frame of generalized Schr(o)dinger equation with the nonlinear term of a general form. General expressions are derived for the dispersion relation, the critical transverse spatial frequency, as well as the instability growth rate.The analysis generalizes the known results reported previously. A detailed discussion on the modulation instability in biased centrosymmetric photorefractive media is also given.
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)
QUANTITATIVE METHODOLOGY FOR STABILITY ANALYSIS OF NONLINEAR ROTOR SYSTEMS
Institute of Scientific and Technical Information of China (English)
ZHENG Hui-ping; XUE Yu-sheng; CHEN Yu-shu
2005-01-01
Rotor-bearings systems applied widely in industry are nonlinear dynamic systems of multi-degree-of-freedom. Modem concepts on design and maintenance call for quantitative stability analysis. Using trajectory based stability-preserving and dimensional-reduction, a quanttative stability analysis method for rotor systems is presented. At first, an n-dimensional nonlinear non-autonomous rotor system is decoupled into n subsystems after numerical integration. Each of them has only onedegree-of-freedom and contains time-varying parameters to represent all other state variables. In this way, n-dimensional trajectory is mapped into a set of one-dimensional trajectories. Dynamic central point (DCP) of a subsystem is then defined on the extended phase plane, namely, force-position plane. Characteristics of curves on the extended phase plane and the DCP's kinetic energy difference sequence for general motion in rotor systems are studied. The corresponding stability margins of trajectory are evaluated quantitatively. By means of the margin and its sensitivity analysis, the critical parameters of the period doubling bifurcation and the Hopf bifurcation in a flexible rotor supported by two short journal beatings with nonlinear suspensionare are determined.
Stability of GOY Model Under Modulation of Periodic External Force
Institute of Scientific and Technical Information of China (English)
ZHAO Ying-Kui; CHEN Shi-Gang; WANG Guang-Rui
2008-01-01
There is a phase transition between quasi-periodic state and intermittent chaos in GOY model with a critical value δ0. When we add a modulated periodic external force to the system, the phase transition can also be found with a critical value δe. Due to coupling between the force and the intrinsic fluctuation of the velocity on shells in GOY model, the stability of the system has been changed, which results in the variation of the critical value. For proper intensity and period of the force, δe is unequal to δ0. The critical value is a nonlinear function of amplitude of the force, and the fluctuation of the velocity can resonate with the external force for certain period Te.
Modulational instability in fractional nonlinear Schrödinger equation
Zhang, Lifu; He, Zenghui; Conti, Claudio; Wang, Zhiteng; Hu, Yonghua; Lei, Dajun; Li, Ying; Fan, Dianyuan
2017-07-01
Fractional calculus is entering the field of nonlinear optics to describe unconventional regimes, as disorder biological media and soft-matter. Here we investigate spatiotemporal modulational instability (MI) in a fractional nonlinear Schrödinger equation. We derive the MI gain spectrum in terms of the Lévy indexes and a varying number of spatial dimensions. We show theoretically and numerically that the Lévy indexes affect fastest growth frequencies and MI bandwidth and gain. Our results unveil a very rich scenario that may occur in the propagation of ultrashort pulses in random media and metamaterials, and may sustain novel kinds of propagation invariant optical bullets.
Robust Stabilization of Nonlinear Systems with Uncertain Varying Control Coefficient
Directory of Open Access Journals (Sweden)
Zaiyue Yang
2014-01-01
Full Text Available This paper investigates the stabilization problem for a class of nonlinear systems, whose control coefficient is uncertain and varies continuously in value and sign. The study emphasizes the development of a robust control that consists of a modified Nussbaum function to tackle the uncertain varying control coefficient. By such a method, the finite-time escape phenomenon has been prevented when the control coefficient is crossing zero and varying its sign. The proposed control guarantees the asymptotic stabilization of the system and boundedness of all closed-loop signals. The control performance is illustrated by a numerical simulation.
Stability Analysis of Some Nonlinear Anaerobic Digestion Models
Directory of Open Access Journals (Sweden)
Ivan Simeonov
2010-04-01
Full Text Available Abstract: The paper deals with local asymptotic stability analysis of some mass balance dynamic models (based on one and on two-stage reaction schemes of the anaerobic digestion (AD in CSTR. The equilibrium states for models based on one (with Monod, Contois and Haldane shapes for the specific growth rate and on two-stage (only with Monod shapes for both the specific growth rate of acidogenic and methanogenic bacterial populations reaction schemes have been determined solving sets of nonlinear algebraic equations using Maples. Their stability has been analyzed systematically, which provides insight and guidance for AD bioreactors design, operation and control.
Robust stabilization of uncertain nonholonomic systems with strong nonlinear drifts
Institute of Scientific and Technical Information of China (English)
Yuqiang WU; Xiuyun ZHENG
2008-01-01
This paper investigates the robust stabilization of the nonholonomic control systems with strongly nonlinear uncertainties.In order to make the state scaling effective and to prevent the fiflite time escape phenomenon from happening.the switching control strategy based on the state measurement of the first subsystem is employed to achieve the asymptotic stabilization.The recurslve integrator backstepping technique is applied to the design of the robust controller.The simulation example demonstrates the efficiency and robust features of the proposed method.
The numerical stability of nonlinear floating body calculations
Park, Jong-Hwan
1992-01-01
The numerical stability of nonlinear body-wave interaction problems is investigated by applying potential flow assumptions to oscillating, non-wallsided two-dimensional and three-dimensional axisymmetric bodies. This body-wave interaction problem is solved using a mixed two-step Eulerian-Lagrangian method. In the first step, Laplace's equation is solved to determine the unknown potential values on the body and the unknown derivatives of the potentials on the free surface. In the second step, free surface boundary conditions are applied using the results of the first step to find the evolved free surface location and new potential values on the new location. Each step has particular mathematical characteristics (elliptic or parabolic-like), so that each step requires different numerical schemes. Consequently, the numerical stability of this body-wave interaction problem contains the characteristics of both of these two steps. The major contributions made to this body-wave interaction problem are the effects of the various parameters (i.e. time increments, panel length, etc.) and the different forms of the Boundary Integral Method (BIM) on numerical stability and accuracy. The far-field truncation requirement is met by matching the linear outer solution to the nonlinear inner solution at the truncation boundary. The intersection point is traced by the extrapolation method with a special boundary condition at the intersection point. To determine the evolution of the free surface according to a Lagrangian model, a regridding scheme is utilized to prevent the concentration of the Lagrangian markers in the vicinity of high gradients. A parameter for the numerical stability of free surface waves, the Free Surface Stability (FSS) number, is defined as a function of the time step size and the discretized panel length. The various stability regions are investigated by changing the FSS number, Green's function constant c, and numerical schemes. A nonlinear stability analysis
Paradoxical stabilization of forced oscillations by strong nonlinear friction
Esirkepov, Timur Zh.; Bulanov, Sergei V.
2017-08-01
In a dissipative dynamic system driven by an oscillating force, a strong nonlinear highly oscillatory friction force can create a quasi-steady tug, which is always directed opposite to the ponderomotive force induced due to a spatial inhomogeneity of oscillations. When the friction-induced tug exceeds the ponderomotive force, the friction stabilizes the system oscillations near the maxima of the oscillation spatial amplitude of the driving force.
Stability, Nonlinearity and Reliability of Electrostatically Actuated MEMS Devices
Directory of Open Access Journals (Sweden)
Di Chen
2007-05-01
Full Text Available Electrostatic micro-electro-mechanical system (MEMS is a special branch with a wide range of applications in sensing and actuating devices in MEMS. This paper provides a survey and analysis of the electrostatic force of importance in MEMS, its physical model, scaling effect, stability, nonlinearity and reliability in detail. It is necessary to understand the effects of electrostatic forces in MEMS and then many phenomena of practical importance, such as pull-in instability and the effects of effective stiffness, dielectric charging, stress gradient, temperature on the pull-in voltage, nonlinear dynamic effects and reliability due to electrostatic forces occurred in MEMS can be explained scientifically, and consequently the great potential of MEMS technology could be explored effectively and utilized optimally. A simplified parallel-plate capacitor model is proposed to investigate the resonance response, inherent nonlinearity, stiffness softened effect and coupled nonlinear effect of the typical electrostatically actuated MEMS devices. Many failure modes and mechanisms and various methods and techniques, including materials selection, reasonable design and extending the controllable travel range used to analyze and reduce the failures are discussed in the electrostatically actuated MEMS devices. Numerical simulations and discussions indicate that the effects of instability, nonlinear characteristics and reliability subjected to electrostatic forces cannot be ignored and are in need of further investigation.
Optimal frequency conversion in the nonlinear stage of modulation instability
Bendahmane, A; Kudlinski, A; Szriftgiser, P; Conforti, M; Wabnitz, S; Trillo, S
2015-01-01
We investigate multi-wave mixing associated with the strongly pump depleted regime of induced modulation instability (MI) in optical fibers. For a complete transfer of pump power into the sideband modes, we theoretically and experimentally demonstrate that it is necessary to use a much lower seeding modulation frequency than the peak MI gain value. Our analysis shows that a record 95 % of the input pump power is frequency converted into the comb of sidebands, in good quantitative agreement with analytical predictions based on the simplest exact breather solution of the nonlinear Schr\\"odinger equation.
Finite-Time Stability and Stabilization of Nonlinear Quadratic Systems with Jumps
Directory of Open Access Journals (Sweden)
Minsong Zhang
2014-01-01
Full Text Available This paper investigates the problems of finite-time stability and finite-time stabilization for nonlinear quadratic systems with jumps. The jump time sequences here are assumed to satisfy some given constraints. Based on Lyapunov function and a particular presentation of the quadratic terms, sufficient conditions for finite-time stability and finite-time stabilization are developed to a set containing bilinear matrix inequalities (BLIMs and linear matrix inequalities (LMIs. Numerical examples are given to illustrate the effectiveness of the proposed methodology.
Indian Academy of Sciences (India)
HONG-YU WU; LI-HONG JIANG
2017-09-01
From a generic transformation, a $(3+1)$-dimensional nonlinear Schrödinger equation with spatially modulated nonlinearity is studied and exact spatiotemporal soliton cluster solutions are derived. When the azimuthal parameter $m = 0$, Gaussian solitons are constructed. For the modulation depth $q = 1$ and the azimuthal parameter $m \
Wu, Hong-Yu; Jiang, Li-Hong
2017-09-01
From a generic transformation, a (3+1)-dimensional nonlinear Schrödinger equation with spatially modulated nonlinearity is studied and exact spatiotemporal soliton cluster solutions are derived. When the azimuthal parameter m = 0, Gaussian solitons are constructed. For the modulation depth q = 1 and the azimuthal parameter m\
Design for robust stabilization of nonlinear systems with uncertain parameters
Institute of Scientific and Technical Information of China (English)
赖旭芝; 文静; 吴敏
2004-01-01
Based on Lyapunov stability theory, a design method for the robust stabilization problem of a class of nonlinear systems with uncertain parameters is presented. The design procedure is divided into two steps: the first is to design controllers for the nominal system and make the system asymptotically stabilize at the expected equilibrium point; the second is to construct closed-loop nominal system based on the first step, then design robust controller to make the error of state between the original system and the nominal system converge to zero, thereby a dynamic controller with the constructed closed-loop nominal system served as interior dynamic is obtained. A numerical simulation verifies the correctness of the design method.
Slope stability analysis using limit equilibrium method in nonlinear criterion.
Lin, Hang; Zhong, Wenwen; Xiong, Wei; Tang, Wenyu
2014-01-01
In slope stability analysis, the limit equilibrium method is usually used to calculate the safety factor of slope based on Mohr-Coulomb criterion. However, Mohr-Coulomb criterion is restricted to the description of rock mass. To overcome its shortcomings, this paper combined Hoek-Brown criterion and limit equilibrium method and proposed an equation for calculating the safety factor of slope with limit equilibrium method in Hoek-Brown criterion through equivalent cohesive strength and the friction angle. Moreover, this paper investigates the impact of Hoek-Brown parameters on the safety factor of slope, which reveals that there is linear relation between equivalent cohesive strength and weakening factor D. However, there are nonlinear relations between equivalent cohesive strength and Geological Strength Index (GSI), the uniaxial compressive strength of intact rock σ ci , and the parameter of intact rock m i . There is nonlinear relation between the friction angle and all Hoek-Brown parameters. With the increase of D, the safety factor of slope F decreases linearly; with the increase of GSI, F increases nonlinearly; when σ ci is relatively small, the relation between F and σ ci is nonlinear, but when σ ci is relatively large, the relation is linear; with the increase of m i , F decreases first and then increases.
Modulational instability in a PT-symmetric vector nonlinear Schrödinger system
Cole, J. T.; Makris, K. G.; Musslimani, Z. H.; Christodoulides, D. N.; Rotter, S.
2016-12-01
A class of exact multi-component constant intensity solutions to a vector nonlinear Schrödinger (NLS) system in the presence of an external PT-symmetric complex potential is constructed. This type of uniform wave pattern displays a non-trivial phase whose spatial dependence is induced by the lattice structure. In this regard, light can propagate without scattering while retaining its original form despite the presence of inhomogeneous gain and loss. These constant-intensity continuous waves are then used to perform a modulational instability analysis in the presence of both non-hermitian media and cubic nonlinearity. A linear stability eigenvalue problem is formulated that governs the dynamical evolution of the periodic perturbation and its spectrum is numerically determined using Fourier-Floquet-Bloch theory. In the self-focusing case, we identify an intensity threshold above which the constant-intensity modes are modulationally unstable for any Floquet-Bloch momentum belonging to the first Brillouin zone. The picture in the self-defocusing case is different. Contrary to the bulk vector case, where instability develops only when the waves are strongly coupled, here an instability occurs in the strong and weak coupling regimes. The linear stability results are supplemented with direct (nonlinear) numerical simulations.
Geometrical nonlinear stability analyses of cable-truss domes
Institute of Scientific and Technical Information of China (English)
高博青; 卢群鑫; 董石麟
2003-01-01
The nonlinear finite element method is used to analyze the geometrical nonlinear stability of cable-truss domes with different cable distributions. The results indicate that the critical load increases evidently when cables, especially diagonal cables, are distributed in the structure. The critical loads of the structure at different rise-span ratios are also discussed in this paper. It was shown that the effect of the tensional cable is more evident at small rise-span ratio. The buckling of the structure is characterized by a global collapse at small rise-span ratio; that the torsional buckling of the radial truss occurs at big rise-span ratio; and that at proper rise-span ratio, the global collapse and the lateral buckling of the truss occur nearly simultaneously.
Geometrical nonlinear stability analyses of cable-truss domes
Institute of Scientific and Technical Information of China (English)
高博青; 卢群鑫; 董石麟
2003-01-01
The nonlinear finite element method is used to analyze the geometrical nonlinear stability of cabletruss domes with different cable distributions. The results indicate that the critical load increases evidently when cables, especially diagonal cables, are distributed in the structure. The critical loads of the structure at different rise-span ratios are also discussed in this paper. It was shown that the effect of the tensional cable is more evident at small rise-span ratio. The buckling of the structure is characterized by a global collapse at small rlse-span ratio ; that the torsional buckling of the radial truss occurs at big rise-span ratio; and that at proper rise-span ratio, the global collapse and the lateral buckling of the truss occur nearly simultaneously.
Transient stability improvement by nonlinear controllers based on tracking
Energy Technology Data Exchange (ETDEWEB)
Ramirez, Juan M. [Centro de Investigacion y Estudios Avanzados, Guadalajara, Mexico. Av. Cientifica 1145. Col. El Bajio. Zapopan, Jal. 45015 (Mexico); Arroyave, Felipe Valencia; Correa Gutierrez, Rosa Elvira [Universidad Nacional de Colombia, Sede Medellin. Facultad de Minas, Escuela de Mecatronica (Colombia)
2011-02-15
This paper deals with the control problem in multi-machine electric power systems, which represent complex great scale nonlinear systems. Thus, the controller design is a challenging problem. These systems are subjected to different perturbations, such as short circuits, connection and/or disconnection of loads, lines, or generators. Then, the utilization of controllers which guarantee good performance under those perturbations is required in order to provide electrical energy to the loads with admissible stability margins. The proposed controllers are based on a systematic strategy, which calculate nonlinear controllers for generating units in a power plant, both for voltage and velocity regulation. The formulation allows designing controllers in a multi-machine power system without intricate calculations. Results on a power system of the open research indicate the proposition's suitability. The problem is formulated as a tracking problem. The designed controllers may be implemented in any electric power system. (author)
Linear Feedback Stabilization of Nonlinear Systems with an Uncontrollable Critical Mode
1992-11-17
mode that is uncontrollable. The results complement previous work on the synthesis of nonlinear stabilizing control laws. The present work addresses...analysis and stabilizing control design employ results on stability of bifurcations of parametrized systems.
Stability analysis of a class of fractional order nonlinear systems with order lying in (0, 2).
Zhang, Ruoxun; Tian, Gang; Yang, Shiping; Cao, Hefei
2015-05-01
This paper investigates the stability of n-dimensional fractional order nonlinear systems with commensurate order 0 nonlinear systems with order lying in (0, 2). According to this theory, stabilizing a class of fractional order nonlinear systems only need a linear state feedback controller. Simulation results demonstrate the effectiveness of the proposed theory.
Adaptive steady-state stabilization for nonlinear dynamical systems
Braun, David J.
2008-07-01
By means of LaSalle’s invariance principle, we propose an adaptive controller with the aim of stabilizing an unstable steady state for a wide class of nonlinear dynamical systems. The control technique does not require analytical knowledge of the system dynamics and operates without any explicit knowledge of the desired steady-state position. The control input is achieved using only system states with no computer analysis of the dynamics. The proposed strategy is tested on Lorentz, van der Pol, and pendulum equations.
Wu, Huilan; Yao, Yuqin
2017-01-01
The time- and space-modulated nonlinearity is the important character of the Bose-Einstein condensates (BECs). Many works have been done on atomic BECs with spatially modulated nonlinearity, but there is little work on atomic-molecular BECs. In this paper, we construct one family of explicitly exact solutions of the atomic-molecular BECs with time- and space-modulated nonlinearities and trapping potential by similarity transformations. We discuss the dynamics of matter waves including breathing solitons, quasi-breathing solitons, resonant solitons and moving solitons. We analyze the linear stability of the solutions by adding various initial stochastic noise. We also provide the experimental parameters to produce these phenomena in future experiments.
Stability analysis for nonlinear multi－variable delay perturbation problems
Institute of Scientific and Technical Information of China (English)
WangHongshan; ZhangChengjian
2003-01-01
This paper discusses the stability of theoretical solutions for nonlinear multi-variable delay perturbation problems(MVDPP) of the form x′(t) = f(x(t),x(t - τ1(t)),…,x(t -τm(t)),y(t),y(t - τ1(t)),…,y(t - τm(t))), and gy′(t) = g(x(t),x(t- τ1(t)),…,x(t- τm(t)),y(t),y(t- τ1(t)),…,y(t- τm(t))), where 0 < ε <<1. A sufficient condition of stability for the systems is obtained. Additionally we prove the numerical solutions of the implicit Euler method are stable under this condition.
Stability of the accelerated expansion in nonlinear electrodynamics
Energy Technology Data Exchange (ETDEWEB)
Sharif, M.; Mumtaz, Saadia [University of the Punjab, Department of Mathematics, Lahore (Pakistan)
2017-02-15
This paper is devoted to the phase space analysis of an isotropic and homogeneous model of the universe by taking a noninteracting mixture of the electromagnetic and viscous radiating fluids whose viscous pressure satisfies a nonlinear version of the Israel-Stewart transport equation. We establish an autonomous system of equations by introducing normalized dimensionless variables. In order to analyze the stability of the system, we find corresponding critical points for different values of the parameters. We also evaluate the power-law scale factor whose behavior indicates different phases of the universe in this model. It is concluded that the bulk viscosity as well as electromagnetic field enhances the stability of the accelerated expansion of the isotropic and homogeneous model of the universe. (orig.)
Chaotic saddles in nonlinear modulational interactions in a plasma
Energy Technology Data Exchange (ETDEWEB)
Miranda, Rodrigo A. [Institute of Aeronautical Technology (ITA) and World Institute for Space Environment Research (WISER), Sao Jose dos Campos, SP 12228-900 (Brazil); National Institute for Space Research (INPE) and World Institute for Space Environment Research (WISER), P.O. Box 515, Sao Jose dos Campos, SP 12227-010 (Brazil); University of Brasilia (UnB), Gama Campus, and Plasma Physics Laboratory, Institute of Physics, Brasilia, DF 70910-900 (Brazil); Rempel, Erico L. [Institute of Aeronautical Technology (ITA) and World Institute for Space Environment Research (WISER), Sao Jose dos Campos, SP 12228-900 (Brazil); National Institute for Space Research (INPE) and World Institute for Space Environment Research (WISER), P.O. Box 515, Sao Jose dos Campos, SP 12227-010 (Brazil); Chian, Abraham C.-L. [Institute of Aeronautical Technology (ITA) and World Institute for Space Environment Research (WISER), Sao Jose dos Campos, SP 12228-900 (Brazil); National Institute for Space Research (INPE) and World Institute for Space Environment Research (WISER), P.O. Box 515, Sao Jose dos Campos, SP 12227-010 (Brazil); Observatoire de Paris, LESIA, CNRS, 92195 Meudon (France)
2012-11-15
A nonlinear model of modulational processes in the subsonic regime involving a linearly unstable wave and two linearly damped waves with different damping rates in a plasma is studied numerically. We compute the maximum Lyapunov exponent as a function of the damping rates in a two-parameter space, and identify shrimp-shaped self-similar structures in the parameter space. By varying the damping rate of the low-frequency wave, we construct bifurcation diagrams and focus on a saddle-node bifurcation and an interior crisis associated with a periodic window. We detect chaotic saddles and their stable and unstable manifolds, and demonstrate how the connection between two chaotic saddles via coupling unstable periodic orbits can result in a crisis-induced intermittency. The relevance of this work for the understanding of modulational processes observed in plasmas and fluids is discussed.
Chaotic saddles in nonlinear modulational interactions in a plasma
Miranda, Rodrigo A; Chian, Abraham C -L
2012-01-01
A nonlinear model of modulational processes in the subsonic regime involving a linearly unstable wave and two linearly damped waves with different damping rates in a plasma is studied numerically. We compute the maximum Lyapunov exponent as a function of the damping rates in a two-parameter space, and identify shrimp-shaped self-similar structures in the parameter space. By varying the damping rate of the low-frequency wave, we construct bifurcation diagrams and focus on a saddle-node bifurcation and an interior crisis associated with a periodic window. We detect chaotic saddles and their stable and unstable manifolds, and demonstrate how the connection between two chaotic saddles via coupling unstable periodic orbits can result in a crisis-induced intermittency. The relevance of this work for the understanding of modulational processes observed in plasmas and fluids is discussed.
Complete modulational-instability gain spectrum of nonlinear quasi-phase-matching gratings
DEFF Research Database (Denmark)
Corney, Joel F.; Bang, Ole
2004-01-01
We consider plane waves propagating in quadratic nonlinear slab waveguides with nonlinear quasi-phasematching gratings. We predict analytically and verify numerically the complete gain spectrum for transverse modulational instability, including hitherto undescribed higher-order gain bands....
Global stabilizer of a general class of feedback nonlinear systems and its exponential convergence
Institute of Scientific and Technical Information of China (English)
Runing MA; Jundi DIAN
2005-01-01
We discuss the global stabilization procedure which renders a general class of feedback nonlinear systems exponential convergent. Our stabilizer consists of a nested saturation function, which is a nonlinear combination of satrration functions. Here we prove the exponential convergence of the stabilizer for the first time and give numerical examples to illustrate the efficiency of the result given above.
Absolute stability of nonlinear systems with time delays and applications to neural networks
Directory of Open Access Journals (Sweden)
Xinzhi Liu
2001-01-01
Full Text Available In this paper, absolute stability of nonlinear systems with time delays is investigated. Sufficient conditions on absolute stability are derived by using the comparison principle and differential inequalities. These conditions are simple and easy to check. In addition, exponential stability conditions for some special cases of nonlinear delay systems are discussed. Applications of those results to cellular neural networks are presented.
The power spectral density of digital modulations transmitted over nonlinear channels
Divsalar, D.; Simon, M. K.
1982-01-01
This paper examines by analytical methods the power spectral densities of digital modulations (in particular, staggered and unstaggered quadrature modulations) passed through band-limited nonlinear channels. Previously observed (by computer simulation or hardware measurement) behavior of such spectra with regard to the suppression or restoration of its sidelobes after passing through the nonlinearity is verified analytically. Several examples corresponding to specific quadrature modulations and filter-nonlinearity combinations are presented as illustrations of the general results.
AMABILI, M.; PELLICANO, F.; PAÏDOUSSIS, M. P.
1999-08-01
The study presented is an investigation of the non-linear dynamics and stability of simply supported, circular cylindrical shells containing inviscid incompressible fluid flow. Non-linearities due to large-amplitude shell motion are considered by using the non-linear Donnell's shallow shell theory, with account taken of the effect of viscous structural damping. Linear potential flow theory is applied to describe the fluid-structure interaction. The system is discretiszd by Galerkin's method, and is investigated by using a model involving seven degrees of freedom, allowing for travelling wave response of the shell and shell axisymmetric contraction. Two different boundary conditions are applied to the fluid flow beyond the shell, corresponding to: (i) infinite baffles (rigid extensions of the shell), and (ii) connection with a flexible wall of infinite extent in the longitudinal direction, permitting solution by separation of variables; they give two different kinds of dynamical behaviour of the system, as a consequence of the fact that axisymmetric contraction, responsible for the softening non-linear dynamical behaviour of shells, is not allowed if the fluid flow beyond the shell is constrained by rigid baffles. Results show that the system loses stability by divergence.
Robust Absolute Stability of General Interval Lur'e Type Nonlinear Control Systems
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
In this paper, Lyapunov function method isused to study the robust absolute stability of general interval Lur'e type nonlinear control systems. As a result, algebraically sufficient conditions with interval matrix inequality form are obtained for the general interval Lur'e type nonlinear control systems, thus the relationship between the stability of symmetrical interval matrix and the robust absolute stability of general interval Lur'e type nonlinear control systems is established.
Improving Stability of Pulse Modulator Technology
Institute of Scientific and Technical Information of China (English)
ZHANG; Li-feng; ZHU; Zhi-bin; LIU; Bao-jie; YANG; Sheng
2015-01-01
In high voltage pulse modulator,the RD loop and the primary winding of the pulse transformer is parallel,and the negative peak loop and the PFN is parallel.When the modulator is running,the resistor temperature of RD loops and the resistor temperature of reverse peak loop are too high,exceeding 100℃.It can work normally,
Collapse arrest and soliton stabilization in nonlocal nonlinear media
DEFF Research Database (Denmark)
Bang, Ole; Krolikowski, Wieslaw; Wyller, John
2002-01-01
We investigate the properties of localized waves in cubic nonlinear materials with a symmetric nonlocal nonlinear response of arbitrary shape and degree of nonlocality, described by a general nonlocal nonlinear Schrodinger type equation. We prove rigorously by bounding the Hamiltonian that nonloc......We investigate the properties of localized waves in cubic nonlinear materials with a symmetric nonlocal nonlinear response of arbitrary shape and degree of nonlocality, described by a general nonlocal nonlinear Schrodinger type equation. We prove rigorously by bounding the Hamiltonian...
Analysis of Stability and Bifurcation in Nonlinear Mechanics with Dissipation
Directory of Open Access Journals (Sweden)
Claude Stolz
2011-01-01
Full Text Available The analysis of stability and bifurcation is studied in nonlinear mechanics with dissipative mechanisms: plasticity, damage, fracture. The description is based on introduction of a set of internal variables. This framework allows a systematic description of the material behaviour via two potentials: the free energy and the potential of dissipation. In the framework of standard generalized materials the internal state evolution is governed by a variational inequality which depends on the mechanism of dissipation. This inequality is obtained through energetic considerations in an unified description based upon energy and driving forces associated to the dissipative process. This formulation provides criterion for existence and uniqueness of the system evolution. Examples are presented for plasticity, fracture and for damaged materials.
On nonlinear stability in various random normed spaces
Directory of Open Access Journals (Sweden)
Saadati Reza
2011-01-01
Full Text Available Abstract In this article, we prove the nonlinear stability of the quartic functional equation 1 6 f ( x + 4 y + f ( 4 x - y = 3 0 6 9 f x + y 3 + f ( x + 2 y (1 + 1 3 6 f ( x - y - 1 3 9 4 f ( x + y + 4 2 5 f ( y - 1 5 3 0 f ( x (2 (3 in the setting of random normed spaces Furthermore, the interdisciplinary relation among the theory of random spaces, the theory of non-Archimedean space, the theory of fixed point theory, the theory of intuitionistic spaces and the theory of functional equations are also presented in the article.
Multivariable nonlinear control of STATCOM for synchronous generator stabilization
Energy Technology Data Exchange (ETDEWEB)
Sahoo, N.C. [Multimedia Univ., Melaka (Malaysia). Faculty of Engineering and Technology; Panigrahi, B.K.; Panda, G. [Multimedia Univ., Selangor (Malaysia); Dash, P.K. [National Inst. of Technology, Rourkela (India)
2004-01-01
A static synchronous compensator (STATCOM) is a typical flexible ac transmission system device playing a vital role as a stability aid for small and large transient disturbances in an interconnected power system. This article deals with design and evaluation of a feedback linearizing nonlinear controller for STATCOM installed in a single-machine infinite-bus power system. In addition to the coordinated control of ac and dc bus voltages, the proposed controller also provides good damping to the electromechanical oscillation of the synchronous generator under transient disturbances. The efficiency of the control strategy is evaluated by computer simulation studies. The comparative study of these results with the conventional cascade control structure establishes the elegance of the proposed control scheme. (author)
STABILITY ANALYSIS OF RUNGE-KUTTA METHODS FOR NONLINEAR SYSTEMS OF PANTOGRAPH EQUATIONS
Institute of Scientific and Technical Information of China (English)
Yue-xin Yu; Shou-fu Li
2005-01-01
This paper is concerned with numerical stability of nonlinear systems of pantograph equations. Numerical methods based on (k, l)-algebraically stable Runge-Kutta methods are suggested. Global and asymptotic stability conditions for the presented methods are derived.
STABILIZATION OF NONLINEAR TIME-VARYING SYSTEMS: A CONTROL LYAPUNOV FUNCTION APPROACH
Institute of Scientific and Technical Information of China (English)
Zhongping JIANG; Yuandan LIN; Yuan WANG
2009-01-01
This paper presents a control Lyapunov function approach to the global stabilization problem for general nonlinear and time-varying systems. Explicit stabilizing feedback control laws are proposed based on the method of control Lyapunov functions and Sontag's universal formula.
Stability analysis of Runge-Kutta methods for nonlinear neutral delay integro-differential equations
Institute of Scientific and Technical Information of China (English)
2007-01-01
The sufficient conditions for the stability and asymptotic stability of Runge-Kutta methods for nonlinear neutral delay integro-differential equations are derived. A numerical test that confirms the theoretical results is given in the end.
Singh, S. N.
1982-03-01
Using the invariance principle of LaSalle (1962) sufficient conditions for the existence of linear and nonlinear control laws for local and global asymptotic stability of nonlinear Hamiltonian systems are derived. An instability theorem is also presented which identifies the control laws from the given class which cannot achieve asymptotic stability. Some of the stability results are based on certain results for the univalence of nonlinear maps. A similar approach for the stabilization of bilinear systems which include nonconservative systems in elasticity is used and a necessary and sufficient condition for stabilization is obtained. An application to attitude control of a gyrostat Satellite is presented.
NONLINEAR STABILITY OF NATURAL RUNGE-KUTTA METHODS FOR NEUTRAL DELAY DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
Cheng-jian Zhang
2002-01-01
This paper first presents the stability analysis of theoretical solutions for a class of nonlinear neutral delay-differential equations (NDDEs). Then the numerical analogous results, of the natural Runge-Kutta (NRK) methods for the same class of nonlinear NDDEs,are given. In particular, it is shown that the (k, l)-algebraic stability of a RK method for ODEs implies the generalized asymptotic stability and the global stability of the induced NRK method.
An Enhanced Asymptotic Expansion for the Stability of Nonlinear Elastic Structures
DEFF Research Database (Denmark)
Christensen, Claus Dencker; Byskov, Esben
2010-01-01
A new, enhanced asymptotic expansion applicable to stability of structures made of nonlinear elastic materials is established. The method utilizes “hyperbolic” terms instead of the conventional polynomial terms, covers full kinematic nonlinearity and is applied to nonlinear elastic Euler columns ...
Stability of dithered non-linear systems with backlash or hysteresis
Desoer, C. A.; Shahruz, S. M.
1986-01-01
A study is conducted of the effect of dither on the nonlinear element of a single-input single-outout feedback system. Nonlinearities are considered with memory (backlash, hysteresis), in the feedforward loop; a dither of a given amplitude is injected at the input of the nonlinearity. The nonlinearity is followed by a linear element with low-pass characteristic. The stability of the dithered system and an approximate equivalent system (in which the nonlinearity is a smooth function) are compared. Conditions on the input and on the dither frequency are obtained so that the approximate-system stability guarantees that of the given hysteretic system.
Directory of Open Access Journals (Sweden)
Xiaoguang Deng
2015-01-01
Full Text Available Based on the nonlinear stability analysis method, the 3D nonlinear finite element model of a composite girder cable-stayed bridge with three pylons is established to research the effect of factors including geometric nonlinearity, material nonlinearity, static wind load, and unbalanced construction load on the structural stability during construction. Besides, the structural nonlinear stability in different construction schemes and the determination of temporary pier position are also studied. The nonlinear stability safety factors are calculated to demonstrate the rationality and safety of construction schemes. The results show that the nonlinear stability safety factors of this bridge during construction meet the design requirement and the minimum value occurs in the maximum double cantilever stage. Besides, the nonlinear stability of the structure in the side of edge-pylon meets the design requirement in the two construction schemes. Furthermore, the temporary pier can improve the structure stability, effectively, and the actual position is reasonable. In addition, the local buckling of steel girder occurs earlier than overall instability under load in some cable tension stages. Finally, static wind load and the unbalanced construction load should be considered in the stability analysis for the adverse impact.
Integral input-to-state stability of nonlinear control systems with delays
Energy Technology Data Exchange (ETDEWEB)
Zhu Wenli [Department of Economics Mathematics, South Western University of Finance and Economics, Chengdu 610074 (China)]. E-mail: zhuwl@swufe.edu.cn; Yi Zhang [Computational Intelligence Laboratory, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054 (China)]. E-mail: zhangyi@uestc.edu.cn
2007-10-15
Integral input-to-state stability is an interesting concept that has been recently introduced to nonlinear control systems. This paper generalizes this concept to nonlinear control systems with delays. These delays can be bounded, unbounded, and even infinite. Theorems for integral input-to-state stability are derived by developing the method of Razumikhin technique in the theory of functional differential equations.
Mittag-Leffler Stability Theorem for Fractional Nonlinear Systems with Delay
Directory of Open Access Journals (Sweden)
S. J. Sadati
2010-01-01
Full Text Available Fractional calculus started to play an important role for analysis of the evolution of the nonlinear dynamical systems which are important in various branches of science and engineering. In this line of taught in this paper we studied the stability of fractional order nonlinear time-delay systems for Caputo's derivative, and we proved two theorems for Mittag-Leffler stability of the fractional nonlinear time delay systems.
Delay-dependent robust stabilization for a class of neutral systems with nonlinear perturbations
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
This note deals with the problem of stabilization/stability for neutral systems with nonlinear perturbations.A new stabilization/stability scheme is presented.Using improved Lyapunov functionals.less conservative stabilization/stability conditions are derived for such systems based on linear matrix inequalities(LMI).Numerical examples are provided to show that the proposed results significantly improve the allowed upper bounds of the delay size over some existing ones in the literature.
Power meter ratio method of stabilizing a resonant modulator
Lentine, Anthony L.; Cox, Jonathan Albert
2016-10-11
Methods and systems for stabilizing a resonant modulator include receiving pre-modulation and post-modulation portions of a carrier signal, determining the average power from these portions, comparing an average input power to the average output power, and operating a heater coupled to the modulator based on the comparison. One system includes a pair of input structures, one or more processing elements, a comparator, and a control element. The input structures are configured to extract pre-modulation and post-modulation portions of a carrier signal. The processing elements are configured to determine average powers from the extracted portions. The comparator is configured to compare the average input power and the average output power. The control element operates a heater coupled to the modulator based on the comparison.
Large thermally induced nonlinear refraction of gold nanoparticles stabilized by cyclohexanone
Energy Technology Data Exchange (ETDEWEB)
Sarkhosh, Leila; Aleali, Hoda; Karimzadeh, Rouhollah; Mansour, Nastaran [Physics Department, Shahid Beheshti University, Evin 19839, Tehran (Iran, Islamic Republic of)
2010-10-15
Stabilized gold nanoparticle (AuNP) colloids have been fabricated by nanosecond pulsed laser ablation of a pure gold plate in cyclohexanone. The AuNPs colloid exhibits a UV-Vis absorption spectrum with a surface plasmon absorption peak at about 540 nm. Scanning electron microscopy has shown the formation of spherical AuNPs with average size about 53 nm. The shift of 24 cm{sup -1} is observed in the carbonyl band of the colloid using FTIR spectroscopy. This shift indicates that the monomer carbonyl group of cyclohexanone interacts with the surface of the AuNPs and leads to stabilizing the colloid. A large nonlinear refractive index of -2.92 x 10{sup -7} cm{sup 2}/W is measured using the Z-scan technique under continuous wave laser irradiation at 532 nm. Our results show that the large induced nonlinear refraction is attributed to the surface plasmon resonance (SPR) enhancement effect of AuNPs, high thermo-optic coefficient and low thermal conductivity of cyclohexanone. Observation of far-field diffraction ring patterns confirm a thermally induced negative lens effect and spatial self-phase modulation in the laser beam as it traverses the colloids. (Abstract Copyright [2010], Wiley Periodicals, Inc.)
Weakly nonlinear stability of vicsous vortices in three-dimensional boundary layers
Bassom, Andrew P.; Otto, S. R.
1993-01-01
Attention is given to the weakly nonlinear stability of essentially viscous vortices in 3D boundary layers. These modes are unstable in the absence of crossflow, but the imposition of small crossflow has a stabilizing effect. Bassom and Hall (1991) demonstrated the existence of neutrally stable vortices for certain crossflow/wave number combinations, and the weakly nonlinear stability properties of these disturbances are described. It is shown that the effect of crossflow is to stabilize the nonlinear modes, and the present calculations allow stable finite-amplitude vortices to be found. Predictions are made concerning the likelihood of observing some of these viscous modes within a practical setting.
Solution behaviors in coupled Schrödinger equations with full-modulated nonlinearities
Pınar, Zehra; Deliktaş, Ekin
2017-02-01
The nonlinear partial differential equations have an important role in real life problems. To obtain the exact solutions of the nonlinear partial differential equations, a number of approximate methods are known in the literature. In this work, a time- space modulated nonlinearities of coupled Schrödinger equations are considered. We provide a large class of Jacobi-elliptic solutions via the auxiliary equation method with sixth order nonlinearity and the Chebyshev approximation.
Institute of Scientific and Technical Information of China (English)
LI Shoufu
2005-01-01
A series of stability, contractivity and asymptotic stability results of the solutions to nonlinear stiff Volterra functional differential equations (VFDEs) in Banach spaces is obtained, which provides the unified theoretical foundation for the stability analysis of solutions to nonlinear stiff problems in ordinary differential equations(ODEs), delay differential equations(DDEs), integro-differential equations(IDEs) and VFDEs of other type which appear in practice.
Nonlinear Stability of a SIRS Epidemic Model with Convex Incidence Rate
Buonomo, B.; Rionero, S.
2010-09-01
We study an epidemic model for infections with non permanent acquired immunity (SIRS). The incidence rate is assumed to be convex respect to the infective class. By using a peculiar Lyapunov function, we obtain necessary and sufficient conditions for the local nonlinear stability of equilibria. Conditions ensuring the global stability of the endemic equilibrium are also obtained. Our procedure allows to enlarge the class of incidence rates ensuring the Lyapunov nonlinear stability of the endemic equilibrium for SIRS models.
Stabilization of solitons under competing nonlinearities by external potentials
Energy Technology Data Exchange (ETDEWEB)
Zegadlo, Krzysztof B., E-mail: zegadlo@if.pw.edu.pl; Karpierz, Miroslaw A. [Faculty of Physics, Warsaw University of Technology, Warsaw, ul. Koszykowa 75, PL-00-662 Warszawa (Poland); Wasak, Tomasz; Trippenbach, Marek [Faculty of Physics, University of Warsaw, ul. Hoza 69, PL-00-681 Warszawa (Poland); Malomed, Boris A. [Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel)
2014-12-15
We report results of the analysis for families of one-dimensional (1D) trapped solitons, created by competing self-focusing (SF) quintic and self-defocusing (SDF) cubic nonlinear terms. Two trapping potentials are considered, the harmonic-oscillator (HO) and delta-functional ones. The models apply to optical solitons in colloidal waveguides and other photonic media, and to matter-wave solitons in Bose-Einstein condensates loaded into a quasi-1D trap. For the HO potential, the results are obtained in an approximate form, using the variational and Thomas-Fermi approximations, and in a full numerical form, including the ground state and the first antisymmetric excited one. For the delta-functional attractive potential, the results are produced in a fully analytical form, and verified by means of numerical methods. Both exponentially localized solitons and weakly localized trapped modes are found for the delta-functional potential. The most essential conclusions concern the applicability of competing Vakhitov-Kolokolov (VK) and anti-VK criteria to the identification of the stability of solitons created under the action of the competing SF and SDF terms.
Sakly, Anis; Kermani, Marwen
2015-07-01
This paper is concerned with the problems of stability analysis and stabilization with a state feedback controller through pole placement for a class of both continuous and discrete-time switched nonlinear systems. These systems are modeled by differential or difference equations. Then, a transformation under the arrow form is employed. Note that, the main contribution in this work is twofold: firstly, based on the construction of an appropriated common Lyapunov function, as well the use of the vector norms notion, the recourse to the Kotelyanski lemma, the M-matrix proprieties, the aggregation techniques and the application of the Borne-Gentina criterion, new sufficient stability conditions under arbitrary switching for the autonomous system are deduced. Secondly, this result is extended for designing a state feedback controller by using pole assignment control, which guarantee that the corresponding closed-loop system is globally asymptotically stable under arbitrary switching. The main novelties features of these obtained results are the explicitness and the simplicity in their application. Moreover, they allow us to avoid the search of a common Lyapunov function which is a difficult matter. Finally, as validation to stabilize a shunt DC motor under variable mechanical loads is performed to demonstrate the effectiveness of the proposed results.
Nonlinear and Variable Structure Excitation Controller for Power System Stability
Institute of Scientific and Technical Information of China (English)
Wang Ben; Ronnie Belmans
2006-01-01
A new nonlinear variable structure excitation controller is proposed. Its design combines the differential geometry theory and the variable structure controlling theory. The mathematical model in the form of "an affine nonlinear system" is set up for the control of a large-scale power system. The static and dynamic performances of the nonlinear variable structure controller are simulated. The response of system with the controller proposed is compared to that of the nonlinear optimal controller when the system is subjected to a variety of disturbances. Simulation results show that the nonlinear variable structure excitation controller gives more satisfactorily static and dynamic performance and better robustness.
Thermal stabilization of a microring modulator using feedback control.
Padmaraju, Kishore; Chan, Johnnie; Chen, Long; Lipson, Michal; Bergman, Keren
2012-12-17
We describe and demonstrate the use of a feedback control system to thermally stabilize a silicon microring modulator subjected to a thermally volatile environment. Furthermore, we establish power monitoring as an effective and appropriate mechanism to infer the temperature drift of a microring modulator. Our demonstration shows that a high-performance silicon microring-based device, normally inoperable in thermally volatile environments, can maintain error-free performance when a feedback control system is implemented.
Exact control of parity-time symmetry in periodically modulated nonlinear optical couplers
Yang, Baiyuan; Hu, QiangLin; Yu, XiaoGuang
2016-01-01
We propose a mechanism for realization of exact control of parity-time (PT) symmetry by using a periodically modulated nonlinear optical coupler with balanced gain and loss. It is shown that for certain appropriately chosen values of the modulation parameters, we can construct a family of exact analytical solutions for the two-mode equations describing the dynamics of such nonlinear couplers. These exact solutions give explicit examples that allow us to precisely manipulate the system from nonlinearity-induced symmetry breaking to PT symmetry, thus providing an analytical approach to the all-optical signal control in nonlinear PT-symmetric structures.
Robust stability of discrete-time nonlinear system with time-delay
Institute of Scientific and Technical Information of China (English)
LIU Xin-ge; WU Min
2005-01-01
The robustly asymptotical stability problem for discrete-time nonlinear systems with time-delay was investigated. Positive definite matrix are constructed through Lyapunov functional. With the identity transform, property of matrix inverse and S-procedure, a new sufficient condition independent of the size of time-delay for robust stability of discrete-time nonlinear systems with time-delay is established. With Schur complement, another equivalent sufficient condition for robust stability of discrete-time nonlinear systems with time-delay is given. Finally, a sufficient condition dependent on the size of time-delay for robust stability of discrete-time nonlinear systems with time-delay is obtained. A unified approach is used to cast the robust stability problem into a convex optimization involving linear matrix inequalities.
Stabilization and regulation of nonlinear systems a robust and adaptive approach
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...
Baseline-free fatigue crack detection based on spectral correlation and nonlinear wave modulation
Liu, Peipei; Sohn, Hoon; Yang, Suyoung; Lim, Hyung Jin
2016-12-01
By generating ultrasonic waves at two different frequencies onto a cracked structure, modulations due to crack-induced nonlinearity can be observed in the corresponding ultrasonic response. This nonlinear wave modulation phenomenon has been widely studied and proven capable of detecting a fatigue crack at a very early stage. However, under field conditions, other exogenous vibrations exist and the modulation components can be buried under ambient noises, making it difficult to extract the modulation components simply by using a spectral density function. In this study, the nonlinear modulation components in the ultrasonic response were extracted using a spectral correlation function (the double Fourier transform) with respect to time and time lag of a signal’s autocorrelation. Using spectral correlation, noise or interference, which is spectrally overlapped with the nonlinear modulation components in the ultrasonic response, can be effectively removed or reduced. Only the nonlinear modulation components are accentuated at specific coordinates of the spectral correlation plot. A damage feature is defined by comparing the spectral correlation value between nonlinear modulation components with other spectral correlation values among randomly selected frequencies. Then, by analyzing the statistical characteristics of the multiple damage feature values obtained from different input frequency combinations, fatigue cracks can be detected without relying on baseline data obtained from the pristine condition of the target structure. In the end, an experimental test was conducted on aluminum plates with a real fatigue crack and the test signals were contaminated by simulated noises with varying signal-to-noise ratios. The results validated the proposed technique.
ON THE PARTIAL EQUIASYMPTOTIC STABILITY OF NONLINEAR TIME-VARYING DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
JianJigui; JiangMinghui; ShenYanjun
2005-01-01
In this paper, the problem of partial equiasymptotic stability for nonlinear time-varying differential equations are analyzed. A sufficient condition of partial stability and a set of sufficient conditions of partial equiasymptotic stability are given. Some of these conditions allow the derivative of Lyapunov function to be positive. Finally, several numerical examples are also given to illustrate the main results.
Directory of Open Access Journals (Sweden)
Meng-Meng Jiang
2016-01-01
Full Text Available Under the weaker assumption on nonlinear functions, the adaptive finite-time stabilization of more general high-order nonlinear systems with dynamic and parametric uncertainties is solved in this paper. To solve this problem, finite-time input-to-state stability (FTISS is used to characterize the unmeasured dynamic uncertainty. By skillfully combining Lyapunov function, sign function, backstepping, and finite-time input-to-state stability approaches, an adaptive state feedback controller is designed to guarantee high-order nonlinear systems are globally finite-time stable.
Institute of Scientific and Technical Information of China (English)
Shu-jun Liu; Ji-feng Zhang; Zhong-ping Jiang
2008-01-01
In this paper, the property of practical input-to-state stability and its application to stability of cascaded nonlinear systems are investigated in the stochastic framework. Firstly, the notion of (practical)stochastic input-to-state stability with respect to a stochastic input is introduced, and then by the method of changing supply functions, (a) an (practical) SISS-Lyapunov function for the overall system is obtained from the corresponding Lyapunov functions for cascaded (practical) SISS subsystems.
Kuehl, Joseph
2016-11-01
The parabolized stability equations (PSE) have been developed as an efficient and powerful tool for studying the stability of advection-dominated laminar flows. In this work, a new "wavepacket" formulation of the PSE is presented. This method accounts for the influence of finite-bandwidth-frequency distributions on nonlinear stability calculations. The methodology is motivated by convolution integrals and is found to appropriately represent nonlinear energy transfer between primary modes and harmonics, in particular nonlinear feedback, via a "nonlinear coupling coefficient." It is found that traditional discrete mode formulations overestimate nonlinear feedback by approximately 70%. This results in smaller maximum disturbance amplitudes than those observed experimentally. The new formulation corrects this overestimation, accounts for the generation of side lobes responsible for spectral broadening and results in disturbance saturation amplitudes consistent with experiment. A Mach 6 flared-cone example is presented. Support from the AFOSR Young Investigator Program via Grant FA9550-15-1-0129 is gratefully acknowledges.
Weakly Nonlinear Stability Analysis of a Thin Magnetic Fluid during Spin Coating
Directory of Open Access Journals (Sweden)
Cha'o-Kuang Chen
2010-01-01
Full Text Available This paper investigates the stability of a thin electrically conductive fluid under an applied uniform magnetic filed during spin coating. A generalized nonlinear kinematic model is derived by the long-wave perturbation method to represent the physical system. After linearizing the nonlinear evolution equation, the method of normal mode is applied to study the linear stability. Weakly nonlinear dynamics of film flow is studied by the multiple scales method. The Ginzburg-Landau equation is determined to discuss the necessary conditions of the various critical flow states, namely, subcritical stability, subcritical instability, supercritical stability, and supercritical explosion. The study reveals that the rotation number and the radius of the rotating circular disk generate similar destabilizing effects but the Hartmann number gives a stabilizing effect. Moreover, the optimum conditions can be found to alter stability of the film flow by controlling the applied magnetic field.
NONLINEAR BOUNDARY STABILIZATION OF WAVE EQUATIONS WITH VARIABLE C OEFFICIENTS
Institute of Scientific and Technical Information of China (English)
冯绍继; 冯德兴
2003-01-01
The wave equation with variable coefficients with a nonlinear dissipative boundary feedbackis studied. By the Riemannian geometry method and the multiplier technique, it is shown thatthe closed loop system decays exponentially or asymptotically, and hence the relation betweenthe decay rate of the system energy and the nonlinearity behavior of the feedback function isestablished.
Directory of Open Access Journals (Sweden)
Qiang Yang
2016-01-01
Full Text Available Based on adaptive nonlinear damping, a novel decentralized robust adaptive output feedback stabilization comprising a decentralized robust adaptive output feedback controller and a decentralized robust adaptive observer is proposed for a large-scale interconnected nonlinear system with general uncertainties, such as unknown nonlinear parameters, bounded disturbances, unknown nonlinearities, unmodeled dynamics, and unknown interconnections, which are nonlinear function of not only states and outputs but also unmodeled dynamics coming from other subsystems. In each subsystem, the proposed stabilization only has two adaptive parameters, and it is not needed to generate an additional dynamic signal or estimate the unknown parameters. Under certain assumptions, the proposed scheme guarantees that all the dynamic signals in the interconnected nonlinear system are bounded. Furthermore, the system states and estimate errors can approach arbitrarily small values by choosing the design parameters appropriately large. Finally, simulation results illustrated the effectiveness of the proposed scheme.
Theory and analysis of nonlinear dynamics and stability in storage rings: A working group summary
Energy Technology Data Exchange (ETDEWEB)
Chattopadhyay, S.; Audy, P.; Courant, E.D.; Forest, E.; Guignard, G.; Hagel, J.; Heifets, S.; Keil, E.; Kheifets, S.; Mais, H.; Moshammer, H.; Pellegrini, C.; Pilat, F.; Suzuki, T.; Turchetti, G.; Warnock, R.L.
1988-07-01
A summary and commentary of the available theoretical and analytical tools and recent advances in the nonlinear dynamics, stability and aperture issues in storage rings are presented. 11 refs., 4 figs.
ON THE BOUNDEDNESS AND THE STABILITY OF SOLUTION TO THIRD ORDER NON-LINEAR DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
In this paper we investigate the global asymptotic stability,boundedness as well as the ultimate boundedness of solutions to a general third order nonlinear differential equation,using complete Lyapunov function.
Nonlinear Pulse Compression and Reshaping Using Cross-Phase Modulation in a Dispersion-Shifted Fiber
Institute of Scientific and Technical Information of China (English)
S.; W.; Chan; K.; K.; Chow; C.; Shu
2003-01-01
Nonlinear pulse compression has been demonstrated by cross-phase modulation in a dispersion-shifted fiber. The output is obtained from filtering of the broadened optical spectrum and a pulse width reduction from 61 to 28 ps is achieved.
Stabilization of nonlinear sandwich systems via state feedback-Discrete-time systems
Wang, Xu; Stoorvogel, Anton A.; Saberi, Ali; Grip, H°avard Fjær; Sannuti, Peddapullaiah
2011-01-01
A recent paper (IEEE Trans. Aut. Contr. 2010; 55(9):2156–2160) considered stabilization of a class of continuous-time nonlinear sandwich systems via state feedback. This paper is a discrete-time counterpart of it. The class of nonlinear sandwich systems consists of saturation elements sandwiched bet
Stabilization of solutions to higher-order nonlinear Schrodinger equation with localized damping
Directory of Open Access Journals (Sweden)
Eleni Bisognin
2007-01-01
Full Text Available We study the stabilization of solutions to higher-order nonlinear Schrodinger equations in a bounded interval under the effect of a localized damping mechanism. We use multiplier techniques to obtain exponential decay in time of the solutions of the linear and nonlinear equations.
Stability of two-dimensional spatial solitons in nonlocal nonlinear media
DEFF Research Database (Denmark)
Skupin, S.; Bang, Ole; Edmundson, D.;
2006-01-01
We discuss the existence and stability of two-dimensional solitons in media with spatially nonlocal nonlinear response. We show that such systems, which include thermal nonlinearity and dipolar Bose-Einstein condensates, may support a variety of stationary localized structures, including rotating...
Institute of Scientific and Technical Information of China (English)
Wan-sheng WANG; Shou-fu LI; Run-sheng YANG
2012-01-01
A series of contractivity and exponential stability results for the solutions to nonlinear neutral functional differential equations (NFDEs) in Banach spaces are obtained,which provide unified theoretical foundation for the contractivity analysis of solutions to nonlinear problems in functional differential equations (FDEs),neutral delay differential equations (NDDEs) and NFDEs of other types which appear in practice.
Global stabilization of nonlinear systems based on vector control lyapunov functions
Karafyllis, Iasson
2012-01-01
This paper studies the use of vector Lyapunov functions for the design of globally stabilizing feedback laws for nonlinear systems. Recent results on vector Lyapunov functions are utilized. The main result of the paper shows that the existence of a vector control Lyapunov function is a necessary and sufficient condition for the existence of a smooth globally stabilizing feedback. Applications to nonlinear systems are provided: simple and easily checkable sufficient conditions are proposed to guarantee the existence of a smooth globally stabilizing feedback law. The obtained results are applied to the problem of the stabilization of an equilibrium point of a reaction network taking place in a continuous stirred tank reactor.
2011-01-01
International audience; In this paper, stabilizing control design for a class of nonlinear affine systems is presented by using a new generalized Gronwall-Bellman lemma approach. The nonlinear systems under consideration can be non Lipschitz. Two cases are treated for the exponential stabilization~: the static state feedback and the static output feedback. The robustness of the proposed control laws with regards to parameter uncertainties is also studied. A numerical example is given to show ...
P-th moment and almost sure stability of stochastic switched nonlinear systems.
Gu, Haibo; Gao, Caixia
2016-01-01
This paper mainly tends to utilize [Formula: see text]-type function to investigate p-th moment and almost sure stability for a class of stochastic switched nonlinear systems. Based on the multiple Lyapunov functions approach, some sufficient conditions are derived to check the stability criteria of stochastic switched nonlinear systems. One numerical example is provided to demonstrate the effectiveness of the proposed results.
Improved Stability Analysis of Nonlinear Networked Control Systems over Multiple Communication Links
Delavar, Rahim; Tavassoli, Babak; Beheshti, Mohammad Taghi Hamidi
2015-01-01
In this paper, we consider a nonlinear networked control system (NCS) in which controllers, sensors and actuators are connected via several communication links. In each link, networking effects such as the transmission delay, packet loss, sampling jitter and data packet miss-ordering are captured by time-varying delays. Stability analysis is carried out based on the Lyapunov Krasovskii method to obtain a condition for stability of the nonlinear NCS in the form of linear matrix inequality (LMI...
Switching management by adiabatic passage in two periodically modulated nonlinear waveguides
Luo, Xiaobing; Yu, Xiaoguang
2016-01-01
We theoretically investigate light propagation in two periodically modulated nonlinear waveguides with certain propagation constant detuning between two guides. By slowly varying the amplitude of modulation, we can steer the light to the desired output waveguide when equal amounts of lights are launched into each waveguide. We also reveal that the light propagation dynamics depends sensitively on the detuning between two guides. Our findings can be explained qualitatively by means of adiabatic navigation of the extended nonlinear Floquet states.
Asymmetrically pumped Bragg scattering with the effects of nonlinear phase modulation
DEFF Research Database (Denmark)
Andersen, Lasse Mejling; Friis, Søren Michael Mørk; Reddy, Dileep V.
2014-01-01
We derive exact solutions to asymmetrically pumped Bragg scattering with nonlinear phase-modulation (NPM) and show that this setup allows for the frequency conversion of many temporal modes, while reducing the effects due to NPM.......We derive exact solutions to asymmetrically pumped Bragg scattering with nonlinear phase-modulation (NPM) and show that this setup allows for the frequency conversion of many temporal modes, while reducing the effects due to NPM....
Sudarshanam, V. S.; Claus, Richard O.
1993-03-01
A new cylindrical coil configuration for polyvinylidene flouride (PVF2) film based fiber optic phase modulator is studied for the frequency response and nonlinearity of phase shift at the resonance frequency. This configuration, hitherto unapproached for PVF2 film modulators, offers resonance at well defined, controllable and higher frequencies than possible for the flat-strip configuration. Two versions of this configuration are presented that differ strongly in both the resonance frequency and the phase shift nonlinearity coefficient.
Modulation instability, solitons and beam propagation in spatially nonlocal nonlinear media
DEFF Research Database (Denmark)
Krolikowski, Wieslaw; Bang, Ole; Nikolov, Nikola Ivanov
2004-01-01
We present an overview of recent advances in the understanding of optical beams in nonlinear media with a spatially nonlocal nonlinear response. We discuss the impact of nonlocality on the modulational instability of plane waves, the collapse of finite-size beams, and the formation and interaction...
Kevrekidis, P G; Saxena, A; Frantzeskakis, D J; Bishop, A R
2014-01-01
We consider a two-dimensional (2D) generalization of a recently proposed model [Phys. Rev. E 88, 032905 (2013)], which gives rise to bright discrete solitons supported by the defocusing nonlinearity whose local strength grows from the center to the periphery. We explore the 2D model starting from the anti-continuum (AC) limit of vanishing coupling. In this limit, we can construct a wide variety of solutions including not only single-site excitations, but also dipole and quadrupole ones. Additionally, two separate families of solutions are explored: the usual "extended" unstaggered bright solitons, in which all sites are excited in the AC limit, with the same sign across the lattice (they represent the most robust states supported by the lattice, their 1D counterparts being what was considered as 1D bright solitons in the above-mentioned work), and the vortex cross, which is specific to the 2D setting. For all the existing states, we explore their stability (analytically, whenever possible). Typical scenarios ...
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.
Robust adaptive dynamic programming and feedback stabilization of nonlinear systems.
Jiang, Yu; Jiang, Zhong-Ping
2014-05-01
This paper studies the robust optimal control design for a class of uncertain nonlinear systems from a perspective of robust adaptive dynamic programming (RADP). The objective is to fill up a gap in the past literature of adaptive dynamic programming (ADP) where dynamic uncertainties or unmodeled dynamics are not addressed. A key strategy is to integrate tools from modern nonlinear control theory, such as the robust redesign and the backstepping techniques as well as the nonlinear small-gain theorem, with the theory of ADP. The proposed RADP methodology can be viewed as an extension of ADP to uncertain nonlinear systems. Practical learning algorithms are developed in this paper, and have been applied to the controller design problems for a jet engine and a one-machine power system.
Stability for a class of nonlinear time-delay systems via Hamiltonian functional method
Institute of Scientific and Technical Information of China (English)
YANG RenMing; WANG YuZhen
2012-01-01
This paper investigates the stability of a class of nonlinear time-delay systems via Hamiltonian functional method,and proposes a number of new results on generalized Hamiltonian realization (GHR) and stability analysis for this class of systems.Firstly,the concept of GHR of general nonlinear time-delay systems is proposed,and several new GHR methods are given.Then,based on the new GHR methods obtained,the stability of time-delay systems is investigated,and several delay-dependent sufficient conditions in term of matrix inequalities are derived for the stability analysis by constructing suitable Lyapunov-Krasovskii (L-K) functionals.Finally,an illustrative example shows that the results obtained in this paper have less conservatism,and work very well in the stability analysis of some nonlinear time-delay Hamiltonian systems.
Static feedback stabilization of nonlinear systems with single sensor and single actuator.
Wang, Jiqiang; Hu, Zhongzhi; Ye, Zhifeng
2014-01-01
This paper considers a single sensor and single actuator approach to the static feedback stabilization of nonlinear systems. This is essentially a remote control problem that is present in many engineering applications. The proposed method solves this problem that is less expensive to implement and more reliable in practice. Significant results are obtained on the design of controllers for stabilizing the nonlinear systems. Important issues on control implementation are also discussed. The proposed design method is validated through its application to nonlinear control of aircraft engines.
A Novel Analog-to-digital conversion Technique using nonlinear duty-cycle modulation
Directory of Open Access Journals (Sweden)
Jean Mbihi
2012-06-01
Full Text Available A new type of analog-to-digital conversion technique is presented in this paper. The interfacing hardware is a very simple nonlinear circuit with 1-bit modulated output. As a implication, behind the hardware simplicity retained is hidden a dreadful nonlinear duty-cycle modulation ratio. However, the overall nonlinear behavior embeds a sufficiently wide linear range, for a rigorous digital reconstitution of the analog input signal using a standard linear filter. Simulation and experimental results obtained using a well tested prototyping system, show the feasibility and good quality of the proposed conversion technique.
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.
Frequency domain stability analysis of nonlinear active disturbance rejection control system.
Li, Jie; Qi, Xiaohui; Xia, Yuanqing; Pu, Fan; Chang, Kai
2015-05-01
This paper applies three methods (i.e., root locus analysis, describing function method and extended circle criterion) to approach the frequency domain stability analysis of the fast tool servo system using nonlinear active disturbance rejection control (ADRC) algorithm. Root locus qualitative analysis shows that limit cycle is generated because the gain of the nonlinear function used in ADRC varies with its input. The parameters in the nonlinear function are adjustable to suppress limit cycle. In the process of root locus analysis, the nonlinear function is transformed based on the concept of equivalent gain. Then, frequency domain description of the nonlinear function via describing function is presented and limit cycle quantitative analysis including estimating prediction error is presented, which virtually and theoretically demonstrates that the describing function method cannot guarantee enough precision in this case. Furthermore, absolute stability analysis based on extended circle criterion is investigated as a complement.
Stability analysis of nonlinear systems by multiple time scaling. [using perturbation methods
Morino, L.
1974-01-01
The asymptotic solution for the transient analysis of a general nonlinear system in the neighborhood of the stability boundary was obtained by using the multiple-time-scaling asymptotic-expansion method. The nonlinearities are assumed to be of algebraic nature. Terms of order epsilon to the 3rd power (where epsilon is the order of amplitude of the unknown) are included in the solution. The solution indicates that there is always a limit cycle which is stable (unstable) and exists above (below) the stability boundary if the nonlinear terms are stabilizing (destabilizing). Extension of the solution to include fifth order nonlinear terms is also presented. Comparisons with harmonic balance and with multiple-time-scaling solution of panel flutter equations are also included.
Directory of Open Access Journals (Sweden)
B.S. Bhadauria
2014-02-01
Full Text Available The present paper deals with a weak nonlinear stability problem of magneto-convection in an electrically conducting Newtonian liquid, confined between two horizontal surfaces, under a constant vertical magnetic field, and subjected to an imposed time-periodic boundary temperature (ITBT along with internal heating effects. In the case of (ITBT, the temperature gradient between the walls of the fluid layer consists of a steady part and a time-dependent oscillatory part. The temperature of both walls is modulated in this case. The disturbance is expanded in terms of power series of amplitude of convection, which is assumed to be small. It is found that the response of the convective system to the internal Rayleigh number is destabilizing. Using Ginzburg-Landau equation, the effect of modulations on heat transport is analyzed. Effect of various parameters on the heat transport is also discussed. Further, it is found that the heat transport can be controlled by suitably adjusting the external parameters of the system.
Stupishin, L.; Nikitin, K.; Kolesnikov, A.
2017-05-01
A methodology for shell stability research and determining buckling load, based on the mixed finite element method are proposed. Axisymmetric geometrically nonlinear shallow shells made of orthotropic material are considered. The results of numerical research of stability by changing the shape of shells, ratio of elastic modulus of the material and parameters of the support contour are presented.
Results on stabilization of nonlinear systems under finite data-rate constraints
Persis, Claudio De
2004-01-01
We discuss in this paper a result concerning the stabilization problem of nonlinear systems under data-rate constraints using output feedback. To put the result in a broader context, we shall first review a number of recent contributions on the stabilization problem under data-rate constraints when
RESEARCH OF THE PERIODIC MOTION AND STABILITY OF TWO-DEGREE-OF-FREEDOM NONLINEAR OSCILLATING SYSTEMS
Institute of Scientific and Technical Information of China (English)
刘俊
2002-01-01
The periodic motion and stability for a class of two-degree-of freedom nonlinear oscillating systems are studied by using the method of Liapunov function.The sufficient conditions which guarantee the existence, uniqueness and asymptotic stability of the periodic solutions are obtained.
Non-smooth finite-time stabilization for a class of nonlinear systems
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper, global finite-time stabilization problem for a large class of nonlinear control systems is considered. An iterative design approach is given based on Lyapunov function. The finite time stabilizing control laws are constructed in the form of continuous but non-smooth time-invariant feedback.
Asymptotic stability for a class of boundary control systems with non-linear damping
Zwart, Heiko J.; Ramirez, Hector; Le Gorrec, Yann
2016-01-01
The asymptotic stability of boundary controlled port-Hamiltonian systems defined on a 1D spatial domain interconnected to a class of non-linear boundary damping is addressed. It is shown that if the port-Hamiltonian system is approximately observable, then any boundary damping which behaves linear for small velocities asymptotically stabilizes the system.
THE EXISTENCE, UNIQUENESS AND STABILITY OF ALMOST PERIODIC SOLUTION FOR A CLASS OF NONLINEAR SYSTEM
Institute of Scientific and Technical Information of China (English)
方聪娜; 王全义
2004-01-01
In this paper, we study the problems on the existence, uniqueness and stability of almost periodic solution for a class of nonlinear system. Using fixed point theorem and Lyapunov functional, the sufficient conditions are given which guarantee the existence, uniqueness and stability of almost periodic solution for the system.
Nonlinear behaviour and stability of thin-walled shells
Obodan, Natalia I; Gromov, Vasilii A
2013-01-01
This book focuses on the nonlinear behaviour of thin-wall shells (single- and multilayered with delamination areas) under various uniform and non-uniform loadings. The dependence of critical (buckling) load upon load variability is revealed to be highly non-monotonous, showing minima when load variability is close to the eigenmode variabilities of solution branching points of the respective nonlinear boundary problem. A novel numerical approach is employed to analyze branching points and to build primary, secondary, and tertiary bifurcation paths of the nonlinear boundary problem for the case of uniform loading. The load levels of singular points belonging to the paths are considered to be critical load estimates for the case of non-uniform loadings.
Optmized stability of a modulated driver in a plasma wakefield
Martorelli, Roberto
2016-01-01
We analyze the transverse stability for a configuration of multiple gaussian bunches subject to the self-generated plasma wakefield. Through a semi-analytical approach we first study the equilibrium configuration for the modulated beam and then we investigate the evolution of the equilibrium configuration due to the emittance-driven expansion of the beam front that results in a rigid backward shift. The rear-directed shift brings the modulated beam out of the equilibrium, with the possibility for some of the bunch particles to be lost with a consequent deterioration of the driver. We look therefore for the proper position of the single bunches that maximize the stability without severely affecting the accelerating field behind the driver. We then compare the results with 3D PIC simulations.
Laser frequency stabilization and shifting by using modulation transfer spectroscopy
Cheng, Bing; Wang, Zhao-Ying; Wu, Bin; Xu, Ao-Peng; Wang, Qi-Yu; Xu, Yun-Fei; Lin, Qiang
2014-10-01
The stabilizing and shifting of laser frequency are very important for the interaction between the laser and atoms. The modulation transfer spectroscopy for the 87Rb atom with D2 line transition F = 2 → F' = 3 is used for stabilizing and shifting the frequency of the external cavity grating feedback diode laser. The resonant phase modulator with electro—optical effect is used to generate frequency sideband to lock the laser frequency. In the locking scheme, circularly polarized pump- and probe-beams are used. By optimizing the temperature of the vapor, the pump- and probe-beam intensity, the laser linewidth of 280 kHz is obtained. Furthermore, the magnetic field generated by a solenoid is added into the system. Therefore the system can achieve the frequency locking at any point in a range of hundreds of megahertz frequency shifting with very low power loss.
Institute of Scientific and Technical Information of China (English)
SUN LiYing; WANG YuZhen
2009-01-01
This paper studies simultaneous stabilization of a class of nonlinear descriptor systems via the Hamiltonlan function method.Firstly,based on the Hamiltonian realization of the nonlinear descriptor systems and a suitable output feedback,two nonlinear descriptor systems are equivalently transformed into two nonlinear Hamiltonian differential-algebraic systems by a nonsingular transformation,and a sufficient condition for two closed-loop systems to be impulse-free is given.The two systems are then combined to generate an augmented dissipative Hamiltonian differential-algebraic system by using the system-augmentation technique,based on which a simultaneous stabilization controller and a robust simultaneous stabilization controller are designed for the two systems.Secondly,the case of more than two nonlinear descriptor systems is investigated,and two new results are proposed for the simultaneous stabilization and robust simultaneous stabilization,respectively.Finally,an illustrative example is studied by using the results proposed in this paper,and simulations show that the simultaneous stabilization controllers obtained in this paper work very well.
Modeling and stability analysis of the nonlinear reactive sputtering process
Directory of Open Access Journals (Sweden)
György Katalin
2011-12-01
Full Text Available The model of the reactive sputtering process has been determined from the dynamic equilibrium of the reactive gas inside the chamber and the dynamic equilibrium of the sputtered metal atoms which form the compound with the reactive gas atoms on the surface of the substrate. The analytically obtained dynamical model is a system of nonlinear differential equations which can result in a histeresis-type input/output nonlinearity. The reactive sputtering process has been simulated by integrating these differential equations. Linearization has been applied for classical analysis of the sputtering process and control system design.
Multi-bi- and tri-stability using nonlinear plasmonic Fano resonators
Amin, Muhammad
2013-09-01
A plasmonic Fano resonator embedding Kerr nonlinearity is used to achieve multi-bi- and tri-stability. Fano resonance is obtained by inducing higher-order plasmon modes on metallic surfaces via geometrical symmetry breaking. The presence of the multiple higher order plasmon modes provides the means for producing multi-bi- or tri-stability in the response of the resonator when it is loaded with a material with Kerr nonlinearity. The multi-stability in the response of the proposed resonator enables its use in three-state all optical memory and switching applications. © 2013 IEEE.
Full-State Linearization and Stabilization of SISO Markovian Jump Nonlinear Systems
Directory of Open Access Journals (Sweden)
Zhongwei Lin
2013-01-01
Full Text Available This paper investigates the linearization and stabilizing control design problems for a class of SISO Markovian jump nonlinear systems. According to the proposed relative degree set definition, the system can be transformed into the canonical form through the appropriate coordinate changes followed with the Markovian switchings; that is, the system can be full-state linearized in every jump mode with respect to the relative degree set n,…,n. Then, a stabilizing control is designed through applying the backstepping technique, which guarantees the asymptotic stability of Markovian jump nonlinear systems. A numerical example is presented to illustrate the effectiveness of our results.
Feedback diagonal canonical form and its application to stabilization of nonlinear systems
Institute of Scientific and Technical Information of China (English)
CHENG Daizhan; HU Qingxi; QIN Huashu
2005-01-01
This paper considers the problem of stabilization of a class of nonlinear systems, which are possibly of non-minimum phase. A new feedback-equivalent canonical form, called diagonal normal form, of linear control systems is proposed. Using it, the corresponding normal form of affine nonlinear control systems is obtained. Based on this new normal form and the design technique of center manifold, a new constructing method for stabilizing control is presented. Certain examples are included to demonstrate the design strategy of stabilizers.
DEFF Research Database (Denmark)
Fuhrmann, David R.; Bingham, Harry B.; Madsen, Per A.;
2004-01-01
This paper considers a method of lines stability analysis for finite difference discretizations of a recently published Boussinesq method for the study of highly nonlinear and extremely dispersive water waves. The analysis demonstrates the near-equivalence of classical linear Fourier (von Neumann......) techniques with matrix-based methods for formulations in both one and two horizontal dimensions. The matrix-based method is also extended to show the local de-stabilizing effects of the nonlinear terms, as well as the stabilizing effects of numerical dissipation. A comparison of the relative stability...... moderately non-normal, suggesting that the eigenvalues are likely suitable for analysis purposes. Numerical experiments demonstrate excellent agreement with the linear analysis, and good qualitative agreement with the local nonlinear analysis. The various methods of analysis combine to provide significant...
Yang, Jianke
2012-01-01
Linear stability of both sign-definite (positive) and sign-indefinite solitary waves near pitchfork bifurcations is analyzed for the generalized nonlinear Schroedinger equations with arbitrary forms of nonlinearity and external potentials in arbitrary spatial dimensions. Bifurcations of linear-stability eigenvalues associated with pitchfork bifurcations are analytically calculated. It is shown that the smooth solution branch switches stability at the bifurcation point. In addition, the two bifurcated solution branches and the smooth branch have the opposite (same) stability when their power slopes have the same (opposite) sign. One unusual feature on the stability of these pitchfork bifurcations is that the smooth and bifurcated solution branches can be both stable or both unstable, which contrasts such bifurcations in finite-dimensional dynamical systems where the smooth and bifurcated branches generally have opposite stability. For the special case of positive solitary waves, stronger and more explicit stab...
Dynamic Nonlinear Focal Shift in Amplitude Modulated Moderately Focused Acoustic Beams
Jiménez, Noé; González-Salido, Nuria
2016-01-01
The phenomenon of the displacement of the position of the pressure, intensity and acoustic radiation force maxima along the axis of focused acoustic beams under increasing driving amplitudes (nonlinear focal shift) is studied for the case of a moderately focused beam excited with continuous and 25 kHz amplitude modulated signals, both in water and tissue. We prove that in amplitude modulated beams the linear and nonlinear propagation effects coexist in a semi-period of modulation, giving place to a complex dynamic behaviour, where the singular points of the beam (peak pressure, rarefaction, intensity and acoustic radiation force) locate at different points on axis as a function of time. These entire phenomena are explained in terms of harmonic generation and absorption during the propagation in a lossy nonlinear medium both, for a continuous and an amplitude modulated beam. One of the possible applications of the acoustic radiation force displacement is the generation of shear waves at different locations by ...
Chaves Filho, V. L.; Lima, R. P. A.; Lyra, M. L.
2015-06-01
We investigate the modulational instability of uniform wavepackets governed by the discrete nonlinear Schrodinger equation in finite linear chains and square lattices. We show that, while the critical nonlinear coupling χMI above which modulational instability occurs remains finite in square lattices, it decays as 1/L in linear chains. In square lattices, there is a direct transition between the regime of stable uniform wavefunctions and the regime of asymptotically localized solutions with stationary probability distributions. On the other hand, there is an intermediate regime in linear chains for which the wavefunction dynamics develops complex breathing patterns. We analytically compute the critical nonlinear strengths for modulational instability in both lattices, as well as the characteristic time τ governing the exponential increase of perturbations in the vicinity of the transition. We unveil that the interplay between modulational instability and self-trapping phenomena is responsible for the distinct wavefunction dynamics in linear and square lattices.
Energy Technology Data Exchange (ETDEWEB)
Belmonte-Beitia, Juan [Departamento de Matematicas, E.T.S. de Ingenieros Industriales and Instituto de Matematica Aplicada a la Ciencia y la Ingenieria (IMACI), Avda. Camilo Jose Cela 3, Universidad de Castilla-La Mancha, 13071 Ciudad Real (Spain)], E-mail: juan.belmonte@uclm.es; Calvo, Gabriel F. [Departamento de Matematicas, E.T.S. de Ingenieros Industriales and Instituto de Matematica Aplicada a la Ciencia y la Ingenieria (IMACI), Avda. Camilo Jose Cela 3, Universidad de Castilla-La Mancha, 13071 Ciudad Real (Spain)], E-mail: gabriel.fernandez@uclm.es
2009-01-19
In this Letter, by means of similarity transformations, we construct explicit solutions to the quintic nonlinear Schroedinger equation with potentials and nonlinearities depending both on time and on the spatial coordinates. We present the general approach and use it to study some examples and find nontrivial explicit solutions such as periodic (breathers), quasiperiodic and bright and dark soliton solutions.
STABILITY OF INNOVATION DIFFUSION MODEL WITH NONLINEAR ACCEPTANCE
Institute of Scientific and Technical Information of China (English)
Yu Yumei; Wang Wendi
2007-01-01
In this article, an innovation diffusion model with the nonlinear acceptance is proposed to describe the dynamics of three competing products in a market. It is proved that the model admits a unique positive equilibrium, which is globally stable by excluding the existence of periodic solutions and by using the theory of three dimensional competition systems.
Stability of planar diffusion wave for nonlinear evolution equation
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
It is known that the one-dimensional nonlinear heat equation ut = f(u)x1x1,f'(u) 0,u(±∞,t) = u±,u+ = u_ has a unique self-similar solution u(x1/1+t).In multi-dimensional space,u(x1/1+t) is called a planar diffusion wave.In the first part of the present paper,it is shown that under some smallness conditions,such a planar diffusion wave is nonlinearly stable for the nonlinear heat equation:ut-△f(u) = 0,x ∈ Rn.The optimal time decay rate is obtained.In the second part of this paper,it is further shown that this planar diffusion wave is still nonlinearly stable for the quasilinear wave equation with damping:utt + utt+ △f(u) = 0,x ∈ Rn.The time decay rate is also obtained.The proofs are given by an elementary energy method.
STABILITY OF NONLINEAR NEUTRAL DIFFERENTIAL EQUATION VIA FIXED POINT
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
In this paper,a nonlinear neutral differential equation is considered.By a fixed point theory,we give some conditions to ensure that the zero solution to the equation is asymptotically stable.Some existing results are improved and generalized.
Robust Stability Analysis of Nonlinear Switched Systems with Filippov Solutions
DEFF Research Database (Denmark)
Ahmadi, Mohamadreza; Mojallali, Hamed; Wisniewski, Rafal
2012-01-01
. Based on the theory of differential inclusions, a Lyapunov stability theorem is brought forward. These results are also extended to autonomous switched systems subject to polytopic uncertainty. Furthermore, the proposed stability theorems are reformulated using the sum of squares decomposition method...... which provides sufficient means to construct the corresponding Lyapunov functions via available semi-definite programming techniques....
On the nonlinear stability of mKdV breathers
DEFF Research Database (Denmark)
Alejo Plana, Miguel Angel; Muñoz, Claudio
2012-01-01
Breather modes of the mKdV equation on the real line are known to be elastic under collisions with other breathers and solitons. This fact indicates very strong stability properties of breathers. In this communication we describe a rigorous, mathematical proof of the stability of breathers under...
Tilt stability in nonlinear programming under Mangasarian-Fromovitz constraint qualification
Mordukhovich, B. S.; Outrata, J. (Jiří)
2013-01-01
The paper concerns the study of tilt stability of local minimizers in standard problems of nonlinear programming. This notion plays an important role in both theoretical and numerical aspects of optimization and has drawn a lot of attention in optimization theory and its applications, especially in recent years. Under the classical Mangasarian–Fromovitz Constraint Qualification, we establish relationships between tilt stability and some other stability notions in constrained optimization. I...
Energy Technology Data Exchange (ETDEWEB)
Prill, Dennis; Class, Andreas G. [Karlsruhe Institute of Technology (KIT), Eggenstein-Leopoldshafen (Germany). AREVA Nuclear Professional School (ANPS)
2013-07-01
Unexpected non-linear boiling water reactor (BWR) instability events in various plants, e.g. LaSalle II in 1988 and Oskarshamn II in 1990 amongst others, emphasize the major safety relevance and the existence of parameter regions with unstable behavior. A detailed description of the complete dynamical non-linear behavior is of paramount importance for BWR operation. An extension of state-of-the-art methodology towards a more general stability description, also applicable in the non-linear region, could lead to a deeper understanding of non-linear BWR stability phenomena. With the intention of a full non-linear stability analysis of the two-phase BWR system, the present paper aims at a general non-linear methodology capable to achieve reliable and numerical stable reduced order models (ROMs), representing the dynamical behavior of an original system based on a small number of transients. Model-specific options and aspects of the proposed methodology are focused on and illustrated by means of a strongly non-linear dynamical system showing complex oscillating behavior. Prediction capability of the proposed methodology is also addressed. (orig.)
Autonomous non-linear classification of LPI radar signal modulations
Gulum, Taylan O.
2007-01-01
In this thesis, an autonomous feature extraction algorithm for classification of Low Probability of Intercept (LPI) radar modulations is investigated. A software engineering architecture that allows a full investigation of various preprocessing algorithms and classification techniques is applied to a database of important LPI radar waveform modulations including Frequency Modulation Continuous Waveform (FMCW), Phase Shift Keying (PSK), Frequency Shift Keying (FSK) and combined PSK and FSK. Th...
DEFF Research Database (Denmark)
Bang, Ole; Graversen, T. W.; Clausen, Carl A. Balslev
2000-01-01
Quasi-phase-matching gratings induces Kerr effects in quadratic nonlinear materials. We show analytically and confirm numerically how modulating the grating changes the effective quadratic and cubic nonlinearities and allows for multi-wavelength second-harmonic generation....
Indian Academy of Sciences (India)
R Ganapathy; V C Kuriakose
2002-04-01
We obtain conditions for the occurrence of cross-phase modulational instability in the normal dispersion regime for the coupled higher order nonlinear Schrödinger equation with higher order dispersion and nonlinear terms.
PARTIAL STABILIZATION OF A CLASS OF CONTINUOUS NONLINEAR CONTROL SYSTEMS WITH SEPARATED VARIABLES
Institute of Scientific and Technical Information of China (English)
Jigui JIAN; Xiaoxin LIAO
2005-01-01
In this paper, the partial stabilization problem for a class of nonlinear continuous control systems with separated variables is investigated. Several stabilizing controllers are constructed based on the partial stability theory of Lyapunov and the property of M-matrix, and some of these stabilizing controllers are only related to partial state variables. The controllers constructed here are shown to guarantee partial asymptotic stability of the closed-loop systems and these sufficient conditions may give some instructions to actual engineering application. A example is also given to illustrate the design method.
Generalized exponential input-to-state stability of nonlinear systems with time delay
Sun, Fenglan; Gao, Lingxia; Zhu, Wei; Liu, Feng
2017-03-01
This paper studies the general input-to-state stability problem of the nonlinear delay systems. By employing Lypaunov-Razumikhin technique, several general input-to-state stability concepts, that is generalized globally exponential integral input-to-state stability (GGE-iISS), generalized globally integral exponential integral input-to-state stability (GGIE-iISS), and eλt-weighted generalized globally integral exponential integral input-to-state stability (eλt-weighted GGIE-iISS) are studied. An example is given to illustrate the correctness of the obtained theoretical results.
Stabilization and utilization of nonlinear phenomena based on bifurcation control for slow dynamics
Yabuno, Hiroshi
2008-08-01
Mechanical systems may experience undesirable and unexpected behavior and instability due to the effects of nonlinearity of the systems. Many kinds of control methods to decrease or eliminate the effects have been studied. In particular, bifurcation control to stabilize or utilize nonlinear phenomena is currently an active topic in the field of nonlinear dynamics. This article presents some types of bifurcation control methods with the aim of realizing vibration control and motion control for mechanical systems. It is also indicated through every control method that slowly varying components in the dynamics play important roles for the control and the utilizations of nonlinear phenomena. In the first part, we deal with stabilization control methods for nonlinear resonance which is the 1/3-order subharmonic resonance in a nonlinear spring-mass-damper system and the self-excited oscillation (hunting motion) in a railway vehicle wheelset. The second part deals with positive utilizations of nonlinear phenomena by the generation and the modification of bifurcation phenomena. We propose the amplitude control method of the cantilever probe of an atomic force microscope (AFM) by increasing the nonlinearity in the system. Also, the motion control of a two link underactuated manipulator with a free link and an active link is considered by actuating the bifurcations produced under high-frequency excitation. This article is a discussion on the bifurcation control methods presented by the author and co-researchers by focusing on the actuation of the slowly varying components included in the original dynamics.
Preservation of stability and synchronization in nonlinear systems
Energy Technology Data Exchange (ETDEWEB)
Fernandez-Anaya, G. [Departamento de Fisica y Matematicas, Universidad Iberoamericana, Prol. Paseo de la Reforma 880, Lomas de Santa Fe, Mexico, D.F. 01210 (Mexico)], E-mail: guillermo.fernandez@uia.mx; Flores-Godoy, J.J. [Departamento de Fisica y Matematicas, Universidad Iberoamericana, Prol. Paseo de la Reforma 880, Lomas de Santa Fe, Mexico, D.F. 01210 (Mexico)], E-mail: job.flores@uia.mx; Femat, R. [Division de Matematicas Aplicadas y Sistemas Computacionales, IPICyT, Camino a la Presa San Jose 2055, Col. Lomas 4a. seccion, San Luis Potosi, San Luis Potosi 78216 (Mexico)], E-mail: rfemat@ipicyt.edu.mx; Alvarez-Ramirez, J.J. [Ingenieria de Procesos e Hidraulica, Universidad Autonoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, Mexico, D.F. 09340 (Mexico)], E-mail: jjar@xanum.uam.mx
2007-11-12
Preservation of stability in the presence of structural and/or parametric changes is an important issue in the study of dynamical systems. A specific case is the synchronization of chaos in complex networks where synchronization should be preserved in spite of changes in the network parameters and connectivity. In this work, a methodology to establish conditions for preservation of stability in a class of dynamical system is given in terms of Lyapunov methods. The idea is to construct a group of dynamical transformations under which stability is retained along certain manifolds. Some synchronization examples illustrate the results.
Stabilization and Stochastic Control of a Class of Nonlinear Systems.
1980-10-01
0 is infinite. Thus it is not sufficient that our composite control be only a stabilizing control . To qualify as a candidate for near-optimality uc...completes the proof. 8. Near Optimality The question can now be posed whether uc, being a stabilizing control which produces a bounded cost, is also...procedure when jjc is a small but unknown parameter. For u to be a meaningful feedback control of the system (2.1), it c must first of all be a stabilizing
Stability Analysis of Nonlinear Vibrations of a Deploying Flexible Beam
Institute of Scientific and Technical Information of China (English)
JunfengLI; ZhaolinWANG
1996-01-01
Consider a rigid-flexible coupled system which consists of a central rigid body deploying a flexible appendage,The appendage is modeled as a finite deflection beam having linear constitutive equations.By taking the energy integral as Lyapunov function,it is proved that nonlinear transverse vibrations of the beam undergoing uniform extension or retrieval are stable when there are not controlling moment in the central rigid body and driving force on the beam,according to the partial stablity theorem.
Negative Kerr Nonlinearity of Graphene as seen via Chirped-Pulse-Pumped Self-Phase Modulation
Vermeulen, Nathalie; Castelló-Lurbe, David; Cheng, JinLuo; Pasternak, Iwona; Krajewska, Aleksandra; Ciuk, Tymoteusz; Strupinski, Wlodek; Thienpont, Hugo; Van Erps, Jürgen
2016-10-01
We experimentally demonstrate a negative Kerr nonlinearity for quasiundoped graphene. Hereto, we introduce the method of chirped-pulse-pumped self-phase modulation and apply it to graphene-covered silicon waveguides at telecom wavelengths. The extracted Kerr-nonlinear index for graphene equals n2 ,gr=-10-13 m2 /W . Whereas the sign of n2 ,gr turns out to be negative in contrast to what has been assumed so far, its magnitude is in correspondence with that observed in earlier experiments. Graphene's negative Kerr nonlinearity strongly impacts how graphene should be exploited for enhancing the nonlinear response of photonic (integrated) devices exhibiting a positive nonlinearity. It also opens up the possibility of using graphene to annihilate unwanted nonlinear effects in such devices, to develop unexplored approaches for establishing Kerr processes, and to extend the scope of the "periodic poling" method often used for second-order nonlinearities towards third-order Kerr processes. Because of the generic nature of the chirped-pulse-pumped self-phase modulation method, it will allow fully characterizing the Kerr nonlinearity of essentially any novel (2D) material.
Stabilization of nonlinear system using uniform eigenvalue assignment in linear model
Siahaan, Sahat P.; Pangaribuan, Timbang
2017-09-01
Some plant in control system has nonlinear dynamic, so it is not easy to do in analysis to see its behavior using eigenstructure assignment. From many observations which have been made, some literature give methods to design nonlinear control system. The modern control theory uses state-space method to explain the behaviour on stability of a plant. To improve the stability of the closed-loop system, designer commonly use the state feedback control law. For the case inverted pendulum plant with the nonlinear dynamics, its need to perform the nonlinear control law with the concepts of modern control theory to satisfy the closed-loop system characteristic, and all the behaviour of the closed-loop system only determined from the given linear pole specifications.
Stabilization of nonlinear systems with parametric uncertainty using variable structure techniques
Energy Technology Data Exchange (ETDEWEB)
Schoenwald, D.A. [Oak Ridge National Lab., TN (United States); Oezguener, Ue. [Ohio State Univ., Columbus, OH (United States). Dept. of Electrical Engineering
1995-07-01
The authors present a result on the robust stabilization of a class of nonlinear systems exhibiting parametric uncertainty. They consider feedback linearizable nonlinear systems with a vector of unknown constant parameters perturbed about a known value. A Taylor series of the system about the nominal parameter vector coupled with a feedback linearizing control law yields a linear system plus nonlinear perturbations. Via a structure matching condition, a variable structure control law is shown to exponentially stabilize the full system. The novelty of the result is that the linearizing coordinates are completely known since they are defined about the nominal parameter vector, and fewer restrictions are imposed on the nonlinear perturbations than elsewhere in the literature.
Non-Linear Langmuir Wave Modulation in Collisionless Plasmas
DEFF Research Database (Denmark)
Dysthe, K. B.; Pécseli, Hans
1977-01-01
A non-linear Schrodinger equation for Langmuir waves is presented. The equation is derived by using a fluid model for the electrons, while both a fluid and a Vlasov formulation are considered for the ion dynamics. The two formulations lead to significant differences in the final results, especially...
Energy Technology Data Exchange (ETDEWEB)
Lebedev, M. E., E-mail: gloriouslair@gmail.com, E-mail: galfimov@yahoo.com; Alfimov, G. L., E-mail: gloriouslair@gmail.com, E-mail: galfimov@yahoo.com [National Research University of Electronic Technology MIET, Zelenograd, Moscow 124498 (Russian Federation); Malomed, Boris A., E-mail: malomed@post.tau.ac.il [Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel); Laboratory of Nonlinear-Optical Informatics, ITMO University, St. Petersburg 197101 (Russian Federation)
2016-07-15
We develop a general classification of the infinite number of families of solitons and soliton complexes in the one-dimensional Gross-Pitaevskii/nonlinear Schrödinger equation with a nonlinear lattice pseudopotential, i.e., periodically modulated coefficient in front of the cubic term, which takes both positive and negative local values. This model finds direct implementations in atomic Bose-Einstein condensates and nonlinear optics. The most essential finding is the existence of two branches of dipole solitons (DSs), which feature an antisymmetric shape, being essentially squeezed into a single cell of the nonlinear lattice. This soliton species was not previously considered in nonlinear lattices. We demonstrate that one branch of the DS family (namely, which obeys the Vakhitov-Kolokolov criterion) is stable, while unstable DSs spontaneously transform into stable fundamental solitons (FSs). The results are obtained in numerical and approximate analytical forms, the latter based on the variational approximation. Some stable bound states of FSs are found too.
Stability of switched nonlinear systems via extensions of LaSalle's invariance principle
Institute of Scientific and Technical Information of China (English)
WANG JinHuan; CHENG DaiZhan
2009-01-01
This paper studies the extension of LaSalle's invariance principle for switched nonlinear systems. Unlike most existing results in which each switching mode in the system needs to be asymptotically stable, this paper allows the switching modes to be only stable. Under certain ergodicity assumptions of the switching signals, two extensions of LaSalle's invariance principle for global asymptotic stability of switched nonlinear systems are obtained using the method of common joint Lyapunov function.
Directory of Open Access Journals (Sweden)
Amit kumar Mishra
2015-01-01
Full Text Available In this paper, we have analyzed the effect of time periodic temperature modulation on convective stability in anisotropic porous cavity. The cavity is heated from below and cooled from above. A weakly non-linear stability analysis is done to find Nusselt number governing the heat transport. The infinitely small disturbances are expanded in terms of power series of amplitude of modulation. Analytically the nonautonomous Ginzburg- landau amplitude equation is obtained for the stationary mode of convection. The effects of various parameters like Vadasz number, mechanical and thermal anisotropic parameters, amplitude of oscillations, frequency of modulation and aspect ratio of the cavity on heat transport is studied and plotted graphically. It is observed that the heat transport can also be controlled by suitably adjusting the external and internal parameters of the system.
Directory of Open Access Journals (Sweden)
Bhadauria B.S.
2016-12-01
Full Text Available In this paper, we investigate the combined effect of internal heating and time periodic gravity modulation in a viscoelastic fluid saturated porous medium by reducing the problem into a complex non-autonomous Ginzgburg-Landau equation. Weak nonlinear stability analysis has been performed by using power series expansion in terms of the amplitude of gravity modulation, which is assumed to be small. The Nusselt number is obtained in terms of the amplitude for oscillatory mode of convection. The influence of viscoelastic parameters on heat transfer has been discussed. Gravity modulation is found to have a destabilizing effect at low frequencies and a stabilizing effect at high frequencies. Finally, it is found that overstability advances the onset of convection, more with internal heating. The conditions for which the complex Ginzgburg-Landau equation undergoes Hopf bifurcation and the amplitude equation undergoes supercritical pitchfork bifurcation are studied.
Tavassoli, Vahid
This thesis studies and mathematically models nonlinear interactions among channels of modern high bit rate (amplitude/) phase modulated optical systems. First, phase modulated analogue systems are studied and a differential receiving method is suggested with experimental validation. The main focus of the rest of the thesis is on digital advanced modulation format systems. Cross-talk due to fiber Kerr nonlinearity in two-format hybrid systems as well as 16-QAM systems is mathematically modelled and verified by simulation for different system parameters. A comparative study of differential receivers and coherent receivers is also given for hybrid systems. The model is based on mathematically proven assumptions and provides an intuitive analytical understanding of nonlinear cross-talk in such systems.
Indian Academy of Sciences (India)
P A Subha; C P Jisha; V C Kuriakose
2007-08-01
The nonlinear Schrödinger equation which governs the dynamics of two-dimensional spatial solitons in Kerr media with periodically varying diffraction and nonlinearity has been analyzed in this paper using variational approach and numerical studies. Analytical expressions for soliton parameters have been derived using variational analysis. Variational equations and partial differential equation have been simulated numerically. Analytical and numerical studies have shown that nonlinearity management and diffraction management stabilize the pulse against decay or collapse providing undisturbed propagation even for larger energies of the incident beam.
Institute of Scientific and Technical Information of China (English)
周少波; 薛明皋
2014-01-01
The paper develops exponential stability of the analytic solution and convergence in probability of the numerical method for highly nonlinear hybrid stochastic pantograph equation. The classical linear growth condition is replaced by polynomial growth conditions, under which there exists a unique global solution and the solution is almost surely exponen-tially stable. On the basis of a series of lemmas, the paper establishes a new criterion on convergence in probability of the Euler-Maruyama approximate solution. The criterion is very general so that many highly nonlinear stochastic pantograph equations can obey these conditions. A highly nonlinear example is provided to illustrate the main theory.
Komech, A I; Stuart, D
2008-01-01
The long-time asymptotics is analyzed for finite energy solutions of the 1D Schr\\"odinger equation coupled to a nonlinear oscillator; mathematically the system under study is a nonlinear Schr\\"odinger equation, whose nonlinear term includes a Dirac delta. The coupled system is invariant with respect to the phase rotation group U(1). This article, which extends the results of a previous one, provides a proof of asymptotic stability of solitary wave solutions in the case that the linearization contains a single discrete oscillatory mode satisfying a non-degeneracy assumption of the type known as the Fermi Golden Rule.
Characterization of the shape stability for nonlinear elliptic problems
Bucur, Dorin
We characterize all geometric perturbations of an open set, for which the solution of a nonlinear elliptic PDE of p-Laplacian type with Dirichlet boundary condition is stable in the L-norm. The necessary and sufficient conditions are jointly expressed by a geometric property associated to the γ-convergence. If the dimension N of the space satisfies N-1
Optimization of coherent optical OFDM transmitter using DP-IQ modulator with nonlinear response
Chang, Sun Hyok; Kang, Hun-Sik; Moon, Sang-Rok; Lee, Joon Ki
2016-07-01
In this paper, we investigate the performance of dual polarization orthogonal frequency division multiplexing (DP-OFDM) signal generation when the signal is generated by a DP-IQ optical modulator. The DP-IQ optical modulator is made of four parallel Mach-Zehnder modulators (MZMs) which have nonlinear responses and limited extinction ratios. We analyze the effects of the MZM in the DP-OFDM signal generation by numerical simulation. The operating conditions of the DP-IQ modulator are optimized to have the best performance of the DP-OFDM signal.
Stability of Gain Scheduling Control for Aircraft with Highly Nonlinear Behavior
Directory of Open Access Journals (Sweden)
Fany Mendez-Vergara
2014-01-01
Full Text Available The main goal of this work is to study the stability properties of an aircraft with nonlinear behavior, controlled using a gain scheduled approach. An output feedback is proposed which is able to guarantee asymptotical stability of the task-coordinates origin and safety of the operation in the entire flight envelope. The results are derived using theory of hybrid and singular perturbed systems. It is demonstrated that both body velocity and orientation asymptotic tracking can be obtained in spite of nonlinearities and uncertainty. The results are illustrated using numerical simulations in F16 jet.
Stability analysis of a general family of nonlinear positive discrete time-delay systems
Nam, P. T.; Phat, V. N.; Pathirana, P. N.; Trinh, H.
2016-07-01
In this paper, we propose a new approach to analyse the stability of a general family of nonlinear positive discrete time-delay systems. First, we introduce a new class of nonlinear positive discrete time-delay systems, which generalises some existing discrete time-delay systems. Second, through a new technique that relies on the comparison and mathematical induction method, we establish explicit criteria for stability and instability of the systems. Three numerical examples are given to illustrate the feasibility of the obtained results.
On Robust Stability of a Class of Uncertain Nonlinear Systems with Time-Varying Delay
Institute of Scientific and Technical Information of China (English)
NIAN Xiao-hong
2002-01-01
The problem of robust stability of a class of uncertain nonlinear dynamical systems with time-delay is considered. Based on the assumption that the nominal system is stable, some sufficient conditions onrobust stability of uncertain nonlinear dynamical systems with time-delay are derived. Some analytical methods and a type of Lyapunov functional are used to investigate such sufficient conditions. The results obtained in this paper are applicable to perturbed time-delay systems with unbounded time-varying delay.Some previous results are improved and a numerical example is given to demonstrate the validity of our results.
Nonlinear model predictive control with guaraneed stability based on pesudolinear neural networks
Institute of Scientific and Technical Information of China (English)
WANG Yongji; WANG Hong
2004-01-01
A nonlinear model predictive control problem based on pseudo-linear neural network (PNN) is discussed, in which the second order on-line optimization method is adopted. The recursive computation of Jacobian matrix is investigated. The stability of the closed loop model predictive control system is analyzed based on Lyapunov theory to obtain the sufficient condition for the asymptotical stability of the neural predictive control system. A simulation was carried out for an exothermic first-order reaction in a continuous stirred tank reactor. It is demonstrated that the proposed control strategy is applicable to some of nonlinear systems.
STABILITY AND BIFURCATION BEHAVIORS ANALYSIS IN A NONLINEAR HARMFUL ALGAL DYNAMICAL MODEL
Institute of Scientific and Technical Information of China (English)
WANG Hong-li; FENG Jian-feng; SHEN Fei; SUN Jing
2005-01-01
A food chain made up of two typical algae and a zooplankton was considered. Based on ecological eutrophication, interaction of the algal and the prey of the zooplankton, a nutrient nonlinear dynamic system was constructed. Using the methods of the modern nonlinear dynamics, the bifurcation behaviors and stability of the model equations by changing the control parameter r were discussed. The value of r for bifurcation point was calculated, and the stability of the limit cycle was also discussed. The result shows that through quasi-periodicity bifurcation the system is lost in chaos.
Finite-time stabilization for a class of stochastic nonlinear systems via output feedback.
Zha, Wenting; Zhai, Junyong; Fei, Shumin; Wang, Yunji
2014-05-01
This paper investigates the problem of global finite-time stabilization in probability for a class of stochastic nonlinear systems. The drift and diffusion terms satisfy lower-triangular or upper-triangular homogeneous growth conditions. By adding one power integrator technique, an output feedback controller is first designed for the nominal system without perturbing nonlinearities. Based on homogeneous domination approach and stochastic finite-time stability theorem, it is proved that the solution of the closed-loop system will converge to the origin in finite time and stay at the origin thereafter with probability one. Two simulation examples are presented to illustrate the effectiveness of the proposed design procedure.
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The nonlinear dynamical behaviors of artificial neural network (ANN) and their application to science and engineering were summarized. The mechanism of two kinds of dynamical processes, i.e. weight dynamics and activation dynamics in neural networks, and the stability of computing in structural analysis and design were stated briefly. It was successfully applied to nonlinear neural network to evaluate the stability of underground stope structure in a gold mine. With the application of BP network, it is proven that the neuro-computing is a practical and advanced tool for solving large-scale underground rock engineering problems.
Practical stabilization of a class of uncertain time-varying nonlinear delay systems
Institute of Scientific and Technical Information of China (English)
Bassem Ben HAMED; Mohamed Ali HAMMAMI
2009-01-01
In this paper we deal with a class of uncertain time-varying nonlinear systems with a state delay. Under some assumptions, we construct some stabilizing continuous feedback, i.e. linear and nonlinear in the state, which can guarantee global uniform exponential stability and global uniform practical convergence of the considered system. The quadratic Lyapunov function for the nominal stable system is used as a Lyapunov candidate function for the global system. The results developed in this note are applicable to a class of dynamical systems with uncertain time-delay. Our result is illustrated by a numerical example.
Modulating light with light via giant nano-opto-mechanical nonlinearity of plasmonic metamaterial
Ou, Jun-Yu; Zhang, Jianfa; Zheludev, Nikolay I
2015-01-01
From the demonstration of saturable absorption by Vavilow and Levshin in 1926, and with invention of the laser, unavailability of strongly nonlinear materials was a key obstacle for developing optical signal processing, in particular in transparent telecommunication networks. Today, most advanced photonic switching materials exploit gain dynamics and near-band and excitonic effects in semiconductors, nonlinearities in organic media with weakly-localized electrons and nonlinearities enhanced by hybridization with metamaterials. Here we report on a new type of artificial nonlinearity that is nano-opto-mechanical in nature. It was observed in an artificial metamaterial array of plasmonic meta-molecules supported by a flexible nano-membrane. Here nonlinearity is underpinned by the reversible reconfiguration of its structure induced by light. In a film of only 100 nanometres thickness we demonstrated modulation of light with light using milliwatt power telecom diode lasers.
ROBUST STABILITY WITH GUARANTEEING COST FOR DISCRETE TIME-DELAY SYSTEMS WITH NONLINEAR PERTURBATION
Institute of Scientific and Technical Information of China (English)
JIA Xinchun; ZHENG Nanning; LIU Yuehu
2005-01-01
The problems of robust stability and robust stability with a guaranteeing cost for discrete time-delay systems with nonlinear perturbation are discussed. A sufficient criterion for robust stability is established in an LMI framework and a linear convex optimization problem with LMI constraints for computing maximal perturbation bound is proposed. Meanwhile, a sufficient criterion for robust stability with a guaranteeing cost for such systems is obtained, and an optimal procedure for decreasing the value of guaranteeing cost is put forward. Two examples are used to illustrate the efficiency of the results.
DEFF Research Database (Denmark)
Thomsen, Jon Juel; Blekhman, Iliya I.
2007-01-01
, and to call these dynamic materials or spatiotemporal composites. Also, according to theoretical predictions, structural nonlinearity enhances the possibilities of achieving specific effective properties. For example, with an elastic rod having cubical elastic nonlinearities, it seems possible to control......, and exemplified. Then simple approximate analytical expressions are derived for the effective wave speed and natural frequencies for one-dimensional wave propagation in a nonlinear elastic rod, where the spatiotemporal modulation is imposed as a high-frequency standing wave, supposed to be given. Finally the more...
Nonlinear Image Restoration in Confocal Microscopy : Stability under Noise
Roerdink, J.B.T.M.
1995-01-01
In this paper we study the noise stability of iterative algorithms developed for attenuation correction in Fluorescence Confocal Microscopy using FT methods. In each iteration the convolution of the previous estimate is computed. It turns out that the estimators are robust to noise perturbation.
Nonlinear Image Restoration in Confocal Microscopy : Stability under Noise
Roerdink, J.B.T.M.
1995-01-01
In this paper we study the noise stability of iterative algorithms developed for attenuation correction in Fluorescence Confocal Microscopy using FT methods. In each iteration the convolution of the previous estimate is computed. It turns out that the estimators are robust to noise perturbation.
Nonlinear response studies and corrections for a liquid crystal spatial light modulator
Indian Academy of Sciences (India)
Ravinder Kumar Banyal; B Raghavendra Prasad
2010-06-01
The nonlinear response of light transmission characteristics of a liquid crystal (LC) spatial light modulator (SLM) is studied. The results show that the device exhibits a wide range of variations with different control parameters and input settings. Experiments were performed to obtain intensity modulation that is best described by either power-law or sigmoidal functions. Based on the inverse transformation, an appropriate pre-processing scheme for electrically addressed input gray-scale images, particularly important in several optical processing and imaging applications, is suggested. Further, the necessity to compensate the SLM image nonlinearities in a volume holographic data storage and retrieval system is demonstrated.
Enhanced nonlinear spectral compression in fiber by external sinusoidal phase modulation
Boscolo, S.; Mouradian, L. Kh; Finot, C.
2016-10-01
We propose a new, simple approach to enhance the spectral compression process arising from nonlinear pulse propagation in an optical fiber. We numerically show that an additional sinusoidal temporal phase modulation of the pulse enables efficient reduction of the intensity level of the side lobes in the spectrum that are produced by the mismatch between the initial linear negative chirp of the pulse and the self-phase modulation-induced nonlinear positive chirp. Remarkable increase of both the extent of spectrum narrowing and the quality of the compressed spectrum is afforded by the proposed approach across a wide range of experimentally accessible parameters.
Directory of Open Access Journals (Sweden)
Cha'o-Kuang Chen
2009-01-01
Full Text Available The main object of this paper is to study the weakly nonlinear hydrodynamic stability of the thin Newtonian fluid flowing on a rotating circular disk. A long-wave perturbation method is used to derive the nonlinear evolution equation for the film flow. The linear behaviors of the spreading wave are investigated by normal mode approach, and its weakly nonlinear behaviors are explored by the method of multiple scales. The Ginzburg-Landau equation is determined to discuss the necessary condition for the existence of such flow pattern. The results indicate that the superctitical instability region increases, and the subcritical stability region decreases with the increase of the rotation number or the radius of circular disk. It is found that the rotation number and the radius of circular disk not only play the significant roles in destabilizing the flow in the linear stability analysis but also shrink the area of supercritical stability region at high Reynolds number in the weakly nonlinear stability analysis.
Non-Linear Stability of an Electrified Plane Interface in Porous Media
El-Dib, Yusry O.; Moatimid, Galal M.
2004-03-01
The non-linear electrohydrodynamic stability of capillary-gravity waves on the interface between two semi-infinite dielectric fluids is investigated. The system is stressed by a vertical electric field in the presence of surface charges. The work examines a few representative porous media configurations. The analysis includes Rayleigh-Taylor and Kelvin-Helmholtz instabilities. The boundary - value problem leads to a non-linear equation governing the surface evolution. Taylor theory is adopted to expand this equation, in the light of multiple scales, in order to obtain a non-linear Schr¨odinger equation describing the behavior of the perturbed interface. The latter equation, representing the amplitude of the quasi-monochromatic traveling wave, is used to describe the stability criteria. These criteria are discussed both analytically and numerically. In order to identifiy regions of stability and instability, the electric field intensity is plotted versus the wave number. Through a linear stability approach it is found that Darcy's coefficients have a destabilizing influence, while in the non-linear scope these coefficients as well as the electric field intensity play a dual role on the stability.
STABILITY, BIFURCATIONS AND CHAOS IN UNEMPLOYMENT NON-LINEAR DYNAMICS
Directory of Open Access Journals (Sweden)
Pagliari Carmen
2013-07-01
Full Text Available The traditional analysis of unemployment in relation to real output dynamics is based on some empirical evidences deducted from Okun’s studies. In particular the so called Okun’s Law is expressed in a linear mathematical formulation, which cannot explain the fluctuation of the variables involved. Linearity is an heavy limit for macroeconomic analysis and especially for every economic growth study which would consider the unemployment rate among the endogenous variables. This paper deals with an introductive study about the role of non-linearity in the investigation of unemployment dynamics. The main idea is the existence of a non-linear relation between the unemployment rate and the gap of GDP growth rate from its trend. The macroeconomic motivation of this idea moves from the consideration of two concatenate effects caused by a variation of the unemployment rate on the real output growth rate. These two effects are concatenate because there is a first effect that generates a secondary one on the same variable. When the unemployment rate changes, the first effect is the variation in the level of production in consequence of the variation in the level of such an important factor as labour force; the secondary effect is a consecutive variation in the level of production caused by the variation in the aggregate demand in consequence of the change of the individual disposal income originated by the previous variation of production itself. In this paper the analysis of unemployment dynamics is carried out by the use of the logistic map and the conditions for the existence of bifurcations (cycles are determined. The study also allows to find the range of variability of some characteristic parameters that might be avoided for not having an absolute unpredictability of unemployment dynamics (deterministic chaos: unpredictability is equivalent to uncontrollability because of the total absence of information about the future value of the variable to
Global asymptotic stability of a class of nonlinear systems with parametric uncertainty
Institute of Scientific and Technical Information of China (English)
Cai Xiushan; Lǜ Ganyun; Zhang Changfiang; He Xiuhui
2009-01-01
Stability of a class of nonlinear systems with parametric uncertainty is dealt with. This kind of systems can be viewed as feedback interconnection systems. By constructing the Lyapunov function for one of the feedback interconnection systems, the Lyapunov function for this kind of systems is obtained. Sufficient conditions of global asymptotic stability for this class of systems axe deduced. The simulation shows the effectiveness of the method.
A NEW APPROACH TO THE NONLINEAR STABILITY OF PARALLEL SHEAR FLOWS
Institute of Scientific and Technical Information of China (English)
XU Lan-xi; HUANG Yong-nian
2005-01-01
Lyapunov's second method was used to study the nonlinear stability of parallel shear flows for stress-free boundaries. By introducing an energy functional, it was shown that the plane Couette and plane Poiseuille flows are conditionally and asymptotically stable for all Reynolds numbers. In particular, to two-dimensional perturbations, by defining new energy functionals the unconditional stability of the basic flows was proved.
Adaptive Stabilization for a Class of Dynamical Systems with Nonlinear Delayed State Perturbations
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The problem of adaptive stabilization for a class of systems with nonlinear delayed state perturbations is considered. The bound of the perturbations is assumed to be unknown, by using the adaptive control method, an adaptive controller is designed. Based on the Lyapunov- Karasovskii functional, it is shown that the dynamical system can be stabilized by the adaptive controller. The effectiveness of the proposed controller is demonstrated by some simulations.
Circuits and systems based on delta modulation linear, nonlinear and mixed mode processing
Zrilic, Djuro G
2005-01-01
This book is intended for students and professionals who are interested in the field of digital signal processing of delta-sigma modulated sequences. The overall focus is on the development of algorithms and circuits for linear, non-linear, and mixed mode processing of delta-sigma modulated pulse streams. The material presented here is directly relevant to applications in digital communication, DSP, instrumentation, and control.
Indian Academy of Sciences (India)
A Ghosh; B K Goswami; R Vijaya
2010-11-01
Our experiments with an erbium-doped fibre ring laser (CW, single transverse mode and multiaxial mode) with an intracavity LiNbO3 electro-optic modulator (EOM) display the characteristic features of a nonlinear oscillator (e.g., harmonic and period-2 sub-harmonic resonances) when the EOM driver voltage is modulated periodically. Harmonic resonance leads to period-1 bistability and hysteresis. Inside the period-2 sub-harmonic resonance region, the laser exhibits Feigenbaum sequence and generalized bistability.
Frequency-domain L2-stability conditions for time-varying linear and nonlinear MIMO systems
Institute of Scientific and Technical Information of China (English)
Zhihong HUANG; Y. V. VENKATESH; Cheng XIANG; Tong Heng LEE
2014-01-01
The paper deals with the L2-stability analysis of multi-input-multi-output (MIMO) systems, governed by integral equations, with a matrix of periodic/aperiodic time-varying gains and a vector of monotone, non-monotone and quasi-monotone nonlin-earities. For nonlinear MIMO systems that are described by differential equations, most of the literature on stability is based on an application of quadratic forms as Lyapunov-function candidates. In contrast, a non-Lyapunov framework is employed here to derive new and more general L2-stability conditions in the frequency domain. These conditions have the following features:i) They are expressed in terms of the positive definiteness of the real part of matrices involving the transfer function of the linear time-invariant block and a matrix multiplier function that incorporates the minimax properties of the time-varying linear/nonlinear block. ii) For certain cases of the periodic time-varying gain, they contain, depending on the multiplier function chosen, no restrictions on the normalized rate of variation of the time-varying gain, but, for other periodic/aperiodic time-varying gains, they do. Overall, even when specialized to periodic-coefficient linear and nonlinear MIMO systems, the stability conditions are distinct from and less restrictive than recent results in the literature. No comparable results exist in the literature for aperiodic time-varying gains. Furthermore, some new stability results concerning the dwell-time problem and time-varying gain switching in linear and nonlinear MIMO systems with periodic/aperiodic matrix gains are also presented. Examples are given to illustrate a few of the stability theorems.
Effects of nonlinear strength parameters on stability of 3D soil slopes
Institute of Scientific and Technical Information of China (English)
高玉峰; 吴迪; 张飞; 秦红玉; 朱德胜
2016-01-01
Actual slope stability problems have three-dimensional (3D) characteristics and the soils of slopes have curved failure envelopes. This incorporates a power-law nonlinear failure criterion into the kinematic approach of limit analysis to conduct the evaluation of the stability of 3D slopes. A tangential technique is adopted to simplify the nonlinear failure criterion in the form of equivalent Mohr-Coulomb strength parameters. A class of 3D admissible rotational failure mechanisms is selected for soil slopes including three types of failure mechanisms: face failure, base failure, and toe failure. The upper-bound solutions and corresponding critical slip surfaces can be obtained by an efficient optimization method. The results indicate that the nonlinear parameters have significant influences on the assessment of slope stability, especially on the type of failure mechanism. The effects of nonlinear parameters appear to be pronounced for gentle slopes constrained to a narrow width. Compared with the solutions derived from plane-strain analysis, the 3D solutions are more sensitive to the values of nonlinear parameters.
Directory of Open Access Journals (Sweden)
Changchuan Xie
2016-01-01
Full Text Available VFAs (very flexible aircraft have begun to attract significant attention because of their good flight performances and significant application potentials; however, they also bring some challenges to researchers due to their unusual lightweight designs and large elastic deformations. A framework for the geometrically nonlinear aeroelastic stability analysis of very flexible wings is constructed in this paper to illustrate the unique aeroelastic characteristics and convenient use of these designs in engineering analysis. The nonlinear aeroelastic analysis model includes the geometrically nonlinear structure finite elements and steady and unsteady nonplanar aerodynamic computations (i.e., the nonplanar vortex lattice method and nonplanar doublet-lattice method. Fully nonlinear methods are used to analyse static aeroelastic features, and linearized structural dynamic equations are established at the structural nonlinear equilibrium state to estimate the stability of the system through the quasimode of the stressed and deformed structure. The exact flutter boundary is searched via an iterative procedure. A wind tunnel test is conducted to validate this theoretical analysis framework, and reasonable agreement is obtained. Both the analysis and test results indicate that the geometric nonlinearity of very flexible wings presents significantly different aeroelastic characteristics under different load cases with large deformations.
Nonlinear stability of cylindrical shells subjected to axial flow: Theory and experiments
Karagiozis, K. N.; Païdoussis, M. P.; Amabili, M.; Misra, A. K.
2008-01-01
This paper, is concerned with the nonlinear dynamics and stability of thin circular cylindrical shells clamped at both ends and subjected to axial fluid flow. In particular, it describes the development of a nonlinear theoretical model and presents theoretical results displaying the nonlinear behaviour of the clamped shell subjected to flowing fluid. The theoretical model employs the Donnell nonlinear shallow shell equations to describe the geometrically nonlinear structure. The clamped beam eigenfunctions are used to describe the axial variations of the shell deformation, automatically satisfying the boundary conditions and the circumferential continuity condition exactly. The fluid is assumed to be incompressible and inviscid, and the fluid-structure interaction is described by linear potential flow theory. The partial differential equation of motion is discretized using the Galerkin method and the final set of ordinary differential equations are integrated numerically using a pseudo-arclength continuation and collocation techniques and the Gear backward differentiation formula. A theoretical model for shells with simply supported ends is presented as well. Experiments are also described for (i) elastomer shells subjected to annular (external) air-flow and (ii) aluminium and plastic shells with internal water flow. The experimental results along with the theoretical ones indicate loss of stability by divergence with a subcritical nonlinear behaviour. Finally, theory and experiments are compared, showing good qualitative and reasonable quantitative agreement.
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.
Rodríguez, Hugo; Schaft, Arjan J. van der; Ortega, Romeo
2001-01-01
Energy-shaping techniques have been successfully used for stabilization of nonlinear finite dimensional systems for 20 years now. In particular, for systems described by Port-Controlled Hamiltonian (PCH) models, the “control by interconnection” method provides a simple and elegant procedure for stab
On Stability of Flat Band Modes in a Rhombic Nonlinear Optical Waveguide Array
Maimistov, Andrey I
2016-01-01
The quasi-one-dimensional rhombic array of the waveguides is considered. In the nonlinear case the system of equations describing coupled waves in the waveguides has the solutions that represent the superposition of the flat band modes. The property of stability of these solutions is considered. It was found that the flat band solution is unstable until the power threshold be attained.
Rodríguez, Hugo; Schaft, van der Arjan J.; Ortega, Romeo
2001-01-01
Energy-shaping techniques have been successfully used for stabilization of nonlinear finite dimensional systems for 20 years now. In particular, for systems described by Port-Controlled Hamiltonian (PCH) models, the "control by interconnection" method provides a simple and elegant procedure for stab
Explicit Conditions for Stability of Nonlinear Scalar Delay Impulsive Difference Equation
Directory of Open Access Journals (Sweden)
Bo Zheng
2010-01-01
Full Text Available Sufficient conditions are obtained for the uniform stability and global attractivity of the zero solution of nonlinear scalar delay impulsive difference equation, which extend and improve the known results in the literature. An example is also worked out to verify that the global attractivity condition is a sharp condition.
Bonito, Andrea
2013-10-03
We establish the L2-stability of an entropy viscosity technique applied to nonlinear scalar conservation equations. First-and second-order explicit time-stepping techniques using continuous finite elements in space are considered. The method is shown to be stable independently of the polynomial degree of the space approximation under the standard CFL condition. © 2013 American Mathematical Society.
DEFF Research Database (Denmark)
Fuhrmann, David R.; Bingham, Harry B.; Madsen, Per A.
2004-01-01
This paper considers a method of lines stability analysis for finite difference discretizations of a recently published Boussinesq method for the study of highly nonlinear and extremely dispersive water waves. The analysis demonstrates the near-equivalence of classical linear Fourier (von Neumann...
Minimal data rate stabilization of nonlinear systems over networks with large delays
Persis, Claudio De
2007-01-01
We consider the problem of designing encoders, decoders and controllers which stabilize feedforward nonlinear systems over a communication network with finite bandwidth and large delay. The control scheme guarantees minimal data-rate semi-global asymptotic and local exponential stabilizatioln of the
A Nonlinear Observer for Estimating Transverse Stability Parameters of Marine Surface Vessels
DEFF Research Database (Denmark)
Galeazzi, Roberto; Perez, Tristan
2011-01-01
This paper presents a nonlinear observer for estimating parameters associated with the restoring term of a roll motion model of a marine vessel in longitudinal waves. Changes in restoring, also referred to as transverse stability, can be the result of changes in the vessel’s centre of gravity due...
Asymptotic stability for a class of boundary control systems with non-linear damping
Zwart, Heiko J.; Ramirez, Hector; Le Gorrec, Yann
2016-01-01
The asymptotic stability of boundary controlled port-Hamiltonian systems defined on a 1D spatial domain interconnected to a class of non-linear boundary damping is addressed. It is shown that if the port-Hamiltonian system is approximately observable, then any boundary damping which behaves linear
Nonlinear Stability for the Periodic and Non-Periodic Zakharov System
Angulo, Jaime
2010-01-01
We prove the existence of a smooth curve of periodic traveling wave solutions for the Zakharov system. We also show that this type of solutions are nonlinear stable by the periodic flow generated for the system mentioned before. An improvement of the work of Ya Ping is made, we prove the stability of the solitary wave solutions associated to the Zakharov system.
A DELAY-DEPENDENT STABILITY CRITERION FOR NONLINEAR STOCHASTIC DELAY-INTEGRO-DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
Niu Yuanling; Zhang Chengjian; Duan Jinqiao
2011-01-01
A type of complex systems under both random influence and memory effects is considered.The systems are modeled by a class of nonlinear stochastic delay-integrodifferential equations.A delay-dependent stability criterion for such equations is derived under the condition that the time lags are small enough.Numerical simulations are presented to illustrate the theoretical result.
At the edge of nuclear stability nonlinear quantum amplifiers, pt. 2
Csoto, A; Schlattl, H; Csoto, Attila; Oberhummer, Heinz; Schlattl, Helmut
2000-01-01
We show that nuclei lying at the edge of stability can behave as nonlinear quantum amplifiers. A tiny change in the nucleon-nucleon interaction can trigger a much bigger change in the binding energy of these systems, relative to the few-cluster breakup threshold.
Oscillation and asymptotic stability of a delay differential equation with Richard's nonlinearity
Directory of Open Access Journals (Sweden)
Leonid Berezansky
2005-04-01
Full Text Available We obtain sufficient conditions for oscillation of solutions, and for asymptotical stability of the positive equilibrium, of the scalar nonlinear delay differential equation $$ frac{dN}{dt} = r(tN(tBig[a-Big(sum_{k=1}^m b_k N(g_k(tBig^{gamma}Big], $$ where $ g_k(tleq t$.
Stabilization of solitons under competing nonlinearities by external potentials
Zegadlo, Krzysztof B; Malomed, Boris A; Karpierz, Miroslaw A; Trippenbach, Marek
2014-01-01
We report results of the analysis for families of one-dimensional (1D) trapped solitons, created by competing self-focusing (SF) quintic and self-defocusing (SDF) cubic nonlinear terms. Two trapping potentials are considered, the harmonic-oscillator (HO) and delta-functional ones. The models apply to optical solitons in colloidal waveguides and other photonic media, and to matter-wave solitons in Bose-Einstein condensates (BEC) loaded into a quasi-1D trap. For the HO potential, the results are obtained in an approximate form, using the variational and Thomas-Fermi approximations (VA and TFA), and in a full numerical form, including the ground state and the first antisymmetric excited one. For the delta-functional attractive potential, the results are produced in a fully analytical form, and verified by means of numerical methods. Both exponentially localized solitons and weakly localized trapped modes are found for the delta-functional potential. The most essential conclusions concern the applicability of com...
Linear and nonlinear stability of periodic orbits in annular billiards.
Dettmann, Carl P; Fain, Vitaly
2017-04-01
An annular billiard is a dynamical system in which a particle moves freely in a disk except for elastic collisions with the boundary and also a circular scatterer in the interior of the disk. We investigate the stability properties of some periodic orbits in annular billiards in which the scatterer is touching or close to the boundary. We analytically show that there exist linearly stable periodic orbits of an arbitrary period for scatterers with decreasing radii that are located near the boundary of the disk. As the position of the scatterer moves away from a symmetry line of a periodic orbit, the stability of periodic orbits changes from elliptic to hyperbolic, corresponding to a saddle-center bifurcation. When the scatterer is tangent to the boundary, the periodic orbit is parabolic. We prove that slightly changing the reflection angle of the orbit in the tangential situation leads to the existence of Kolmogorov-Arnold-Moser islands. Thus, we show that there exists a decreasing to zero sequence of open intervals of scatterer radii, along which the billiard table is not ergodic.
Directory of Open Access Journals (Sweden)
Florian Hartig
Full Text Available If two species exhibit different nonlinear responses to a single shared resource, and if each species modifies the resource dynamics such that this favors its competitor, they may stably coexist. This coexistence mechanism, known as relative nonlinearity of competition, is well understood theoretically, but less is known about its evolutionary properties and its prevalence in real communities. We address this challenge by using adaptive dynamics theory and individual-based simulations to compare community stabilization and evolutionary stability of species that coexist by relative nonlinearity. In our analysis, evolution operates on the species' density-compensation strategies, and we consider a trade-off between population growth rates at high and low resource availability. We confirm previous findings that, irrespective of the particular model of density dependence, there are many combinations of overcompensating and undercompensating density-compensation strategies that allow stable coexistence by relative nonlinearity. However, our analysis also shows that most of these strategy combinations are not evolutionarily stable and will be outcompeted by an intermediate density-compensation strategy. Only very specific trade-offs lead to evolutionarily stable coexistence by relative nonlinearity. As we find no reason why these particular trade-offs should be common in nature, we conclude that the sympatric evolution and evolutionary stability of relative nonlinearity, while possible in principle, seems rather unlikely. We speculate that this may, at least in part, explain why empirical demonstrations of this coexistence mechanism are rare, noting, however, that the difficulty to detect relative nonlinearity in the field is an equally likely explanation for the current lack of empirical observations, and that our results are limited to communities with non-overlapping generations and constant resource supply. Our study highlights the need for
Hartig, Florian; Münkemüller, Tamara; Johst, Karin; Dieckmann, Ulf
2014-01-01
If two species exhibit different nonlinear responses to a single shared resource, and if each species modifies the resource dynamics such that this favors its competitor, they may stably coexist. This coexistence mechanism, known as relative nonlinearity of competition, is well understood theoretically, but less is known about its evolutionary properties and its prevalence in real communities. We address this challenge by using adaptive dynamics theory and individual-based simulations to compare community stabilization and evolutionary stability of species that coexist by relative nonlinearity. In our analysis, evolution operates on the species' density-compensation strategies, and we consider a trade-off between population growth rates at high and low resource availability. We confirm previous findings that, irrespective of the particular model of density dependence, there are many combinations of overcompensating and undercompensating density-compensation strategies that allow stable coexistence by relative nonlinearity. However, our analysis also shows that most of these strategy combinations are not evolutionarily stable and will be outcompeted by an intermediate density-compensation strategy. Only very specific trade-offs lead to evolutionarily stable coexistence by relative nonlinearity. As we find no reason why these particular trade-offs should be common in nature, we conclude that the sympatric evolution and evolutionary stability of relative nonlinearity, while possible in principle, seems rather unlikely. We speculate that this may, at least in part, explain why empirical demonstrations of this coexistence mechanism are rare, noting, however, that the difficulty to detect relative nonlinearity in the field is an equally likely explanation for the current lack of empirical observations, and that our results are limited to communities with non-overlapping generations and constant resource supply. Our study highlights the need for combining ecological and
Non-linear ultimate strength and stability limit state analysis of a wind turbine blade
DEFF Research Database (Denmark)
Rosemeier, Malo; Berring, Peter; Branner, Kim
2016-01-01
flap-wise loading has been compared with a linear response to determine the blade's resistance in the ultimate strength and stability limit states. The linear analysis revealed an unrealistic failure mechanism and failure mode. Further, it did not capture the highly non-linear response of the blade...... of an imperfection. The more realistic non-linear approaches yielded more optimistic results than the mandatory linear bifurcation analysis. Consequently, the investigated blade designed after the lesser requirements was sufficient. Using the non-linear approaches, considering inter-fibre failure as the critical...... failure mode, yielded still a significant safety margin for the designer (7–28%). The non-linear response was significantly dependent on the scaling of the imperfection. Eurocode's method of applying an imperfection appeared more realistic than the GL method. Since the considered blade withstood 135...
Nonlinear control for global stabilization of multiple-integrator system by bounded controls
Institute of Scientific and Technical Information of China (English)
Bin ZHOU; Guangren DUAN; Liu ZHANG
2008-01-01
The global stabilization problem of the multiple-integrator system by bounded controls is considered.A nonlinear feedback law consisting of nested saturation functions is proposed.This type of nonlinear feedback law that is a modification and generalization of the result given in[1] needs only[(n+1)/2](n is the dimensions of the system)saturation elements,which is fewer than that which the other nonlinear laws need.Funhermore.the poles of the closedloop system Can be placed on any location on the left real axis when none of the saturafion elements in the control laws is saturated.This type of nonlinear control law exhibits a simpler structure and call significantly improve the transient performances of the closed-loop system,and is very superior to the other existing methods.Simulation on a fourth-order system is used to validate the proposed method.
OI,Shigemitsu
1993-01-01
Sufficient conditions for finite pulse stability of interconnected systems with combined pulse frequency and pulse width modulation are developed in this paper using a direct method. The stability criteria established provide upper bounds on the number of pulses emitted by each modulator. The results are also applicable to those systems which contain a finite number of pulse frequency modulators and a finite number of combined pulse frequency and pulse width modulators
Effects of nonlinear phase modulation on Bragg scattering in the low-conversion regime
DEFF Research Database (Denmark)
Andersen, Lasse Mejling; Cargill, D. S.; McKinstrie, C. J.
2012-01-01
In this paper, we consider the effects of nonlinear phase modulation on frequency conversion by four-wave mixing (Bragg scattering) in the low-conversion regime. We derive the Green functions for this process using the time-domain collision method, for partial collisions, in which the four fields...
Effects of nonlinear phase modulation on low-conversion four-wave mixing Bragg scattering
DEFF Research Database (Denmark)
Andersen, Lasse Mejling; McKinstrie, C. J.; Rottwitt, Karsten
We consider the effects of nonlinear phase modulation (NPM) on frequency converseon by Bragg scattering. Previously we found that arbitrary mode reshaping without temporal entanglement (separability) was possible. When NPM is included, the modes are chirped and the separability is no longer compl...
A versatile all-optical modulator based on nonlinear Mach-Zehnder interferometers
Krijnen, G.J.M.; Villeneuve, A.; Stegeman, G.I.; Lambeck, P.V.; Hoekstra, H.J.W.M.
1994-01-01
A device based on a Nonlinear Mach-Zehnder interferometer (NMI) which exploits cross-phase modulation of two co-propagating modes in bimodal branches has been described in this paper. The advantage of this device is that it becomes polarisation independent while keeping phase insensitive by using di
Nonlinear evolution of Airy-like beams generated by modulated waveguide arrays.
Cao, Zheng; Tan, Qinggui; Li, Xiaojun; Qi, Xinyuan
2016-08-20
We numerically study the formation of modulated waveguide generated Airy-like beams and their subsequent evolution in homogeneous medium. The results show that the Airy-like beams could be generated from narrow Gaussian beams propagating in one-dimensional transverse separation modulated unbent, cosine bent, or logarithm bent waveguide arrays, respectively. The waveguide-generated Airy-like beams maintain their characteristics when propagating without nonlinearity or under the self-defocusing nonlinearity in homogeneous medium, while the beams are distorted under the self-focusing nonlinearity. The deformation depends on the waveguide bending and the outgoing angles of the Airy-like beams. Our results provide a new way to generate and manipulate the Airy-like beam.
Interharmonic modulation products as a means to quantify nonlinear D-region interactions
Moore, Robert
Experimental observations performed during dual beam ionospheric HF heating experiments at the High frequency Active Auroral Research Program (HAARP) HF transmitter in Gakona, Alaska are used to quantify the relative importance of specific nonlinear interactions that occur within the D region ionosphere. During these experiments, HAARP broadcast two amplitude modulated HF beams whose center frequencies were separated by less than 20 kHz. One beam was sinusoidally modulated at 500 Hz while the second beam was sinusoidally modulated using a 1-7 kHz linear frequency-time chirp. ELF/VLF observations performed at two different locations (3 and 98 km from HAARP) provide clear evidence of strong interactions between all field components of the two HF beams in the form of low and high order interharmonic modulation products. From a theoretical standpoint, the observed interharmonic modulation products could be produced by several different nonlinearities. The two primary nonlinearities take the form of wave-medium interactions (i.e., cross modulation), wherein the ionospheric conductivity modulation produced by one signal crosses onto the other signal via collision frequency modification, and wave-wave interactions, wherein the conduction current associated with one wave mixes with the electric field of the other wave to produce electron temperature oscillations. We are able to separate and quantify these two different nonlinearities, and we conclude that the wave-wave interactions dominate the wave-medium interactions by a factor of two. These results are of great importance for the modeling of transioinospheric radio wave propagation, in that both the wave-wave and the wave-medium interactions could be responsible for a significant amount of anomalous absorption.
Nonlinear optical microscopy improvement by focal-point axial modulation
Dashtabi, Mahdi Mozdoor; Massudi, Reza
2016-05-01
Among the most important challenges of microscopy-even more important than the resolution enhancement, especially in biological and neuroscience applications-is noninvasive and label-free imaging deeper into live scattering samples. However, the fundamental limitation on imaging depth is the signal-to-background ratio in scattering biological tissues. Here, using a vibrating microscope objective in conjunction with a lock-in amplifier, we demonstrate the background cancellation in imaging the samples surrounded by turbid and scattering media, which leads to more clear images deeper into the samples. Furthermore, this technique offers the localization and resolution enhancement as well as resolves ambiguities in signal interpretation, using a single-color laser. This technique is applicable to most nonlinear as well as some linear point-scanning optical microscopies.
Opsin stability and folding: modulation by phospholipid bicelles.
McKibbin, Craig; Farmer, Nicola A; Jeans, Chris; Reeves, Philip J; Khorana, H Gobind; Wallace, B A; Edwards, Patricia C; Villa, Claudio; Booth, Paula J
2007-12-14
Integral membrane proteins do not fare well when extracted from biological membranes and are unstable or lose activity in detergents commonly used for structure and function investigations. We show that phospholipid bicelles provide a valuable means of preserving alpha-helical membrane proteins in vitro by supplying a soluble lipid bilayer fragment. Both 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC)/3-[(cholamidopropyl)dimethyl-ammonio]-1-propane sulfonate (Chaps) and DMPC/l-alpha-1,2-dihexanoyl-sn-glycero-3-phosphocholine (DHPC) bicelles dramatically increase the stability of the mammalian vision receptor rhodopsin as well as its apoprotein, opsin. Opsin is particularly unstable in detergent solution but can be directly purified into DMPC/Chaps. We show that opsin can also be directly purified in DMPC/DHPC bicelles to give correctly folded functional opsin, as shown by the ability to regenerate rhodopsin to approximately 70% yield. These well-characterised DMPC/DHPC bicelles enable us to probe the influence of bicelle properties on opsin stability. These bicelles are thought to provide DMPC bilayer fragments with most DHPC capping the bilayer edge, giving a soluble bilayer disc. Opsin stability is shown to be modulated by the q value, the ratio of DMPC to DHPC, which reflects changes in the bicelle size and, thus, proportion of DMPC bilayer present. The observed changes in stability also correlate with loss of opsin secondary structure as determined by synchrotron far-UV circular dichroism spectroscopy; the most stable bicelle results in the least helix loss. The inclusion of Chaps rather than DHPC in the DMPC/Chaps bicelles, however, imparts the greatest stability. This suggests that it is not just the DMPC bilayer fragment in the bicelles that stabilises the protein, but that Chaps provides additional stability either through direct interaction with the protein or by altering the DMPC/Chaps bilayer properties within the bicelle. The significant stability
UNCONDITIONAL NONLINEAR EXPONENTIAL STABILITY OF THE MOTIONLESS CONDUCTION-DIFFUSION SOLUTION
Institute of Scientific and Technical Information of China (English)
许兰喜
2000-01-01
Nonlinear stability of the motionless state of a heterogeneous fluid with constant temperature-gradient and concentration-gradient is studied for both cases of stress-free and rigid boundary conditions. By introducing new energy functionals we have shown that for τ = PC/PT _＜ 1, α = C/R ＞ 1 the motionless state is always stable and for τ＜ 1, α ＜ 1 the sufficient and necessary conditions for stability coincide, where PC, PT, C and R are the Schmidt number, Prandtl number,Rayleigh number for solute and heat, respectively. Moreover, the criteria guarantees the exponential stability.
Directory of Open Access Journals (Sweden)
Kanit Mukdasai
2012-01-01
Full Text Available This paper investigates the problem of robust exponential stability for linear parameter-dependent (LPD systems with discrete and distributed time-varying delays and nonlinear perturbations. Parameter dependent Lyapunov-Krasovskii functional, Leibniz-Newton formula, and linear matrix inequality are proposed to analyze the stability. On the basis of the estimation and by utilizing free-weighting matrices, new delay-dependent exponential stability criteria are established in terms of linear matrix inequalities (LMIs. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.
Model Predictive Control of Nonlinear Systems: Stability Region and Feasible Initial Control
Institute of Scientific and Technical Information of China (English)
Xiao-Bing Hu; Wen-Hua Chen
2007-01-01
This paper proposes a new method for model predictive control (MPC) of nonlinear systems to calculate stability region and feasible initial control profile/sequence, which are important to the implementations of MPC. Different from many existing methods,this paper distinguishes stability region from conservative terminal region. With global linearization, linear differential inclusion (LDI)and linear matrix inequality (LMI) techniques, a nonlinear system is transformed into a convex set of linear systems, and then the vertices of the set are used off-line to design the controller, to estimate stability region, and also to determine a feasible initial control profile/sequence. The advantages of the proposed method are demonstrated by simulation study.
Zamani, Iman; Shafiee, Masoud; Ibeas, Asier
2014-05-01
The issue of exponential stability of a class of continuous-time switched nonlinear singular systems consisting of a family of stable and unstable subsystems with time-varying delay is considered in this paper. Based on the free-weighting matrix approach, the average dwell-time approach and by constructing a Lyapunov-like Krasovskii functional, delay-dependent sufficient conditions are derived and formulated to check the exponential stability of such systems in terms of linear matrix inequalities (LMIs). By checking the corresponding LMI conditions, the average dwell-time and switching signal conditions are obtained. This paper also highlights the relationship between the average dwell-time of the switched nonlinear singular time-delay system, its stability and the exponential convergence rate of differential and algebraic states. A numerical example shows the effectiveness of the proposed method.
Colburn, B. K.; Boland, J. S., III
1976-01-01
A new nonlinear stability criterion is developed by use of a class of Lyapunov functionals for model-reference adaptive systems (MRAS). Results are compared with traditional results, and a comparative design technique is used to illustrate its function in improving the transient response of an MRAS controller. For a particular system structure and class of input signals, the new stability criterion is shown to include traditional sufficiency stability conditions as a special case. An example is cited to illustrate the use of the nonlinear criterion and its definite advantages in helping improve the adaptive error transient response of a system. Analysis of results is effected by use of a linearization technique on the resulting adaptive equations.
Stability and nonlinear regimes of flow over a saturated porous medium
Directory of Open Access Journals (Sweden)
T. P. Lyubimova
2013-07-01
Full Text Available The paper deals with the investigation of stability and nonlinear regimes of flow over the saturated porous medium applied to the problem of stability of water flow over the bottom covered with vegetation. It is shown that the velocity profile of steady plane-parallel flow has two inflection points, which results in instability of this flow. The neutral stability curves, the dependencies of critical Reynolds number and the wave number of most dangerous perturbations on the ratio of porous layer thickness to the total thickness are obtained. The nonlinear flow regimes are investigated numerically by finite difference method. It is found that at supercritical parameter values waves travelling in the direction of the base flow take place.
A steady-state solver and stability calculator for nonlinear internal wave flows
Viner, Kevin C.; Epifanio, Craig C.; Doyle, James D.
2013-10-01
A steady solver and stability calculator is presented for the problem of nonlinear internal gravity waves forced by topography. Steady-state solutions are obtained using Newton's method, as applied to a finite-difference discretization in terrain-following coordinates. The iteration is initialized using a boundary-inflation scheme, in which the nonlinearity of the flow is gradually increased over the first few Newton steps. The resulting method is shown to be robust over the full range of nonhydrostatic and rotating parameter space. Examples are given for both nonhydrostatic and rotating flows, as well as flows with realistic upstream shear and static stability profiles. With a modest extension, the solver also allows for a linear stability analysis of the steady-state wave fields. Unstable modes are computed using a shifted-inverse method, combined with a parameter-space search over a set of realistic target values. An example is given showing resonant instability in a nonhydrostatic mountain wave.
Colburn, B. K.; Boland, J. S., III
1976-01-01
A new nonlinear stability criterion is developed by use of a class of Lyapunov functionals for model-reference adaptive systems (MRAS). Results are compared with traditional results, and a comparative design technique is used to illustrate its function in improving the transient response of an MRAS controller. For a particular system structure and class of input signals, the new stability criterion is shown to include traditional sufficiency stability conditions as a special case. An example is cited to illustrate the use of the nonlinear criterion and its definite advantages in helping improve the adaptive error transient response of a system. Analysis of results is effected by use of a linearization technique on the resulting adaptive equations.
Dynamic nonlinear focal shift in amplitude modulated moderately focused acoustic beams.
Jiménez, Noé; Camarena, Francisco; González-Salido, Nuria
2017-03-01
The phenomenon of the displacement of the position of the pressure, intensity and acoustic radiation force maxima along the axis of focused acoustic beams under increasing driving amplitudes (nonlinear focal shift) is studied for the case of a moderately focused beam excited with continuous and 25kHz amplitude modulated signals, both in water and tissue. We prove that in amplitude modulated beams the linear and nonlinear propagation effects coexist in a semi-period of modulation, giving place to a complex dynamic behavior, where the singular points of the beam (peak pressure, rarefaction, intensity and acoustic radiation force) locate at different points on axis as a function of time. These entire phenomena are explained in terms of harmonic generation and absorption during the propagation in a lossy nonlinear medium both for a continuous and an amplitude modulated beam. One of the possible applications of the acoustic radiation force displacement is the generation of shear waves at different locations by using a focused mono-element transducer excited by an amplitude modulated signal.
Nonlinear Slewing Spacecraft Control Based on Exergy, Power Flow, and Static and Dynamic Stability
Robinett, Rush D.; Wilson, David G.
2009-10-01
This paper presents a new nonlinear control methodology for slewing spacecraft, which provides both necessary and sufficient conditions for stability by identifying the stability boundaries, rigid body modes, and limit cycles. Conservative Hamiltonian system concepts, which are equivalent to static stability of airplanes, are used to find and deal with the static stability boundaries: rigid body modes. The application of exergy and entropy thermodynamic concepts to the work-rate principle provides a natural partitioning through the second law of thermodynamics of power flows into exergy generator, dissipator, and storage for Hamiltonian systems that is employed to find the dynamic stability boundaries: limit cycles. This partitioning process enables the control system designer to directly evaluate and enhance the stability and performance of the system by balancing the power flowing into versus the power dissipated within the system subject to the Hamiltonian surface (power storage). Relationships are developed between exergy, power flow, static and dynamic stability, and Lyapunov analysis. The methodology is demonstrated with two illustrative examples: (1) a nonlinear oscillator with sinusoidal damping and (2) a multi-input-multi-output three-axis slewing spacecraft that employs proportional-integral-derivative tracking control with numerical simulation results.
Arshad, M.; Seadawy, Aly R.; Lu, Dianchen
2017-08-01
The higher-order nonlinear Schrödinger equation (NLSE) with fourth-order dispersion, cubic-quintic terms, self-steepening and nonlinear dispersive terms describes the propagation of extremely short pulses in optical fibers. In this paper, the elliptic function, bright and dark solitons and solitary wave solutions of higher-order NLSE are constructed by employing a modified extended direct algebraic method, which has important applications in applied mathematics and physics. Furthermore, we also present the formation conditions of the bright and dark solitons for this equation. The modulation instability is utilized to discuss the stability of these solutions, which shows that all solutions are exact and stable. Many other higher-order nonlinear evolution equations arising in applied sciences can also be solved by this powerful, effective and reliable method.
Negative Kerr nonlinearity of graphene as seen via chirped-pulse-pumped self-phase modulation
Vermeulen, Nathalie; Cheng, JinLuo; Pasternak, Iwona; Krajewska, Aleksandra; Ciuk, Tymoteusz; Strupinski, Wlodek; Thienpont, Hugo; Van Erps, Jurgen
2016-01-01
We experimentally demonstrate a negative Kerr nonlinearity for quasi-undoped graphene. Hereto, we introduce the method of chirped-pulse-pumped self-phase modulation and apply it to graphene-covered silicon waveguides at telecom wavelengths. The extracted Kerr-nonlinear index for graphene equals n2,gr = -10^(-13) m^2/W. Whereas the sign of n2,gr turns out to be negative in contrast to what has been assumed so far, its magnitude is in correspondence with that observed in earlier experiments. Graphene's negative Kerr nonlinearity strongly impacts how graphene should be exploited for enhancing the nonlinear response of photonic (integrated) devices exhibiting a positive nonlinearity. It also opens up the possibility of using graphene to annihilate unwanted nonlinear effects in such devices, to develop unexplored approaches for establishing Kerr processes, and to extend the scope of the "periodic poling" method often used for second-order nonlinearities towards third-order Kerr processes. Because of the generic na...
Non-linear modulation of short wavelength compressional Alfven eigenmodes
Energy Technology Data Exchange (ETDEWEB)
Fredrickson, E. D.; Gorelenkov, N. N.; Podesta, M.; Gerhardt, S. P.; Bell, R. E.; Diallo, A.; LeBlanc, B. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543 (United States); Bortolon, A. [University of California, Irvine, California 92697 (United States); Crocker, N. A. [University of California, Los Angeles, California 90095 (United States); Levinton, F. M.; Yuh, H. [Nova Photonics, Princeton, New Jersey 08543 (United States)
2013-04-15
Most Alfvenic activity in the frequency range between toroidal Alfven eigenmodes and roughly one half of the ion cyclotron frequency on National Spherical Torus eXperiment [Ono et al., Nucl. Fusion 40, 557 (2000)], that is, approximately 0.3 MHz up to Almost-Equal-To 1.2 MHz, are modes propagating counter to the neutral beam ions. These have been modeled as Compressional and Global Alfven Eigenmodes (CAE and GAE) and are excited through a Doppler-shifted cyclotron resonance with the beam ions. There is also a class of co-propagating modes at higher frequency than the counter-propagating CAE and GAE. These modes have been identified as CAE, and are seen mostly in the company of a low frequency, n = 1 kink-like mode. In this paper, we present measurements of the spectrum of these high frequency CAE (hfCAE) and their mode structure. We compare those measurements to a simple model of CAE and present a predator-prey type model of the curious non-linear coupling of the hfCAE and the low frequency kink-like mode.
Masuda, Arata; Sato, Takeru
2016-04-01
This paper presents an experimental verification of a wideband nonlinear vibration energy harvester which has a globally stabilized high-energy resonating response. For the conventional linear vibration energy harvester, the maximum performance of the power generation and its bandwidth are in a relation of trade-off. The resonance frequency band can be expanded by introducing a Duffing-type nonlinear resonator in order to enable the harvester to generate larger electric power in a wider frequency range. However, since such nonlinear resonators often have multiple stable steady-state solutions in the resonance band, it is diﬃcult for the nonlinear harvester to maintain the high performance of the power generation constantly. The principle of self-excitation and entrainment has been utilized to provide the global stability to the highest-energy solution by destabilizing other unexpected lower-energy solutions by introducing a switching circuit of the load resistance between positive and the negative values depending on the response amplitude of the oscillator. In this study, an experimental verification of this concept are carried out. An experimental prototype harvester is designed and fabricated and the performance of the proposed harvester is experimentally verified. It has been shown that the numerical and experimental results agreed very well, and the highest-energy solutions above the threshold value were successfully stabilized globally.
Geometrical Nonlinear Aeroelastic Stability Analysis of a Composite High-Aspect-Ratio Wing
Directory of Open Access Journals (Sweden)
Chang Chuan Xie
2008-01-01
Full Text Available A composite high-aspect-ratio wing of a high-altitude long-endurance (HALE aircraft was modeled with FEM by MSC/NASTRAN, and the nonlinear static equilibrium state is calculated under design load with follower force effect, but without load redistribution. Assuming the little vibration amplitude of the wing around the static equilibrium state, the system is linearized and the natural frequencies and mode shapes of the deformed structure are obtained. Planar doublet lattice method is used to calculate unsteady aerodynamics in frequency domain ignoring the bending effect of the deflected wing. And then, the aeroelastic stability analysis of the system under a given load condition is successively carried out. Comparing with the linear results, the nonlinear displacement of the wing tip is higher. The results indicate that the critical nonlinear flutter is of the flap/chordwise bending type because of the chordwise bending having quite a large torsion component, with low critical speed and slowly growing damping, which dose not appear in the linear analysis. Furthermore, it is shown that the variation of the nonlinear flutter speed depends on the scale of the load and on the chordwise bending frequency. The research work indicates that, for the very flexible HALE aircraft, the nonlinear aeroelastic stability is very important, and should be considered in the design progress. Using present FEM software as the structure solver (e.g. MSC/NASTRAN, and the unsteady aerodynamic code, the nonlinear aeroelastic stability margin of a complex system other than a simple beam model can be determined.
Carrier frequency modulation of an acousto-optic modulator for laser stabilization.
Aldous, Matthew; Woods, Jonathan; Dragomir, Andrei; Roy, Ritayan; Himsworth, Matt
2017-05-29
The stabilization of lasers to absolute frequency references is a fundamental requirement in several areas of atomic, molecular and optical physics. A range of techniques are available to produce a suitable reference onto which one can 'lock' the laser, many of which depend on the specific internal structure of the reference or are sensitive to laser intensity noise. We present a novel method using the frequency modulation of an acousto-optic modulator's carrier (drive) signal to generate two spatially separated beams, with a frequency difference of only a few MHz. These beams are used to probe a narrow absorption feature and the difference in their detected signals leads to a dispersion-like feature suitable for wavelength stabilization of a diode laser. This simple and versatile method only requires a narrow absorption line and is therefore suitable for both atomic and cavity based stabilization schemes. To demonstrate the suitability of this method we lock an external cavity diode laser near the (85)Rb 5S1/2 → 5P3/2, F = 3 → F' = 4 using sub-Doppler pump probe spectroscopy and also demonstrate excellent agreement between the measured signal and a theoretical model.
Directory of Open Access Journals (Sweden)
Wu Huaiqin
2009-01-01
Full Text Available This paper considers a new class of additive neural networks where the neuron activations are modelled by discontinuous functions with nonlinear growth. By Leray-Schauder alternative theorem in differential inclusion theory, matrix theory, and generalized Lyapunov approach, a general result is derived which ensures the existence and global asymptotical stability of a unique periodic solution for such neural networks. The obtained results can be applied to neural networks with a broad range of activation functions assuming neither boundedness nor monotonicity, and also show that Forti's conjecture for discontinuous neural networks with nonlinear growth activations is true.
Evolutions of matter-wave bright soliton with spatially modulated nonlinearity
Institute of Scientific and Technical Information of China (English)
Yongshan Cheng; Fei Liu
2009-01-01
The evolution characteristics of a matter-wave bright soliton are investigated by means of the variational approach in the presence of spatially varying nonlinearity.It is found that the atom density envelope of the soliton is changed as a result of the spatial variation of the s-wave scattering length.The stable soliton can exist in appropriate initial conditions.The movement of the soliton depends on the sign and value of the coefficient of spatially modulated nonlinearity.These theoretical predictions are confirmed by the full numerical simulations of the one-dimensional Gross-Pitaevskii equation.
Observation of spectral self-imaging by nonlinear parabolic cross-phase modulation.
Lei, Lei; Huh, Jeonghyun; Cortés, Luis Romero; Maram, Reza; Wetzel, Benjamin; Duchesne, David; Morandotti, Roberto; Azaña, José
2015-11-15
We report an experimental demonstration of spectral self-imaging on a periodic frequency comb induced by a nonlinear all-optical process, i.e., parabolic cross-phase modulation in a highly nonlinear fiber. The comb free spectral range is reconfigured by simply tuning the temporal period of the pump parabolic pulse train. In particular, undistorted FSR divisions by factors of 2 and 3 are successfully performed on a 10 GHz frequency comb, realizing new frequency combs with an FSR of 5 and 3.3 GHz, respectively. The pump power requirement associated to the SSI phenomena is also shown to be significantly relaxed by the use of dark parabolic pulses.
Magri, Luca; Juniper, Matthew
2016-01-01
We present an adjoint-based method for the calculation of eigenvalue perturbations in nonlinear, degenerate and non self-adjoint eigenproblems. This method is applied to a thermo-acoustic annular combustor network, the stability of which is governed by a nonlinear eigenproblem. We calculate the first- and second-order sensitivities of the growth rate and frequency to geometric, flow and flame parameters. Three different configurations are analysed. The benchmark sensitivities are obtained by finite difference, which involves solving the nonlinear eigenproblem at least as many times as the number of parameters. By solving only one adjoint eigenproblem, we obtain the sensitivities to any thermo-acoustic parameter, which match the finite-difference solutions at much lower computational cost.
Institute of Scientific and Technical Information of China (English)
潘子刚; 刘允刚; 施颂椒
2001-01-01
In this paper, we study the problem of output feedback stabilization for stochastic nonlinear systems. We consider a class of stochastic nonlinear systems in observer canonical form with stable zero-dynamics. We introduce a sequence of state transformations that transform the system into a lower triangular structure that is amenable for integrator backstepping design. Then we design the output-feedback controller and prove that the closed-loop system is bounded in probability. Furthermore, when the disturbance vector field vanishes at the origin, the closed-loop system is asymptotically stable in the large. With special care, the controller preserves the equilibrium of the nonlinear system. An example is included to illustrate the theoretical findings.
Energy analysis of stability of twin shallow tunnels based on nonlinear failure criterion
Institute of Scientific and Technical Information of China (English)
张佳华; 许敬叔; 张标
2014-01-01
Based on nonlinear Mohr−Coulomb failure criterion, the analytical solutions of stability number and supporting force on twin shallow tunnels were derived using upper bound theorem of limit analysis. The optimized solutions were obtained by the technique of sequential quadratic programming. When nonlinear coefficient equals 1 and internal friction angle equals 0, the nonlinear Mohr−Coulomb failure criterion degenerates into linear failure criterion. The calculated results of stability number in this work were compared with previous results, and the agreement verifies the effectiveness of the present method. Under the condition of nonlinear Mohr−Coulomb failure criterion, the results show that the supporting force on twin shallow tunnels obviously increases when the nonlinear coefficient, burial depth, ground load or pore water pressure coefficients increase. When the clear distance is 0.5 to 1.0 times the diameter of tunnel, the supporting force of twin shallow tunnels reaches its maximum value, which means that the tunnels are the easiest to collapse. While the clear distance increases to 3.5 times the diameter of tunnel, the calculation for twin shallow tunnels can be carried out by the method for independent single shallow tunnel. Therefore, 3.5 times the diameter of tunnel serves as a critical value to determine whether twin shallow tunnels influence each other. In designing twin shallow tunnels, appropriate clear distance value must be selected according to its change rules and actual topographic conditions, meanwhile, the influences of nonlinear failure criterion of soil materials and pore water must be completely considered. During the excavation process, supporting system should be intensified at the positions of larger burial depth or ground load to avoid collapses.
Phase stabilization of Kerr frequency comb internally without nonlinear optical interferometry
Huang, S -W; Yang, J; Yu, M; Kwong, D -L; Wong, C W
2016-01-01
Optical frequency comb (OFC) technology has been the cornerstone for scientific breakthroughs such as precision frequency metrology, redefinition of time, extreme light-matter interaction, and attosecond sciences. While the current mode-locked laser-based OFC has had great success in extending the scientific frontier, its use in real-world applications beyond the laboratory setting remains an unsolved challenge. Microresonator-based OFCs, or Kerr frequency comb, have recently emerged as a candidate solution to the challenge because of their preferable size, weight, and power consumption (SWaP). On the other hand, the current phase stabilization technology requires either external optical references or power-demanding nonlinear processes, overturning the SWaP benefit of Kerr frequency combs. Introducing a new concept in phase control, here we report an internally phase stabilized Kerr frequency comb without the need of any optical references or nonlinear processes. We describe the comb generation analytically ...
A conformal approach for the analysis of the non-linear stability of radiation cosmologies
Energy Technology Data Exchange (ETDEWEB)
Luebbe, Christian, E-mail: c.luebbe@ucl.ac.uk [Department of Mathematics, University College London, Gower Street, London, WC1E 6BT (United Kingdom); Department of Mathematics, University of Leicester, University Road, LE1 8RH (United Kingdom); Valiente Kroon, Juan Antonio, E-mail: j.a.valiente-kroon@qmul.ac.uk [School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS (United Kingdom)
2013-01-15
The conformal Einstein equations for a trace-free (radiation) perfect fluid are derived in terms of the Levi-Civita connection of a conformally rescaled metric. These equations are used to provide a non-linear stability result for de Sitter-like trace-free (radiation) perfect fluid Friedman-Lemaitre-Robertson-Walker cosmological models. The solutions thus obtained exist globally towards the future and are future geodesically complete. - Highlights: Black-Right-Pointing-Pointer We study the Einstein-Euler system in General Relativity using conformal methods. Black-Right-Pointing-Pointer We analyze the structural properties of the associated evolution equations. Black-Right-Pointing-Pointer We establish the non-linear stability of pure radiation cosmological models.
Nonlinear {omega}*-stabilization of the m = 1 mode in tokamaks
Energy Technology Data Exchange (ETDEWEB)
Rogers, B. [Univ. of Maryland, College Park, MD (United States). Inst. for Plasma Research; Zakharov, L. [Princeton Univ., NJ (United States). Plasma Physics Lab.
1995-08-01
Earlier studies of sawtooth oscillations in Tokamak Fusion Test Reactor supershots (Levinton et al, Phys. Rev. Lett. 72, 2895 (1994); Zakharov, et al, Plasma Phys. and Contr. Nucl. Fus. Res., Proc. 15th Int. Conf., Seville 1994, Vienna) have found an apparent contradiction between conventional linear theory and experiment: even in sawtooth-free discharges, the theory typically predicts instability due to a nearly ideal m = 1 mode. Here, the nonlinear evolution of such mode is analyzed using numerical simulations of a two-fluid magnetohydrodynamic (MHD) model. We find the mode saturates nonlinearly at a small amplitude provided the ion and electron drift-frequencies {omega}*{sub i,e} are somewhat above the linear stability threshold of the collisionless m = 1 reconnecting mode. The comparison of the simulation results to m = 1 mode activity in TFTR suggests additional, stabilizing effects outside the present model are also important.
Directory of Open Access Journals (Sweden)
Huang Tingwen
2009-01-01
Full Text Available This paper studies the exponential stability of a class of periodically time-switched nonlinear systems. Three cases of such systems which are composed, respectively, of a pair of unstable subsystems, of both stable and unstable subsystems, and of a pair of stable systems, are considered. For the first case, the proposed result shows that there exists periodically switching rule guaranteeing the exponential stability of the whole system with (sufficient small switching period if there is a Hurwitz linear convex combination of two uncertain linear systems derived from two subsystems by certain linearization. For the second case, we present two general switching criteria by means of multiple and single Lyapunov function, respectively. We also investigate the stability issue of the third case, and the switching criteria of exponential stability are proposed. The present results for the second case are further applied to the periodically intermittent control. Several numerical examples are also given to show the effectiveness of theoretical results.
Sinou, Jean-Jacques; Thouverez, Fabrice; Jezequel, Louis
2006-01-01
International audience; Herein, a novel non-linear procedure for producing non-linear behaviour and stable limit cycle amplitudes of non-linear systems subjected to super-critical Hopf bifurcation point is presented. This approach, called Complex Non-Linear Modal Analysis (CNLMA), makes use of the non-linear unstable mode which governs the non-linear dynamic of structural systems in unstable areas. In this study, the computational methodology of CNLMA is presented for the systematic estimatio...
Institute of Scientific and Technical Information of China (English)
LIU Yungang; ZHANG Jifeng
2004-01-01
A minimal-order observer and output-feedback stabilization control are given for single-input multi-output stochastic nonlinear systems with unobservable states, unmodelled dynamics and stochastic disturbances. Based on the observer designed, the estimates of all observable states of the system are given, and the convergence of the estimation errors are analyzed. In addition, by using the integrator backstepping approach,an output-feedback stabilization control is constructively designed, and sufficient conditions are obtained under which the closed-loop system is asymptotically stable in the large or bounded in probability, respectively.
Institute of Scientific and Technical Information of China (English)
Weihai ZHANG; Xuezhen LIU; Shulan KONG; Qinghua LI
2006-01-01
This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally (globally) robustly stabilizable conditions are given in terms of matrix inequalities that are independent of the delay size. When it is applied to linear stochastic time-delay systems, sufficient conditions for the state-feedback stabilization are presented via linear matrix inequalities. Several previous results are extended to more general systems with both state and control-dependent noise, and easy computation algorithms are also given.
Directory of Open Access Journals (Sweden)
Xia Zhou
2013-01-01
Full Text Available The problem of bounded-input bounded-output (BIBO stabilization in mean square for a class of discrete-time stochastic control systems with mixed time-varying delays and nonlinear perturbations is investigated. Some novel delay-dependent stability conditions for the previously mentioned system are established by constructing a novel Lyapunov-Krasovskii function. These conditions are expressed in the forms of linear matrix inequalities (LMIs, whose feasibility can be easily checked by using MATLAB LMI Toolbox. Finally, a numerical example is given to illustrate the validity of the obtained results.
Nonlinear theory of combustion stability in liquid rocket engine based on chemistry dynamics
Institute of Scientific and Technical Information of China (English)
黄玉辉; 王振国; 周进
2002-01-01
Detailed models of combustion instability based on chemistry dynamics are developed. The results show that large activation energy goes against the combustion stability. The heat transfer coefficient between the wall and the combust gas is an important bifurcation parameter for the combustion instability. The acoustics modes of the chamber are in competition and cooperation with each other for limited vibration energy. Thermodynamics criterion of combustion stability can be deduced from the nonlinear thermodynamics. Correlations of the theoretical results and historical experiments indicate that chemical kinetics play a critical role in the combustion instability.
Global Stabilization of High-Order Time-Delay Nonlinear Systems under a Weaker Condition
Directory of Open Access Journals (Sweden)
Nengwei Zhang
2014-01-01
Full Text Available Under the weaker condition on the system growth, this paper further investigates the problem of global stabilization by state feedback for a class of high-order nonlinear systems with time-varying delays. By skillfully using the homogeneous domination approach, a continuous state feedback controller is successfully designed, which preserves the equilibrium at the origin and guarantees the global asymptotic stability of the resulting closed-loop system. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.
Sequences of nonlinear contractions and stability of fi xed points
Directory of Open Access Journals (Sweden)
Swaminath Mishra
2012-09-01
Full Text Available Stability of fixed points for sequences of nonlinear contractions over a variable domain is studied in a 2-metric space. The results so obtained generalize some recent results of Mishra et al. [Chaos, Soliton & Fractals 45(2012, 1012-1016] and Barbet and Nachi [Monografias del Seminario Matemático García de Galdeano 33(2006, 51--58].
Keshtkar, F.; Erjaee, G.; Boutefnouchet, M.
2014-01-01
In this article, a brief stability analysis of equilibrium points in nonlinear fractional order dynamical systems is given. Then, based on the first integral concept, a definition of planar Hamiltonian systems with fractional order introduced. Some interesting properties of these fractional Hamiltonian systems are also presented. Finally, we illustrate two examples to see the differences between fractional Hamiltonian systems with their classical order counterparts. NPRP . Grant Number: NP...
Nonlinear Stability of Intense Mismatched Beams in a Uniform Focusing Field
Pakter, Renato; Simeoni, Wilson
2005-01-01
We investigate the nonlinear coupling between axisymmetric and elliptic oscillations in the dynamics of intense beams propagating in a uniform magnetic focusing field. It is shown that finite amplitude mismatched oscillations of an initially round beam may destabilize elliptic oscillations, heavily affecting stability and the shape of the beam. This is a potential mechanics for beam particle loss in such systems. Self consistent simulations are performed to verify the findings.
Stability of Nonlinear Systems with Unknown Time-varying Feedback Delay
Chunodkar, Apurva A.; Akella, Maruthi R.
2013-12-01
This paper considers the problem of stabilizing a class of nonlinear systems with unknown bounded delayed feedback wherein the time-varying delay is 1) piecewise constant 2) continuous with a bounded rate. We also consider application of these results to the stabilization of rigid-body attitude dynamics. In the first case, the time-delay in feedback is modeled specifically as a switch among an arbitrarily large set of unknown constant values with a known strict upper bound. The feedback is a linear function of the delayed states. In the case of linear systems with switched delay feedback, a new sufficiency condition for average dwell time result is presented using a complete type Lyapunov-Krasovskii (L-K) functional approach. Further, the corresponding switched system with nonlinear perturbations is proven to be exponentially stable inside a well characterized region of attraction for an appropriately chosen average dwell time. In the second case, the concept of the complete type L-K functional is extended to a class of nonlinear time-delay systems with unknown time-varying time-delay. This extension ensures stability robustness to time-delay in the control design for all values of time-delay less than the known upper bound. Model-transformation is used in order to partition the nonlinear system into a nominal linear part that is exponentially stable with a bounded perturbation. We obtain sufficient conditions which ensure exponential stability inside a region of attraction estimate. A constructive method to evaluate the sufficient conditions is presented together with comparison with the corresponding constant and piecewise constant delay. Numerical simulations are performed to illustrate the theoretical results of this paper.
Institute of Scientific and Technical Information of China (English)
Xiaowu MU; Haijun LIU
2007-01-01
In this paper,a state feedback adaptive stabilization for a class of large-scale stochastic nonlinear systems is designed with Lyapunov and Backstepping method.In the systems there are uncertain terms,whose bounds are governed by a set of unknown parameters.The designed controllers would make the close-loop systems asymptotically stable and adaptive for the unknown parameters.As an application,a second order example is delivered to illustrate the approach.
Global Stability and Dynamics of Strongly Nonlinear Systems Using Koopman Operator Theory
2017-03-01
calculus, applied mathematics, Director’s Research Initiative 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT UU 18...ARL-TR-7959 MAR 2017 US Army Research Laboratory Global Stability and Dynamics of Strongly Nonlinear Systems Using Koopman...report when it is no longer needed. Do not return it to the originator. ARL-TR-7959 ● MAR 2017 US Army Research Laboratory Global
Nungesser, Ernesto
2014-01-01
We show future global non-linear stability of surface symmetric solutions of the Einstein-Vlasov system with a positive cosmological constant. Estimates of higher derivatives of the metric and the matter terms are obtained using an inductive argument. In a recent research monograph Ringstr\\"{o}m shows future non-linear stability of (not necessarily symmetric) solutions of the Einstein-Vlasov system with a non-linear scalar field if certain local estimates on the geometry and the matter terms are fulfilled. We show that these assumptions are satisfied at late times for the case under consideration here which together with Cauchy stability leads to our main conclusion.
Modulational Instability in a Pair of Non-identical Coupled Nonlinear Electrical Transmission Lines
Institute of Scientific and Technical Information of China (English)
Eric Tala-Tebue; Aurelien Kenfack-Jiotsa; Marius Hervé Tatchou-Ntemfack; Timoléon Crépin Kofané
2013-01-01
In this work,we investigate the dynamics of modulated waves non-identical coupled nonlinear transmission lines.Traditional methods for avoiding mode mixing in identical coupled nonlinear electrical lines consist of adding the same number of linear inductors in each branch.Adding linear inductors in a single line leads to asymmetric coupled nonlinear electrical transmission lines which propagate the signal and the mode mixing.On one hand,the difference between the two lines induced the fission for only one mode of propagation.This fission is influenced by the amplitude of the signal and the amount of the input energy as well; it also narrows the width of the input pulse soliton,leading to a possible increasing of the bit rate.On the other hand,the dissymmetry of the two lines converts the network into a good amplifier for the w_ mode which corresponds to the regime admitting low frequencies.
Lim, Hyung Jin; Sohn, Hoon; DeSimio, Martin P.; Brown, Kevin
2014-04-01
This study presents a reference-free fatigue crack detection technique using nonlinear ultrasonic modulation. When low frequency (LF) and high frequency (HF) inputs generated by two surface-mounted lead zirconate titanate (PZT) transducers are applied to a structure, the presence of a fatigue crack can provide a mechanism for nonlinear ultrasonic modulation and create spectral sidebands around the frequency of the HF signal. The crack-induced spectral sidebands are isolated using a combination of linear response subtraction (LRS), synchronous demodulation (SD) and continuous wavelet transform (CWT) filtering. Then, a sequential outlier analysis is performed on the extracted sidebands to identify the crack presence without referring any baseline data obtained from the intact condition of the structure. Finally, the robustness of the proposed technique is demonstrated using actual test data obtained from simple aluminum plate and complex aircraft fitting-lug specimens under varying temperature and loading variations.
Skidin, Anton S; Sidelnikov, Oleg S; Fedoruk, Mikhail P; Turitsyn, Sergei K
2016-12-26
The impact of the fiber Kerr effect on error statistics in the nonlinear (high power) transmission of the OFDM 16-QAM signal over a 2000 km EDFA-based link is examined. We observed and quantified the difference in the error statistics for constellation points located at three power-defined rings. Theoretical analysis of a trade-off between redundancy and error rate reduction using probabilistic coding of three constellation power rings decreasing the symbol-error rate of OFDM 16-QAM signal is presented. Based on this analysis, we propose to mitigate the nonlinear impairments using the adaptive modulation technique applied to the OFDM 16-QAM signal. We demonstrate through numerical modelling the system performance improvement by the adaptive modulation for the large number of OFDM subcarriers (more than 100). We also show that a similar technique can be applied to single carrier transmission.
Nariyuki, Y; Nariyuki, Yasuhiro; Hada, Tohru
2006-01-01
Nonlinear relations among frequencies and phases in modulational instability of circularly polarized Alfven waves are discussed, within the context of one dimensional, dissipation-less, unforced fluid system. We show that generation of phase coherence is a natural consequence of the modulational instability of Alfven waves. Furthermore, we quantitatively evaluate intensity of wave-wave interaction by using bi-coherence, and also by computing energy flow among wave modes, and demonstrate that the energy flow is directly related to the phase coherence generation.
Omura, J. K.; Simon, M. K.
1982-01-01
A theory for deducing and predicting the performance of transmitter/receivers for bandwidth efficient modulations suitable for use on the nonlinear satellite channel is presented. The underlying principle used throughout is the development of receiver structures based on the maximum likelihood decision rule and aproximations to it. The bit error probability transfer function bounds developed in great detail in Part 4 is applied to these modulation/demodulation techniques. The effects of the various degrees of receiver mismatch are considered both theoretically and by numerous illustrative examples.
Kartashov, Yaroslav V
2014-01-01
We study specific features of resonant mode conversion in nonlinear waveguides stimulated by the bi-harmonic longitudinal modulation of its parameters, which includes changes of the waveguide depth as well as its bending (in the one-dimensional case) or spiraling (in the two-dimensional case). We demonstrate the possibility of simultaneous excitation of higher-order modes of different parities and topologies with controllable energy weights. The output mode composition is highly sensitive to the variation in the input power and detuning from the resonant modulation frequency.
Periodic modulations controlling Kuznetsov–Ma soliton formation in nonlinear Schrödinger equations
Energy Technology Data Exchange (ETDEWEB)
Tiofack, C.G.L., E-mail: glatchio@yahoo.fr [Univ. Lille, CNRS, UMR 8523 – PhLAM – Physique des Lasers Atomes et Molécules, F-59000 Lille (France); Coulibaly, S.; Taki, M. [Univ. Lille, CNRS, UMR 8523 – PhLAM – Physique des Lasers Atomes et Molécules, F-59000 Lille (France); De Bièvre, S.; Dujardin, G. [Univ. Lille, CNRS, UMR 8524 – Laboratoire Paul Painlevé, F-59000 Lille (France); Équipe-Projet Mephysto, INRIA Lille-Nord Europe (France)
2017-06-28
We analyze the exact Kuznetsov–Ma soliton solution of the one-dimensional nonlinear Schrödinger equation in the presence of periodic modulations satisfying an integrability condition. We show that, in contrast to the case without modulation, the Kuznetsov–Ma soliton develops multiple compression points whose number, shape and position are controlled both by the intensity of the modulation and by its frequency. In addition, when this modulation frequency is a rational multiple of the natural frequency of the Kuznetsov–Ma soliton, a scenario similar to a nonlinear resonance is obtained: in this case the spatial oscillations of the Kuznetsov–Ma soliton's intensity are periodic. When the ratio of the two frequencies is irrational, the soliton's intensity is a quasiperiodic function. A striking and important result of our analysis is the possibility to suppress any component of the output spectrum of the Kuznetsov–Ma soliton by a judicious choice of the amplitude and frequency of the modulation. - Highlights: • Exact Kuznetsov–Ma soliton solution in presence of periodic coefficients is obtained. • The multiple compression points of the solution are studied. • The quasi-periodicity of the solution is discussed. • The possibility to suppress any component of the spectrum is analyzed.
Femtojoule-Scale All-Optical Latching and Modulation via Cavity Nonlinear Optics
Kwon, Yeong-Dae; Armen, Michael A.; Mabuchi, Hideo
2013-11-01
We experimentally characterize Hopf bifurcation phenomena at femtojoule energy scales in a multiatom cavity quantum electrodynamical (cavity QED) system and demonstrate how such behaviors can be exploited in the design of all-optical memory and modulation devices. The data are analyzed by using a semiclassical model that explicitly treats heterogeneous coupling of atoms to the cavity mode. Our results highlight the interest of cavity QED systems for ultralow power photonic signal processing as well as for fundamental studies of mesoscopic nonlinear dynamics.
Improved stability and performance from sigma-delta modulators using 1-bit vector quantization
DEFF Research Database (Denmark)
Risbo, Lars
1993-01-01
A novel class of sigma-delta modulators is presented. The usual scalar 1-b quantizer in a sigma-delta modulator is replaced by a 1-b vector quantizer with a N-dimensional input state-vector from the linear feedback filter. Generally, the vector quantizer changes the nonlinear dynamics...
Arditi, Tal; Granot, Er'el; Sternklar, Shmuel
2007-09-15
Brillouin amplification with counterpropagating modulated pump and Stokes light leads to nonlinear modulation-phase shifts of the interacting intensity waves. This is due to a partial transformation of the nonmodulated light component at the input into modulated light at the output as a result of a mixing process with the counterpropagating modulated component of the pump and results in an advance or delay of the input modulation. This occurs for interactions over less than half of a modulation wavelength. Milliwatts of power in a kilometer of standard single-mode fiber give significant tunability of the modulation phase.
Linear and nonlinear stability analysis in BWRs applying a reduced order model
Energy Technology Data Exchange (ETDEWEB)
Olvera G, O. A.; Espinosa P, G.; Prieto G, A., E-mail: omar_olverag@hotmail.com [Universidad Autonoma Metropolitana, Unidad Iztapalapa, San Rafael Atlixco No. 186, Col. Vicentina, 09340 Ciudad de Mexico (Mexico)
2016-09-15
Boiling Water Reactor (BWR) stability studies are generally conducted through nonlinear reduced order models (Rom) employing various techniques such as bifurcation analysis and time domain numerical integration. One of those models used for these studies is the March-Leuba Rom. Such model represents qualitatively the dynamic behavior of a BWR through a one-point reactor kinetics, a one node representation of the heat transfer process in fuel, and a two node representation of the channel Thermal hydraulics to account for the void reactivity feedback. Here, we study the effect of this higher order model on the overall stability of the BWR. The change in the stability boundaries is determined by evaluating the eigenvalues of the Jacobian matrix. The nonlinear model is also integrated numerically to show that in the nonlinear region, the system evolves to stable limit cycles when operating close to the stability boundary. We also applied a new technique based on the Empirical Mode Decomposition (Emd) to estimate a parameter linked with stability in a BWR. This instability parameter is not exactly the classical Decay Ratio (Dr), but it will be linked with it. The proposed method allows decomposing the analyzed signal in different levels or mono-component functions known as intrinsic mode functions (Imf). One or more of these different modes can be associated to the instability problem in BWRs. By tracking the instantaneous frequencies (calculated through Hilbert Huang Transform (HHT) and the autocorrelation function (Acf) of the Imf linked to instability. The estimation of the proposed parameter can be achieved. The current methodology was validated with simulated signals of the studied model. (Author)
Chatterjee, Debjani; Misra, A P
2015-12-01
The nonlinear theory of amplitude modulation of electrostatic wave envelopes in a collisionless electron-positron (EP) pair plasma is studied by using a set of Vlasov-Poisson equations in the context of Tsallis' q-nonextensive statistics. In particular, the previous linear theory of Langmuir oscillations in EP plasmas [Saberian and Esfandyari-Kalejahi, Phys. Rev. E 87, 053112 (2013)] is rectified and modified. Applying the multiple scale technique (MST), it is shown that the evolution of electrostatic wave envelopes is governed by a nonlinear Schrödinger (NLS) equation with a nonlocal nonlinear term ∝P∫|ϕ(ξ',τ)|(2)dξ'ϕ/(ξ-ξ') [where P denotes the Cauchy principal value, ϕ is the small-amplitude electrostatic (complex) potential, and ξ and τ are the stretched coordinates in MST], which appears due to the wave-particle resonance. It is found that a subregion 1/3Landau damping) due to the nonlocal nonlinearity in the NLS equation. Furthermore, the effect of the nonlinear Landau damping is to slow down the amplitude of the wave envelope, and the corresponding decay rate can be faster the larger is the number of superthermal particles in pair plasmas.
Coward, Adrian V.; Papageorgiou, Demetrios T.; Smyrlis, Yiorgos S.
1994-01-01
In this paper the nonlinear stability of two-phase core-annular flow in a pipe is examined when the acting pressure gradient is modulated by time harmonic oscillations and viscosity stratification and interfacial tension is present. An exact solution of the Navier-Stokes equations is used as the background state to develop an asymptotic theory valid for thin annular layers, which leads to a novel nonlinear evolution describing the spatio-temporal evolution of the interface. The evolution equation is an extension of the equation found for constant pressure gradients and generalizes the Kuramoto-Sivashinsky equation with dispersive effects found by Papageorgiou, Maldarelli & Rumschitzki, Phys. Fluids A 2(3), 1990, pp. 340-352, to a similar system with time periodic coefficients. The distinct regimes of slow and moderate flow are considered and the corresponding evolution is derived. Certain solutions are described analytically in the neighborhood of the first bifurcation point by use of multiple scales asymptotics. Extensive numerical experiments, using dynamical systems ideas, are carried out in order to evaluate the effect of the oscillatory pressure gradient on the solutions in the presence of a constant pressure gradient.
Applied Time Domain Stability Margin Assessment for Nonlinear Time-Varying Systems
Kiefer, J. M.; Johnson, M. D.; Wall, J. H.; Dominguez, A.
2016-01-01
The baseline stability margins for NASA's Space Launch System (SLS) launch vehicle were generated via the classical approach of linearizing the system equations of motion and determining the gain and phase margins from the resulting frequency domain model. To improve the fidelity of the classical methods, the linear frequency domain approach can be extended by replacing static, memoryless nonlinearities with describing functions. This technique, however, does not address the time varying nature of the dynamics of a launch vehicle in flight. An alternative technique for the evaluation of the stability of the nonlinear launch vehicle dynamics along its trajectory is to incrementally adjust the gain and/or time delay in the time domain simulation until the system exhibits unstable behavior. This technique has the added benefit of providing a direct comparison between the time domain and frequency domain tools in support of simulation validation. This technique was implemented by using the Stability Aerospace Vehicle Analysis Tool (SAVANT) computer simulation to evaluate the stability of the SLS system with the Adaptive Augmenting Control (AAC) active and inactive along its ascent trajectory. The gains for which the vehicle maintains apparent time-domain stability defines the gain margins, and the time delay similarly defines the phase margin. This method of extracting the control stability margins from the time-domain simulation is relatively straightforward and the resultant margins can be compared to the linearized system results. The sections herein describe the techniques employed to extract the time-domain margins, compare the results between these nonlinear and the linear methods, and provide explanations for observed discrepancies. The SLS ascent trajectory was simulated with SAVANT and the classical linear stability margins were evaluated at one second intervals. The linear analysis was performed with the AAC algorithm disabled to attain baseline stability
The beauty of simple adaptive control and new developments in nonlinear systems stability analysis
Barkana, Itzhak
2014-12-01
Although various adaptive control techniques have been around for a long time and in spite of successful proofs of stability and even successful demonstrations of performance, the eventual use of adaptive control methodologies in practical real world systems has met a rather strong resistance from practitioners and has remained limited. Apparently, it is difficult to guarantee or even understand the conditions that can guarantee stable operations of adaptive control systems under realistic operational environments. Besides, it is difficult to measure the robustness of adaptive control system stability and allow it to be compared with the common and widely used measure of phase margin and gain margin that is utilized by present, mainly LTI, controllers. Furthermore, customary stability analysis methods seem to imply that the mere stability of adaptive systems may be adversely affected by any tiny deviation from the pretty idealistic and assumably required stability conditions. This paper first revisits the fundamental qualities of customary direct adaptive control methodologies, in particular the classical Model Reference Adaptive Control, and shows that some of their basic drawbacks have been addressed and eliminated within the so-called Simple Adaptive Control methodology. Moreover, recent developments in the stability analysis methods of nonlinear systems show that prior conditions that were customarily assumed to be needed for stability are only apparent and can be eliminated. As a result, sufficient conditions that guarantee stability are clearly stated and lead to similarly clear proofs of stability. As many real-world applications show, once robust stability of the adaptive systems can be guaranteed, the added value of using Add-On Adaptive Control along with classical Control design techniques is pushing the desired performance beyond any previous limits.
The beauty of simple adaptive control and new developments in nonlinear systems stability analysis
Energy Technology Data Exchange (ETDEWEB)
Barkana, Itzhak, E-mail: ibarkana@gmail.com [BARKANA Consulting, Ramat Hasharon (Israel)
2014-12-10
Although various adaptive control techniques have been around for a long time and in spite of successful proofs of stability and even successful demonstrations of performance, the eventual use of adaptive control methodologies in practical real world systems has met a rather strong resistance from practitioners and has remained limited. Apparently, it is difficult to guarantee or even understand the conditions that can guarantee stable operations of adaptive control systems under realistic operational environments. Besides, it is difficult to measure the robustness of adaptive control system stability and allow it to be compared with the common and widely used measure of phase margin and gain margin that is utilized by present, mainly LTI, controllers. Furthermore, customary stability analysis methods seem to imply that the mere stability of adaptive systems may be adversely affected by any tiny deviation from the pretty idealistic and assumably required stability conditions. This paper first revisits the fundamental qualities of customary direct adaptive control methodologies, in particular the classical Model Reference Adaptive Control, and shows that some of their basic drawbacks have been addressed and eliminated within the so-called Simple Adaptive Control methodology. Moreover, recent developments in the stability analysis methods of nonlinear systems show that prior conditions that were customarily assumed to be needed for stability are only apparent and can be eliminated. As a result, sufficient conditions that guarantee stability are clearly stated and lead to similarly clear proofs of stability. As many real-world applications show, once robust stability of the adaptive systems can be guaranteed, the added value of using Add-On Adaptive Control along with classical Control design techniques is pushing the desired performance beyond any previous limits.
Krishnan, Hariharan
1993-01-01
This thesis is organized in two parts. In Part 1, control systems described by a class of nonlinear differential and algebraic equations are introduced. A procedure for local stabilization based on a local state realization is developed. An alternative approach to local stabilization is developed based on a classical linearization of the nonlinear differential-algebraic equations. A theoretical framework is established for solving a tracking problem associated with the differential-algebraic system. First, a simple procedure is developed for the design of a feedback control law which ensures, at least locally, that the tracking error in the closed loop system lies within any given bound if the reference inputs are sufficiently slowly varying. Next, by imposing additional assumptions, a procedure is developed for the design of a feedback control law which ensures that the tracking error in the closed loop system approaches zero exponentially for reference inputs which are not necessarily slowly varying. The control design methodologies are used for simultaneous force and position control in constrained robot systems. The differential-algebraic equations are shown to characterize the slow dynamics of a certain nonlinear control system in nonstandard singularly perturbed form. In Part 2, the attitude stabilization (reorientation) of a rigid spacecraft using only two control torques is considered. First, the case of momentum wheel actuators is considered. The complete spacecraft dynamics are not controllable. However, the spacecraft dynamics are small time locally controllable in a reduced sense. The reduced spacecraft dynamics cannot be asymptotically stabilized using continuous feedback, but a discontinuous feedback control strategy is constructed. Next, the case of gas jet actuators is considered. If the uncontrolled principal axis is not an axis of symmetry, the complete spacecraft dynamics are small time locally controllable. However, the spacecraft attitude
Jiao, J. P.; Drinkwater, B. W.; Neild, S. A.; Wilcox, P. D.
2009-06-01
Guided wave structural health monitoring offers the prospect of continuous interrogation of large plate-like structures with a sparse network of permanently attached sensors. Currently, the most common approach is to monitor changes in the received signals by subtraction from a reference signal obtained when the structure was known to be defect-free. In this paper a comparison is made between this defect-free subtraction approach and a technique in which low-frequency vibration modulation of guided wave signals is used to detect nonlinear scatterers. The modulation technique potentially overcomes the need for the defect-free reference measurement as the subtraction is now made between different parts of an externally applied low-frequency vibration. Linear defects were simulated by masses bonded onto a plate and nonlinear scatterers were simulated by loading a similar mass against the plate. The experimental results show that the defect-free subtraction technique performs well in detecting the bonded mass whereas the modulation technique is able to discriminate between the bonded and loaded masses. Furthermore, because the modulation technique does not require a defect-free reference, it is shown to be relatively independent of temperature effects, a significant problem for reference based subtraction techniques.
Shahmansouri, M.; Misra, A. P.
2016-12-01
The modulational instability (MI) and the evolution of weakly nonlinear two-dimensional (2D) Langmuir wave (LW) packets are studied in an unmagnetized collisionless plasma with weakly relativistic electron flow. By using a 2D self-consistent relativistic fluid model and employing the standard multiple-scale technique, a coupled set of Davey-Stewartson (DS)-like equations is derived, which governs the slow modulation and the evolution of LW packets in relativistic plasmas. It is found that the relativistic effects favor the instability of LW envelopes in the k - θ plane, where k is the wave number and θ ( 0 ≤ θ ≤ π ) the angle of modulation. It is also found that as the electron thermal velocity or θ increases, the growth rate of MI increases with cutoffs at higher wave numbers of modulation. Furthermore, in the nonlinear evolution of the DS-like equations, it is seen that with an effect of the relativistic flow, a Gaussian wave beam collapses in a finite time, and the collapse can be arrested when the effect of the thermal pressure or the relativistic flow is slightly relaxed. The present results may be useful to the MI and the formation of localized LW envelopes in cosmic plasmas with a relativistic flow of electrons.
Shahmansouri, M
2016-01-01
The modulational instability (MI) and the evolution of weakly nonlinear two-dimensional (2D) Langmuir wave (LW) packets are studied in an unmagnetized collisionless plasma with weakly relativistic electron flow. By using a 2D self-consistent relativistic fluid model and employing the standard multiple-scale technique, a coupled set of Davey-Stewartson (DS)-like equations is derived which governs the slow modulation and the evolution of LW packets in relativistic plasmas. It is found that the relativistic effects favor the instability of LW envelopes in the k{\\theta} plane, where k is the wave number and {\\theta} the angle of modulation. It is also found that as the electron thermal velocity or {\\theta} increases, the growth rate of MI increases with cutoffs at higher wave numbers of modulation. Furthermore, in the nonlinear evolution of the DS-like equations, it is seen that with an effect of the relativistic flow, a Gaussian wave beam collapses in a finite time, and the collapse can be arrested when the effe...
Institute of Scientific and Technical Information of China (English)
Abhijit Sinha; Sourangshu Mukhopadhyay
2004-01-01
In optical soliton propagation through a single mode optical fiber,it is established that self-phase mod ulation is maintained by the third order non-linearity of the silica-based glass material of the fiber.In this paper we show that the fifth order non-linearity has also some contribution in frequency variation of self-phase modulation.
Yang, Jianke
2016-01-01
Stability of soliton families in one-dimensional nonlinear Schroedinger equations with non-parity-time (PT)-symmetric complex potentials is investigated numerically. It is shown that these solitons can be linearly stable in a wide range of parameter values both below and above phase transition. In addition, a pseudo-Hamiltonian-Hopf bifurcation is revealed, where pairs of purely-imaginary eigenvalues in the linear-stability spectra of solitons collide and bifurcate off the imaginary axis, creating oscillatory instability, which resembles Hamiltonian-Hopf bifurcations of solitons in Hamiltonian systems even though the present system is dissipative and non-Hamiltonian. The most important numerical finding is that, eigenvalues of linear-stability operators of these solitons appear in quartets $(\\lambda, -\\lambda, \\lambda^*, -\\lambda^*)$, similar to conservative systems and PT-symmetric systems. This quartet eigenvalue symmetry is very surprising for non-PT-symmetric systems, and it has far-reaching consequences ...
Longitudinal/Lateral Stability Analysis of Vehicle Motion in the Nonlinear Region
Directory of Open Access Journals (Sweden)
Keji Chen
2016-01-01
Full Text Available We focus on the study of motion stability of vehicle nonlinear dynamics. The dynamic model combining with Burckhardt tire model is firstly derived. By phase portrait method, the vehicle stability differences of three cases, front wheels steering/four-wheel steering case, front/rear/four-wheel braking case, and high/low road friction case, are characterized. With the Jacobian matrix, the stable equilibrium point is found and stable areas are calculated out. Similarly, the stability boundaries corresponding to different working conditions are also captured. With vehicle braking or accelerating in the steering process, the relationship between front/rear wheel slippage and the stable area is examined. Comparing with current literatures, the research method and its results present the novelty and provide a guideline for new vehicle controller design.
NONLINEAR STABILITY OF BALANCED ROTOR DUE TO EFFECT OF BALL BEARING INTERNAL CLEARANCE
Institute of Scientific and Technical Information of China (English)
BAI Chang-qing; XU Qing-yu; ZHANG Xiao-long
2006-01-01
Stability and dynamic characteristics of a ball bearing-rotor system are investigated under the effect of the clearance in the ball bearing. Different clearance values are assumed to calculate the nonlinear stability of periodic solution with the aid of the Floquet theory. Bifurcation and chaos behavior are analyzed with variation of the clearance and rotational speed. It is found that there are three routes to unstable periodic solution.The period-doubling bifurcation and the secondary Hopf bifurcation are two usual routes to instability. The third route is the boundary crisis, a chaotic attractor occurs suddenly as the speed passes through its critical value. At last, the instable ranges for different internal clearance values are described. It is useful to investigate the stability property of ball bearing rotor system.
Effects of periodic modulation on the nonlinear Landau-Zener tunneling
Institute of Scientific and Technical Information of China (English)
Wu Li-Hua; Duan Wen-Shan
2009-01-01
We study the Landau-Zener tunneling of a nonlinear two-level system by applying a periodic modulation on its energy bias. We find that the two levels are splitting at the zero points of the zero order Bessel function for high-frequency modulation. Moreover, we obtain the effective coupling constant between two levels at the zero points of the zero order Bessel function by calculating the final tunneling probability at these points. It seems that the effective coupling constant can be regarded as the approximation of the higher order Bessel function at these points. For the low-frequency modulation, we find that the final tunneling probability is a function of the interaction strength. For the weak inter-level coupling case, we find that the final tunneling probability is more disordered as the interaction strength becomes larger.
Institute of Scientific and Technical Information of China (English)
Zhong Xian-Qiong; Cheng Ke; Xiang An-Ping
2013-01-01
On the basis of the standard linear stability analysis and Drude electromagnetic model,the impacts of higher-order dispersions and three kinds of typical saturable nonlinearities on modulation instability (MI) have been analyzed and calculated for negative-refractive metamaterials (MMs).Our results show that the MI gain spectra consist of only one spectral region instead of one or two regions in ordinary materials,which may be close to or far from the zero point.Particularly,the spectrum far from the zero point has a high cut-off frequency but a narrow spectral width,which is obviously beneficial to the generation of high-repetition-rate pulse trains.Moreover,MI characteristics here will vary with the normalized angular frequency which can be modified by adjusting the structures of negative-refractive MMs,signifying the controllability of bistable solitons and MI based applications.The effects of saturable nonlinearities are similar to those in ordinary materials.
Sato, T.; Kato, S.; Masuda, A.
2016-09-01
This paper presents a resonance-type vibration energy harvester with a Duffing-type nonlinear oscillator which is designed to perform effectively in a wide frequency band. For the conventional linear vibration energy harvester, the maximum performance of the power generation and its bandwidth are in a relation of trade-off. Introducing a Duffing-type nonlinearity can expand the resonance frequency band and enable the harvester to generate larger electric power in a wider frequency range. However, since such nonlinear oscillator may have coexisting multiple steady-state solutions in the resonance band, it is difficult for the nonlinear harvester to maintain the high performance of the power generation constantly. The principle of self-excitation and entrainment has been utilized to give global stability to the high-energy orbit by destabilizing other unexpected low-energy orbits by introducing a switching circuit of the load resistance between positive and the negative values depending on the response amplitude of the oscillator. In this paper, an improved control law that switches the load resistance according to a frequency-dependent threshold is proposed to ensure the oscillator to respond in the high-energy orbit without ineffective power consumption. Numerical study shows that the steady-state responses of the harvester with the proposed control low are successfully kept on the high-energy orbit without repeating activation of the excitationmode.
Stability Analysis of Fixed points in a Parity-time symmetric coupler with Kerr nonlinearity
Deka, Jyoti Prasad
2016-01-01
We report our study on nonlinear parity-time (PT) symmetric coupler from a dynamical perspective. In the linear regime, the differential equations governing the dynamics of the coupler, under some parametric changes, can be solved exactly. But with the inclusion of nonlinearity, analytical solution of the system is a rather complicated job. And the sensitiveness of the system on the initial conditions is yet another critical issue. To circumvent the situation, we have employed the mathematical framework of nonlinear dynamics. Considering the parity-time threshold of the linear PT-coupler as the reference point, we find that in nonlinear coupler the parity-time symmetric threshold governs the existence of fixed points. We have found that the stability of the ground state undergoes a phase transition when the gain/loss coefficient is increased from zero to beyond the PT threshold. In the unbroken PT regime, we find that the instabilities in the initial launch conditions can trigger an exponential growth and dec...
Stability Analysis and Design of a Nonlinear Controller for Hot Rolling Coiler
Directory of Open Access Journals (Sweden)
Rui Li
2015-01-01
Full Text Available For the new style hot rolling coiler which adopt AC asynchronous motor as the driving force and with using the algorithm based on differential geometry design nonlinear controller, precise coiling tension control in the rolling process of strip steel is achieved. In this paper, under the rotating orthogonal coordinate system, the fifth-order nonlinear motor model is selected as the controlled plant. By multi-input multioutput (MIMO exact feedback linearization (EFL algorithm, the nonlinear model is transformed to a linear one. In terms of small-gain theorem, it is the first to prove that the nonlinear coiler engine that contains the controller has characteristics of input-to-state stability. Experimental results show that the algorithm can be used for high order tracking control system with time-varying parameters. Even without the traditional flux orientation calculation, the output signals are decoupled. With this controller, the tension deviation is restricted to less than 3% and average rotational speed bias was decreased from 0.5% to 0.1% that ensure high-quality plate cut and surface of strip products.
Directory of Open Access Journals (Sweden)
Hyung Jin Lim
2017-02-01
Full Text Available It has been shown that nonlinear ultrasonics can be more sensitive to local incipient defects, such as a fatigue crack, than conventional linear ultrasonics. Therefore, there is an increasing interest in utilizing nonlinear ultrasonics for structural health monitoring and nondestructive testing applications. While the conditions, which are the necessary conditions that should be satisfied for the generation of nonlinear harmonic components, are extensively studied for distributed material nonlinearity, little work has been done to understand the necessary conditions at the presence of a localized nonlinear source such as a fatigue crack. In this paper, the necessary conditions of nonlinear ultrasonic modulation generation in a plate-like structure are formulated specifically for a localized nonlinear source. Then, the correctness of the formulated necessary conditions is experimentally verified using ultrasounds obtained from aluminum plates.
The global nonlinear stability of self-gravitating irrotational Chaplygin fluids in a FRW geometry
LeFloch, Philippe G
2015-01-01
We analyze the global nonlinear stability of FRW (Friedmann-Robertson-Walker) spacetimes in presence of an irrotational perfect fluid. We assume that the fluid is governed by the so-called (generalized) Chaplygin equation of state relating the pressure to the mass-energy density. We express the Einstein equations in wave gauge as a systems of coupled nonlinear wave equations and by performing a suitable conformal transformation, we are able to analyze the global behavior of solutions in future timelike directions. We establish that the (3+1)-spacetime metric and the mass density and velocity vector describing the evolution of the fluid remain globally close to a reference FRW solution, under small initial data perturbations. Our analysis provides also the precise asymptotic behavior of the perturbed solutions in the future directions.
Global Stabilization of Nonlinear Systems with Byrnes-Isidori Normal Form
Institute of Scientific and Technical Information of China (English)
WU Yu-qiang; YU Xing-huo
2002-01-01
The global stabilization of nonlinear cascade systems with partially linear composite dynamics is discussed in this paper using continuous terminal sliding modes (TSM). A two phase control strategy is proposed. The first phase is to use a linear control, called pre-TSM control, to bring the system state into a region where the TSM control is not singular. The second phase is to employ the TSM control in the region such that the equilibrium of the linear subsystem is reached in a finite time whose value is tunable by parameter setting of the TSMs. The finite time convergence of the proposed control strategy enables elimination of the effect of asymptotic convergence on the nonlinear systems. Although the proposed control strategy is sliding mode based, the control signal is continuous except at a single discontinuous point.Chattering phenomenon commonly associated with sliding mode control does not occur.
STEADY-STATE RESPONSES AND THEIR STABILITY OF NONLINEAR VIBRATION OF AN AXIALLY ACCELERATING STRING
Institute of Scientific and Technical Information of China (English)
吴俊; 陈立群
2004-01-01
The steady-state transverse vibration of an axially moving string with geometric nonlinearity was investigated. The transport speed was assumed to be a constant mean speed with small harmonic variations. The nonlinear partial-differential equation that governs the transverse vibration of the string was derived by use of the Hamilton principle. The method of multiple scales was applied directly to the equation. The solvability condition of eliminating the secular terms was established. Closed form solutions for the amplitude and the existence conditions of nontrivial steady-state response of the two-to-one parametric resonance were obtained. Some numerical examples showing effects of the mean transport speed, the amplitude and the frequency of speed variation were presented. The Liapunov linearized stability theory was employed to derive the instability conditions of the trivial solution and the nontrivial solutions for the two-to-one parametric resonance. Some numerical examples highlighting influences of the related parameters on the instability conditions were presented.
Underlying conservation and stability laws in nonlinear propagation of axicon-generated Bessel beams
Porras, Miguel A; Losada, Juan Carlos
2015-01-01
In light filamentation induced by axicon-generated, powerful Bessel beams, the spatial propagation dynamics in the nonlinear medium determines the geometry of the filament channel and hence its potential applications. We show that the observed steady and unsteady Bessel beam propagation regimes can be understood in a unified way from the existence of an attractor and its stability properties. The attractor is identified as the nonlinear unbalanced Bessel beam (NL-UBB) whose inward H\\"ankel beam amplitude equals the amplitude of the linear Bessel beam that the axicon would generate in linear propagation. A simple analytical formula that determines de NL-UBB attractor is given. Steady or unsteady propagation depends on whether the attracting NL-UBB has a small, exponentially growing, unstable mode. In case of unsteady propagation, periodic, quasi-periodic or chaotic dynamics after the axicon reproduces similar dynamics after the development of the small unstable mode into the large perturbation regime.
Thermal stability analysis of nonlinearly charged asymptotic AdS black hole solutions
Dehghani, M.; Hamidi, S. F.
2017-08-01
In this paper, the four-dimensional nonlinearly charged black hole solutions have been considered in the presence of the power Maxwell invariant electrodynamics. Two new classes of anti-de Sitter (AdS) black hole solutions have been introduced according to different amounts of the parameters in the nonlinear theory of electrodynamics. The conserved and thermodynamical quantities of either of the black hole classes have been calculated from geometrical and thermodynamical approaches, separately. It has been shown that the first law of black hole thermodynamics is satisfied for either of the AdS black hole solutions we just obtained. Through the canonical and grand canonical ensemble methods, the black hole thermal stability or phase transitions have been analyzed by considering the heat capacities with the fixed black hole charge and fixed electric potential, respectively. It has been found that the new AdS black holes are stable if some simple conditions are satisfied.
STUDIES ON NONLINEAR STABILITY OF THREE-DIMENSIONAL H-TYPE DISTURBANCE
Institute of Scientific and Technical Information of China (English)
王伟志; 唐登斌
2003-01-01
The three-dimensional H-type nonlinear evolution process for the problem of boundary layer stability is studied by using a newly developed method called parabolic stability equations (PSE).The key initial conditions for sub-harmonic disturbances are obtained by means of the secondary instability theory. The initial solutions of two-dimensional harmonic waves are expressed in Landau expansions. The numerical techniques developed in this paper, including the higher order spectrum method and the more effective algebraic mapping for dealing with the problem of an infinite region,increase the numerical accuracy and the rate of convergence greatly. With the predictor-corrector approach in the marching procedure, the normalization, which is very important for PSE method, is satisfied and the stability of the numerical calculation can be assured. The effects of different pressure gradients, including the favorable and adverse pressure gradients of the basic flow, on the "H-type"evolution are studied in detail. The results of the three-dimensional nonlinear "H-type" evolution are given accurately and show good agreement with the data of the experiment and the results of the DNS from the curves of the amplitude variation, disturbance velocity profile and the evolution of velocity.
Stochastic Stability of Nonlinear Sampled Data Systems with a Jump Linear Controller
Gonzalez, Oscar R.; Herencia-Zapana, Heber; Gray, W. Steven
2004-01-01
This paper analyzes the stability of a sampled- data system consisting of a deterministic, nonlinear, time- invariant, continuous-time plant and a stochastic, discrete- time, jump linear controller. The jump linear controller mod- els, for example, computer systems and communication net- works that are subject to stochastic upsets or disruptions. This sampled-data model has been used in the analysis and design of fault-tolerant systems and computer-control systems with random communication delays without taking into account the inter-sample response. To analyze stability, appropriate topologies are introduced for the signal spaces of the sampled- data system. With these topologies, the ideal sampling and zero-order-hold operators are shown to be measurable maps. This paper shows that the known equivalence between the stability of a deterministic, linear sampled-data system and its associated discrete-time representation as well as between a nonlinear sampled-data system and a linearized representation holds even in a stochastic framework.
Two-beam nonlinear Kerr effect to stabilize laser frequency with sub-Doppler resolution
Martins, Weliton Soares; de Silans, Thierry Passerat; Oriá, Marcos; Chevrollier, Martine; 10.1364/AO.51.005080
2012-01-01
Avoiding laser frequency drifts is a key issue in many atomic physics experiments. Several techniques have been developed to lock the laser frequency using sub-Doppler dispersive atomic lineshapes as error signals in a feedback loop. We propose here a two-beam technique that uses non-linear properties of an atomic vapor around sharp resonances to produce sub-Doppler dispersive-like lineshapes that can be used as error signals. Our simple and robust technique has the advantage of not needing either modulation or magnetic fields.
Nonlinear instability in flagellar dynamics: a novel modulation mechanism in sperm migration?
Gadelha, H.
2010-05-12
Throughout biology, cells and organisms use flagella and cilia to propel fluid and achieve motility. The beating of these organelles, and the corresponding ability to sense, respond to and modulate this beat is central to many processes in health and disease. While the mechanics of flagellum-fluid interaction has been the subject of extensive mathematical studies, these models have been restricted to being geometrically linear or weakly nonlinear, despite the high curvatures observed physiologically. We study the effect of geometrical nonlinearity, focusing on the spermatozoon flagellum. For a wide range of physiologically relevant parameters, the nonlinear model predicts that flagellar compression by the internal forces initiates an effective buckling behaviour, leading to a symmetry-breaking bifurcation that causes profound and complicated changes in the waveform and swimming trajectory, as well as the breakdown of the linear theory. The emergent waveform also induces curved swimming in an otherwise symmetric system, with the swimming trajectory being sensitive to head shape-no signalling or asymmetric forces are required. We conclude that nonlinear models are essential in understanding the flagellar waveform in migratory human sperm; these models will also be invaluable in understanding motile flagella and cilia in other systems.
Nonlinear Stability Analysis of Long-Span Continuous Rigid Frame Bridge with Thin-Wall High Piers
Institute of Scientific and Technical Information of China (English)
Li Li; Peng Yuancheng; Long Xiaohong; Liao Ping
2005-01-01
By utilizing the current finite element program ANSYS, two types of finite element models (FEM), the beam model (BM) and shell model (SM), are established for the nonlinear stability analysis of a practical rigid frame bridge-Longtanhe Great Bridge. In these analyses, geometrical and material nonlinearities are simultaneously taken into account. For geometrical nonlinearity, updated Lagrangian formulations are adopted to derive the tangent stiffness matrix. In order to simulate the nonlinear behavior of the plastic hinge of the piers, the multi-lines spring element COMBIN39 is used in the SM while the bilinear rotational spring element COMBIN40 is employed in the BM. Numerical calculations show that satisfying results can be obtained in the stability analysis of the bridge when the double coupling nonlinearity effects are considered. In addition, the conclusion is significant for practical engineering.
Two-component vector solitons in defocusing Kerr-type media with spatially modulated nonlinearity
Energy Technology Data Exchange (ETDEWEB)
Zhong, Wei-Ping, E-mail: zhongwp6@126.com [Department of Electronic and Information Engineering, Shunde Polytechnic, Guangdong Province, Shunde 528300 (China); Texas A and M University at Qatar, P.O. Box 23874 Doha (Qatar); Belić, Milivoj [Texas A and M University at Qatar, P.O. Box 23874 Doha (Qatar); Institute of Physics, University of Belgrade, P.O. Box 57, 11001 Belgrade (Serbia)
2014-12-15
We present a class of exact solutions to the coupled (2+1)-dimensional nonlinear Schrödinger equation with spatially modulated nonlinearity and a special external potential, which describe the evolution of two-component vector solitons in defocusing Kerr-type media. We find a robust soliton solution, constructed with the help of Whittaker functions. For specific choices of the topological charge, the radial mode number and the modulation depth, the solitons may exist in various forms, such as the half-moon, necklace-ring, and sawtooth vortex-ring patterns. Our results show that the profile of such solitons can be effectively controlled by the topological charge, the radial mode number, and the modulation depth. - Highlights: • Two-component vector soliton clusters in defocusing Kerr-type media are reported. • These soliton clusters are constructed with the help of Whittaker functions. • The half-moon, necklace-ring and vortex-ring patterns are found. • The profile of these solitons can be effectively controlled by three soliton parameters.
Arefi, Mohammad Mehdi; Jahed-Motlagh, Mohammad Reza; Karimi, Hamid Reza
2015-08-01
In this paper, first, an adaptive neural network (NN) state-feedback controller for a class of nonlinear systems with mismatched uncertainties is proposed. By using a radial basis function NN (RBFNN), a bound of unknown nonlinear functions is approximated so that no information about the upper bound of mismatched uncertainties is required. Then, an observer-based adaptive controller based on RBFNN is designed to stabilize uncertain nonlinear systems with immeasurable states. The state-feedback and observer-based controllers are based on Lyapunov and strictly positive real-Lyapunov stability theory, respectively, and it is shown that the asymptotic convergence of the closed-loop system to zero is achieved while maintaining bounded states at the same time. The presented methods are more general than the previous approaches, handling systems with no restriction on the dimension of the system and the number of inputs. Simulation results confirm the effectiveness of the proposed methods in the stabilization of mismatched nonlinear systems.
GPU linear and non-linear Poisson–Boltzmann solver module for DelPhi
Colmenares, José; Ortiz, Jesús; Rocchia, Walter
2014-01-01
Summary: In this work, we present a CUDA-based GPU implementation of a Poisson–Boltzmann equation solver, in both the linear and non-linear versions, using double precision. A finite difference scheme is adopted and made suitable for the GPU architecture. The resulting code was interfaced with the electrostatics software for biomolecules DelPhi, which is widely used in the computational biology community. The algorithm has been implemented using CUDA and tested over a few representative cases of biological interest. Details of the implementation and performance test results are illustrated. A speedup of ∼10 times was achieved both in the linear and non-linear cases. Availability and implementation: The module is open-source and available at http://www.electrostaticszone.eu/index.php/downloads. Contact: walter.rocchia@iit.it Supplementary information: Supplementary data are available at Bioinformatics online PMID:24292939
Yang, Yunqing; Malomed, Boris A
2015-01-01
We analytically study rogue-wave (RW) solutions and rational solitons of an integrable fifth-order nonlinear Schr\\"odinger (FONLS) equation with three free parameters. It includes, as particular cases, the usual NLS, Hirota, and Lakshmanan-Porsezian-Daniel (LPD) equations. We present continuous-wave (CW) solutions and conditions for their modulation instability in the framework of this model. Applying the Darboux transformation to the CW input, novel first- and second-order RW solutions of the FONLS equation are analytically found. In particular, trajectories of motion of peaks and depressions of profiles of the first- and second-order RWs are produced by means of analytical and numerical methods. The solutions also include newly found rational and W-shaped one- and two-soliton modes. The results predict the corresponding dynamical phenomena in extended models of nonlinear fiber optics and other physically relevant integrable systems.
Institute of Scientific and Technical Information of China (English)
方建印; 慕小武
2005-01-01
In this paper, the nonlinear singular stabilization, H∞ control problem of systems with ordinary homogeneous properties is considered. At first, we discuss the stabilization problems of nonlinear systems with homogeneous. Secondly, by vitue of Hamilton-JacobiIsaacs equations or inequalities, we solve regular H∞ of nonlinear systems with homogeneous properties. To overcome the H∞ problem of singular nonlinear system, we try to transform inputs of the singular nonlinear system into two parts: regular part input and singular part input. Following the previous results, we solve the singular nonlinear system H∞ control,we give the Lyapunov function and the state feedback controller of the singular nonlinear systems with homogeneous properties.
Magri, Luca; Nicoud, Franck; Juniper, Matthew
2016-01-01
Monte Carlo and Active Subspace Identification methods are combined with first- and second-order adjoint sensitivities to perform (forward) uncertainty quantification analysis of the thermo-acoustic stability of two annular combustor configurations. This method is applied to evaluate the risk factor, i.e., the probability for the system to be unstable. It is shown that the adjoint approach reduces the number of nonlinear-eigenproblem calculations by up to $\\sim\\mathcal{O}(M)$, as many as the Monte Carlo samples.
Global stability, periodic solutions, and optimal control in a nonlinear differential delay model
Directory of Open Access Journals (Sweden)
Anatoli F. Ivanov
2010-09-01
Full Text Available A nonlinear differential equation with delay serving as a mathematical model of several applied problems is considered. Sufficient conditions for the global asymptotic stability and for the existence of periodic solutions are given. Two particular applications are treated in detail. The first one is a blood cell production model by Mackey, for which new periodicity criteria are derived. The second application is a modified economic model with delay due to Ramsey. An optimization problem for a maximal consumption is stated and solved for the latter.
Photochemical stability of nonlinear optical chromophores in polymeric and crystalline materials.
Rezzonico, Daniele; Kwon, Seong-Ji; Figi, Harry; Kwon, O-Pil; Jazbinsek, Mojca; Günter, Peter
2008-03-28
We compare the photochemical stability of the nonlinear optical chromophore configurationally locked polyene 2-{3-[2-(4-dimethylaminophenyl)vinyl]-5,5-dimethylcyclohex-2-enylidene} malononitrile (DAT2) embedded in a polymeric matrix and in a single-crystalline configuration. The results show that, under resonant light excitations, the polymeric compound degrades through an indirect process, while the DAT2 crystal follows a slow direct process. We show that chromophores in a crystalline environment exhibit three orders of magnitude better photostability as compared to guest-host polymer composites.
DEFF Research Database (Denmark)
Andersen, Lasse Mejling; McKinstrie, C. J.; Rottwitt, Karsten
2013-01-01
Recently, we solved the coupled-mode equations for Bragg scattering (BS) in the low- and high-conversion regimes, but without the effects of nonlinear phase modulation (NPM). We now present solutions and Green functions in the low-conversion regime that include NPM. We find that NPM does not change...... are still possible, even when the effects of NPM are included. Finally, the effects of using different input signals are considered, and we conclude that using the natural input modes of the system drastically increases the efficiency. © (2013) COPYRIGHT Society of Photo-Optical Instrumentation Engineers...
Nonlinear analysis on purely mechanical stabilization of a wheeled inverted pendulum on a slope
Yoshida, Katsutoshi; Hosomi, Kenta
2015-01-01
This paper investigates the potential for stabilizing an inverted pendulum without electric devices, using gravitational potential energy. We propose a wheeled mechanism on a slope, specifically, a wheeled double pendulum, whose second pendulum transforms gravity force into braking force that acts on the wheel. In this paper, we derive steady-state equations of this system and conduct nonlinear analysis to obtain parameter conditions under which the standing position of the first pendulum becomes asymptotically stable. In this asymptotically stable condition, the proposed mechanism descends the slope in a stable standing position, while dissipating gravitational potential energy via the brake mechanism. By numerically continuing the stability limits in the parameter space, we find that the stable parameter region is simply connected. This implies that the proposed mechanism can be robust against errors in parameter setting.
Stability of the equilibrium positions of an engine with nonlinear quadratic springs
Stănescu, Nicolae-Doru; Popa, Dinel
2014-06-01
Our paper realizes a study of the equilibrium positions for an engine supported by four identical nonlinear springs of quadratic characteristic. The systems with quadratic characteristic are generally avoided because they lead to mathematical complications. Our goal is to realize such a study for an engine supported on quadratic springs. For the model purposed, we established the equations of motion and we discussed the possibilities for the equilibrium positions. Because of the quadratic characteristic of the springs and of the approximations made for the small rotations, the equations obtained for the equilibrium lead us to a paradox, which consists in the existence of an open neighborhood in which there exists an infinity of positions of indifferent equilibrium, or a curve where the equilibrium positions are situated. Moreover, the study of the stability shows that the stability is assured for the position at which the springs are not compressed. Finally, a numerical example is presented and completely solved.
Global stability for delay SIR and SEIR epidemic models with nonlinear incidence rate.
Huang, Gang; Takeuchi, Yasuhiro; Ma, Wanbiao; Wei, Daijun
2010-07-01
In this paper, based on SIR and SEIR epidemic models with a general nonlinear incidence rate, we incorporate time delays into the ordinary differential equation models. In particular, we consider two delay differential equation models in which delays are caused (i) by the latency of the infection in a vector, and (ii) by the latent period in an infected host. By constructing suitable Lyapunov functionals and using the Lyapunov-LaSalle invariance principle, we prove the global stability of the endemic equilibrium and the disease-free equilibrium for time delays of any length in each model. Our results show that the global properties of equilibria also only depend on the basic reproductive number and that the latent period in a vector does not affect the stability, but the latent period in an infected host plays a positive role to control disease development.
New results on stability analysis for time-varying delay systems with non-linear perturbations.
Liu, Pin-Lin
2013-05-01
The problem of stability for linear time-varying delay systems under nonlinear perturbation is discussed, with delay assumed as time-varying. Delay decomposition approach allows information of the delayed plant states to be fully considered. A less conservative delay-dependent robust stability condition is derived, using integral inequality approach to express the relationship of Leibniz-Newton formula terms in the within the framework of linear matrix inequalities (LMIs). Merits of the proposed results lie in lesser conservatism, which are realized by choosing different Lyapunov matrices in the decomposed integral intervals and estimating the upper bound of some cross term more exactly. Numerical examples are given to illustrate the effectiveness and lesser conservatism of the proposed method.
A new neural network model for the feedback stabilization of nonlinear systems
Institute of Scientific and Technical Information of China (English)
Mei-qin LIU; Sen-lin ZHANG; Gang-long YAN
2008-01-01
A new neural network model termed 'standard neural network model' (SNNM) is presented,and a state-feedback control law is then designed for the SNNM to stabilize the closed-loop system.The control design constraints are shown to be a set of linear matrix inequalities (LMIs),which can be easily solved by the MATLAB LMI Control Toolbox to determine the control law.Most recurrent neural networks (including the chaotic neural network) and nonlinear systems modeled by neural networks or Takagi and Sugeno (T-S) fuzzy models can be transformed into the SNNMs to be stabilization controllers synthesized in the framework of a unified SNNM.Finally,three numerical examples are provided to illustrate the design developed in this paper.
Directory of Open Access Journals (Sweden)
Xiaohui Mo
2017-01-01
Full Text Available In this paper, finite-time stabilization problem for a class of nonlinear differential-algebraic systems (NDASs subject to external disturbance is investigated via a composite control manner. A composite finite-time controller (CFTC is proposed with a three-stage design procedure. Firstly, based on the adding a power integrator technique, a finite-time control (FTC law is explicitly designed for the nominal NDAS by only using differential variables. Then, by using homogeneous system theory, a continuous finite-time disturbance observer (CFTDO is constructed to estimate the disturbance generated by an exogenous system. Finally, a composite controller which consists of a feedforward compensation part based on CFTDO and the obtained FTC law is proposed. Rigorous analysis demonstrates that not only the proposed composite controller can stabilize the NDAS in finite time, but also the proposed control scheme exhibits nominal performance recovery property. Simulation examples are provided to illustrate the effectiveness of the proposed control approach.
DEFF Research Database (Denmark)
Fuhrman, David R.; Bingham, Harry B.; Madsen, Per A.;
2004-01-01
This paper considers a method of lines stability analysis for finite difference discretizations of a recently published Boussinesq method for the study of highly non-linear and extremely dispersive water waves. The analysis demonstrates the near-equivalence of classical linear Fourier (von Neumann......) techniques with matrix-based methods for formulations in both one and two horizontal dimensions. The matrix-based method is also extended to show the local de-stabilizing effects of the non-linear terms, as well as the stabilizing effects of numerical dissipation. A comparison of the relative stability...... moderately non-normal, suggesting that the eigenvalues are likely suitable for analysis purposes. Numerical experiments demonstrate excellent agreement with the linear analysis, and good qualitative agreement with the local non-linear analysis. The various methods of analysis combine to provide significant...
The reliability and stability of multijunction amorphous silicon PV modules
Energy Technology Data Exchange (ETDEWEB)
Carlson, D.E. [Solarex, Newtown, PA (United States)
1995-11-01
Solarex is developing a manufacturing process for the commercial production of 8 ft{sup 2} multijunction amorphous silicon (a-Si) PV modules starting in 1996. The device structure used in these multijunction modules is: glass/textured tin oxide/p-i-n/p-i-n/ZnO/Al/EVA/Tedlar where the back junction of the tandem structure contains an amorphous silicon germanium alloy. As an interim step, 4 ft{sup 2} multijunction modules have been fabricated in a pilot production mode over the last several months. The distribution of initial conversion efficiencies for an engineering run of 67 modules (4 ft{sup 2}) is shown. Measurements recently performed at NREL indicate that the actual efficiencies are about 5% higher than those shown, and thus exhibit an average initial conversion efficiency of about 9.5%. The data indicates that the process is relatively robust since there were no modules with initial efficiencies less than 7.5%.
Grain size effects on stability of nonlinear vibration with nanocrystalline NiTi shape memory alloy
Xia, Minglu; Sun, Qingping
2017-10-01
Grain size effects on stability of thermomechanical responses for a nonlinear torsional vibration system with nanocrystalline superelastic NiTi bar are investigated in the frequency and amplitude domains. NiTi bars with average grain size from 10 nm to 100 nm are fabricated through cold-rolling and subsequent annealing. Thermomechanical responses of the NiTi bar as a softening nonlinear damping spring in the torsional vibration system are obtained by synchronised acquisition of rotational angle and temperature under external sinusoidal excitation. It is shown that nonlinearity and damping capacity of the NiTi bar decrease as average grain size of the material is reduced below 100 nm. Therefore jump phenomena of thermomechanical responses become less significant or even vanish and the vibration system becomes more stable. The work in this paper provides a solid experimental base for manipulating the undesired jump phenomena of thermomechanical responses and stabilising the mechanical vibration system through grain refinement of NiTi SMA.
On the ?2-stability of time-varying linear and nonlinear discrete-time MIMO systems
Institute of Scientific and Technical Information of China (English)
Y.V.VENKATESH
2014-01-01
New conditions are derived for the 2-stability of time-varying linear and nonlinear discrete-time multiple-input multiple-output (MIMO) systems, having a linear time time-invariant block with the transfer function Γ(z), in negative feedback with a matrix of periodic/aperiodic gains A(k),k =0,1,2,. . . and a vector of certain classes of non-monotone/monotone nonlinearitiesϕ( · ), without restrictions on their slopes and also not requiring path-independence of their line integrals. The stability conditions, which are derived in the frequency domain, have the following features: i) They involve the positive definiteness of the real part (as evaluated on |z| = 1) of the product of Γ(z) and a matrix multiplier function of z. ii) For periodic A(k), one class of multiplier functions can be chosen so as to impose no constraint on the rate of variations A(k), but for aperiodic A(k), which allows a more general multiplier function, constraints are imposed on certain global averages of the generalized eigenvalues of (A(k+1),A(k)),k=1,2,. . . . iii) They are distinct from and less restrictive than recent results in the literature.
Properties and stability of freely propagating nonlinear density waves in accretion disks
Fromang, S
2007-01-01
In this paper, we study the propagation and stability of nonlinear sound waves in accretion disks. Using the shearing box approximation, we derive the form of these waves using a semi-analytic approach and go on to study their stability. The results are compared to those of numerical simulations performed using finite difference approaches such as employed by ZEUS as well as Godunov methods. When the wave frequency is between Omega and two Omega (where Omega is the disk orbital angular velocity), it can couple resonantly with a pair of linear inertial waves and thus undergo a parametric instability. Neglecting the disk vertical stratification, we derive an expression for the growth rate when the amplitude of the background wave is small. Good agreement is found with the results of numerical simulations performed both with finite difference and Godunov codes. During the nonlinear phase of the instability, the flow remains well organised if the amplitude of the background wave is small. However, strongly nonlin...
Kumar, Rajesh; Srivastava, Smriti; Gupta, J R P
2017-03-01
In this paper adaptive control of nonlinear dynamical systems using diagonal recurrent neural network (DRNN) is proposed. The structure of DRNN is a modification of fully connected recurrent neural network (FCRNN). Presence of self-recurrent neurons in the hidden layer of DRNN gives it an ability to capture the dynamic behaviour of the nonlinear plant under consideration (to be controlled). To ensure stability, update rules are developed using lyapunov stability criterion. These rules are then used for adjusting the various parameters of DRNN. The responses of plants obtained with DRNN are compared with those obtained when multi-layer feed forward neural network (MLFFNN) is used as a controller. Also, in example 4, FCRNN is also investigated and compared with DRNN and MLFFNN. Robustness of the proposed control scheme is also tested against parameter variations and disturbance signals. Four simulation examples including one-link robotic manipulator and inverted pendulum are considered on which the proposed controller is applied. The results so obtained show the superiority of DRNN over MLFFNN as a controller. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
A stabilized complementarity formulation for nonlinear analysis of 3D bimodular materials
Zhang, L.; Zhang, H. W.; Wu, J.; Yan, B.
2016-06-01
Bi-modulus materials with different mechanical responses in tension and compression are often found in civil, composite, and biological engineering. Numerical analysis of bimodular materials is strongly nonlinear and convergence is usually a problem for traditional iterative schemes. This paper aims to develop a stabilized computational method for nonlinear analysis of 3D bimodular materials. Based on the parametric variational principle, a unified constitutive equation of 3D bimodular materials is proposed, which allows the eight principal stress states to be indicated by three parametric variables introduced in the principal stress directions. The original problem is transformed into a standard linear complementarity problem (LCP) by the parametric virtual work principle and a quadratic programming algorithm is developed by solving the LCP with the classic Lemke's algorithm. Update of elasticity and stiffness matrices is avoided and, thus, the proposed algorithm shows an excellent convergence behavior compared with traditional iterative schemes. Numerical examples show that the proposed method is valid and can accurately analyze mechanical responses of 3D bimodular materials. Also, stability of the algorithm is greatly improved.
Mechanical analysis of roof stability under nonlinear compaction of solid backfill body
Institute of Scientific and Technical Information of China (English)
Li Meng⇑; Zhang Jixiong; Liu Zhan; Zhao Xu; Huang Peng
2016-01-01
Based on the compaction characteristic test and the nonlinear compaction deformation characteristics of backfill material, this paper applies the theory of nonlinear elastic foundation of thin plate to establish a mechanical model of backfill body and roof in solid dense backfill coal mining. This study critically anal-yses the deflection equation of the roof by the energy method, derives the conditions of roof breakage and combined with concrete engineering practice analyses, determines roof movement regularity and stabil-ity in solid dense backfill mining. Analysis of the engineering practice of the 13,120 backfill panel of Pingmei 12# mine shows the theoretical maximum of roof convergence in backfill mining to be 415 mm which is in significant agreement with the measured value. During the advancing process of solid backfill mining at the panel, the maximum tensile stress on the roof is less than its tensile strength which does not satisfy the conditions for roof breakage. Drilling results on the roof and ground pressure monitoring show that the integrity of roof is strong, which is consistent with the theoretical calculations described in this study. The results presented in the study provide a basis for further investigation into strata movement theory in solid dense backfill mining.
The effect of nonlinear thermo-fluid-dynamic terms on free-piston Stirling machine stability
Energy Technology Data Exchange (ETDEWEB)
Benvenuto, G. [Univ. of Genoa (Italy). Dipt. di Ingegneria Navale; Monte, F. de [Univ. of L`Aquila (Italy). Dipt. de Energetica
1996-12-31
In this work a new linearization technique of the dynamic balance equations of a free-piston Stirling machine is developed. It takes into account the nonlinear thermo-fluid-dynamic terms inherent in the machine, although keeping the linearity of the differential dynamic equations. This allows the equations of motion to be solved still analytically and, therefore, useful algebraic relations (already established by the authors in past studies) linking together the various machine parameters to be used. The advantages related to the proposed linearization methodology are the following: (1) it gives a right interpretation of the machine working when the operational parameters vary, because the considered nonlinear terms have a stabilizing effect; (2) it can be used to predict the machine performance not only with more accuracy, but especially in a more exhaustive way, allowing to estimate also the piston stroke and, therefore, the delivered power; (3) it enables to design the machine in such a way to enhance its stability, thus eliminating the necessity of power control systems.
Nguyen, Quan M.; Peleg, Avner; Tran, Thinh P.
2015-01-01
We develop a method for transmission stabilization and robust dynamic switching for colliding optical soliton sequences in broadband waveguide systems with nonlinear gain and loss. The method is based on employing hybrid waveguides, consisting of spans with linear gain and cubic loss, and spans with linear loss, cubic gain, and quintic loss. We show that the amplitude dynamics is described by a hybrid Lotka-Volterra (LV) model, and use the model to determine the physical parameter values required for enhanced transmission stabilization and switching. Numerical simulations with coupled nonlinear Schrödinger equations confirm the predictions of the LV model, and show complete suppression of radiative instability and pulse distortion. This enables stable transmission over distances larger by an order of magnitude compared with uniform waveguides with linear gain and cubic loss. Moreover, multiple on-off and off-on dynamic switching events are demonstrated over a wide range of soliton amplitudes, showing the superiority of hybrid waveguides compared with static switching in uniform waveguides.
On the stability and compressive nonlinearity of a physiologically based model of the cochlea
Energy Technology Data Exchange (ETDEWEB)
Nankali, Amir [Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan (United States); Grosh, Karl [Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan (United States); Department of Biomedical Engineering, University of Michigan, Ann Arbor, Michigan (United States)
2015-12-31
Hearing relies on a series of coupled electrical, acoustical (fluidic) and mechanical interactions inside the cochlea that enable sound processing. A positive feedback mechanism within the cochlea, called the cochlear amplifier, provides amplitude and frequency selectivity in the mammalian auditory system. The cochlear amplifier and stability are studied using a nonlinear, micromechanical model of the Organ of Corti (OoC) coupled to the electrical potentials in the cochlear ducts. It is observed that the mechano-electrical transduction (MET) sensitivity and somatic motility of the outer hair cell (OHC), control the cochlear stability. Increasing MET sensitivity beyond a critical value, while electromechanical coupling coefficient is within a specific range, causes instability. We show that instability in this model is generated through a supercritical Hopf bifurcation. A reduced order model of the system is approximated and it is shown that the tectorial membrane (TM) transverse mode effect on the dynamics is significant while the radial mode can be simplified from the equations. The cochlear amplifier in this model exhibits good agreement with the experimental data. A comprehensive 3-dimensional model based on the cross sectional model is simulated and the results are compared. It is indicated that the global model qualitatively inherits some characteristics of the local model, but the longitudinal coupling along the cochlea shifts the stability boundary (i.e., Hopf bifurcation point) and enhances stability.
Institute of Scientific and Technical Information of China (English)
LU Yanjun; LIU Heng; YU Lie; LI Qi; ZHANG Zhiyu; JIANG Ming
2007-01-01
Based on the variational constraint approach, the variational form of Reynolds equation in hydrodynamic lubrication is revised continuously to satisfy certain con- straints in the cavitation zone of oil film field. According to the physical characteristic of oil film, an eight-node isopara- metric finite element method is used to convert the revised variational form of Reynolds equation to a discrete form of finite dimensional algebraic variational equation. By this approach, a perturbance equation can be obtained directly on the finite element equation. Consequently, nonlinear oil film forces and their Jacobian matrices are calculated simul- taneously, and compatible accuracy is obtained without increasing the computational costs. A method, which is a combination ofpredictor-corrector mechanism and Newton- Raphson method, is presented to calculate equilibrium posi- tion and critical speed corresponding to Hopf bifurcation point of bearing-rotor system, as by-product dynamic coe- fficients of bearing are obtained. The timescale, i.e., the unknown whirling period of Hopf bifurcation solution of bearing-rotor system is drawn into the iterative process using Poincaré-Newton-Floquet method. The stability of the Hopf bifurcation solution can be detected when estimating Hopf bifurcation solution and its periods. The nonlinear unbalanced Tperiodic responses of the system are obtained by using PNF method and path-following technique. The local stability and bifurcation behaviors of T periodic motions are analyzed by Floquet theory. Chaotic motions are analyzed by Lyapunov exponents. The numerical results revealed the rich and complex nonlinear behavior of the system, such as periodic, quasiperiodic, jumped solution, chaos, and coexistence of multisolution, and so on.
Frye, Michael Takaichi
This dissertation examines the problem of global decentralized control by output feedback for large-scale uncertain nonlinear systems whose subsystems are interconnected not only by their outputs but also by their unmeasurable states. Several innovative techniques will be developed to create decentralized output feedback controllers rendering the closed-loop systems globally asymptotically stable. This is accomplished by extending an output feedback domination design that requires only limited information about the nonlinear system. We will apply our design to lower, upper, and non-triangular nonlinear systems. A time-varying output feedback controller is also constructed for use with large-scale systems that have unknown parameters. Furthermore, a mixed large-scale system consisting of both lower and upper triangular systems is shown to be stabilizable by employing a combined high and low gain domination technique. The significance of our results is that we do not need to have prior information about the nonlinearities of the system. In addition, a new design technique was developed using homogeneous system theory, which allows for the design of nonsmooth controllers and observers to stabilize a class of feedforward system with uncontrollable and unobservable linearization. An example of a large-scale system is a group of autonomous airships performing the function of a temporary mobile cell phone network. An airship mobile cell phone network is a novel solution to the problem of maintaining communication during the advent of extensive damage to the communication infrastructure; be it from a flood, earthquake, hurricane, or terrorist attack. A first principle force-based dynamic model for the Tri-Turbofan Airship was developed and will be discussed in detail. The mathematical model was based on actual flight test data that has been collected at the Gait Analysis and Innovative Technologies Laboratory. This model was developed to research autonomous airship
Sub-wavelength modulation of χ(2) optical nonlinearity in organic thin films
Yan, Yixin; Yuan, Yakun; Wang, Baomin; Gopalan, Venkatraman; Giebink, Noel C.
2017-01-01
Modulating the second-order nonlinear optical susceptibility (χ(2)) of materials at the nanoscale represents an ongoing technological challenge for a variety of integrated frequency conversion and nonlinear nanophotonic applications. Here we exploit the large hyperpolarizability of intermolecular charge transfer states, naturally aligned at an organic semiconductor donor-acceptor (DA) interface, as a means to control the magnitude and sign of χ(2) at the nanoscale. Focusing initially on a single pentacene-C60 DA interface, we confirm that the charge transfer transition is strongly aligned orthogonal to the heterojunction and find that it is responsible for a large interfacial nonlinearity probed via second harmonic generation that is sufficient to achieve d33>10 pm V-1, when incorporated in a non-centrosymmetric DA multilayer stack. Using grating-shadowed oblique-angle deposition to laterally structure the DA interface distribution in such multilayers subsequently enables the demonstration of a χ(2) grating with 280 nm periodicity, which is the shortest reported to date.
Bright solitons in defocusing media with spatial modulation of the quintic nonlinearity
Zeng, Jianhua
2012-01-01
It has been recently demonstrated that self-defocusing (SDF) media with the cubic nonlinearity, whose local coefficient grows from the center to periphery fast enough, support stable bright solitons, without the use of any linear potential. Our objective is to test the genericity of this mechanism for other nonlinearities, by applying it to one- and two-dimensional (1D and 2D) quintic SDF media. The models may be implemented in optics (in particular, in colloidal suspensions of nanoparticles), and the 1D model may be applied to the description of the Tonks-Girardeau gas of ultracold bosons. In 1D, the nonlinearity-modulation function is taken as $% g_{0}+\\sinh ^{2}(\\beta x) $. This model admits a subfamily of exact solutions for fundamental solitons. Generic \\ soliton solutions are constructed in a numerical form, and also by means of the Thomas-Fermi and variational approximations (TFA and VA). In particular, a new ansatz for the VA is proposed, in the form of "raised $\\mathrm{sech}$", which provides for an ...
Chatterjee, D
2015-01-01
The nonlinear theory of amplitude modulation of electrostatic wave envelopes in a collisionless electron-positron (EP) pair plasma is studied by using a set of Vlasov-Poisson equations in the context of Tsallis' $q$-nonextensive statistics. In particular, the previous linear theory of Langmuir oscillations in EP plasmas [Phys. Rev. E {\\bf87}, 053112 (2013)] is rectified and modified. Applying the multiple scale technique (MST), it is shown that the evolution of electrostatic wave envelopes is governed by a nonlinear Schr{\\"o}dinger (NLS) equation with a nonlocal nonlinear term $\\propto {\\cal{P}}\\int|\\phi(\\xi',\\tau)|^2d\\xi'\\phi/(\\xi-\\xi') $ [where ${\\cal P}$ denotes the Cauchy principal value, $\\phi$ is the small-amplitude electrostatic (complex) potential, and $\\xi$ and $\\tau$ are the stretched coordinates in MST] which appears due to the wave-particle resonance. It is found that a subregion $1/3
Energy Technology Data Exchange (ETDEWEB)
del Cueto, J. A.; Deline, C. A.; Rummel, S. R.; Anderberg, A.
2010-08-01
Cadmium telluride (CdTe) and copper indium gallium diselenide (CIGS) thin-film photovoltaic (PV) modules can exhibit substantial variation in measured performance depending on prior exposure history. This study examines the metastable performance changes in these PV modules with the goal of establishing standard preconditioning or stabilization exposure procedures to mitigate measured variations prior to current-voltage (IV) measurements.
Cai, Runyu; Thitsa, Makhin; Bluiett, Althea; Brown, Ei; Hommerich, Uwe
2017-06-01
We propose a direct modulation method with nonlinear feedback controller which can produce chirp-free modulation of the output pulse without bulky external modulators. This work reports the design of the controller which, via a feedback loop, varies and controls the pump rate in real time by automatically adjusting the pump power to precisely modulate the emission of 550 nm in Er3+ -doped Fluoroindate glass under 1.48 μm pumping. In this interdisciplinary paper, well established theoretical tools from nonlinear control theory are applied to the dynamical system of the laser material in order to produce the desired output of the laser. The controller is simulated in MATLAB Simulink and the simulation results show that our technique yields precise modulation of the output intensity without frequency chirping. Results on both theoretical analysis of the control methodology and simulation are presented.
Institute of Scientific and Technical Information of China (English)
Yuan Guangwei; Sheng Zhiqiang; Hang Xudeng
2007-01-01
For solving nonlinear parabolic equation on massive parallel computers,the construction of parallel difference schemes with simple design, high parallelism and unconditional stability and second order global accuracy in space, has long been desired.In the present work, a new kind of general parallel difference schemes for the nonlinear parabolic system is proposed. The general parallel difference schemes include, among others, two new parallel schemes. In one of them, to obtain the interface values on the interface of sub-domains an explicit scheme of Jacobian type is employed, and then the fully implicit scheme is used in the sub-domains. Here, in the explicit scheme of Jacobian type, the values at the points being adjacent to the interface points are taken as the linear combination of values of previous two time layers at the adjoining points of the inner interface. For the construction of another new parallel difference scheme,the main procedure is as follows. Firstly the linear combination of values of previous two time layers at the interface points among the sub-domains is used as the (Dirichlet)boundary condition for solving the sub-domain problems. Then the values in the subdomains are calculated by the fully implicit scheme. Finally the interface values are computed by the fully implicit scheme, and in fact these calculations of the last step are explicit since the values adjacent to the interface points have been obtained in the previous step. The existence, uniqueness, unconditional stability and the second order accuracy of the discrete vector solutions for the parallel difference schemes are proved.Numerical results are presented to examine the stability, accuracy and parallelism of the parallel schemes.
Cho, Yonggeun
2016-05-04
This paper is devoted to the mathematical analysis of a class of nonlinear fractional Schrödinger equations with a general Hartree-type integrand. We show the well-posedness of the associated Cauchy problem and prove the existence and stability of standing waves under suitable assumptions on the nonlinearity. Our proofs rely on a contraction argument in mixed functional spaces and the concentration-compactness method. © 2015 World Scientific Publishing Company
Yi-You Hou; Zhang-Lin Wan
2014-01-01
This paper considers the problem of the robust stability for the nonlinear system with time-varying delay and parameters uncertainties. Based on the H∞ theorem, Lyapunov-Krasovskii theory, and linear matrix inequality (LMI) optimization technique, the H∞ quasi-sliding mode controller and switching function are developed such that the nonlinear system is asymptotically stable in the quasi-sliding mode and satisfies the disturbance attenuation (H∞-norm performance). The effectiveness and accura...
Tadepalli, Siva Kumar; Krishna Rao Kandanvli, V.; Kar, Haranath
2015-11-01
A recently reported paper (Ji, X., Liu, T., Sun, Y., and Su, H. (2011), 'Stability analysis and controller synthesis for discrete linear time-delay systems with state saturation nonlinearities', International Journal of Systems Science, 42, 397-406) for the global asymptotic stability analysis and controller synthesis for a class of discrete linear time delay systems employing state saturation nonlinearities is reviewed. It is claimed in Ji, Liu, Sun and Su (2011) that a previous approach by Kandanvli and Kar (Kandanvli, V.K.R and Kar, H. (2009), 'Robust stability of discrete-time state-delayed systems with saturation nonlinearities: Linear matrix inequality approach', Signal Processing, 89, 161-173) is recovered from their approach as a special case. It is shown that this claim is not justified.
Wang, Yue
2014-01-01
The classical problem of attitude stability in a central gravity field is generalized to that on a stationary orbit around a uniformly-rotating asteroid. This generalized problem is studied in the framework of geometric mechanics. Based on the natural symplectic structure, the non-canonical Hamiltonian structure of the problem is derived. The Poisson tensor, Casimir functions and equations of motion are obtained in a differential geometric method. The equilibrium of the equations of motion, i.e. the equilibrium attitude of the spacecraft, is determined from a global point of view. Nonlinear stability conditions of the equilibrium attitude are obtained with the energy-Casimir method. The nonlinear attitude stability is then investigated versus three parameters of the asteroid, including the ratio of the mean radius to the stationary orbital radius, the harmonic coefficients C20 and C22. It is found that when the spacecraft is located on the intermediate-moment principal axis of the asteroid, the nonlinear stab...
Indian Academy of Sciences (India)
Aditi Ghosh; R Vijaya
2014-07-01
The continuous-wave output of a single-mode erbium-doped fibre ring laser when subjected to cavity-loss modulation is found to exhibit linear as well as nonlinear resonances. At sufficiently low driving amplitude, the system resembles a linear damped oscillator. At higher amplitudes, the dynamical study of these resonances shows that the behaviour of the system exhibits features of a nonlinear damped oscillator under harmonic modulation. These nonlinear dynamical features, including harmonic and subharmonic resonances, have been studied experimentally and analysed with the help of a simple time-domain and frequency-domain information obtained from the output of the laser. All the studies are restricted to the modulation frequency lying in a regime near the relaxation oscillation frequency.
Amplitude-stabilized frequency-modulated laser diode and its interferometric sensing applications.
Takahashi, Y; Yoshino, T; Ohde, N
1997-08-20
A direct frequency-modulated (FM) laser diode light source without light power variation is developed. The amplitude variation of the FM laser diode is compensated by means of a feedback system with use of a superluminescent diode as an external light power controller. Output power greater than 1 mW is obtained at the modulation frequency to 5 kHz with a >10 stabilization factor. By use of the amplitude-stabilized FM laser diode, we measured subfringes with high accuracy in FM continuous wave interferometry, increased the dynamic range of the displacement measurement, and improved the stabilization factor in the laser diode feedback interferometer.
J, Joy Sebastian Prakash; G, Vinitha; Ramachandran, Murugesan; Rajamanickam, Karunanithi
2017-10-01
Three different stabilizing agents, namely, L-cysteine, Thioglycolic acid and cysteamine hydrochloride were used to synthesize Cd(Zn)Se quantum dots (QDs). It was characterized using UV-vis spectroscopy, x-ray diffraction (XRD) and transmission electron microscopy (TEM). The non-linear optical properties (non-linear absorption and non-linear refraction) of synthesized Cd(Zn)Se quantum dots were studied with z-scan technique using diode pumped continuous wavelaser system at a wavelength of 532 nm. Our (organic) synthesized quantum dots showed optical properties similar to the inorganic materials reported elsewhere.
Directory of Open Access Journals (Sweden)
Fei Chen
2013-01-01
Full Text Available This paper deals with the finite-time stabilization problem for discrete-time Markov jump nonlinear systems with time delays and norm-bounded exogenous disturbance. The nonlinearities in different jump modes are parameterized by neural networks. Subsequently, a linear difference inclusion state space representation for a class of neural networks is established. Based on this, sufficient conditions are derived in terms of linear matrix inequalities to guarantee stochastic finite-time boundedness and stochastic finite-time stabilization of the closed-loop system. A numerical example is illustrated to verify the efficiency of the proposed technique.
On the Stability of a Double Integration Delta Modulator
DEFF Research Database (Denmark)
Nielsen, Palle Tolstrup
1971-01-01
A delta modulator with a second-order network in the feedback path is considered. For zero input signal the possible modes of oscillation are determined as a function of the zero of the linear network. The method could be employed with other types of feedback networks. A comparison is made...
Attraction and Stability of Nonlinear Ode's using Continuous Piecewise Linear Approximations
Garcia, Andres; Agamennoni, Osvaldo
2010-04-01
In this paper, several results concerning attraction and asymptotic stability in the large of nonlinear ordinary differential equations are presented. The main result is very simple to apply yielding a sufficient condition under which the equilibrium point (assuming a unique equilibrium) is attractive and also provides a variety of options among them the classical linearization and other existing results are special cases of the this main theorem in this paper including and extension of the well known Markus-Yamabe conjecture. Several application examples are presented in order to analyze the advantages and drawbacks of the proposed result and to compare such results with successful existing techniques for analysis available in the literature nowadays.
Attraction and Stability of Nonlinear Ode's using Continuous Piecewise Linear Approximations
Garcia, Andres
2010-01-01
In this paper, several results concerning attraction and asymptotic stability in the large of nonlinear ordinary differential equations are presented. The main result is very simple to apply yielding a sufficient condition under which the equilibrium point (assuming a unique equilibrium) is attractive and also provides a variety of options among them the classical linearization and other existing results are special cases of the this main theorem in this paper including and extension of the well known Markus-Yamabe conjecture. Several application examples are presented in order to analyze the advantages and drawbacks of the proposed result and to compare such results with successful existing techniques for analysis available in the literature nowadays.
Reithmeier, Eduard
1991-01-01
Limit cycles or, more general, periodic solutions of nonlinear dynamical systems occur in many different fields of application. Although, there is extensive literature on periodic solutions, in particular on existence theorems, the connection to physical and technical applications needs to be improved. The bifurcation behavior of periodic solutions by means of parameter variations plays an important role in transition to chaos, so numerical algorithms are necessary to compute periodic solutions and investigate their stability on a numerical basis. From the technical point of view, dynamical systems with discontinuities are of special interest. The discontinuities may occur with respect to the variables describing the configuration space manifold or/and with respect to the variables of the vector-field of the dynamical system. The multiple shooting method is employed in computing limit cycles numerically, and is modified for systems with discontinuities. The theory is supported by numerous examples, mainly fro...
On the Nonlinear Stability of Plane Parallel Shear Flow in a Coplanar Magnetic Field
Xu, Lanxi; Lan, Wanli
2016-10-01
Lyapunov direct method has been used to study the nonlinear stability of laminar flow between two parallel planes in the presence of a coplanar magnetic field for streamwise perturbations with stress-free boundary planes. Two Lyapunov functions are defined. By means of the first, it is proved that the transverse components of the perturbations decay unconditionally and asymptotically to zero for all Reynolds numbers and magnetic Reynolds numbers. By means of the second, it is showed that the other components of the perturbations decay conditionally and exponentially to zero for all Reynolds numbers and the magnetic Reynolds numbers below π ^2/2M , where M is the maximum of the absolute value of the velocity field of the laminar flow.
A Mechanism for Stabilization of Dynamics in Nonlinear Systems with Different Time Scales
Lopez, Raquel M; Camacho, Erika T
2009-01-01
There are many natural, physical, and biological systems that exhibit multiple time scales. For example, the dynamics of a population of ticks can be described in continuous time during their individual life cycle yet discrete time is used to describe the generation of offspring. These characteristics cause the population levels to be reset periodically. A similar phenomenon can be observed in a sociological college drinking model in which the population is reset by the incoming class each year, as described in the 2006 work of Camacho et al. With the latter as our motivation we analytically and numerically investigate the mechanism by which solutions in certain systems with this resetting conditions stabilize. We further utilize the sociological college drinking model as an analogue to analyze certain one-dimensional and two-dimensional nonlinear systems, as we attempt to generalize our results to higher dimensions.
Directory of Open Access Journals (Sweden)
Roseane Cavalcanti dos Santos
2012-08-01
Full Text Available The objective of this work was to estimate the stability and adaptability of pod and seed yield in runner peanut genotypes based on the nonlinear regression and AMMI analysis. Yield data from 11 trials, distributed in six environments and three harvests, carried out in the Northeast region of Brazil during the rainy season were used. Significant effects of genotypes (G, environments (E, and GE interactions were detected in the analysis, indicating different behaviors among genotypes in favorable and unfavorable environmental conditions. The genotypes BRS Pérola Branca and LViPE‑06 are more stable and adapted to the semiarid environment, whereas LGoPE‑06 is a promising material for pod production, despite being highly dependent on favorable environments.
Kerswell, R R; Willis, A P
2014-01-01
This article introduces, and reviews recent work using, a simple optimisation technique for analysing the nonlinear stability of a state in a dynamical system. The technique can be used to identify the most efficient way to disturb a system such that it transits from one stable state to another. The key idea is introduced within the framework of a finite-dimensional set of ordinary differential equations (ODEs) and then illustrated for a very simple system of 2 ODEs which possesses bistability. Then the transition to turbulence problem in fluid mechanics is used to show how the technique can be formulated for a spatially-extended system described by a partial differential equation (the well-known Navier-Stokes equation). Within that context, the optimisation technique bridges the gap between (linear) optimal perturbation theory and the (nonlinear) dynamical systems approach to fluid flows. The fact that the technique has now been recently shown to work in this very high dimensional setting augurs well for its...
Kerswell, R R; Pringle, C C T; Willis, A P
2014-08-01
This article introduces and reviews recent work using a simple optimization technique for analysing the nonlinear stability of a state in a dynamical system. The technique can be used to identify the most efficient way to disturb a system such that it transits from one stable state to another. The key idea is introduced within the framework of a finite-dimensional set of ordinary differential equations (ODEs) and then illustrated for a very simple system of two ODEs which possesses bistability. Then the transition to turbulence problem in fluid mechanics is used to show how the technique can be formulated for a spatially-extended system described by a set of partial differential equations (the well-known Navier-Stokes equations). Within that context, the optimization technique bridges the gap between (linear) optimal perturbation theory and the (nonlinear) dynamical systems approach to fluid flows. The fact that the technique has now been recently shown to work in this very high dimensional setting augurs well for its utility in other physical systems.
Energy Technology Data Exchange (ETDEWEB)
Itasse, Maxime, E-mail: Maxime.Itasse@onera.fr; Brazier, Jean-Philippe, E-mail: Jean-Philippe.Brazier@onera.fr; Léon, Olivier, E-mail: Olivier.Leon@onera.fr; Casalis, Grégoire, E-mail: Gregoire.Casalis@onera.fr [Onera - The French Aerospace Lab, F-31055 Toulouse (France)
2015-08-15
Nonlinear evolution of disturbances in an axisymmetric, high subsonic, high Reynolds number hot jet with forced eigenmodes is studied using the Parabolized Stability Equations (PSE) approach to understand how modes interact with one another. Both frequency and azimuthal harmonic interactions are analyzed by setting up one or two modes at higher initial amplitudes and various phases. While single mode excitation leads to harmonic growth and jet noise amplification, controlling the evolution of a specific mode has been made possible by forcing two modes (m{sub 1}, n{sub 1}), (m{sub 2}, n{sub 2}), such that the difference in azimuth and in frequency matches the desired “target” mode (m{sub 1} − m{sub 2}, n{sub 1} − n{sub 2}). A careful setup of the initial amplitudes and phases of the forced modes, defined as the “killer” modes, has allowed the minimizing of the initially dominant instability in the near pressure field, as well as its estimated radiated noise with a 15 dB loss. Although an increase of the overall sound pressure has been found in the range of azimuth and frequency analyzed, the present paper reveals the possibility to make the initially dominant instability ineffective acoustically using nonlinear interactions with forced eigenmodes.
The global non-linear stability of the Kerr-de Sitter family of black holes
Hintz, Peter
2016-01-01
We establish the full global non-linear stability of the Kerr-de Sitter family of black holes, as solutions of the initial value problem for the Einstein vacuum equations with positive cosmological constant, for small angular momenta, and without any symmetry assumptions on the initial data. We achieve this by extending the linear and non-linear analysis on black hole spacetimes described in a sequence of earlier papers by the authors: We develop a general framework which enables us to deal systematically with the diffeomorphism invariance of Einstein's equations. In particular, the iteration scheme used to solve Einstein's equations automatically finds the parameters of the Kerr-de Sitter black hole that the solution is asymptotic to, the exponentially decaying tail of the solution, and the gauge in which we are able to find the solution; the gauge here is a wave map/DeTurck type gauge, modified by source terms which are treated as unknowns, lying in a suitable finite-dimensional space.
Non-linear Spectroscopy of Sr Atoms in an Optical Cavity for Laser Stabilization
Christensen, Bjarke T R; Schäffer, Stefan A; Westergaard, Philip G; Ye, Jun; Holland, Murray; Thomsen, Jan W
2015-01-01
We study the non-linear interaction of a cold sample of strontium-88 atoms coupled to a single mode of a low finesse optical cavity in the so-called bad cavity limit and investigate the implications for applications to laser stabilization. The atoms are probed on the weak inter-combination line $\\lvert 5s^{2} \\, ^1 \\textrm{S}_0 \\rangle \\,-\\, \\lvert 5s5p \\, ^3 \\textrm{P}_1 \\rangle$ at 689 nm in a strongly saturated regime. Our measured observables include the atomic induced phase shift and absorption of the light field transmitted through the cavity represented by the complex cavity transmission coefficient. We demonstrate high signal-to-noise-ratio measurements of both quadratures - the cavity transmitted phase and absorption - by employing FM spectroscopy (NICE-OHMS). We also show that when FM spectroscopy is employed in connection with a cavity locked to the probe light, observables are substantially modified compared to the free space situation where no cavity is present. Furthermore, the non-linear dynami...
Nonlinear Modulation of Cutaneous Reflexes with Increasing Speed of Locomotion in Spinal Cats.
Hurteau, Marie-France; Thibaudier, Yann; Dambreville, Charline; Chraibi, Anass; Desrochers, Etienne; Telonio, Alessandro; Frigon, Alain
2017-04-05
Cutaneous reflexes are important for responding rapidly to perturbations, correcting limb trajectory, and strengthening support. During locomotion, they are modulated by phase to generate functionally appropriate responses. The goal of the present study was to determine whether cutaneous reflexes and their phase-dependent modulation are altered with increasing speed and if this is accomplished at the spinal level. Four adult cats that recovered stable hindlimb locomotion after spinal transection were implanted with electrodes to record hindlimb muscle activity chronically and to stimulate the superficial peroneal nerve electrically to evoke cutaneous reflexes. The speed-dependent modulation of cutaneous reflexes was assessed by evoking and characterizing ipsilateral and contralateral responses in semitendinosus, vastus lateralis, and lateral gastrocnemius muscles at four treadmill speeds: 0.2, 0.4, 0.6, and 0.8 m/s. The amplitudes of ipsilateral and contralateral responses were largest at intermediate speeds of 0.4 and 0.6 m/s, followed by the slowest and fastest speeds of 0.2 and 0.8 m/s, respectively. The phase-dependent modulation of reflexes was maintained across speeds, with ipsilateral and contralateral responses peaking during the stance-to-swing transition and swing phase of the ipsilateral limb or midstance of the contralateral limb. Reflex modulation across speeds also correlated with the spatial symmetry of the locomotor pattern, but not with temporal symmetry. That the cutaneous reflex amplitude in all muscles was similarly modulated with increasing speed independently of the background level of muscle activity is consistent with a generalized premotoneuronal spinal control mechanism that could help to stabilize the locomotor pattern when changing speed.SIGNIFICANCE STATEMENT When walking, receptors located in the skin respond to mechanical pressure and send signals to the CNS to correct the trajectory of the limb and to reinforce weight support. These
Designing Non-linear Frequency Modulated Signals For Medical Ultrasound Imaging
DEFF Research Database (Denmark)
Gran, Fredrik; Jensen, Jørgen Arendt
2006-01-01
is tested experimentally using the RASMUS ultrasound system with a 7 MHz linear array transducer. Synthetic transmit aperture ultrasound imaging is applied to acquire data. The proposed design method was compared to a linear FM signal. Due to more efficient spectral usage, a gain in SNR of 4.3plusmn1.2 d......In this paper a new method for designing non-linear frequency modulated (NLFM) waveforms for ultrasound imaging is proposed. The objective is to control the amplitude spectrum of the designed waveform and still keep a constant transmit amplitude, so that the transmitted energy is maximized...... in the transducer can be decreased. Secondly, by choosing an appropriate amplitude spectrum, no additional temporal tapering has to be applied to the matched filter to achieve sufficient range sidelobe suppression. Proper design results in waveforms with a range sidelobe level beyond -80 dB. The design method...
Yan, Zhenya
2013-01-01
The higher-order dispersive and nonlinear effects (alias {\\it the perturbation terms}) like the third-order dispersion, the self-steepening, and the self-frequency shift play important roles in the study of the ultra-short optical pulse propagation. We consider optical rogue wave solutions and interactions for the generalized higher-order nonlinear Schr\\"odinger (NLS) equation with space- and time-modulated parameters. A proper transformation is presented to reduce the generalized higher-order NLS equation to the integrable Hirota equation with constant coefficients. This transformation allows us to relate certain class of exact solutions of the generalized higher-order NLS equation to the variety of solutions of the integrable Hirota equation. In particular, we illustrate the approach in terms of two lowest-order rational solutions of the Hirota equation as seeding functions to generate rogue wave solutions localized in time that have complicated evolution in space with or without the differential gain or lo...
Institute of Scientific and Technical Information of China (English)
张佳华; 王成洋
2015-01-01
On the basis of upper bound theorem, non-associated flow rule and non-linear failure criterion were considered together. The modified shear strength parameters of materials were obtained with the help of the tangent method. Employing the virtual power principle and strength reduction technique, the effects of dilatancy of materials, non-linear failure criterion, pore water pressure, surface loads and buried depth, on the stability of shallow tunnel were studied. In order to validate the effectiveness of the proposed approach, the solutions in the present work agree well with the existing results when the non-associated flow rule is reduced to the associated flow rule and the non-linear failure criterion is degenerated to the linear failure criterion. Compared with dilatancy of materials, the non-linear failure criterion exerts greater impact on the stability of shallow tunnels. The safety factor of shallow tunnels decreases and the failure surface expands outward when the dilatancy coefficient decreases. While the increase of nonlinear coefficient, the pore water pressure coefficient, the surface load and the buried depth results in the small safety factor. Therefore, the dilatancy as well as non-linear failure criterion should be taken into account in the design of shallow tunnel supporting structure. The supporting structure must be reinforced promptly to prevent potential mud from gushing or collapse accident in the areas with abundant pore water, large surface load or buried depth.
Stability for Function Trade-Offs in the Enolase Superfamily 'Catalytic Module'
Energy Technology Data Exchange (ETDEWEB)
Nagatani, R.A.; Gonzalez, A.; Shoichet, B.K.; Brinen, L.S.; Babbitt, P.C.; /UC, San Francisco /SLAC, SSRL
2007-07-12
Enzyme catalysis reflects a dynamic interplay between charged and polar active site residues that facilitate function, stabilize transition states, and maintain overall protein stability. Previous studies show that substituting neutral for charged residues in the active site often significantly stabilizes a protein, suggesting a stability trade-off for functionality. In the enolase superfamily, a set of conserved active site residues (the ''catalytic module'') has repeatedly been used in nature in the evolution of many different enzymes for the performance of unique overall reactions involving a chemically diverse set of substrates. This catalytic module provides a robust solution for catalysis that delivers the common underlying partial reaction that supports all of the different overall chemical reactions of the superfamily. As this module has been so broadly conserved in the evolution of new functions, we sought to investigate the extent to which it follows the stability-function trade-off. Alanine substitutions were made for individual residues, groups of residues, and the entire catalytic module of o-succinylbenzoate synthase (OSBS), a member of the enolase superfamily from Escherichia coli. Of six individual residue substitutions, four (K131A, D161A, E190A, and D213A) substantially increased protein stability (by 0.46-4.23 kcal/mol), broadly consistent with prediction of a stability-activity trade-off. The residue most conserved across the superfamily, E190, is by far the most destabilizing. When the individual substitutions were combined into groups (as they are structurally and functionally organized), nonadditive stability effects emerged, supporting previous observations that residues within the module interact as two functional groups within a larger catalytic system. Thus, whereas the multiple-mutant enzymes D161A/E190A/D213A and K131A/K133A/D161A/E190A/D213A/K235A (termed 3KDED) are stabilized relative to the wild-type enzyme (by 1
Weak Nonlinear Double-Diffusive Magnetoconvection in a Newtonian Liquid under Temperature Modulation
Directory of Open Access Journals (Sweden)
B. S. Bhadauria
2014-01-01
Full Text Available The present paper deals with a weak nonlinear theory of double-diffusive magnetoconvection in an electrically conducting Newtonian liquid, confined between two horizontal surfaces, under a constant vertical magnetic field, and subjected to imposed time-periodic thermal boundaries. The temperature of both walls is varied time periodic in this case. The disturbances are expanded in terms of power series of amplitude of convection, which is assumed to be small. Using nonautonomous Ginzburg-Landau equation, the Nusselt and Sherwood numbers obtained analytically and studied heat and mass transport in the system. Effect of various parameters on the heat and mass transport is discussed extensively. It is found that the effect of magnetic field is to stabilize the system. Further, it is also notified that the heat and mass transport can be controlled by suitably adjusting the external parameters of the system.
Liu, Yunqiao; Calvisi, Michael L.; Wang, Qianxi
2017-04-01
Encapsulated microbubbles (EMBs) are widely used in medical ultrasound imaging as contrast-enhanced agents. However, the potential damaging effects of violent collapsing EMBs to cells and tissues in clinical settings have remained a concern. Dual-frequency ultrasound is a promising technique for improving the efficacy and safety of sonography. The system modeled consists of the external liquid, membrane and internal gases of an EMB. The microbubble dynamics are simulated using a simple nonlinear interactive theory, considering the compressibility of the internal gas, viscosity of the liquid flow and viscoelasticity of the membrane. The radial oscillation and interfacial stability of an EMB under single- and dual-frequency excitations are compared. The simulation results show that the dual-frequency technique produces larger backscatter pressure at higher harmonics of the primary driving frequency—this enriched acoustic spectrum can enhance blood-tissue contrast and improve the quality of sonographic images. The results further show that the acoustic pressure threshold associated with the onset of shape instability is greater for dual-frequency driving. This suggests that the dual-frequency technique stabilizes the encapsulated bubble, thereby improving the efficacy and safety of contrast-enhanced agents.
Liu, Shuang; Zhao, Shuang-Shuang; Wang, Zhao-Long; Li, Hai-Bin
2015-01-01
The stability and the Hopf bifurcation of a nonlinear electromechanical coupling system with time delay feedback are studied. By considering the energy in the air-gap field of the AC motor, the dynamical equation of the electromechanical coupling transmission system is deduced and a time delay feedback is introduced to control the dynamic behaviors of the system. The characteristic roots and the stable regions of time delay are determined by the direct method, and the relationship between the feedback gain and the length summation of stable regions is analyzed. Choosing the time delay as a bifurcation parameter, we find that the Hopf bifurcation occurs when the time delay passes through a critical value. A formula for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is given by using the normal form method and the center manifold theorem. Numerical simulations are also performed, which confirm the analytical results. Project supported by the National Natural Science Foundation of China (Grant No. 61104040), the Natural Science Foundation of Hebei Province, China (Grant No. E2012203090), and the University Innovation Team of Hebei Province Leading Talent Cultivation Project, China (Grant No. LJRC013).
Zhao, Xudong; Yin, Yunfei; Niu, Ben; Zheng, Xiaolong
2016-08-01
In this paper, the problem of switching stabilization for a class of switched nonlinear systems is studied by using average dwell time (ADT) switching, where the subsystems are possibly all unstable. First, a new concept of ADT is given, which is different from the traditional definition of ADT. Based on the new proposed switching signals, a sufficient condition of stabilization for switched nonlinear systems with unstable subsystems is derived. Then, the T-S fuzzy modeling approach is applied to represent the underlying nonlinear system to make the obtained condition easily verified. A novel multiple quadratic Lyapunov function approach is also proposed, by which some conditions are provided in terms of a set of linear matrix inequalities to guarantee the derived T-S fuzzy system to be asymptotically stable. Finally, a numerical example is given to demonstrate the effectiveness of our developed results.
Directory of Open Access Journals (Sweden)
X. Gao
2014-01-01
Full Text Available A methodology is presented to study the resonance and stability for a single-degree-of-freedom (SDOF system with a piecewise linear-nonlinear stiffness term (i.e., one piece is linear and the other is weakly nonlinear. Firstly, the exact response of the linear governing equation is obtained, and a modified perturbation method is applied to finding the approximate solution of the weakly nonlinear equation. Then, the primary and 1/2 subharmonic resonances are obtained by imposing continuity conditions and periodicity conditions. Furthermore, Jacobian matrix is derived to investigate the stability of resonance responses. Finally, the results of theoretical study are compared with numerical results, and a good agreement is observed.
DEFF Research Database (Denmark)
Fuhrman, David R.; Bingham, Harry B.; Madsen, Per A.
2004-01-01
This paper considers a method of lines stability analysis for finite difference discretizations of a recently published Boussinesq method for the study of highly non-linear and extremely dispersive water waves. The analysis demonstrates the near-equivalence of classical linear Fourier (von Neumann...
Ayten, B.; Westerhof, E.; ASDEX Upgrade team,
2014-01-01
Due to the smallness of the volumes associated with the flux surfaces around the O-point of a magnetic island, the electron cyclotron power density applied inside the island for the stabilization of neoclassical tearing modes (NTMs) can exceed the threshold for non-linear effects as derived
Gou, Pengqi; Wang, Kaihui; Qin, Chaoyi; Yu, Jianjun
2017-03-01
We experimentally demonstrate a 16-ary quadrature amplitude modulation (16QAM) DFT-spread optical orthogonal frequency division multiplexing (OFDM) transmission system utilizing a cost-effective directly modulated laser (DML) and direct detection. For 20-Gbaud 16QAM-OFDM signal, with the aid of nonlinear equalization (NLE) algorithm, we respectively provide 6.2-dB and 5.2-dB receiver sensitivity improvement under the hard-decision forward-error-correction (HD-FEC) threshold of 3.8×10-3 for the back-to-back (BTB) case and after transmission over 10-km standard single mode fiber (SSMF) case, related to only adopt post-equalization scheme. To our knowledge, this is the first time to use dynamic nonlinear equalizer (NLE) based on the summation of the square of the difference between samples in one IM/DD OFDM system with DML to mitigate nonlinear distortion.
Nonlinear photoacoustic microscopy via a loss modulation technique: from detection to imaging.
Lai, Yu-Hung; Lee, Szu-Yu; Chang, Chieh-Feng; Cheng, Yu-Hsiang; Sun, Chi-Kuang
2014-01-13
In order to achieve high-resolution deep-tissue imaging, multi-photon fluorescence microscopy and photoacoustic tomography had been proposed in the past two decades. However, combining the advantages of these two imaging systems to achieve optical-spatial resolution with an ultrasonic-penetration depth is still a field with challenges. In this paper, we investigate the detection of the two-photon photoacoustic ultrasound, and first demonstrate background-free two-photon photoacoustic imaging in a phantom sample. To generate the background-free two-photon photoacoustic signals, we used a high-repetition rate femtosecond laser to induce narrowband excitation. Combining a loss modulation technique, we successfully created a beating on the light intensity, which not only provides pure sinusoidal modulation, but also ensures the spectrum sensitivity and frequency selectivity. By using the lock-in detection, the power dependency experiment validates our methodology to frequency-select the source of the nonlinearity. This ensures our capability of measuring the background-free two-photon photoacoustic waves by detecting the 2nd order beating signal directly. Furthermore, by mixing the nanoparticles and fluorescence dyes as contrast agents, the two-photon photoacoustic signal was found to be enhanced and detected. In the end, we demonstrate subsurface two-photon photoacoustic bio-imaging based on the optical scanning mechanism inside phantom samples.
Directory of Open Access Journals (Sweden)
MUHAMMAD ARIF
2017-01-01
Full Text Available Ultrasound imaging with the subharmonic component from contrast microbubbles provide improved CTR (Contrast-to-Tissue Ratio, however it is susceptible to the low amplitude of the subharmonic component. In this simulation study, NLFM (Nonlinear Frequency Modulated signals are proposed in order to enhance the subharmonic response from microbubbles. NLFM signals having fractional bandwidths of 10, 20, and 40% with up and down sweeps were used as excitation. The performance of NLFM signals were compared with the reference tone-burst and LFM (Linear Frequency Modulated signals. The results show that the ultrasound contrast microbubbles can produce subharmonic response which is dependent on the applied signal pressure and bandwidth. It is observed that the subharmonic component of the scattered NLFM signal is 3.2dB higher than the LFM signal, whereas it is 9dB higher compared to the sinusoidal tone-burst signal. The results are also presented which show that the up and down sweeps NLFM signals performed better than the LFM signals at the same acoustic pressure and bandwidth.
Song, Byeongju; Park, Byeongjin; Sohn, Hoon; Lim, Cheol-Woo; Park, Jae-Roung
2015-04-01
Rotating shafts in drop lifts of manufacturing facilities are susceptible to fatigue cracks as they are under repetitive heavy loading and high speed spins. However, it is challenging to use conventional contact transducers to monitor these shafts as they are continuously spinning with a high speed. In this study, a noncontact crack detection technique for a rotating shaft is proposed using air-coupled transducers (ACTs). (1) Low frequency (LF) and high frequency (HF) sinusoidal inputs are simultaneously applied to a shaft using two ACTs, respectively. A fatigue crack can provide a mechanism for nonlinear ultrasonic modulation and create spectral sidebands at the modulation frequencies, which are the sum and difference of the two input frequencies Then LF and HF inputs are independently applied to the shaft using each ACT. These three ultrasonic responses are measured using another ACT. (2) The damage index (DI) is defined as the energy of the first sideband components, which corresponding to the frequency sum and difference between HF and LF inputs. (3) Steps 1 and 2 are repeated with various combinations of HF and LF inputs. Crack existence is detected through an outlier analysis of the DIs. The effectiveness of the proposed technique is investigated using a steel shaft with a real fatigue crack.
Dissipative parametric modulation instability and pattern formation in nonlinear optical systems
Perego, A. M.; Tarasov, N.; Churkin, D. V.; Turitsyn, S. K.; Staliunas, K.
2016-04-01
We present the essential features of the dissipative parametric instability, in the universal complex Ginzburg- Landau equation. Dissipative parametric instability is excited through a parametric modulation of frequency dependent losses in a zig-zag fashion in the spectral domain. Such damping is introduced respectively for spectral components in the +ΔF and in the -ΔF region in alternating fashion, where F can represent wavenumber or temporal frequency depending on the applications. Such a spectral modulation can destabilize the homogeneous stationary solution of the system leading to growth of spectral sidebands and to the consequent pattern formation: both stable and unstable patterns in one- and in two-dimensional systems can be excited. The dissipative parametric instability provides an useful and interesting tool for the control of pattern formation in nonlinear optical systems with potentially interesting applications in technological applications, like the design of mode- locked lasers emitting pulse trains with tunable repetition rate; but it could also find realizations in nanophotonics circuits or in dissipative polaritonic Bose-Einstein condensates.
Stability of Phase-modulated Quantum Key Distribution System
Han, Z F; Gui, Y Z; Guo, G C; Han, Zheng-Fu; Mo, Xiao-Fan; Gui, You-Zhen; Guo, Guang-Can
2004-01-01
Phase drift and random fluctuation of interference visibility in double unbalanced M-Z QKD system are observed and distinguished. It has been found that the interference visibilities are influenced deeply by the disturbance of transmission fiber. Theory analysis shows that the fluctuation is derived from the envioronmental disturbance on polarization characteristic of fiber, especially including transmission fiber. Finally, stability conditions of one-way anti-disturbed M-Z QKD system are given out, which provides a theoretical guide in pragmatic anti-disturbed QKD.
Lam, H K; Leung, Frank H F
2007-10-01
This correspondence presents the stability analysis and performance design of the continuous-time fuzzy-model-based control systems. The idea of the nonparallel-distributed-compensation (non-PDC) control laws is extended to the continuous-time fuzzy-model-based control systems. A nonlinear controller with non-PDC control laws is proposed to stabilize the continuous-time nonlinear systems in Takagi-Sugeno's form. To produce the stability-analysis result, a parameter-dependent Lyapunov function (PDLF) is employed. However, two difficulties are usually encountered: 1) the time-derivative terms produced by the PDLF will complicate the stability analysis and 2) the stability conditions are not in the form of linear-matrix inequalities (LMIs) that aid the design of feedback gains. To tackle the first difficulty, the time-derivative terms are represented by some weighted-sum terms in some existing approaches, which will increase the number of stability conditions significantly. In view of the second difficulty, some positive-definitive terms are added in order to cast the stability conditions into LMIs. In this correspondence, the favorable properties of the membership functions and nonlinear control laws, which allow the introduction of some free matrices, are employed to alleviate the two difficulties while retaining the favorable properties of PDLF-based approach. LMI-based stability conditions are derived to ensure the system stability. Furthermore, based on a common scalar performance index, LMI-based performance conditions are derived to guarantee the system performance. Simulation examples are given to illustrate the effectiveness of the proposed approach.
Wang, Lei; Zhang, Jian-Hui; Liu, Chong; Li, Min; Qi, Feng-Hua
2016-06-01
We study a variable-coefficient nonlinear Schrödinger (vc-NLS) equation with higher-order effects. We show that the breather solution can be converted into four types of nonlinear waves on constant backgrounds including the multipeak solitons, antidark soliton, periodic wave, and W -shaped soliton. In particular, the transition condition requiring the group velocity dispersion (GVD) and third-order dispersion (TOD) to scale linearly is obtained analytically. We display several kinds of elastic interactions between the transformed nonlinear waves. We discuss the dispersion management of the multipeak soliton, which indicates that the GVD coefficient controls the number of peaks of the wave while the TOD coefficient has compression effect. The gain or loss has influence on the amplitudes of the multipeak soliton. We further derive the breather multiple births and Peregrine combs by using multiple compression points of Akhmediev breathers and Peregrine rogue waves in optical fiber systems with periodic GVD modulation. In particular, we demonstrate that the Peregrine comb can be converted into a Peregrine wall by the proper choice of the amplitude of the periodic GVD modulation. The Peregrine wall can be seen as an intermediate state between rogue waves and W -shaped solitons. We finally find that the modulational stability regions with zero growth rate coincide with the transition condition using rogue wave eigenvalues. Our results could be useful for the experimental control and manipulation of the formation of generalized Peregrine rogue waves in diverse physical systems modeled by vc-NLS equation with higher-order effects.
Direct Modulation of Microtubule Stability Contributes to Anthracene General Anesthesia
Emerson, Daniel J.; Weiser, Brian P.; Psonis, John; Liao, Zhengzheng; Taratula, Olena; Fiamengo, Ashley; Wang, Xiaozhao; Sugasawa, Keizo; Smith, Amos B.; Eckenhoff, Roderic G; Dmochowski, Ivan J.
2013-01-01
Recently, we identified 1-aminoanthracene as a fluorescent general anesthetic. To investigate the mechanism of action, a photoactive analogue, 1-azidoanthracene, was synthesized. Administration of 1-azidoanthracene to albino stage 40–47 tadpoles was found to immobilize animals upon near-UV irradiation of the forebrain region. The immobilization was often reversible, but it was characterized by a longer duration consistent with covalent attachment of the ligand to functionally important targets. IEF/SDS-PAGE examination of irradiated tadpole brain homogenate revealed labeled protein, identified by mass spectrometry as β-tubulin. In vitro assays with aminoanthracene-cross-linked tubulin indicated inhibition of microtubule polymerization, similar to colchicine. Tandem mass spectrometry confirmed anthracene binding near the colchicine site. Stage 40–47 tadpoles were also incubated 1 h with microtubule stabilizing agents, epothilone D or discodermolide, followed by dosing with 1-aminoanthracene. The effective concentration of 1-aminoanthracene required to immobilize the tadpoles was significantly increased in the presence of either microtubule stabilizing agent. Epothilone D similarly mitigated the effects of a clinical neurosteroid general anesthetic, allopregnanolone, believed to occupy the colchicine site in tubulin. We conclude that neuronal microtubules are “on-pathway” targets for anthracene general anesthetics and may also represent functional targets for some neurosteroid general anesthetics. PMID:23484901
From Cell to Module: Fabrication and Long-term Stability of Dye-sensitized Solar Cells
Nursam, N. M.; Hidayat, J.; Muliani, L.; Anggraeni, P. N.; Retnaningsih, L.; Idayanti, N.
2017-07-01
Dye-sensitized solar cell (DSSC), which has been firstly developed by Graetzel et al back in 1991, has attracted a considerable interest since its discovery. However, two of the main challenges that the DSSC technology will have to overcome towards commercialization involve device scale-up and long-term stability. In our group, the fabrication technology of DSSC has been developed from laboratory to module scale over the past few years, nevertheless, the long-term stability has still became a major concern. In this contribution, the long-term DSSC performance in relation to their scale-up from cell to module is investigated. The photoelectrode of the DSSCs were fabricated using nanocrystalline titanium dioxide materials that were subsequently sensitized using ruthenium-based dye. Additionally, TiCl4 pre- and post-treatment were carried out to enhance the overall device efficiency. When fabricated as cells, the DSSC prototypes showed relatively stable performance during repeated tests over three months. In order to increase the output power of the solar cells, the DSSCs were then connected in a Z-type series connection to obtain sub-module panels. The DSSC sub-modules exhibit poor stability, particularly as indicated by the significant decrease in the short circuit current (ISC ). Herein, the effect of photoelectrode and sealant materials as well as module design are investigated, highlighting their profound influence upon the DSSC efficiency and long-term stability.
A miniature frequency-stabilized VCSEL system emitting at 795 nm based on LTCC modules
Gruet, Florian; Vecchio, Fabrizio; Affolderbach, Christoph; Pétremand, Yves; de Rooij, Nico F.; Maeder, Thomas; Mileti, Gaetano
2013-08-01
We present a compact frequency-stabilized laser system locked to the Rubidium absorption line of a micro-fabricated reference cell. A printed circuit board (PCB) is used to carry all the components and part of the electronics, and low-temperature co-fired ceramic (LTCC) modules are used to temperature-stabilize the laser diode and the miniature Rubidium cell (cell inner dimensions: 5 mm diameter and 2 mm height). The measured frequency stability of the laser, in terms of Allan deviation, is ≤8×10-10 for integration times of 103-105s. The current overall dimensions of the system are 70×40×50 mm3, with good potential for realization of a frequency-stabilized laser module with few cm3 volume.
Energy Technology Data Exchange (ETDEWEB)
Belmonte-Beitia, J [Departamento de Matematicas, E T S de Ingenieros Industriales and Instituto de Matematica Aplicada a la Ciencia y la IngenierIa (IMACI), Avda Camilo Jose Cela, 3 Universidad de Castilla-La Mancha 13071 Ciudad Real (Spain); Cuevas, J [Grupo de Fisica No Lineal, Departamento de Fisica Aplicada I, Escuela Universitaria Politecnica, C/Virgen de Africa, 7, 41011 Sevilla (Spain)], E-mail: juan.belmonte@uclm.es, E-mail: jcuevas@us.es
2009-04-24
In this paper, we construct, by means of similarity transformations, explicit solutions to the cubic-quintic nonlinear Schroedinger equation with potentials and nonlinearities depending on both time and spatial coordinates. We present the general approach and use it to calculate bright and dark soliton solutions for nonlinearities and potentials of physical interest in applications to Bose-Einstein condensates and nonlinear optics.
Directory of Open Access Journals (Sweden)
Philippe eTerrier
2013-09-01
Full Text Available It has been observed that times series of gait parameters (stride length (SL, stride time (ST and stride speed (SS, exhibit long-term persistence and fractal-like properties. Synchronizing steps with rhythmic auditory stimuli modifies the persistent fluctuation pattern to anti-persistence. Another nonlinear method estimates the degree of resilience of gait control to small perturbations, i.e. the local dynamic stability (LDS. The method makes use of the maximal Lyapunov exponent, which estimates how fast a nonlinear system embedded in a reconstructed state space (attractor diverges after an infinitesimal perturbation. We propose to use an instrumented treadmill to simultaneously measure basic gait parameters (time series of SL, ST and SS from which the statistical persistence among consecutive strides can be assessed, and the trajectory of the center of pressure (from which the LDS can be estimated. In 20 healthy participants, the response to rhythmic auditory cueing (RAC of LDS and of statistical persistence (assessed with detrended fluctuation analysis (DFA was compared. By analyzing the divergence curves, we observed that long-term LDS (computed as the reverse of the average logarithmic rate of divergence between the 4th and the 10th strides downstream from nearest neighbors in the reconstructed attractor was strongly enhanced (relative change +47%. That is likely the indication of a more dampened dynamics. The change in short-term LDS (divergence over one step was smaller (+3%. DFA results (scaling exponents confirmed an anti-persistent pattern in ST, SL and SS. Long-term LDS (but not short-term LDS and scaling exponents exhibited a significant correlation between them (r=0.7. Both phenomena probably result from the more conscious/voluntary gait control that is required by RAC. We suggest that LDS and statistical persistence should be used to evaluate the efficiency of cueing therapy in patients with neurological gait disorders.
Institute of Scientific and Technical Information of China (English)
Xianqiong Zhong; Anping Xiang
2007-01-01
@@ The synthetic effects of group-velocity mismatch and cubic-quintic nonlinearity on cross-phase modulation induced modulation instability in loss single-mode optical fibers have been numerically investigated. The results show that the quintic nonlinearity plays a role similar to the case of neglecting the group-velocity mismatch in modifying the modulation instability, namely, the positive and negative quintic nonlinearities can still enhance and weaken the modulation instability, respectively. The group-velocity mismatch can considerably change the gain spectrum of modulation instability in terms of its shape, peak value, and position. In the normal dispersion regime, with the increase of the group-velocity mismatch parameter,the gain spectrum widens and then narrows, shifts to higher frequencies, and the peak value gets higher before approaching a saturable value. In the abnormal dispersion regime, two separated spectra may occur when the group-velocity mismatch is taken into account. With the increase of the group-velocity mismatch parameter, the peak value of the gain spectrum gets higher and shorter before tending to a saturable value for the first and second spectral regimes, respectively.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A two-layer quasi-geostrophic model is used to study the stability and sensitivity of motions on small-scale vortices in Jupiter's atmosphere. Conditional nonlinear optimal perturbations (CNOPs) and linear singular vectors (LSVs) are both obtained numerically and compared in this paper. The results show that CNOPs can capture the nonlinear characteristics of motions in small-scale vortices in Jupiter's atmosphere and show great difference from LSVs under the condition that the initial constraint condition is large or the optimization time is not very short or both. Besides, in some basic states, local CNOPs are found.The pattern of LSV is more similar to local CNOP than global CNOP in some cases. The elementary application of the method of CNOP to the Jovian atmosphere helps us to explore the stability of variousscale motions of Jupiter's atmosphere and to compare the stability of motions in Jupiter's atmosphere and Earth's atmosphere further.
Carrassi, Alberto; Ghil, Michael; Trevisan, Anna; Uboldi, Francesco
2008-06-01
We study prediction-assimilation systems, which have become routine in meteorology and oceanography and are rapidly spreading to other areas of the geosciences and of continuum physics. The long-term, nonlinear stability of such a system leads to the uniqueness of its sequentially estimated solutions and is required for the convergence of these solutions to the system's true, chaotic evolution. The key ideas of our approach are illustrated for a linearized Lorenz system. Stability of two nonlinear prediction-assimilation systems from dynamic meteorology is studied next via the complete spectrum of their Lyapunov exponents; these two systems are governed by a large set of ordinary and of partial differential equations, respectively. The degree of data-induced stabilization is crucial for the performance of such a system. This degree, in turn, depends on two key ingredients: (i) the observational network, either fixed or data-adaptive, and (ii) the assimilation method.
Li, Yongming; Tong, Shaocheng
2016-03-16
This paper proposes an fuzzy adaptive output-feedback stabilization control method for nonstrict feedback uncertain switched nonlinear systems. The controlled system contains unmeasured states and unknown nonlinearities. First, a switched state observer is constructed in order to estimate the unmeasured states. Second, a variable separation approach is introduced to solve the problem of nonstrict feedback. Third, fuzzy logic systems are utilized to identify the unknown uncertainties, and an adaptive fuzzy output feedback stabilization controller is set up by exploiting the backstepping design principle. At last, by applying the average dwell time method and Lyapunov stability theory, it is proven that all the signals in the closed-loop switched system are bounded, and the system output converges to a small neighborhood of the origin. Two examples are given to further show the effectiveness of the proposed switched control approach.
Cooper, Nathan; Dunning, Alexander; Freegarde, Tim
2012-01-01
We demonstrate a simple and robust technique for removal of the carrier wave from a phase-modulated laser beam, using a non-interferometric method that is insensitive to the modulation frequency and instead exploits the polarization-dependence of electro-optic modulation. An actively stabilized system using feedback via a liquid crystal cell yields long-term carrier suppression in excess of 28 dB at the expense of a 6.5 dB reduction in sideband power.
Jumps and bi-stability in the phase-gain characteristics of a nonlinear parametric amplifier
DEFF Research Database (Denmark)
Neumeyer, Stefan; van de Looij, Ruud; Thomsen, Jon Juel
2014-01-01
This work experimentally investigates the impact of nonlinearity on macromechanical parametric amplification. For a strong cubic stiffness nonlinearity we observe jumps in gain (ratio of steady-state vibration amplitude of the externally and parametrically excited system, to vibration amplitude...
Karafyllis, Iasson
2010-01-01
Sampling arises simultaneously with input and output delays in networked control systems. When the delay is left uncompensated, the sampling period is generally required to be sufficiently small, the delay sufficiently short, and, for nonlinear systems, only semiglobal practical stability is generally achieved. For example, global stabilization of strict-feedforward systems under sampled measurements, sampled-data stabilization of the nonholonomic unicycle with arbitrarily sparse sampling, and sampled-data stabilization of LTI systems over networks with long delays, are open problems. In this paper we present two general results that address these example problems as special cases. First, we present global asymptotic stabilizers for forward complete systems under arbitrarily long input and output delays, with arbitrarily long sampling periods, and with continuous application of the control input. Second, we consider systems with sampled measurements and with control applied through a zero-order hold, under th...
Application of HPEM to investigate the response and stability of nonlinear problems in vibration
DEFF Research Database (Denmark)
Mohammadi, M.H.; Mohammadi, A.; Kimiaeifar, A.;
2010-01-01
In this work, a powerful analytical method, called He's Parameter Expanding Methods (HPEM) is used to obtain the exact solution of nonlinear problems in nonlinear vibration. In this work, the governing equation is obtained by using Lagrange method, then the nonlinear governing equation is solved...... and convenient for solving these problems....
Directory of Open Access Journals (Sweden)
Yi-You Hou
2014-01-01
Full Text Available This paper considers the problem of the robust stability for the nonlinear system with time-varying delay and parameters uncertainties. Based on the H∞ theorem, Lyapunov-Krasovskii theory, and linear matrix inequality (LMI optimization technique, the H∞ quasi-sliding mode controller and switching function are developed such that the nonlinear system is asymptotically stable in the quasi-sliding mode and satisfies the disturbance attenuation (H∞-norm performance. The effectiveness and accuracy of the proposed methods are shown in numerical simulations.
Directory of Open Access Journals (Sweden)
Ruofeng Rao
2013-01-01
Full Text Available The robust exponential stability of delayed fuzzy Markovian-jumping Cohen-Grossberg neural networks (CGNNs with nonlinear p-Laplace diffusion is studied. Fuzzy mathematical model brings a great difficulty in setting up LMI criteria for the stability, and stochastic functional differential equations model with nonlinear diffusion makes it harder. To study the stability of fuzzy CGNNs with diffusion, we have to construct a Lyapunov-Krasovskii functional in non-matrix form. But stochastic mathematical formulae are always described in matrix forms. By way of some variational methods in W1,p(Ω, Itô formula, Dynkin formula, the semi-martingale convergence theorem, Schur Complement Theorem, and LMI technique, the LMI-based criteria on the robust exponential stability and almost sure exponential robust stability are finally obtained, the feasibility of which can efficiently be computed and confirmed by computer MatLab LMI toolbox. It is worth mentioning that even corollaries of the main results of this paper improve some recent related existing results. Moreover, some numerical examples are presented to illustrate the effectiveness and less conservatism of the proposed method due to the significant improvement in the allowable upper bounds of time delays.
Ermolenko, M. V.; Stankevich, V. V.; Buganov, O. V.; Tikhomirov, S. A.; Ganonenko, S. V.; Kuznetsov, P. I.; Yakushcheva, G. G.
2009-04-01
The nonlinear optical properties of multilayer heterostructures based on zinc chalcogenides are studied. Rapid variations in the reflection and transmission of samples excited by ultrashort laser pulses are demonstrated. The characteristic relaxation times of the induced nonlinearity are 2-5 ps and are almost independent within the experimental error on the excitation energy and temperature of a sample.
Energy Technology Data Exchange (ETDEWEB)
Deline, C. A.; del Cueto, J. A.; Albin, D. S.; Rummel, S. R.
2011-09-01
The significant features of a series of stabilization experiments conducted at the National Renewable Energy Laboratory (NREL) between May 2009 and the present are reported. These experiments evaluated a procedure to stabilize the measured performance of thin-film polycrystalline cadmium telluride (CdTe) and copper indium gallium diselenide (CIGS) thin-film photovoltaic (PV) modules. The current-voltage (I-V) characteristics of CdTe and CIGS thin-film PV devices and modules exhibit transitory changes in electrical performance after thermal exposure in the dark and/or bias and light exposures. We present the results of our case studies of module performance versus exposure: light-soaked at 65 degrees C; exposed in the dark under forward bias at 65 degrees C; and, finally, longer-term outdoor exposure. We find that stabilization can be achieved to varying degrees using either light-soaking or dark bias methods and that the existing IEC 61646 light-soaking interval may be appropriate for CdTe and CIGS modules with one caveat: it is likely that at least three exposure intervals are required for stabilization.
Stability of a Bi-Additive Functional Equation in Banach Modules Over a C⋆-Algebra
Directory of Open Access Journals (Sweden)
Won-Gil Park
2012-01-01
Full Text Available We solve the bi-additive functional equation f(x+y,z−w+f(x−y,z+w=2f(x,z−2f(y,w and prove that every bi-additive Borel function is bilinear. And we investigate the stability of a bi-additive functional equation in Banach modules over a unital C⋆-algebra.
Geometric method for stability of non-linear elastic thin shells
Ivanova, Jordanka
2002-01-01
PREFACE This book deals with the new developments and applications of the geometric method to the nonlinear stability problem for thin non-elastic shells. There are no other published books on this subject except the basic ones of A. V. Pogorelov (1966,1967,1986), where variational principles defined over isometric surfaces, are postulated, and applied mainly to static and dynamic problems of elastic isotropic thin shells. A. V. Pogorelov (Harkov, Ukraine) was the first to provide in his monographs the geometric construction of the deformed shell surface in a post-critical stage and deriving explicitely the asymptotic formulas for the upper and lower critical loads. In most cases, these formulas were presented in a closed analytical form, and confirmed by experimental data. The geometric method by Pogorelov is one of the most important analytical methods developed during the last century. Its power consists in its ability to provide a clear geometric picture of the postcritical form of a deformed shell surfac...
Gottlieb, Sigal
2015-04-10
High order spatial discretizations with monotonicity properties are often desirable for the solution of hyperbolic PDEs. These methods can advantageously be coupled with high order strong stability preserving time discretizations. The search for high order strong stability time-stepping methods with large allowable strong stability coefficient has been an active area of research over the last two decades. This research has shown that explicit SSP Runge-Kutta methods exist only up to fourth order. However, if we restrict ourselves to solving only linear autonomous problems, the order conditions simplify and this order barrier is lifted: explicit SSP Runge-Kutta methods of any linear order exist. These methods reduce to second order when applied to nonlinear problems. In the current work we aim to find explicit SSP Runge-Kutta methods with large allowable time-step, that feature high linear order and simultaneously have the optimal fourth order nonlinear order. These methods have strong stability coefficients that approach those of the linear methods as the number of stages and the linear order is increased. This work shows that when a high linear order method is desired, it may still be worthwhile to use methods with higher nonlinear order.
Fernandez, Fernando R; Malerba, Paola; White, John A
2015-04-01
The presence of voltage fluctuations arising from synaptic activity is a critical component in models of gain control, neuronal output gating, and spike rate coding. The degree to which individual neuronal input-output functions are modulated by voltage fluctuations, however, is not well established across different cortical areas. Additionally, the extent and mechanisms of input-output modulation through fluctuations have been explored largely in simplified models of spike generation, and with limited consideration for the role of non-linear and voltage-dependent membrane properties. To address these issues, we studied fluctuation-based modulation of input-output responses in medial entorhinal cortical (MEC) stellate cells of rats, which express strong sub-threshold non-linear membrane properties. Using in vitro recordings, dynamic clamp and modeling, we show that the modulation of input-output responses by random voltage fluctuations in stellate cells is significantly limited. In stellate cells, a voltage-dependent increase in membrane resistance at sub-threshold voltages mediated by Na+ conductance activation limits the ability of fluctuations to elicit spikes. Similarly, in exponential leaky integrate-and-fire models using a shallow voltage-dependence for the exponential term that matches stellate cell membrane properties, a low degree of fluctuation-based modulation of input-output responses can be attained. These results demonstrate that fluctuation-based modulation of input-output responses is not a universal feature of neurons and can be significantly limited by subthreshold voltage-gated conductances.
Krishnan, Hariharan; Reyhanoglu, Mahmut; McClamroch, Harris
1994-06-01
The attitude stabilization problem of a rigid spacecraft using control torques supplied by gas jet actuators about only two of its principal axes is considered. If the uncontrolled principal axis of the spacecraft is not an axis of symmetry, then the complete spacecraft dynamics are small time locally controllable. However, the spacecraft cannot be asymptotically stabilized to any equilibrium attitude using time-invariant continuous feedback. A discontinuous stabilizing feedback control strategy is constructed which stabilizes the spacecraft to any equilibrium attitude. If the uncontrolled principal axis of the spacecraft is an axis of symmetry, the complete spacecraft dynamics are not even assessible. However, the spacecraft dynamics are strongly accessible and small time locally controllable in a reduced sense. The reduced spacecraft dynamics cannot be asymptotically stabilized to any equilibrium attitude using time-invariant continuous feedback, but again a discontinuous stabilizing feedback control strategy is constructed. In both cases, the discontinuous feedback controllers are constructed by switching between several feedback functions which are selected to accomplish a sequence of spacecraft maneuvers. The results of the paper show that although standard nonlinear control techniques are not applicable, it is possible to construct a nonlinear discontinuous control law based on the dynamics of the particular physical system.
Zhou, Hao-Miao; Liu, Hui; Zhou, Yun; Hu, Wen-Wen
2016-12-01
Based on the tri-layer symmetrical magnetoelectric laminates, a equivalent circuit for the nonlinear resonance converse magnetoelectric coupling effect is established. Because the nonlinear thermo-magneto-mechanical constitutive equations of magnetostrictive material were introduced, a converse magnetoelectric coefficient model was derived from the equivalent circuit, which can describe the influence of bias electric field, bias magnetic field and ambient temperature on the resonance converse magnetoelectric coupling effect. Especially, the model can well predict the modulation effect of bias electric field/voltage on the magnetism of magnetoelectric composite or the converse magnetoelectric coefficient, which is absolutely vital in applications. Both of the converse magnetoelectric coefficient and the resonance frequency predicted by the model have good agreements with the existing experimental results in qualitatively and quantitatively, and the validity of the model is confirmed. On this basis, according to the model, the nonlinear trends of the resonance converse magnetoelectric effect under different bias voltages, bias magnetic fields and ambient temperatures are predicted. From the results, it can be found that the bias voltage can effectively modulate the curve of the resonance converse magnetoelectric coefficient versus bias magnetic field, and then change the corresponding optimal bias magnetic field of the maximum converse magnetoelectric coefficient; with the increasing volume ratio of piezoelectric layers, the modulation effect of bias voltage becomes more obvious; under different bias magnetic fields, the modulation effect of bias voltage on the converse magnetoelectric effect has nonvolatility in a wide temperature region.
Wheeler, A. A.; Mcfadden, G. B.; Murray, B. T.; Coriell, S. R.
1991-01-01
The effect of vertical, sinusoidal, time-dependent gravitational acceleration on the onset of solutal convection during directional solidification is analyzed in the limit of large modulation frequency. When the unmodulated state is unstable, the modulation amplitude required to stabilize the system is determined by the method of averaging. When the unmodulated state is stable, resonant modes of instability occur at large modulation amplitude. These are analyzed using matched asymptotic expansions to elucidate the boundary-layer structure for both the Rayleigh-Benard and directional solidification configurations. Based on these analyses, a thorough examination of the dependence of the stability criteria on the unmodulated Rayleigh number, Schmidt number, and distribution coefficient, is carried out.
Stability issues pertaining large area perovskite and dye-sensitized solar cells and modules
Castro-Hermosa, S.; Yadav, S. K.; Vesce, L.; Guidobaldi, A.; Reale, A.; Di Carlo, A.; Brown, T. M.
2017-01-01
Perovskite and dye-sensitized solar cells are PV technologies which hold promise for PV application. Arguably, the biggest issue facing these technologies is stability. The vast majority of studies have been limited to small area laboratory cells. Moisture, oxygen, UV light, thermal and electrical stresses are leading the degradation causes. There remains a shortage of stability investigations on large area devices, in particular modules. At the module level there exist particular challenges which can be different from those at the small cell level such as encapsulation (not only of the unit cells but of interconnections and contacts), non-uniformity of the layer stacks and unit cells, reverse bias stresses, which are important to investigate for technologies that aim for industrial acceptance. Herein we present a review of stability investigations published in the literature pertaining large area perovskite and dye-sensitized solar devices fabricated both on rigid (glass) and flexible substrates.
Hong, Xiaobin; Lin, Xiaohui; Yang, Bo; Li, Maodong
2017-10-01
As a common kind of failure, crack damages account for major losses in plastic pipeline systems, which are now increasingly being used. In this study, a crack detection method for plastic pipes using piezoelectric transducers based on nonlinear ultrasonic modulation is developed. First, the low frequency and the high frequency (HF) inputs generated by two lead zirconate titanate (PZT) transducers that are bonded to the outer surface of a plastic pipe are used to induce stress waves along the pipe. For the response signal detected by another PZT, the first spectral sideband is extracted using filtering and synchronous demodulation and then modified by a proposed mean equalization method. Subsequently, by applying wavelet packet analysis, the wavelet energy of the signal can be obtained and is used as an index to determine the damaged state. Finally, a series of experiments on plastic pipes of different crack damaged states were conducted using several ways to verify their effectiveness. Experimental results show that wavelet energy of the response signal decreases as the crack grows and it is mainly determined by the HF component of the response signal, while the wavelet energy of the modified first spectral sideband tends to become larger when the crack grows. Among the investigated approaches, it is found that the first spectral sideband can detect the crack damage state effectively.
Collapse of optical wave arrested by cross-phase modulation in nonlinear metamaterials
Zhang, Jinggui; Li, Ying; Xiang, Yuanjiang; Lei, Dajun; Zhang, Lifu
2016-03-01
In this article, we put forward a novel strategy to realize the management of wave collapse through designing probe-pump configuration where probe wave is assumed to propagate in the positive-index region of metamaterials (MMs), while pump wave is assumed to propagate in the negative-index region. We disclose that cross-phase modulation (XPM) in MMs as a new physical mechanism that can be used to arrest the collapse of probe wave in the positive-index region by copropagating it together with pump wave in the negative-index region. Further, we observe that pump wave will evolve into a ring while probe wave will develop a side lob in the wings during the course of coupled waves propagation, different from the corresponding counterpart in the ordinary positive-index materials (OMs) where they simultaneously exhibit the catastrophic self-focusing behavior. Meanwhile, we also discuss how to control the collapse of probe wave by adjusting intensity-detuned pump wave. Our analysis is performed by directly numerically solving the coupled nonlinear Schrödinger equations, as well as using the variational approximation, both showing consistent results. The finding demonstrates XPM as a specific physical mechanism in MMs can provide us unique opportunities unattainable in OMs to manipulate self-focusing of high-power laser.
Energy Technology Data Exchange (ETDEWEB)
Li, S.; Pons, R. (Autonoma de Barcelona (Spain). Dept. of Fisica); Zhang, Y. (Chongqing Inst. of Posts and Telecommunications, Sichuan (China). Telecommunications Engineering Dept.)
1994-08-01
In this paper, the authors study a laser using a nonlinear Fabry-Perot etalon as a cavity mirror. First, using the semiclassical laser theory and the differential equation for the lossy nonlinear Fabry-Perot etalon, they develop dynamic equations describing this system for single-mode operation. In this model, the frequency-pulling effect, a finite response time of the nonlinear medium, and a finite-cavity round-trip time of the Fabry-Perot etalon are included. Second, based on this model, they analyze the stability of this laser and give some numerical results. The results show that (1) this system can exist in the stable state and in the unstable state; (2) there are not only saddle-node bifurcations but also Hopf bifurcations; (3) the detuning parameter will effect the characteristics of the bistability and the number and distribution of Hopf bifurcation points.
Giannakis, D.; Slawinska, J. M.
2016-12-01
The variability of the Indo-Pacific Ocean on interannual to multidecadal timescales is investigated in a millennial control run of CCSM4 and in observations using a recently introduced technique called Nonlinear Laplacian Spectral Analysis (NLSA). Through this technique, drawbacks associated with ad hoc pre-filtering of the input data are avoided, enabling recovery of low-frequency and intermittent modes not accessible previously via classical approaches. Here, a multiscale hierarchy of modes is identified for Indo-Pacific SST and numerous linkages between these patterns are revealed. On interannual timescales, a mode with spatiotemporal pattern corresponding to the fundamental component of ENSO emerges, along with modulations of the annual cycle by ENSO in agreement with ENSO combination mode theory. In spatiotemporal reconstructions, these patterns capture the seasonal southward migration of SST and zonal wind anomalies associated with termination of El Niño and La Niña events. Notably, this family of modes explains a significant portion of SST variance in Eastern Indian Ocean regions employed in the definition of Indian Ocean dipole (IOD) indices, suggesting that it should be useful for understanding the linkage of these indices with ENSO and the interaction of the Indian and Pacific Oceans. In model data, we find that the ENSO and ENSO combination modes are modulated on multidecadal timescales by a mode predominantly active in the western tropical Pacific - we call this mode West Pacific Multidecadal Oscillation (WPMO). Despite the relatively low variance explained by this mode, its dynamical role appears to be significant as it has clear sign-dependent modulating relationships with the interannual modes carrying most of the variance. In particular, cold WPMO events are associated with anomalous Central Pacific westerlies favoring stronger ENSO events, while warm WPMO events suppress ENSO activity. Moreover, the WPMO has significant climatic impacts as
Overview of Orion Crew Module and Launch Abort Vehicle Dynamic Stability
Owens, Donald B.; Aibicjpm. Vamessa V.
2011-01-01
With the retirement of the Space Shuttle, NASA is designing a new spacecraft, called Orion, to fly astronauts to low earth orbit and beyond. Characterization of the dynamic stability of the Orion spacecraft is important for the design of the spacecraft and trajectory construction. Dynamic stability affects the stability and control of the Orion Crew Module during re-entry, especially below Mach = 2.0 and including flight under the drogues. The Launch Abort Vehicle is affected by dynamic stability as well, especially during the re-orientation and heatshield forward segments of the flight. The dynamic stability was assessed using the forced oscillation technique, free-to-oscillate, ballistic range, and sub-scale free-flight tests. All of the test techniques demonstrated that in heatshield-forward flight the Crew Module and Launch Abort Vehicle are dynamically unstable in a significant portion of their flight trajectory. This paper will provide a brief overview of the Orion dynamic aero program and a high-level summary of the dynamic stability characteristics of the Orion spacecraft.
Rezaee, Mousa; Jahangiri, Reza
2015-05-01
In this study, in the presence of supersonic aerodynamic loading, the nonlinear and chaotic vibrations and stability of a simply supported Functionally Graded Piezoelectric (FGP) rectangular plate with bonded piezoelectric layer have been investigated. It is assumed that the plate is simultaneously exposed to the effects of harmonic uniaxial in-plane force and transverse piezoelectric excitations and aerodynamic loading. It is considered that the potential distribution varies linearly through the piezoelectric layer thickness, and the aerodynamic load is modeled by the first order piston theory. The von-Karman nonlinear strain-displacement relations are used to consider the geometrical nonlinearity. Based on the Classical Plate Theory (CPT) and applying the Hamilton's principle, the nonlinear coupled partial differential equations of motion are derived. The Galerkin's procedure is used to reduce the equations of motion to nonlinear ordinary differential Mathieu equations. The validity of the formulation for analyzing the Limit Cycle Oscillation (LCO), aero-elastic stability boundaries is accomplished by comparing the results with those of the literature, and the convergence study of the FGP plate is performed. By applying the Multiple Scales Method, the case of 1:2 internal resonance and primary parametric resonance are taken into account and the corresponding averaged equations are derived and analyzed numerically. The results are provided to investigate the effects of the forcing/piezoelectric detuning parameter, amplitude of forcing/piezoelectric excitation and dynamic pressure, on the nonlinear dynamics and chaotic behavior of the FGP plate. It is revealed that under the certain conditions, due to the existence of bi-stable region of non-trivial solutions, system shows the hysteretic behavior. Moreover, in absence of airflow, it is observed that variation of control parameters leads to the multi periodic and chaotic motions.
Schamel, Hans; Mandal, Debraj; Sharma, Devendra
2017-03-01
An outstanding notion for collisionless plasmas is the essential nonlinear character of their coherent structures, which in the stationary, weak amplitude limit are described by a continuum of cnoidal electron and ion hole modes governed by a multiparametric nonlinear dispersion relation. The well-known discrete structure of undamped linear plasma modes is seamlessly embedded in this nonlinear continuum as the microscopic texture of plasma begins to reveal itself in the high temperature collisionless plasma limit. This transforms the linear-threshold-based operating mechanism of plasma turbulence into a fundamental nonlinear, multifaceted one. Based on a comprehensive three-level description of increasing profundity, a proof of this novel dictum is presented, which makes use of the joint properties of such structures, their coherency and stationarity, and uses in succession a fluid, linear Vlasov and a full Vlasov description. It unifies discrete and continuum limits by resolving the inevitable resonant region and shows that coherent electrostatic equilibria are generally controlled by kinetic particle trapping and are hence fundamentally nonlinear. By forging a link between damped and growing wave solutions, these modes render plasma stability complex and difficult to evaluate due to the entangled pattern of the stability boundary in function and parameter space, respectively. A direct consequence is the existence of negative energy modes of arbitrarily small amplitudes in the subcritical region of the two-stream instability as well as the failure of linear Landau (Vlasov, van Kampen) theory, whenever resonant particles are involved, in addressing the onset of instability in a current-carrying plasma. Responsible for this subtle phase space behavior is hence the thresholdless omnipresence of the trapping nonlinearity originating from coherency. A high resolution, exact-mass-ratio, multispecies, and collisionless plasma simulation is employed to illustrate
Theoretical and experimental research on nonlinear hydrodynamic stability and transition is presented. Bifurcations, amplitude equations, pattern in experiments, and shear flows are considered. Particular attention is given to bifurcations of plane viscous fluid flow and transition to turbulence, chaotic traveling wave covection, chaotic behavior of parametrically excited surface waves in square geometry, amplitude analysis of the Swift-Hohenberg equation, traveling wave convection in finite containers, focus instability in axisymmetric Rayleigh-Benard convection, scaling and pattern formation in flowing sand, dynamical behavior of instabilities in spherical gap flows, and nonlinear short-wavelength Taylor vortices. Also discussed are stability of a flow past a two-dimensional grid, inertia wave breakdown in a precessing fluid, flow-induced instabilities in directional solidification, structure and dynamical properties of convection in binary fluid mixtures, and instability competition for convecting superfluid mixtures.
Dmitriev, Mikhail G.; Makarov, Dmitry A.
2016-08-01
We carried out analysis of near optimality of one computationally effective nonlinear stabilizing control built for weakly nonlinear systems with coefficients depending on the state and the formal small parameter. First investigation of that problem was made in [M. G. Dmitriev, and D. A. Makarov, "The suboptimality of stabilizing regulator in a quasi-linear system with state-depended coefficients," in 2016 International Siberian Conference on Control and Communications (SIBCON) Proceedings, National Research University, Moscow, 2016]. In this paper, another optimal control and gain matrix representations were used and theoretical results analogous to cited work above were obtained. Also as in the cited work above the form of quality criterion on which this close-loop control is optimal was constructed.
Institute of Scientific and Technical Information of China (English)
Zongyao SUN; Yungang LIU
2007-01-01
In this paper, a new approach is successfully addressed to design the state-feedback adaptive stabilizing control law for a class of high-order nonlinear systems in triangular form and with unknown and nonidentical control coefficients, whose stabilizing control has been investigated recently under the knowledge that the lower bounds of the control coefficients are exactly known. In the present paper,without any knowledge of the lower bounds of the control coefficients, based on the adaptive technique and appropriately choosing design parameters, we give the recursive design procedure of the stabilizing control law by utilizing the approach of adding a power integrator together with tuning functions. The state-feedback adaptive control law designed not only preserves the equilibrium at the origin, but also guarantees the global asymptotic stability of the closed-loop states and the uniform boundedness of all the other closed-loop signals.
Li, Shukai; Yang, Lixing; Gao, Ziyou; Li, Keping
2014-11-01
In this paper, the stabilization strategies of a general nonlinear car-following model with reaction-time delay of the drivers are investigated. The reaction-time delay of the driver is time varying and bounded. By using the Lyapunov stability theory, the sufficient condition for the existence of the state feedback control strategy for the stability of the car-following model is given in the form of linear matrix inequality, under which the traffic jam can be well suppressed with respect to the varying reaction-time delay. Moreover, by considering the external disturbance for the running cars, the robust state feedback control strategy is designed, which ensures robust stability and a smaller prescribed H∞ disturbance attenuation level for the traffic flow. Numerical examples are given to illustrate the effectiveness of the proposed methods.
Terry, Emmanuelle; Marvel, Jacqueline; Arpin, Christophe; Gandrillon, Olivier; Crauste, Fabien
2012-08-01
The primary CD8 T cell immune response, due to a first encounter with a pathogen, happens in two phases: an expansion phase, with a fast increase of T cell count, followed by a contraction phase. This contraction phase is followed by the generation of memory cells. These latter are specific of the antigen and will allow a faster and stronger response when encountering the antigen for the second time. We propose a nonlinear mathematical model describing the T CD8 immune response to a primary infection, based on three nonlinear ordinary differential equations and one nonlinear age-structured partial differential equation, describing the evolution of CD8 T cell count and pathogen amount. We discuss in particular the roles and relevance of feedback controls that regulate the response. First we reduce our system to a system with a nonlinear differential equation with a distributed delay. We study the existence of two steady states, and we analyze the asymptotic stability of these steady states. Second we study the system with a discrete delay, and analyze global asymptotic stability of steady states. Finally, we show some simulations that we can obtain from the model and confront them to experimental data.
Ayten, B
2013-01-01
Due to the smallness of the volumes associated with the flux surfaces around the O-point of a magnetic island, the electron cyclotron power density applied inside the island for the stabilization of neoclassical tearing modes (NTMs) can exceed the threshold for non-linear effects as derived previously by Harvey et al, Phys. Rev. Lett. 62 (1989) 426. We study the non-linear electron cyclotron current drive (ECCD) efficiency through bounce-averaged, quasi-linear Fokker-Planck calculations in the magnetic geometry as created by the islands. The calculations are performed for the parameters of a typical NTM stabilization experiment on ASDEX Upgrade. A particular feature of these experiments is that the rays of the EC wave beam propagate tangential to the flux surfaces in the power deposition region. The calculations show significant non-linear effects on the ECCD efficiency, when the ECCD power is increased from its experimental value of 1 MW to a larger value of 4 MW. The nonlinear effects are largest in case of...
Gao, Fangzheng; Wu, Yuqiang
2015-03-01
This paper considers the problem of global stabilization by state feedback for a class of high-order nonlinear systems with time-varying delays. Comparing with the existing relevant literature, the systems under investigation allow more uncertainties, to which the existing control methods are inapplicable. By introducing sign function and necessarily modifying the method of adding a power integrator, a state feedback controller is successfully constructed to preserve the equilibrium at the origin and guarantee the global asymptotic stability of the resulting closed-loop system. Finally, two simulation examples are provided to illustrate the effectiveness of the proposed approach.
Yang, Jianke
2012-03-01
Saddle-node bifurcations arise frequently in solitary waves of diverse physical systems. Previously it was believed that solitary waves always undergo stability switching at saddle-node bifurcations, just as in finite-dimensional dynamical systems. Here we show that this is not true. For a large class of generalized nonlinear Schrödinger equations with real or complex potentials, we prove that stability of solitary waves does not switch at saddle-node bifurcations. This analytical result is confirmed by numerical examples where both soliton branches are stable at saddle-node bifurcations.
Modeling and Stability Analysis for Non-linear Network Control System Based on T-S Fuzzy Model
Institute of Scientific and Technical Information of China (English)
ZHANG Hong; FANG Huajing
2007-01-01
Based on the T-S fuzzy model, this paper presents a new model of non-linear network control system with stochastic transfer delay. Sufficient criterion is proposed to guarantee globally asymptotically stability of this two-levels T-S fuzzy model. Also a T-S fuzzy observer of NCS is designed base on this two-levels T-S fuzzy model. All these results present a new approach for networked control system analysis and design.
Stoller, Patrick C.; Kim, Beop-Min; Rubenchik, Alexander M.; Reiser, Karen M.; Da Silva, Luiz B.
2001-05-01
The measurement of the second order nonlinear susceptibility of collagen in various biological tissues has potential applications in the detection of structural changes which are related to different pathological conditions. We investigate second harmonic generation in a rat-tail tendon, a highly organized collagen structure consisting of parallel fibers. Using an electro-optic modulator and a quarter-wave plate, we modulate the linear polarization of an ultra-short pulse laser beam that is used to measure second harmonic generation in a confocal microscopy setup. Phase-sensitive detection of the generated signal, coupled with a simple model of the collagen protein structures, allows us to measure a parameter (gamma) related to nonlinear susceptibility and to determine the relative orientation of the structures. Our preliminary results indicate that it may be possible to use this parameter to characterize the structure.
Energy Technology Data Exchange (ETDEWEB)
Stoller, P; Kim, B-M; Rubenchik, A M; Reiser, K M; Da Silva, L B
2001-03-03
The measurement of the second order nonlinear susceptibility of collagen in various biological tissues has potential applications in the detection of structural changes which are related to different pathological conditions. We investigate second harmonic generation in rat-tail tendon, a highly organized collagen structure consisting of parallel fibers. Using an electro-optic modulator and a quarter-wave plate, we modulate the linear polarization of an ultra-short pulse laser beam that is used to measure second harmonic generation (SHG) in a confocal microscopy setup. Phase-sensitive detection of the generated signal, coupled with a simple model of the collagen protein structures, allows us to measure a parameter {gamma} related to nonlinear susceptibility and to determine the relative orientation of the structures. Our preliminary results indicate that it may be possible to use this parameter to characterize the structure.
Li, Chung-Yi; Ying, Cheng-Ling; Lin, Chun-Yu; Chu, Chien-An
2015-12-01
This study evaluated a directly modulated distributed feedback (DFB) laser diode (LD) for cable TV systems with respect to carrier-to-nonlinear distortion of LDs. The second-order distortion-to-carrier ratio is found to be proportional to that of the second-order coefficient-to-first-order coefficient of the DFB laser diode driving current and to the optical modulation index (OMI). Furthermore, the third-order distortion-to-carrier ratio is proportional to that of the third-order coefficient-to-first-order coefficient of the DFB laser diode driving current, and to the OMI2.
State-of-the-art MCT IR-modules with enhanced long term and cycle stability
Breiter, R.; Wendler, J.; Lutz, H.; Rutzinger, S.; Schallenberg, T.; Ziegler, J.; Rühlich, I.
2012-06-01
Current trends on the enhancement of MCT FPA IR-modules are reduction of size, weight and power (SWaP), increase of resolution with large detector arrays, provision of staring LWIR or dual-band capability. This is achieved by reduction of pixel size, higher operating temperatures (HOT) or complex pixel structures together with the optimization of dewars, adapted cooling engines and proximity electronics. To meet these demands AIM is working on MCT single-band MWIR or LWIR modules with formats 640x512 or 1280x1024 in 15μm pitch and a dual-band MWIR/LWIR module 640x512 in 20μm pitch. As a first step high operating temperatures for MWIR 120K and LWIR 80K were demonstrated, development for MWIR >= 150K and LWIR >= 90K is ongoing. The modules are realized as integrated detector cooler assemblies (IDCA) with proximity electronics. The 640x512/15μm pitch modules are already available in application specific configurations e.g. having integral rotary or split linear cooling engines. Besides implementation of the above mentioned capabilities also improvement in long term and cycle stability of IRmodules has been achieved which is important to fully benefit from increased mission times and longer maintenance periods by HOT. Especially staring MCT LWIR modules so far required sophisticated non-uniformity correction (NUC) processing to provide acceptable long term image quality while former scanning systems usually used implemented temperature references for NUC update. For a thermal imager setup with the LWIR 640x512/15μm module two-point correction with factory calibrated gain coefficients together with a new offset calibration after every cool down cycle is used. The paper will present the results of AIM's current staring single-band MCT IR-modules in MWIR or LWIR configuration especially regarding to their long term and cycle stability.
Senthilkumar, D V; Lakshmanan, M
2007-03-01
Existence of a new type of oscillating synchronization that oscillates between three different types of synchronizations (anticipatory, complete, and lag synchronizations) is identified in unidirectionally coupled nonlinear time-delay systems having two different time-delays, that is feedback delay with a periodic delay time modulation and a constant coupling delay. Intermittent anticipatory, intermittent lag, and complete synchronizations are shown to exist in the same system with identical delay time modulations in both the delays. The transition from anticipatory to complete synchronization and from complete to lag synchronization as a function of coupling delay with suitable stability condition is discussed. The intermittent anticipatory and lag synchronizations are characterized by the minimum of the similarity functions and the intermittent behavior is characterized by a universal asymptotic -32 power law distribution. It is also shown that the delay time carved out of the trajectories of the time-delay system with periodic delay time modulation cannot be estimated using conventional methods, thereby reducing the possibility of decoding the message by phase space reconstruction.
Subrahmanyam, K. B.; Kaza, K. R. V.; Brown, G. V.; Lawrence, C.
1987-01-01
The coupled bending-bending-torsional equations of dynamic motion of rotating, linearly pretwisted blades are derived including large precone, second degree geometric nonlinearities and Coriolis effects. The equations are solved by the Galerkin method and a linear perturbation technique. Accuracy of the present method is verified by conparisons of predicted frequencies and steady state deflections with those from MSC/NASTRAN and from experiments. Parametric results are generated to establish where inclusion of only the second degree geometric nonlinearities is adequate. The nonlinear terms causing torsional divergence in thin blades are identified. The effects of Coriolis terms and several other structurally nonlinear terms are studied, and their relative importance is examined.